TSTP Solution File: LCL834_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL834_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 : Sun May 5 07:54:09 EDT 2024
% Result : Theorem 11.66s 2.03s
% Output : Refutation 11.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL834_5 : TPTP v8.1.2. Released v6.0.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 13:29:34 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (17282)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.34 % (17285)WARNING: value z3 for option sas not known
% 0.17/0.34 % (17289)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)
% 0.17/0.34 % (17288)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)
% 0.17/0.34 % (17287)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)
% 0.17/0.34 % (17286)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.34 % (17283)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.34 % (17284)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.34 % (17285)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)
% 0.17/0.35 % (17289)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.35 % Exception at run slice level
% 0.17/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.35 % Exception at run slice level
% 0.17/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.35 % Exception at run slice level
% 0.17/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.36 % (17290)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.17/0.36 % (17292)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)
% 0.17/0.36 % (17291)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)
% 0.17/0.37 % (17290)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.37 % Exception at run slice level
% 0.17/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.37 % (17291)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.38 % (17293)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)
% 11.12/1.97 % (17287)First to succeed.
% 11.66/2.03 % (17287)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17282"
% 11.66/2.03 % (17287)Refutation found. Thanks to Tanya!
% 11.66/2.03 % SZS status Theorem for theBenchmark
% 11.66/2.03 % SZS output start Proof for theBenchmark
% 11.66/2.03 tff(type_def_5, type, bool: $tType).
% 11.66/2.03 tff(type_def_6, type, dB: $tType).
% 11.66/2.03 tff(type_def_7, type, list: $tType > $tType).
% 11.66/2.03 tff(type_def_8, type, nat: $tType).
% 11.66/2.03 tff(type_def_9, type, type: $tType).
% 11.66/2.03 tff(type_def_10, type, fun: ($tType * $tType) > $tType).
% 11.66/2.03 tff(func_def_0, type, combb: !>[X0: $tType, X1: $tType, X2: $tType]:(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))))).
% 11.66/2.03 tff(func_def_1, type, combc: !>[X0: $tType, X1: $tType, X2: $tType]:((fun(X0,fun(X1,X2)) * X1) > fun(X0,X2))).
% 11.66/2.03 tff(func_def_2, type, zero_zero: !>[X0: $tType]:(X0)).
% 11.66/2.03 tff(func_def_3, type, beta: fun(dB,fun(dB,bool))).
% 11.66/2.03 tff(func_def_4, type, abs: dB > dB).
% 11.66/2.03 tff(func_def_5, type, app: fun(dB,fun(dB,dB))).
% 11.66/2.03 tff(func_def_6, type, var: nat > dB).
% 11.66/2.03 tff(func_def_7, type, dB_size: dB > nat).
% 11.66/2.03 tff(func_def_8, type, liftn: (nat * dB * nat) > dB).
% 11.66/2.03 tff(func_def_9, type, subst: (dB * dB * nat) > dB).
% 11.66/2.03 tff(func_def_10, type, substn: (dB * dB * nat) > dB).
% 11.66/2.03 tff(func_def_11, type, foldl: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0)) * X0 * list(X1)) > X0)).
% 11.66/2.03 tff(func_def_12, type, foldr: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X1)) * list(X0) * X1) > X1)).
% 11.66/2.03 tff(func_def_13, type, insert: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 11.66/2.03 tff(func_def_14, type, cons: !>[X0: $tType]:((X0 * list(X0)) > list(X0))).
% 11.66/2.03 tff(func_def_15, type, nil: !>[X0: $tType]:(list(X0))).
% 11.66/2.03 tff(func_def_16, type, list_case: !>[X0: $tType, X1: $tType]:((X0 * fun(X1,fun(list(X1),X0)) * list(X1)) > X0)).
% 11.66/2.03 tff(func_def_17, type, sublist: !>[X0: $tType]:((list(X0) * fun(nat,bool)) > list(X0))).
% 11.66/2.03 tff(func_def_18, type, shift: !>[X0: $tType]:((fun(nat,X0) * nat * X0) > fun(nat,X0))).
% 11.66/2.03 tff(func_def_19, type, fun1: fun(type,fun(type,type))).
% 11.66/2.03 tff(func_def_20, type, type_case: !>[X0: $tType]:((fun(nat,X0) * fun(type,fun(type,X0)) * type) > X0)).
% 11.66/2.03 tff(func_def_21, type, typing: (fun(nat,type) * dB) > fun(type,bool)).
% 11.66/2.03 tff(func_def_22, type, typings: (fun(nat,type) * list(dB)) > fun(list(type),bool)).
% 11.66/2.03 tff(func_def_23, type, aa: !>[X0: $tType, X1: $tType]:((fun(X0,X1) * X0) > X1)).
% 11.66/2.03 tff(func_def_24, type, fFalse: bool).
% 11.66/2.03 tff(func_def_25, type, fTrue: bool).
% 11.66/2.03 tff(func_def_26, type, fconj: fun(bool,fun(bool,bool))).
% 11.66/2.03 tff(func_def_27, type, t1: type).
% 11.66/2.03 tff(func_def_28, type, t_a: type).
% 11.66/2.03 tff(func_def_29, type, t: type).
% 11.66/2.03 tff(func_def_30, type, a: dB).
% 11.66/2.03 tff(func_def_31, type, as: list(dB)).
% 11.66/2.03 tff(func_def_32, type, e: fun(nat,type)).
% 11.66/2.03 tff(func_def_33, type, ea: fun(nat,type)).
% 11.66/2.03 tff(func_def_34, type, i: nat).
% 11.66/2.03 tff(func_def_35, type, ia: nat).
% 11.66/2.03 tff(func_def_36, type, r: dB).
% 11.66/2.03 tff(func_def_37, type, t2: dB).
% 11.66/2.03 tff(func_def_38, type, u: dB).
% 11.66/2.03 tff(func_def_39, type, ua: dB).
% 11.66/2.03 tff(func_def_40, type, sK3: !>[X0: $tType]:((list(X0)) > X0)).
% 11.66/2.03 tff(func_def_41, type, sK4: !>[X0: $tType]:((list(X0)) > list(X0))).
% 11.66/2.03 tff(func_def_42, type, sK5: (dB * dB) > dB).
% 11.66/2.03 tff(func_def_43, type, sK6: !>[X0: $tType]:((list(X0)) > X0)).
% 11.66/2.03 tff(func_def_44, type, sK7: !>[X0: $tType]:((list(X0)) > list(X0))).
% 11.66/2.03 tff(func_def_45, type, sK8: (dB * fun(nat,type)) > type).
% 11.66/2.03 tff(func_def_46, type, sK9: (dB * fun(nat,type)) > type).
% 11.66/2.03 tff(func_def_47, type, sK10: (type * dB * fun(nat,type)) > type).
% 11.66/2.03 tff(func_def_48, type, sK11: (type * dB * fun(nat,type)) > type).
% 11.66/2.03 tff(func_def_49, type, sK12: (dB * list(dB) * dB) > dB).
% 11.66/2.03 tff(func_def_50, type, sK13: (dB * list(dB) * dB) > dB).
% 11.66/2.03 tff(func_def_51, type, sK14: (dB * list(dB) * dB) > list(dB)).
% 11.66/2.03 tff(func_def_52, type, sK15: (dB * list(dB) * dB) > list(dB)).
% 11.66/2.03 tff(func_def_53, type, sK16: (dB * list(dB) * dB) > dB).
% 11.66/2.03 tff(func_def_54, type, sK17: (dB * list(dB) * nat) > list(dB)).
% 11.66/2.03 tff(func_def_55, type, sK18: (dB * dB * dB) > dB).
% 11.66/2.03 tff(func_def_56, type, sK19: (dB * dB * dB) > dB).
% 11.66/2.03 tff(func_def_57, type, sK20: (dB * dB * dB) > dB).
% 11.66/2.03 tff(func_def_58, type, sK21: (type * list(dB) * dB * fun(nat,type)) > list(type)).
% 11.66/2.03 tff(func_def_59, type, sK22: (type * list(dB) * dB * fun(nat,type)) > list(type)).
% 11.66/2.03 tff(func_def_60, type, sK23: (type * list(dB) * nat * fun(nat,type)) > list(type)).
% 11.66/2.03 tff(func_def_61, type, sK24: (type * dB * dB * fun(nat,type)) > type).
% 11.66/2.03 tff(func_def_62, type, sK25: !>[X0: $tType, X1: $tType]:((fun(X1,X0) * fun(X1,X0)) > X1)).
% 11.66/2.03 tff(func_def_63, type, sK26: !>[X0: $tType]:((list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool))) > list(X0))).
% 11.66/2.03 tff(func_def_64, type, sK27: !>[X0: $tType]:((list(X0) * X0 * list(X0) * fun(X0,fun(X0,bool))) > X0)).
% 11.66/2.03 tff(func_def_65, type, sK28: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 11.66/2.03 tff(func_def_66, type, sK29: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X1)).
% 11.66/2.03 tff(func_def_67, type, sK30: !>[X0: $tType, X1: $tType]:((fun(X0,fun(X1,X0))) > X0)).
% 11.66/2.03 tff(func_def_68, type, sK31: (type * type * list(dB) * fun(nat,type)) > list(type)).
% 11.66/2.03 tff(pred_def_1, type, zero: !>[X0: $tType]:($o)).
% 11.66/2.03 tff(pred_def_2, type, it: dB > $o).
% 11.66/2.03 tff(pred_def_3, type, step1: !>[X0: $tType]:((fun(X0,fun(X0,bool)) * list(X0) * list(X0)) > $o)).
% 11.66/2.03 tff(pred_def_4, type, member: !>[X0: $tType]:((X0 * fun(X0,bool)) > $o)).
% 11.66/2.03 tff(pred_def_5, type, pp: bool > $o).
% 11.66/2.03 tff(pred_def_6, type, sP0: (dB * list(dB) * dB) > $o).
% 11.66/2.03 tff(pred_def_7, type, sP1: (dB * dB * dB) > $o).
% 11.66/2.03 tff(pred_def_8, type, sP2: !>[X0: $tType]:((list(X0) * list(X0) * fun(X0,fun(X0,bool)) * X0 * X0) > $o)).
% 11.66/2.03 tff(f18565,plain,(
% 11.66/2.03 $false),
% 11.66/2.03 inference(avatar_sat_refutation,[],[f551,f556,f561,f566,f571,f576,f581,f585,f589,f593,f597,f601,f605,f609,f616,f620,f624,f628,f633,f638,f642,f646,f650,f654,f666,f670,f674,f678,f689,f694,f701,f706,f710,f722,f726,f730,f735,f739,f749,f753,f760,f764,f769,f775,f779,f783,f787,f794,f805,f810,f816,f821,f827,f831,f835,f839,f843,f847,f851,f861,f866,f870,f874,f883,f889,f893,f902,f906,f910,f914,f918,f943,f947,f951,f955,f959,f963,f967,f971,f997,f1002,f1008,f1012,f1016,f1026,f1030,f1036,f1041,f1045,f1062,f1066,f1086,f1100,f1104,f1262,f1275,f1279,f1284,f1295,f1299,f1303,f1307,f1311,f1315,f1319,f1323,f1327,f1448,f1454,f1467,f1473,f1488,f1493,f1497,f1516,f1520,f1524,f1529,f1571,f1632,f1646,f1652,f1665,f1670,f1682,f1686,f1692,f1696,f1727,f1732,f1747,f1753,f1769,f1781,f1785,f1790,f1803,f1844,f1849,f1857,f1861,f1891,f1896,f1915,f1920,f1935,f1940,f1955,f1959,f1979,f1985,f1990,f2014,f2019,f2043,f2059,f2064,f2086,f2091,f2125,f2130,f2152,f2158,f2180,f2184,f2196,f2201,f2224,f2232,f2246,f2254,f2276,f2282,f2303,f2309,f2323,f2338,f2344,f2348,f2370,f2388,f2406,f2414,f2430,f2438,f2442,f2458,f2466,f2482,f2490,f2506,f2676,f2680,f2684,f2715,f2719,f2723,f2727,f2731,f2778,f2782,f2786,f2790,f2794,f2798,f2806,f2814,f2818,f2822,f2826,f2830,f2839,f2885,f2889,f2893,f2897,f2901,f2905,f2909,f2913,f2917,f2922,f2955,f2959,f2963,f2980,f2985,f3000,f3004,f3008,f3012,f3016,f3020,f3024,f3065,f3069,f3073,f3077,f3081,f3101,f3105,f3109,f3175,f3179,f3183,f3187,f3191,f3195,f3200,f3205,f3235,f3315,f3319,f3323,f3330,f3334,f3338,f3342,f3390,f3397,f3401,f3405,f3409,f3413,f3417,f3421,f3425,f3794,f3798,f3802,f3806,f3810,f3814,f3818,f3822,f3826,f3830,f4141,f4145,f4149,f4153,f4157,f4161,f4165,f4170,f4175,f4179,f4262,f4266,f4270,f4309,f4313,f4317,f4321,f4325,f4339,f4343,f4347,f4351,f4355,f4359,f4363,f4367,f4371,f4375,f4388,f4392,f4500,f4603,f4625,f4629,f4633,f4637,f4641,f4645,f4649,f4653,f4657,f4661,f4665,f4669,f4673,f4678,f4682,f4686,f4691,f4695,f4989,f5301,f5550,f5593,f5597,f5601,f5605,f5609,f5613,f5617,f5621,f5878,f5882,f5886,f5890,f5895,f5918,f5919,f7426,f7430,f7446,f7514,f7519,f7524,f7529,f7534,f7538,f7542,f7546,f7550,f7598,f7602,f7618,f7746,f7750,f7754,f7758,f7773,f7777,f7781,f7785,f7789,f7793,f7798,f7802,f7806,f7810,f7821,f7826,f7831,f8408,f8412,f8416,f8599,f8603,f8608,f8612,f8617,f8622,f8626,f8630,f8634,f8638,f8642,f8670,f8674,f8825,f8829,f8833,f8837,f8841,f8846,f8851,f9153,f9158,f9261,f9265,f9269,f9648,f9652,f9656,f9936,f10392,f10396,f10473,f10477,f10482,f10487,f10507,f10529,f10533,f10538,f10562,f10629,f10633,f10656,f10661,f10667,f10673,f10690,f10694,f10698,f10702,f10706,f10742,f10746,f10750,f10754,f10758,f10762,f10781,f11581,f11586,f11591,f11595,f11601,f11607,f11611,f11615,f11619,f12103,f12108,f12112,f12116,f12120,f12124,f12130,f12135,f12191,f12298,f12303,f12307,f12311,f12315,f12320,f12596,f12803,f12805,f13214,f13218,f13225,f13405,f13482,f13620,f13667,f13696,f13703,f13707,f17295,f17816,f17864,f17869,f17874,f17878,f17882,f17984,f18139,f18145,f18149,f18153,f18157,f18161,f18437,f18441,f18445,f18564])).
% 11.66/2.03 tff(f18564,plain,(
% 11.66/2.03 ~spl32_7 | ~spl32_18 | spl32_32 | ~spl32_89 | ~spl32_110 | ~spl32_275 | ~spl32_489),
% 11.66/2.03 inference(avatar_split_clause,[],[f18553,f18439,f3812,f1452,f1039,f698,f626,f578])).
% 11.66/2.03 tff(f578,plain,(
% 11.66/2.03 spl32_7 <=> pp(fTrue)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_7])])).
% 11.66/2.03 tff(f626,plain,(
% 11.66/2.03 spl32_18 <=> ! [X0 : bool] : (~pp(X0) | fTrue = X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_18])])).
% 11.66/2.03 tff(f698,plain,(
% 11.66/2.03 spl32_32 <=> pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_32])])).
% 11.66/2.03 tff(f1039,plain,(
% 11.66/2.03 spl32_89 <=> ! [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)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_89])])).
% 11.66/2.03 tff(f1452,plain,(
% 11.66/2.03 spl32_110 <=> ! [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))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_110])])).
% 11.66/2.03 tff(f3812,plain,(
% 11.66/2.03 spl32_275 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X1,X2 : fun(X0,fun(X1,X1))] : aa(X1,X1,aa(X0,fun(X1,X1),X2,X4),X3) = foldr(X0,X1,X2,insert(X0,X4,nil(X0)),X3)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_275])])).
% 11.66/2.03 tff(f18439,plain,(
% 11.66/2.03 spl32_489 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X3),foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X3,X2)),foldl(dB,dB,app,X0,cons(dB,X1,X2)))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_489])])).
% 11.66/2.03 tff(f18553,plain,(
% 11.66/2.03 ~pp(fTrue) | (~spl32_18 | spl32_32 | ~spl32_89 | ~spl32_110 | ~spl32_275 | ~spl32_489)),
% 11.66/2.03 inference(forward_demodulation,[],[f18515,f5961])).
% 11.66/2.03 tff(f5961,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (fTrue = aa(dB,bool,combc(dB,dB,bool,beta,subst(X0,X1,zero_zero(nat))),foldr(dB,dB,app,insert(dB,abs(X0),nil(dB)),X1))) ) | (~spl32_18 | ~spl32_89 | ~spl32_110 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f1457,f3939])).
% 11.66/2.03 tff(f3939,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(X0,X0)),X3 : X1,X4 : X0] : (foldr(X1,X0,X2,insert(X1,X3,nil(X1)),X4) = aa(X1,X0,combc(X1,X0,X0,X2,X4),X3)) ) | (~spl32_89 | ~spl32_275)),
% 11.66/2.03 inference(superposition,[],[f3813,f1040])).
% 11.66/2.03 tff(f1040,plain,(
% 11.66/2.03 ( ! [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)) ) | ~spl32_89),
% 11.66/2.03 inference(avatar_component_clause,[],[f1039])).
% 11.66/2.03 tff(f3813,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X1)),X3 : X1,X4 : X0] : (aa(X1,X1,aa(X0,fun(X1,X1),X2,X4),X3) = foldr(X0,X1,X2,insert(X0,X4,nil(X0)),X3)) ) | ~spl32_275),
% 11.66/2.03 inference(avatar_component_clause,[],[f3812])).
% 11.66/2.03 tff(f1457,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (fTrue = aa(dB,bool,combc(dB,dB,bool,beta,subst(X0,X1,zero_zero(nat))),aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X0)))) ) | (~spl32_18 | ~spl32_110)),
% 11.66/2.03 inference(resolution,[],[f1453,f627])).
% 11.66/2.03 tff(f627,plain,(
% 11.66/2.03 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | ~spl32_18),
% 11.66/2.03 inference(avatar_component_clause,[],[f626])).
% 11.66/2.03 tff(f1453,plain,(
% 11.66/2.03 ( ! [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))))) ) | ~spl32_110),
% 11.66/2.03 inference(avatar_component_clause,[],[f1452])).
% 11.66/2.03 tff(f18515,plain,(
% 11.66/2.03 ~pp(aa(dB,bool,combc(dB,dB,bool,beta,subst(r,a,zero_zero(nat))),foldr(dB,dB,app,insert(dB,abs(r),nil(dB)),a))) | (spl32_32 | ~spl32_489)),
% 11.66/2.03 inference(resolution,[],[f18440,f700])).
% 11.66/2.03 tff(f700,plain,(
% 11.66/2.03 ~pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as)))) | spl32_32),
% 11.66/2.03 inference(avatar_component_clause,[],[f698])).
% 11.66/2.03 tff(f18440,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X3,X2)),foldl(dB,dB,app,X0,cons(dB,X1,X2)))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X3),foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1)))) ) | ~spl32_489),
% 11.66/2.03 inference(avatar_component_clause,[],[f18439])).
% 11.66/2.03 tff(f18445,plain,(
% 11.66/2.03 spl32_490 | ~spl32_89 | ~spl32_108 | ~spl32_152 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12880,f3812,f1983,f1325,f1039,f18443])).
% 11.66/2.03 tff(f18443,plain,(
% 11.66/2.03 spl32_490 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1)),X3)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,cons(dB,X1,X2))),foldl(dB,dB,app,X3,X2))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_490])])).
% 11.66/2.03 tff(f1325,plain,(
% 11.66/2.03 spl32_108 <=> ! [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)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_108])])).
% 11.66/2.03 tff(f1983,plain,(
% 11.66/2.03 spl32_152 <=> ! [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))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_152])])).
% 11.66/2.03 tff(f12880,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1)),X3)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,cons(dB,X1,X2))),foldl(dB,dB,app,X3,X2)))) ) | (~spl32_89 | ~spl32_108 | ~spl32_152 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2008,f3939])).
% 11.66/2.03 tff(f2008,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),X3)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,cons(dB,X1,X2))),foldl(dB,dB,app,X3,X2)))) ) | (~spl32_89 | ~spl32_108 | ~spl32_152)),
% 11.66/2.03 inference(forward_demodulation,[],[f1998,f1040])).
% 11.66/2.03 tff(f1998,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,cons(dB,X1,X2))),foldl(dB,dB,app,X3,X2))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)),X3))) ) | (~spl32_108 | ~spl32_152)),
% 11.66/2.03 inference(superposition,[],[f1984,f1326])).
% 11.66/2.03 tff(f1326,plain,(
% 11.66/2.03 ( ! [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)) ) | ~spl32_108),
% 11.66/2.03 inference(avatar_component_clause,[],[f1325])).
% 11.66/2.03 tff(f1984,plain,(
% 11.66/2.03 ( ! [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,combc(dB,dB,bool,beta,X1),X2))) ) | ~spl32_152),
% 11.66/2.03 inference(avatar_component_clause,[],[f1983])).
% 11.66/2.03 tff(f18441,plain,(
% 11.66/2.03 spl32_489 | ~spl32_89 | ~spl32_108 | ~spl32_152 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12879,f3812,f1983,f1325,f1039,f18439])).
% 11.66/2.03 tff(f12879,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X3),foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X3,X2)),foldl(dB,dB,app,X0,cons(dB,X1,X2))))) ) | (~spl32_89 | ~spl32_108 | ~spl32_152 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2010,f3939])).
% 11.66/2.03 tff(f2010,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X3),aa(dB,dB,combc(dB,dB,dB,app,X1),X0))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X3,X2)),foldl(dB,dB,app,X0,cons(dB,X1,X2))))) ) | (~spl32_89 | ~spl32_108 | ~spl32_152)),
% 11.66/2.03 inference(forward_demodulation,[],[f2000,f1040])).
% 11.66/2.03 tff(f2000,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X3,X2)),foldl(dB,dB,app,X0,cons(dB,X1,X2)))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X3),aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1)))) ) | (~spl32_108 | ~spl32_152)),
% 11.66/2.03 inference(superposition,[],[f1984,f1326])).
% 11.66/2.03 tff(f18437,plain,(
% 11.66/2.03 spl32_488 | ~spl32_107 | ~spl32_159),
% 11.66/2.03 inference(avatar_split_clause,[],[f2092,f2084,f1321,f18435])).
% 11.66/2.03 tff(f18435,plain,(
% 11.66/2.03 spl32_488 <=> ! [X1 : $tType,X0 : $tType,X3 : list(fun(X1,X1)),X4 : fun(X0,X1),X5 : X0,X2 : fun(X1,X1)] : aa(X1,X1,X2,aa(X0,X1,foldr(fun(X1,X1),fun(X0,X1),combb(X1,X1,X0),X3,X4),X5)) = aa(X0,X1,foldr(fun(X1,X1),fun(X0,X1),combb(X1,X1,X0),cons(fun(X1,X1),X2,X3),X4),X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_488])])).
% 11.66/2.03 tff(f1321,plain,(
% 11.66/2.03 spl32_107 <=> ! [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))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_107])])).
% 11.66/2.03 tff(f2084,plain,(
% 11.66/2.03 spl32_159 <=> ! [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))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_159])])).
% 11.66/2.03 tff(f2092,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X1),X3 : list(fun(X1,X1)),X4 : fun(X0,X1),X5 : X0] : (aa(X1,X1,X2,aa(X0,X1,foldr(fun(X1,X1),fun(X0,X1),combb(X1,X1,X0),X3,X4),X5)) = aa(X0,X1,foldr(fun(X1,X1),fun(X0,X1),combb(X1,X1,X0),cons(fun(X1,X1),X2,X3),X4),X5)) ) | (~spl32_107 | ~spl32_159)),
% 11.66/2.03 inference(superposition,[],[f2085,f1322])).
% 11.66/2.03 tff(f1322,plain,(
% 11.66/2.03 ( ! [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))) ) | ~spl32_107),
% 11.66/2.03 inference(avatar_component_clause,[],[f1321])).
% 11.66/2.03 tff(f2085,plain,(
% 11.66/2.03 ( ! [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))) ) | ~spl32_159),
% 11.66/2.03 inference(avatar_component_clause,[],[f2084])).
% 11.66/2.03 tff(f18161,plain,(
% 11.66/2.03 spl32_487 | ~spl32_89 | ~spl32_275 | ~spl32_482),
% 11.66/2.03 inference(avatar_split_clause,[],[f18141,f18137,f3812,f1039,f18159])).
% 11.66/2.03 tff(f18159,plain,(
% 11.66/2.03 spl32_487 <=> ! [X0 : $tType,X3 : type,X4 : fun(nat,fun(type,X0)),X6 : fun(nat,X0),X5 : type,X2 : type,X1 : fun(type,fun(type,fun(type,X0)))] : aa(type,X0,type_case(fun(type,X0),X4,X1,foldr(type,type,fun1,insert(type,X2,nil(type)),X3)),X5) = type_case(X0,X6,aa(type,fun(type,fun(type,X0)),X1,X2),foldr(type,type,fun1,insert(type,X3,nil(type)),X5))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_487])])).
% 11.66/2.03 tff(f18137,plain,(
% 11.66/2.03 spl32_482 <=> ! [X0 : $tType,X3 : type,X4 : fun(nat,fun(type,X0)),X6 : fun(nat,X0),X5 : type,X2 : type,X1 : fun(type,fun(type,fun(type,X0)))] : type_case(X0,X6,aa(type,fun(type,fun(type,X0)),X1,X2),aa(type,type,combc(type,type,type,fun1,X5),X3)) = aa(type,X0,type_case(fun(type,X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_482])])).
% 11.66/2.03 tff(f18141,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,fun(type,X0))),X6 : fun(nat,X0),X4 : fun(nat,fun(type,X0)),X5 : type] : (aa(type,X0,type_case(fun(type,X0),X4,X1,foldr(type,type,fun1,insert(type,X2,nil(type)),X3)),X5) = type_case(X0,X6,aa(type,fun(type,fun(type,X0)),X1,X2),foldr(type,type,fun1,insert(type,X3,nil(type)),X5))) ) | (~spl32_89 | ~spl32_275 | ~spl32_482)),
% 11.66/2.03 inference(forward_demodulation,[],[f18140,f3939])).
% 11.66/2.03 tff(f18140,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,fun(type,X0))),X6 : fun(nat,X0),X4 : fun(nat,fun(type,X0)),X5 : type] : (type_case(X0,X6,aa(type,fun(type,fun(type,X0)),X1,X2),aa(type,type,combc(type,type,type,fun1,X5),X3)) = aa(type,X0,type_case(fun(type,X0),X4,X1,foldr(type,type,fun1,insert(type,X2,nil(type)),X3)),X5)) ) | (~spl32_89 | ~spl32_275 | ~spl32_482)),
% 11.66/2.03 inference(forward_demodulation,[],[f18138,f3939])).
% 11.66/2.03 tff(f18138,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,fun(type,X0))),X6 : fun(nat,X0),X4 : fun(nat,fun(type,X0)),X5 : type] : (type_case(X0,X6,aa(type,fun(type,fun(type,X0)),X1,X2),aa(type,type,combc(type,type,type,fun1,X5),X3)) = aa(type,X0,type_case(fun(type,X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X5)) ) | ~spl32_482),
% 11.66/2.03 inference(avatar_component_clause,[],[f18137])).
% 11.66/2.03 tff(f18157,plain,(
% 11.66/2.03 spl32_486 | ~spl32_28 | ~spl32_179),
% 11.66/2.03 inference(avatar_split_clause,[],[f2354,f2342,f676,f18155])).
% 11.66/2.03 tff(f18155,plain,(
% 11.66/2.03 spl32_486 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X1,nil(dB),X0)),X0)) | sP0(X1,nil(dB),X0) | foldl(dB,dB,app,X0,sK15(X1,nil(dB),X0)) = X1)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_486])])).
% 11.66/2.03 tff(f676,plain,(
% 11.66/2.03 spl32_28 <=> ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : foldl(X1,X0,X3,X2,nil(X0)) = X2),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_28])])).
% 11.66/2.03 tff(f2342,plain,(
% 11.66/2.03 spl32_179 <=> ! [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,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_179])])).
% 11.66/2.03 tff(f2354,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X1,nil(dB),X0)),X0)) | sP0(X1,nil(dB),X0) | foldl(dB,dB,app,X0,sK15(X1,nil(dB),X0)) = X1) ) | (~spl32_28 | ~spl32_179)),
% 11.66/2.03 inference(superposition,[],[f2343,f677])).
% 11.66/2.03 tff(f677,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : (foldl(X1,X0,X3,X2,nil(X0)) = X2) ) | ~spl32_28),
% 11.66/2.03 inference(avatar_component_clause,[],[f676])).
% 11.66/2.03 tff(f2343,plain,(
% 11.66/2.03 ( ! [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,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0) ) | ~spl32_179),
% 11.66/2.03 inference(avatar_component_clause,[],[f2342])).
% 11.66/2.03 tff(f18153,plain,(
% 11.66/2.03 spl32_485 | ~spl32_33 | ~spl32_179),
% 11.66/2.03 inference(avatar_split_clause,[],[f2352,f2342,f704,f18151])).
% 11.66/2.03 tff(f18151,plain,(
% 11.66/2.03 spl32_485 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | ~member(dB,foldl(dB,dB,app,X2,X1),combc(dB,dB,bool,beta,X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_485])])).
% 11.66/2.03 tff(f704,plain,(
% 11.66/2.03 spl32_33 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~member(X0,X2,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_33])])).
% 11.66/2.03 tff(f2352,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | ~member(dB,foldl(dB,dB,app,X2,X1),combc(dB,dB,bool,beta,X0))) ) | (~spl32_33 | ~spl32_179)),
% 11.66/2.03 inference(resolution,[],[f2343,f705])).
% 11.66/2.03 tff(f705,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~member(X0,X2,X1)) ) | ~spl32_33),
% 11.66/2.03 inference(avatar_component_clause,[],[f704])).
% 11.66/2.03 tff(f18149,plain,(
% 11.66/2.03 spl32_484 | ~spl32_33 | ~spl32_177),
% 11.66/2.03 inference(avatar_split_clause,[],[f2327,f2321,f704,f18147])).
% 11.66/2.03 tff(f18147,plain,(
% 11.66/2.03 spl32_484 <=> ! [X2 : nat,X0 : fun(nat,type),X1 : dB,X3 : type] : (~pp(aa(type,bool,typing(X0,X1),t)) | ~it(X1) | it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X1,X2)) | ~member(type,X3,typing(shift(type,X0,X2,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_484])])).
% 11.66/2.03 tff(f2321,plain,(
% 11.66/2.03 spl32_177 <=> ! [X0 : dB,X3 : fun(nat,type),X2 : nat,X1 : type] : (it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),t)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_177])])).
% 11.66/2.03 tff(f2327,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,X1),t)) | ~it(X1) | it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X1,X2)) | ~member(type,X3,typing(shift(type,X0,X2,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)))) ) | (~spl32_33 | ~spl32_177)),
% 11.66/2.03 inference(resolution,[],[f2322,f705])).
% 11.66/2.03 tff(f2322,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type] : (~pp(aa(type,bool,typing(shift(type,X3,X2,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),X1)) | ~pp(aa(type,bool,typing(X3,X0),t)) | ~it(X0) | it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X0,X2))) ) | ~spl32_177),
% 11.66/2.03 inference(avatar_component_clause,[],[f2321])).
% 11.66/2.03 tff(f18145,plain,(
% 11.66/2.03 spl32_483 | ~spl32_78 | ~spl32_150),
% 11.66/2.03 inference(avatar_split_clause,[],[f1970,f1957,f961,f18143])).
% 11.66/2.03 tff(f18143,plain,(
% 11.66/2.03 spl32_483 <=> ! [X0 : $tType,X2 : X0,X3 : X0,X4 : list(X0),X5 : fun(X0,fun(X0,bool)),X1 : list(X0)] : (cons(X0,X3,X4) = cons(X0,sK27(X0,X1,X2,cons(X0,X3,X4),X5),X1) | cons(X0,X3,X4) = cons(X0,X2,sK26(X0,X1,X2,cons(X0,X3,X4),X5)) | ~sP2(X0,X1,X4,X5,X3,X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_483])])).
% 11.66/2.03 tff(f961,plain,(
% 11.66/2.03 spl32_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)) | ~sP2(X0,X1,X3,X5,X4,X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_78])])).
% 11.66/2.03 tff(f1957,plain,(
% 11.66/2.03 spl32_150 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3 | cons(X0,sK27(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_150])])).
% 11.66/2.03 tff(f1970,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : list(X0),X4 : list(X0),X5 : fun(X0,fun(X0,bool))] : (cons(X0,X3,X4) = cons(X0,sK27(X0,X1,X2,cons(X0,X3,X4),X5),X1) | cons(X0,X3,X4) = cons(X0,X2,sK26(X0,X1,X2,cons(X0,X3,X4),X5)) | ~sP2(X0,X1,X4,X5,X3,X2)) ) | (~spl32_78 | ~spl32_150)),
% 11.66/2.03 inference(resolution,[],[f1958,f962])).
% 11.66/2.03 tff(f962,plain,(
% 11.66/2.03 ( ! [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)) | ~sP2(X0,X1,X3,X5,X4,X2)) ) | ~spl32_78),
% 11.66/2.03 inference(avatar_component_clause,[],[f961])).
% 11.66/2.03 tff(f1958,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (~step1(X0,X4,X3,cons(X0,X2,X1)) | cons(X0,sK27(X0,X1,X2,X3,X4),X1) = X3 | cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3) ) | ~spl32_150),
% 11.66/2.03 inference(avatar_component_clause,[],[f1957])).
% 11.66/2.03 tff(f18139,plain,(
% 11.66/2.03 spl32_482 | ~spl32_119),
% 11.66/2.03 inference(avatar_split_clause,[],[f1530,f1527,f18137])).
% 11.66/2.03 tff(f1527,plain,(
% 11.66/2.03 spl32_119 <=> ! [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))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_119])])).
% 11.66/2.03 tff(f1530,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,fun(type,X0))),X6 : fun(nat,X0),X4 : fun(nat,fun(type,X0)),X5 : type] : (type_case(X0,X6,aa(type,fun(type,fun(type,X0)),X1,X2),aa(type,type,combc(type,type,type,fun1,X5),X3)) = aa(type,X0,type_case(fun(type,X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X5)) ) | ~spl32_119),
% 11.66/2.03 inference(superposition,[],[f1528,f1528])).
% 11.66/2.03 tff(f1528,plain,(
% 11.66/2.03 ( ! [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))) ) | ~spl32_119),
% 11.66/2.03 inference(avatar_component_clause,[],[f1527])).
% 11.66/2.03 tff(f17984,plain,(
% 11.66/2.03 spl32_481 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1074,f1060,f17982])).
% 11.66/2.03 tff(f17982,plain,(
% 11.66/2.03 spl32_481 <=> ! [X0 : $tType,X1 : $tType,X5 : fun(list(list(X0)),X1),X4 : list(X0),X6 : X1,X3 : X0,X2 : fun(X0,fun(list(X0),fun(list(list(X0)),X1))),X7 : list(list(X0))] : list_case(X1,list(X0),X6,aa(X0,fun(list(X0),fun(list(list(X0)),X1)),X2,X3),cons(list(X0),X4,X7)) = aa(list(list(X0)),X1,list_case(fun(list(list(X0)),X1),X0,X5,X2,cons(X0,X3,X4)),X7)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_481])])).
% 11.66/2.03 tff(f1060,plain,(
% 11.66/2.03 spl32_91 <=> ! [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)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_91])])).
% 11.66/2.03 tff(f1074,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),fun(list(list(X0)),X1))),X3 : X0,X6 : X1,X7 : list(list(X0)),X4 : list(X0),X5 : fun(list(list(X0)),X1)] : (list_case(X1,list(X0),X6,aa(X0,fun(list(X0),fun(list(list(X0)),X1)),X2,X3),cons(list(X0),X4,X7)) = aa(list(list(X0)),X1,list_case(fun(list(list(X0)),X1),X0,X5,X2,cons(X0,X3,X4)),X7)) ) | ~spl32_91),
% 11.66/2.03 inference(superposition,[],[f1061,f1061])).
% 11.66/2.03 tff(f1061,plain,(
% 11.66/2.03 ( ! [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)) ) | ~spl32_91),
% 11.66/2.03 inference(avatar_component_clause,[],[f1060])).
% 11.66/2.03 tff(f17882,plain,(
% 11.66/2.03 spl32_480 | ~spl32_28 | ~spl32_174),
% 11.66/2.03 inference(avatar_split_clause,[],[f2288,f2280,f676,f17880])).
% 11.66/2.03 tff(f17880,plain,(
% 11.66/2.03 spl32_480 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X1,nil(dB),X0)),X0)) | sP0(X1,nil(dB),X0) | step1(dB,beta,nil(dB),sK15(X1,nil(dB),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_480])])).
% 11.66/2.03 tff(f2280,plain,(
% 11.66/2.03 spl32_174 <=> ! [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,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_174])])).
% 11.66/2.03 tff(f2288,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X1,nil(dB),X0)),X0)) | sP0(X1,nil(dB),X0) | step1(dB,beta,nil(dB),sK15(X1,nil(dB),X0))) ) | (~spl32_28 | ~spl32_174)),
% 11.66/2.03 inference(superposition,[],[f2281,f677])).
% 11.66/2.03 tff(f2281,plain,(
% 11.66/2.03 ( ! [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,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2))) ) | ~spl32_174),
% 11.66/2.03 inference(avatar_component_clause,[],[f2280])).
% 11.66/2.03 tff(f17878,plain,(
% 11.66/2.03 spl32_479 | ~spl32_129 | ~spl32_158),
% 11.66/2.03 inference(avatar_split_clause,[],[f2069,f2062,f1694,f17876])).
% 11.66/2.03 tff(f17876,plain,(
% 11.66/2.03 spl32_479 <=> ! [X4 : type,X0 : dB,X3 : fun(nat,type),X2 : list(dB),X1 : list(dB)] : (cons(dB,X0,sK26(dB,X1,X0,X2,beta)) = X2 | ~step1(dB,beta,X2,cons(dB,X0,X1)) | pp(aa(type,bool,typing(X3,X0),X4)) | ~pp(aa(type,bool,typing(X3,sK27(dB,X1,X0,X2,beta)),X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_479])])).
% 11.66/2.03 tff(f1694,plain,(
% 11.66/2.03 spl32_129 <=> ! [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)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_129])])).
% 11.66/2.03 tff(f2062,plain,(
% 11.66/2.03 spl32_158 <=> ! [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),sK27(X0,X1,X2,X3,X4))) | cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_158])])).
% 11.66/2.03 tff(f2069,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : list(dB),X4 : type] : (cons(dB,X0,sK26(dB,X1,X0,X2,beta)) = X2 | ~step1(dB,beta,X2,cons(dB,X0,X1)) | pp(aa(type,bool,typing(X3,X0),X4)) | ~pp(aa(type,bool,typing(X3,sK27(dB,X1,X0,X2,beta)),X4))) ) | (~spl32_129 | ~spl32_158)),
% 11.66/2.03 inference(resolution,[],[f2063,f1695])).
% 11.66/2.03 tff(f1695,plain,(
% 11.66/2.03 ( ! [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))) ) | ~spl32_129),
% 11.66/2.03 inference(avatar_component_clause,[],[f1694])).
% 11.66/2.03 tff(f2063,plain,(
% 11.66/2.03 ( ! [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),sK27(X0,X1,X2,X3,X4))) | cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | ~spl32_158),
% 11.66/2.03 inference(avatar_component_clause,[],[f2062])).
% 11.66/2.03 tff(f17874,plain,(
% 11.66/2.03 spl32_478 | ~spl32_149 | ~spl32_156),
% 11.66/2.03 inference(avatar_split_clause,[],[f2046,f2041,f1953,f17872])).
% 11.66/2.03 tff(f17872,plain,(
% 11.66/2.03 spl32_478 <=> ! [X4 : nat,X0 : fun(nat,type),X3 : list(dB),X2 : type,X1 : list(dB)] : (~pp(aa(list(type),bool,typings(X0,X1),sK23(X2,X3,X4,X0))) | pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X4),X1)),X2)) | ~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X4),X3)),X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_478])])).
% 11.66/2.03 tff(f1953,plain,(
% 11.66/2.03 spl32_149 <=> ! [X0 : type,X3 : fun(nat,type),X2 : nat,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK23(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_149])])).
% 11.66/2.03 tff(f2041,plain,(
% 11.66/2.03 spl32_156 <=> ! [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))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_156])])).
% 11.66/2.03 tff(f2046,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : list(dB),X0 : fun(nat,type),X1 : list(dB),X4 : nat] : (~pp(aa(list(type),bool,typings(X0,X1),sK23(X2,X3,X4,X0))) | pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X4),X1)),X2)) | ~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X4),X3)),X2))) ) | (~spl32_149 | ~spl32_156)),
% 11.66/2.03 inference(resolution,[],[f2042,f1954])).
% 11.66/2.03 tff(f1954,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK23(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0))) ) | ~spl32_149),
% 11.66/2.03 inference(avatar_component_clause,[],[f1953])).
% 11.66/2.03 tff(f2042,plain,(
% 11.66/2.03 ( ! [X2 : list(type),X3 : dB,X0 : list(dB),X1 : type,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))) ) | ~spl32_156),
% 11.66/2.03 inference(avatar_component_clause,[],[f2041])).
% 11.66/2.03 tff(f17869,plain,(
% 11.66/2.03 spl32_477 | ~spl32_91 | ~spl32_119),
% 11.66/2.03 inference(avatar_split_clause,[],[f1543,f1527,f1060,f17867])).
% 11.66/2.03 tff(f17867,plain,(
% 11.66/2.03 spl32_477 <=> ! [X0 : $tType,X5 : X0,X3 : type,X4 : fun(nat,fun(list(type),X0)),X6 : list(type),X2 : type,X1 : fun(type,fun(type,fun(list(type),X0)))] : list_case(X0,type,X5,aa(type,fun(type,fun(list(type),X0)),X1,X2),cons(type,X3,X6)) = aa(list(type),X0,type_case(fun(list(type),X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X6)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_477])])).
% 11.66/2.03 tff(f1543,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,fun(list(type),X0))),X6 : list(type),X4 : fun(nat,fun(list(type),X0)),X5 : X0] : (list_case(X0,type,X5,aa(type,fun(type,fun(list(type),X0)),X1,X2),cons(type,X3,X6)) = aa(list(type),X0,type_case(fun(list(type),X0),X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)),X6)) ) | (~spl32_91 | ~spl32_119)),
% 11.66/2.03 inference(superposition,[],[f1061,f1528])).
% 11.66/2.03 tff(f17864,plain,(
% 11.66/2.03 spl32_476 | ~spl32_89 | ~spl32_119),
% 11.66/2.03 inference(avatar_split_clause,[],[f1531,f1527,f1039,f17862])).
% 11.66/2.03 tff(f17862,plain,(
% 11.66/2.03 spl32_476 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : type,X6 : fun(nat,X0),X5 : type,X2 : fun(X1,fun(type,fun(type,X0)))] : type_case(X0,X6,aa(X1,fun(type,fun(type,X0)),X2,X3),aa(type,type,combc(type,type,type,fun1,X5),X4)) = aa(type,X0,aa(X1,fun(type,X0),combc(X1,type,fun(type,X0),X2,X4),X3),X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_476])])).
% 11.66/2.03 tff(f1531,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(type,fun(type,X0))),X3 : X1,X6 : fun(nat,X0),X4 : type,X5 : type] : (type_case(X0,X6,aa(X1,fun(type,fun(type,X0)),X2,X3),aa(type,type,combc(type,type,type,fun1,X5),X4)) = aa(type,X0,aa(X1,fun(type,X0),combc(X1,type,fun(type,X0),X2,X4),X3),X5)) ) | (~spl32_89 | ~spl32_119)),
% 11.66/2.03 inference(superposition,[],[f1528,f1040])).
% 11.66/2.03 tff(f17816,plain,(
% 11.66/2.03 spl32_475 | ~spl32_89 | ~spl32_275 | ~spl32_463),
% 11.66/2.03 inference(avatar_split_clause,[],[f12941,f12318,f3812,f1039,f17814])).
% 11.66/2.03 tff(f17814,plain,(
% 11.66/2.03 spl32_475 <=> ! [X4 : type,X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (~member(type,foldr(type,type,fun1,insert(type,X4,nil(type)),X3),typing(X0,X2)) | pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_475])])).
% 11.66/2.03 tff(f12318,plain,(
% 11.66/2.03 spl32_463 <=> ! [X4 : type,X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~member(type,aa(type,type,combc(type,type,type,fun1,X3),X4),typing(X0,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_463])])).
% 11.66/2.03 tff(f12941,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB,X4 : type] : (~member(type,foldr(type,type,fun1,insert(type,X4,nil(type)),X3),typing(X0,X2)) | pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4))) ) | (~spl32_89 | ~spl32_275 | ~spl32_463)),
% 11.66/2.03 inference(forward_demodulation,[],[f12940,f3939])).
% 11.66/2.03 tff(f12940,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB,X4 : type] : (pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~member(type,aa(type,type,combc(type,type,type,fun1,X3),X4),typing(X0,X2))) ) | (~spl32_89 | ~spl32_275 | ~spl32_463)),
% 11.66/2.03 inference(forward_demodulation,[],[f12319,f3939])).
% 11.66/2.03 tff(f12319,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB,X4 : type] : (pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~member(type,aa(type,type,combc(type,type,type,fun1,X3),X4),typing(X0,X2))) ) | ~spl32_463),
% 11.66/2.03 inference(avatar_component_clause,[],[f12318])).
% 11.66/2.03 tff(f17295,plain,(
% 11.66/2.03 spl32_474 | ~spl32_12 | ~spl32_89 | ~spl32_159),
% 11.66/2.03 inference(avatar_split_clause,[],[f2118,f2084,f1039,f599,f17293])).
% 11.66/2.03 tff(f17293,plain,(
% 11.66/2.03 spl32_474 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : fun(X0,X1),X2 : fun(X1,bool)] : (fTrue = aa(X0,bool,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2),X4) | fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_474])])).
% 11.66/2.03 tff(f599,plain,(
% 11.66/2.03 spl32_12 <=> ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_12])])).
% 11.66/2.03 tff(f2118,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,bool),X3 : fun(X0,X1),X4 : X0] : (fTrue = aa(X0,bool,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2),X4) | fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4))) ) | (~spl32_12 | ~spl32_89 | ~spl32_159)),
% 11.66/2.03 inference(forward_demodulation,[],[f2100,f1040])).
% 11.66/2.03 tff(f2100,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,bool),X3 : fun(X0,X1),X4 : X0] : (fFalse = aa(X1,bool,X2,aa(X0,X1,X3,X4)) | fTrue = aa(X0,bool,aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3),X4)) ) | (~spl32_12 | ~spl32_159)),
% 11.66/2.03 inference(superposition,[],[f2085,f600])).
% 11.66/2.03 tff(f600,plain,(
% 11.66/2.03 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) ) | ~spl32_12),
% 11.66/2.03 inference(avatar_component_clause,[],[f599])).
% 11.66/2.03 tff(f13707,plain,(
% 11.66/2.03 spl32_473 | ~spl32_89 | ~spl32_186 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12857,f3812,f2436,f1039,f13705])).
% 11.66/2.03 tff(f13705,plain,(
% 11.66/2.03 spl32_473 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (foldr(dB,dB,app,insert(dB,X2,nil(dB)),sK19(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK20(X0,X1,X2)),X2)) | sP1(X2,X0,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_473])])).
% 11.66/2.03 tff(f2436,plain,(
% 11.66/2.03 spl32_186 <=> ! [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,sK20(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(X2,X0,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_186])])).
% 11.66/2.03 tff(f12857,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (foldr(dB,dB,app,insert(dB,X2,nil(dB)),sK19(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK20(X0,X1,X2)),X2)) | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_186 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f12856,f3939])).
% 11.66/2.03 tff(f12856,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK20(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_186 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2437,f3939])).
% 11.66/2.03 tff(f2437,plain,(
% 11.66/2.03 ( ! [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,sK20(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(X2,X0,X1)) ) | ~spl32_186),
% 11.66/2.03 inference(avatar_component_clause,[],[f2436])).
% 11.66/2.03 tff(f13703,plain,(
% 11.66/2.03 spl32_472 | ~spl32_89 | ~spl32_189 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12836,f3812,f2464,f1039,f13701])).
% 11.66/2.03 tff(f13701,plain,(
% 11.66/2.03 spl32_472 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (foldr(dB,dB,app,insert(dB,sK20(X0,X1,X2),nil(dB)),X1) = X0 | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_472])])).
% 11.66/2.03 tff(f2464,plain,(
% 11.66/2.03 spl32_189 <=> ! [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),sK20(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_189])])).
% 11.66/2.03 tff(f12836,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (foldr(dB,dB,app,insert(dB,sK20(X0,X1,X2),nil(dB)),X1) = X0 | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_189 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f12835,f3939])).
% 11.66/2.03 tff(f12835,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1))) | aa(dB,dB,combc(dB,dB,dB,app,X1),sK20(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_189 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2465,f3939])).
% 11.66/2.03 tff(f2465,plain,(
% 11.66/2.03 ( ! [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),sK20(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | ~spl32_189),
% 11.66/2.03 inference(avatar_component_clause,[],[f2464])).
% 11.66/2.03 tff(f13696,plain,(
% 11.66/2.03 spl32_471 | ~spl32_89 | ~spl32_184 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12833,f3812,f2412,f1039,f13694])).
% 11.66/2.03 tff(f13694,plain,(
% 11.66/2.03 spl32_471 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK20(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_471])])).
% 11.66/2.03 tff(f2412,plain,(
% 11.66/2.03 spl32_184 <=> ! [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,sK20(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_184])])).
% 11.66/2.03 tff(f12833,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1))) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK20(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_184 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2413,f3939])).
% 11.66/2.03 tff(f2413,plain,(
% 11.66/2.03 ( ! [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,sK20(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | ~spl32_184),
% 11.66/2.03 inference(avatar_component_clause,[],[f2412])).
% 11.66/2.03 tff(f13667,plain,(
% 11.66/2.03 spl32_470 | ~spl32_89 | ~spl32_176 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12903,f3812,f2307,f1039,f13665])).
% 11.66/2.03 tff(f13665,plain,(
% 11.66/2.03 spl32_470 <=> ! [X2 : type,X4 : fun(nat,type),X0 : dB,X3 : dB,X1 : type] : (pp(aa(type,bool,typing(X4,foldr(dB,dB,app,insert(dB,X3,nil(dB)),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,insert(type,X2,nil(type)),X1))) | ~pp(aa(type,bool,typing(X4,X0),X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_470])])).
% 11.66/2.03 tff(f2307,plain,(
% 11.66/2.03 spl32_176 <=> ! [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)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_176])])).
% 11.66/2.03 tff(f12903,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (pp(aa(type,bool,typing(X4,foldr(dB,dB,app,insert(dB,X3,nil(dB)),X0)),X1)) | ~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,insert(type,X2,nil(type)),X1))) | ~pp(aa(type,bool,typing(X4,X0),X2))) ) | (~spl32_89 | ~spl32_176 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f12902,f3939])).
% 11.66/2.03 tff(f12902,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : dB,X1 : type,X4 : fun(nat,type)] : (~pp(aa(type,bool,typing(X4,X3),foldr(type,type,fun1,insert(type,X2,nil(type)),X1))) | 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))) ) | (~spl32_89 | ~spl32_176 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2308,f3939])).
% 11.66/2.03 tff(f2308,plain,(
% 11.66/2.03 ( ! [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))) ) | ~spl32_176),
% 11.66/2.03 inference(avatar_component_clause,[],[f2307])).
% 11.66/2.03 tff(f13620,plain,(
% 11.66/2.03 spl32_469 | ~spl32_89 | ~spl32_164 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12907,f3812,f2156,f1039,f13618])).
% 11.66/2.03 tff(f13618,plain,(
% 11.66/2.03 spl32_469 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (~pp(aa(type,bool,typing(X3,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X0)) | pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,insert(type,sK24(X0,X1,X2,X3),nil(type)),X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_469])])).
% 11.66/2.03 tff(f2156,plain,(
% 11.66/2.03 spl32_164 <=> ! [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),sK24(X0,X1,X2,X3)))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_164])])).
% 11.66/2.03 tff(f12907,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (~pp(aa(type,bool,typing(X3,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X0)) | pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,insert(type,sK24(X0,X1,X2,X3),nil(type)),X0)))) ) | (~spl32_89 | ~spl32_164 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f12906,f3939])).
% 11.66/2.03 tff(f12906,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,insert(type,sK24(X0,X1,X2,X3),nil(type)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X0))) ) | (~spl32_89 | ~spl32_164 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2157,f3939])).
% 11.66/2.03 tff(f2157,plain,(
% 11.66/2.03 ( ! [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),sK24(X0,X1,X2,X3)))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X0))) ) | ~spl32_164),
% 11.66/2.03 inference(avatar_component_clause,[],[f2156])).
% 11.66/2.03 tff(f13482,plain,(
% 11.66/2.03 spl32_468 | ~spl32_89 | ~spl32_148 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12908,f3812,f1938,f1039,f13480])).
% 11.66/2.03 tff(f13480,plain,(
% 11.66/2.03 spl32_468 <=> ! [X0 : type,X3 : fun(nat,type),X2 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,abs(X1)),foldr(type,type,fun1,insert(type,X2,nil(type)),X0))) | ~pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_468])])).
% 11.66/2.03 tff(f1938,plain,(
% 11.66/2.03 spl32_148 <=> ! [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)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_148])])).
% 11.66/2.03 tff(f12908,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,abs(X1)),foldr(type,type,fun1,insert(type,X2,nil(type)),X0))) | ~pp(aa(type,bool,typing(shift(type,X3,zero_zero(nat),X2),X1),X0))) ) | (~spl32_89 | ~spl32_148 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f1939,f3939])).
% 11.66/2.03 tff(f1939,plain,(
% 11.66/2.03 ( ! [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))) ) | ~spl32_148),
% 11.66/2.03 inference(avatar_component_clause,[],[f1938])).
% 11.66/2.03 tff(f13405,plain,(
% 11.66/2.03 spl32_467 | ~spl32_89 | ~spl32_137 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12913,f3812,f1788,f1039,f13403])).
% 11.66/2.03 tff(f13403,plain,(
% 11.66/2.03 spl32_467 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (~pp(aa(type,bool,typing(X3,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X0)) | pp(aa(type,bool,typing(X3,X1),sK24(X0,X1,X2,X3))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_467])])).
% 11.66/2.03 tff(f1788,plain,(
% 11.66/2.03 spl32_137 <=> ! [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),sK24(X0,X1,X2,X3))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_137])])).
% 11.66/2.03 tff(f12913,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (~pp(aa(type,bool,typing(X3,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X0)) | pp(aa(type,bool,typing(X3,X1),sK24(X0,X1,X2,X3)))) ) | (~spl32_89 | ~spl32_137 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f1789,f3939])).
% 11.66/2.03 tff(f1789,plain,(
% 11.66/2.03 ( ! [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),sK24(X0,X1,X2,X3)))) ) | ~spl32_137),
% 11.66/2.03 inference(avatar_component_clause,[],[f1788])).
% 11.66/2.03 tff(f13225,plain,(
% 11.66/2.03 spl32_466 | ~spl32_67 | ~spl32_89 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12832,f3812,f1039,f891,f13223])).
% 11.66/2.03 tff(f13223,plain,(
% 11.66/2.03 spl32_466 <=> ! [X0 : bool,X1 : bool] : (pp(foldr(bool,bool,fconj,insert(bool,X1,nil(bool)),X0)) | ~pp(X0) | ~pp(X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_466])])).
% 11.66/2.03 tff(f891,plain,(
% 11.66/2.03 spl32_67 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_67])])).
% 11.66/2.03 tff(f12832,plain,(
% 11.66/2.03 ( ! [X0 : bool,X1 : bool] : (pp(foldr(bool,bool,fconj,insert(bool,X1,nil(bool)),X0)) | ~pp(X0) | ~pp(X1)) ) | (~spl32_67 | ~spl32_89 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f892,f3939])).
% 11.66/2.03 tff(f892,plain,(
% 11.66/2.03 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1)) ) | ~spl32_67),
% 11.66/2.03 inference(avatar_component_clause,[],[f891])).
% 11.66/2.03 tff(f13218,plain,(
% 11.66/2.03 spl32_465 | ~spl32_53 | ~spl32_89 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12813,f3812,f1039,f819,f13216])).
% 11.66/2.03 tff(f13216,plain,(
% 11.66/2.03 spl32_465 <=> ! [X0 : bool,X1 : bool] : (~pp(foldr(bool,bool,fconj,insert(bool,X1,nil(bool)),X0)) | pp(X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_465])])).
% 11.66/2.03 tff(f819,plain,(
% 11.66/2.03 spl32_53 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_53])])).
% 11.66/2.03 tff(f12813,plain,(
% 11.66/2.03 ( ! [X0 : bool,X1 : bool] : (~pp(foldr(bool,bool,fconj,insert(bool,X1,nil(bool)),X0)) | pp(X1)) ) | (~spl32_53 | ~spl32_89 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f820,f3939])).
% 11.66/2.03 tff(f820,plain,(
% 11.66/2.03 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1)) ) | ~spl32_53),
% 11.66/2.03 inference(avatar_component_clause,[],[f819])).
% 11.66/2.03 tff(f13214,plain,(
% 11.66/2.03 spl32_464 | ~spl32_51 | ~spl32_89 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f12812,f3812,f1039,f808,f13212])).
% 11.66/2.03 tff(f13212,plain,(
% 11.66/2.03 spl32_464 <=> ! [X0 : bool,X1 : bool] : (~pp(foldr(bool,bool,fconj,insert(bool,X1,nil(bool)),X0)) | pp(X0))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_464])])).
% 11.66/2.03 tff(f808,plain,(
% 11.66/2.03 spl32_51 <=> ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_51])])).
% 11.66/2.03 tff(f12812,plain,(
% 11.66/2.03 ( ! [X0 : bool,X1 : bool] : (~pp(foldr(bool,bool,fconj,insert(bool,X1,nil(bool)),X0)) | pp(X0)) ) | (~spl32_51 | ~spl32_89 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f809,f3939])).
% 11.66/2.03 tff(f809,plain,(
% 11.66/2.03 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0)) ) | ~spl32_51),
% 11.66/2.03 inference(avatar_component_clause,[],[f808])).
% 11.66/2.03 tff(f12805,plain,(
% 11.66/2.03 ~spl32_29 | spl32_128),
% 11.66/2.03 inference(avatar_contradiction_clause,[],[f12804])).
% 11.66/2.03 tff(f12804,plain,(
% 11.66/2.03 $false | (~spl32_29 | spl32_128)),
% 11.66/2.03 inference(trivial_inequality_removal,[],[f12652])).
% 11.66/2.03 tff(f12652,plain,(
% 11.66/2.03 fTrue != fTrue | (~spl32_29 | spl32_128)),
% 11.66/2.03 inference(superposition,[],[f1691,f684])).
% 11.66/2.03 tff(f684,plain,(
% 11.66/2.03 ( ! [X0 : bool] : (fTrue = X0) ) | ~spl32_29),
% 11.66/2.03 inference(avatar_component_clause,[],[f683])).
% 11.66/2.03 tff(f683,plain,(
% 11.66/2.03 spl32_29 <=> ! [X0 : bool] : fTrue = X0),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_29])])).
% 11.66/2.03 tff(f1691,plain,(
% 11.66/2.03 fTrue != aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) | spl32_128),
% 11.66/2.03 inference(avatar_component_clause,[],[f1689])).
% 11.66/2.03 tff(f1689,plain,(
% 11.66/2.03 spl32_128 <=> fTrue = aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_128])])).
% 11.66/2.03 tff(f12803,plain,(
% 11.66/2.03 ~spl32_29 | spl32_30),
% 11.66/2.03 inference(avatar_contradiction_clause,[],[f12802])).
% 11.66/2.03 tff(f12802,plain,(
% 11.66/2.03 $false | (~spl32_29 | spl32_30)),
% 11.66/2.03 inference(trivial_inequality_removal,[],[f12777])).
% 11.66/2.03 tff(f12777,plain,(
% 11.66/2.03 fTrue != fTrue | (~spl32_29 | spl32_30)),
% 11.66/2.03 inference(superposition,[],[f688,f684])).
% 11.66/2.03 tff(f688,plain,(
% 11.66/2.03 fFalse != fTrue | spl32_30),
% 11.66/2.03 inference(avatar_component_clause,[],[f686])).
% 11.66/2.03 tff(f686,plain,(
% 11.66/2.03 spl32_30 <=> fFalse = fTrue),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_30])])).
% 11.66/2.03 tff(f12596,plain,(
% 11.66/2.03 spl32_29 | ~spl32_18 | ~spl32_253),
% 11.66/2.03 inference(avatar_split_clause,[],[f5860,f3233,f626,f683])).
% 11.66/2.03 tff(f3233,plain,(
% 11.66/2.03 spl32_253 <=> ! [X4 : bool] : (fTrue = X4 | pp(X4))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_253])])).
% 11.66/2.03 tff(f5860,plain,(
% 11.66/2.03 ( ! [X0 : bool] : (fTrue = X0) ) | (~spl32_18 | ~spl32_253)),
% 11.66/2.03 inference(duplicate_literal_removal,[],[f5811])).
% 11.66/2.03 tff(f5811,plain,(
% 11.66/2.03 ( ! [X0 : bool] : (fTrue = X0 | fTrue = X0) ) | (~spl32_18 | ~spl32_253)),
% 11.66/2.03 inference(resolution,[],[f3234,f627])).
% 11.66/2.03 tff(f3234,plain,(
% 11.66/2.03 ( ! [X4 : bool] : (pp(X4) | fTrue = X4) ) | ~spl32_253),
% 11.66/2.03 inference(avatar_component_clause,[],[f3233])).
% 11.66/2.03 tff(f12320,plain,(
% 11.66/2.03 spl32_463 | ~spl32_33 | ~spl32_176),
% 11.66/2.03 inference(avatar_split_clause,[],[f2312,f2307,f704,f12318])).
% 11.66/2.03 tff(f2312,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB,X4 : type] : (pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~member(type,aa(type,type,combc(type,type,type,fun1,X3),X4),typing(X0,X2))) ) | (~spl32_33 | ~spl32_176)),
% 11.66/2.03 inference(resolution,[],[f2308,f705])).
% 11.66/2.03 tff(f12315,plain,(
% 11.66/2.03 spl32_462 | ~spl32_33 | ~spl32_174),
% 11.66/2.03 inference(avatar_split_clause,[],[f2286,f2280,f704,f12313])).
% 11.66/2.03 tff(f12313,plain,(
% 11.66/2.03 spl32_462 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | ~member(dB,foldl(dB,dB,app,X2,X1),combc(dB,dB,bool,beta,X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_462])])).
% 11.66/2.03 tff(f2286,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | ~member(dB,foldl(dB,dB,app,X2,X1),combc(dB,dB,bool,beta,X0))) ) | (~spl32_33 | ~spl32_174)),
% 11.66/2.03 inference(resolution,[],[f2281,f705])).
% 11.66/2.03 tff(f12311,plain,(
% 11.66/2.03 spl32_461 | ~spl32_33 | ~spl32_168),
% 11.66/2.03 inference(avatar_split_clause,[],[f2205,f2199,f704,f12309])).
% 11.66/2.03 tff(f12309,plain,(
% 11.66/2.03 spl32_461 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~member(dB,foldl(dB,dB,app,X2,X1),combc(dB,dB,bool,beta,X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_461])])).
% 11.66/2.03 tff(f2199,plain,(
% 11.66/2.03 spl32_168 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_168])])).
% 11.66/2.03 tff(f2205,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~member(dB,foldl(dB,dB,app,X2,X1),combc(dB,dB,bool,beta,X0))) ) | (~spl32_33 | ~spl32_168)),
% 11.66/2.03 inference(resolution,[],[f2200,f705])).
% 11.66/2.03 tff(f2200,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0) ) | ~spl32_168),
% 11.66/2.03 inference(avatar_component_clause,[],[f2199])).
% 11.66/2.03 tff(f12307,plain,(
% 11.66/2.03 spl32_460 | ~spl32_89 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1073,f1060,f1039,f12305])).
% 11.66/2.03 tff(f12305,plain,(
% 11.66/2.03 spl32_460 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X6 : X1,X4 : X2,X7 : list(X0),X5 : X0,X3 : fun(X2,fun(X0,fun(list(X0),X1)))] : list_case(X1,X0,X6,aa(X2,fun(X0,fun(list(X0),X1)),X3,X4),cons(X0,X5,X7)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),combc(X2,X0,fun(list(X0),X1),X3,X5),X4),X7)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_460])])).
% 11.66/2.03 tff(f1073,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : fun(X2,fun(X0,fun(list(X0),X1))),X6 : X1,X7 : list(X0),X4 : X2,X5 : X0] : (list_case(X1,X0,X6,aa(X2,fun(X0,fun(list(X0),X1)),X3,X4),cons(X0,X5,X7)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),combc(X2,X0,fun(list(X0),X1),X3,X5),X4),X7)) ) | (~spl32_89 | ~spl32_91)),
% 11.66/2.03 inference(superposition,[],[f1061,f1040])).
% 11.66/2.03 tff(f12303,plain,(
% 11.66/2.03 spl32_459 | ~spl32_89 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1072,f1060,f1039,f12301])).
% 11.66/2.03 tff(f12301,plain,(
% 11.66/2.03 spl32_459 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X6 : X1,X4 : X2,X7 : list(X0),X5 : X0,X3 : fun(X0,fun(X2,fun(list(X0),X1)))] : list_case(X1,X0,X6,combc(X0,X2,fun(list(X0),X1),X3,X4),cons(X0,X5,X7)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),aa(X0,fun(X2,fun(list(X0),X1)),X3,X5),X4),X7)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_459])])).
% 11.66/2.03 tff(f1072,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : fun(X0,fun(X2,fun(list(X0),X1))),X6 : X1,X7 : list(X0),X4 : X2,X5 : X0] : (list_case(X1,X0,X6,combc(X0,X2,fun(list(X0),X1),X3,X4),cons(X0,X5,X7)) = aa(list(X0),X1,aa(X2,fun(list(X0),X1),aa(X0,fun(X2,fun(list(X0),X1)),X3,X5),X4),X7)) ) | (~spl32_89 | ~spl32_91)),
% 11.66/2.03 inference(superposition,[],[f1061,f1040])).
% 11.66/2.03 tff(f12298,plain,(
% 11.66/2.03 spl32_458 | ~spl32_89 | ~spl32_275 | ~spl32_455),
% 11.66/2.03 inference(avatar_split_clause,[],[f12131,f12128,f3812,f1039,f12296])).
% 11.66/2.03 tff(f12296,plain,(
% 11.66/2.03 spl32_458 <=> ! [X4 : type,X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,abs(X2),nil(dB)),X1)),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X4),X2),X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_458])])).
% 11.66/2.03 tff(f12128,plain,(
% 11.66/2.03 spl32_455 <=> ! [X4 : type,X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2))),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X4),X2),X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_455])])).
% 11.66/2.03 tff(f12131,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB,X4 : type] : (pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,abs(X2),nil(dB)),X1)),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X4),X2),X3))) ) | (~spl32_89 | ~spl32_275 | ~spl32_455)),
% 11.66/2.03 inference(forward_demodulation,[],[f12129,f3939])).
% 11.66/2.03 tff(f12129,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB,X4 : type] : (pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2))),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X4),X2),X3))) ) | ~spl32_455),
% 11.66/2.03 inference(avatar_component_clause,[],[f12128])).
% 11.66/2.03 tff(f12191,plain,(
% 11.66/2.03 spl32_457 | ~spl32_74 | ~spl32_252),
% 11.66/2.03 inference(avatar_split_clause,[],[f3324,f3230,f945,f12189])).
% 11.66/2.03 tff(f12189,plain,(
% 11.66/2.03 spl32_457 <=> ! [X2 : $tType,X0 : fun(bool,fun(nat,bool)),X3 : X2,X1 : bool] : (fTrue = foldl(bool,nat,X0,X1,insert(nat,zero_zero(nat),nil(nat))) | nil(X2) = sublist(X2,insert(X2,X3,nil(X2)),aa(bool,fun(nat,bool),X0,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_457])])).
% 11.66/2.03 tff(f945,plain,(
% 11.66/2.03 spl32_74 <=> ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_74])])).
% 11.66/2.03 tff(f3230,plain,(
% 11.66/2.03 spl32_252 <=> ! [X0 : $tType,X3 : X0,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (~member(X0,X3,aa(bool,fun(X0,bool),X1,X2)) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_252])])).
% 11.66/2.03 tff(f3324,plain,(
% 11.66/2.03 ( ! [X2 : $tType,X3 : X2,X0 : fun(bool,fun(nat,bool)),X1 : bool] : (fTrue = foldl(bool,nat,X0,X1,insert(nat,zero_zero(nat),nil(nat))) | nil(X2) = sublist(X2,insert(X2,X3,nil(X2)),aa(bool,fun(nat,bool),X0,X1))) ) | (~spl32_74 | ~spl32_252)),
% 11.66/2.03 inference(resolution,[],[f3231,f946])).
% 11.66/2.03 tff(f946,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (member(nat,zero_zero(nat),X2) | nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2)) ) | ~spl32_74),
% 11.66/2.03 inference(avatar_component_clause,[],[f945])).
% 11.66/2.03 tff(f3231,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool))] : (~member(X0,X3,aa(bool,fun(X0,bool),X1,X2)) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0)))) ) | ~spl32_252),
% 11.66/2.03 inference(avatar_component_clause,[],[f3230])).
% 11.66/2.03 tff(f12135,plain,(
% 11.66/2.03 spl32_456 | ~spl32_12 | ~spl32_89 | ~spl32_158 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f5972,f3812,f2062,f1039,f599,f12133])).
% 11.66/2.03 tff(f12133,plain,(
% 11.66/2.03 spl32_456 <=> ! [X0 : list(bool),X3 : fun(bool,fun(bool,bool)),X2 : list(bool),X1 : bool] : (pp(foldr(bool,bool,X3,insert(bool,fFalse,nil(bool)),X1)) | cons(bool,X1,sK26(bool,X0,X1,X2,X3)) = X2 | ~step1(bool,X3,X2,cons(bool,X1,X0)) | fTrue = sK27(bool,X0,X1,X2,X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_456])])).
% 11.66/2.03 tff(f5972,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X3 : fun(bool,fun(bool,bool)),X0 : list(bool),X1 : bool] : (pp(foldr(bool,bool,X3,insert(bool,fFalse,nil(bool)),X1)) | cons(bool,X1,sK26(bool,X0,X1,X2,X3)) = X2 | ~step1(bool,X3,X2,cons(bool,X1,X0)) | fTrue = sK27(bool,X0,X1,X2,X3)) ) | (~spl32_12 | ~spl32_89 | ~spl32_158 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2076,f3939])).
% 11.66/2.03 tff(f2076,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X3 : fun(bool,fun(bool,bool)),X0 : list(bool),X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,X3,X1),fFalse)) | cons(bool,X1,sK26(bool,X0,X1,X2,X3)) = X2 | ~step1(bool,X3,X2,cons(bool,X1,X0)) | fTrue = sK27(bool,X0,X1,X2,X3)) ) | (~spl32_12 | ~spl32_158)),
% 11.66/2.03 inference(superposition,[],[f2063,f600])).
% 11.66/2.03 tff(f12130,plain,(
% 11.66/2.03 spl32_455 | ~spl32_148 | ~spl32_176),
% 11.66/2.03 inference(avatar_split_clause,[],[f2310,f2307,f1938,f12128])).
% 11.66/2.03 tff(f2310,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB,X4 : type] : (pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2))),X3)) | ~pp(aa(type,bool,typing(X0,X1),X4)) | ~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X4),X2),X3))) ) | (~spl32_148 | ~spl32_176)),
% 11.66/2.03 inference(resolution,[],[f2308,f1939])).
% 11.66/2.03 tff(f12124,plain,(
% 11.66/2.03 spl32_454 | ~spl32_70 | ~spl32_164),
% 11.66/2.03 inference(avatar_split_clause,[],[f2159,f2156,f908,f12122])).
% 11.66/2.03 tff(f12122,plain,(
% 11.66/2.03 spl32_454 <=> ! [X0 : fun(nat,type),X3 : type,X2 : nat,X1 : dB] : (~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),var(X2))),X3)) | aa(nat,type,X0,X2) = aa(type,type,combc(type,type,type,fun1,X3),sK24(X3,X1,var(X2),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_454])])).
% 11.66/2.03 tff(f908,plain,(
% 11.66/2.03 spl32_70 <=> ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_70])])).
% 11.66/2.03 tff(f2159,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),var(X2))),X3)) | aa(nat,type,X0,X2) = aa(type,type,combc(type,type,type,fun1,X3),sK24(X3,X1,var(X2),X0))) ) | (~spl32_70 | ~spl32_164)),
% 11.66/2.03 inference(resolution,[],[f2157,f909])).
% 11.66/2.03 tff(f909,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (~pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) = X0) ) | ~spl32_70),
% 11.66/2.03 inference(avatar_component_clause,[],[f908])).
% 11.66/2.03 tff(f12120,plain,(
% 11.66/2.03 spl32_453 | ~spl32_48 | ~spl32_89 | ~spl32_159),
% 11.66/2.03 inference(avatar_split_clause,[],[f2121,f2084,f1039,f785,f12118])).
% 11.66/2.03 tff(f12118,plain,(
% 11.66/2.03 spl32_453 <=> ! [X0 : $tType,X3 : nat,X2 : fun(nat,X0),X1 : fun(X0,type)] : pp(aa(type,bool,typing(aa(fun(X0,type),fun(nat,type),combc(fun(X0,type),fun(nat,X0),fun(nat,type),combb(X0,type,nat),X2),X1),var(X3)),aa(X0,type,X1,aa(nat,X0,X2,X3))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_453])])).
% 11.66/2.03 tff(f785,plain,(
% 11.66/2.03 spl32_48 <=> ! [X2 : fun(nat,type),X1 : nat] : pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_48])])).
% 11.66/2.03 tff(f2121,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : fun(nat,X0),X3 : nat,X1 : fun(X0,type)] : (pp(aa(type,bool,typing(aa(fun(X0,type),fun(nat,type),combc(fun(X0,type),fun(nat,X0),fun(nat,type),combb(X0,type,nat),X2),X1),var(X3)),aa(X0,type,X1,aa(nat,X0,X2,X3))))) ) | (~spl32_48 | ~spl32_89 | ~spl32_159)),
% 11.66/2.03 inference(forward_demodulation,[],[f2107,f1040])).
% 11.66/2.03 tff(f2107,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : fun(nat,X0),X3 : nat,X1 : fun(X0,type)] : (pp(aa(type,bool,typing(aa(fun(nat,X0),fun(nat,type),aa(fun(X0,type),fun(fun(nat,X0),fun(nat,type)),combb(X0,type,nat),X1),X2),var(X3)),aa(X0,type,X1,aa(nat,X0,X2,X3))))) ) | (~spl32_48 | ~spl32_159)),
% 11.66/2.03 inference(superposition,[],[f786,f2085])).
% 11.66/2.03 tff(f786,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))) ) | ~spl32_48),
% 11.66/2.03 inference(avatar_component_clause,[],[f785])).
% 11.66/2.03 tff(f12116,plain,(
% 11.66/2.03 spl32_452 | ~spl32_135 | ~spl32_156),
% 11.66/2.03 inference(avatar_split_clause,[],[f2045,f2041,f1779,f12114])).
% 11.66/2.03 tff(f12114,plain,(
% 11.66/2.03 spl32_452 <=> ! [X4 : dB,X0 : fun(nat,type),X3 : list(dB),X2 : type,X1 : list(dB)] : (~pp(aa(list(type),bool,typings(X0,X1),sK22(X2,X3,X4,X0))) | pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X4,X1)),X2)) | ~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X4,X3)),X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_452])])).
% 11.66/2.03 tff(f1779,plain,(
% 11.66/2.03 spl32_135 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK22(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_135])])).
% 11.66/2.03 tff(f2045,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : list(dB),X0 : fun(nat,type),X1 : list(dB),X4 : dB] : (~pp(aa(list(type),bool,typings(X0,X1),sK22(X2,X3,X4,X0))) | pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X4,X1)),X2)) | ~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X4,X3)),X2))) ) | (~spl32_135 | ~spl32_156)),
% 11.66/2.03 inference(resolution,[],[f2042,f1780])).
% 11.66/2.03 tff(f1780,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK22(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl32_135),
% 11.66/2.03 inference(avatar_component_clause,[],[f1779])).
% 11.66/2.03 tff(f12112,plain,(
% 11.66/2.03 spl32_451 | ~spl32_134 | ~spl32_156),
% 11.66/2.03 inference(avatar_split_clause,[],[f2044,f2041,f1767,f12110])).
% 11.66/2.03 tff(f12110,plain,(
% 11.66/2.03 spl32_451 <=> ! [X4 : dB,X0 : fun(nat,type),X3 : list(dB),X2 : type,X1 : list(dB)] : (~pp(aa(list(type),bool,typings(X0,X1),sK21(X2,X3,X4,X0))) | pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X4,X1)),X2)) | ~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X4,X3)),X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_451])])).
% 11.66/2.03 tff(f1767,plain,(
% 11.66/2.03 spl32_134 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_134])])).
% 11.66/2.03 tff(f2044,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : list(dB),X0 : fun(nat,type),X1 : list(dB),X4 : dB] : (~pp(aa(list(type),bool,typings(X0,X1),sK21(X2,X3,X4,X0))) | pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X4,X1)),X2)) | ~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X4,X3)),X2))) ) | (~spl32_134 | ~spl32_156)),
% 11.66/2.03 inference(resolution,[],[f2042,f1768])).
% 11.66/2.03 tff(f1768,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl32_134),
% 11.66/2.03 inference(avatar_component_clause,[],[f1767])).
% 11.66/2.03 tff(f12108,plain,(
% 11.66/2.03 spl32_450 | ~spl32_129 | ~spl32_155),
% 11.66/2.03 inference(avatar_split_clause,[],[f2024,f2017,f1694,f12106])).
% 11.66/2.03 tff(f12106,plain,(
% 11.66/2.03 spl32_450 <=> ! [X4 : type,X0 : dB,X3 : fun(nat,type),X2 : list(dB),X1 : list(dB)] : (step1(dB,beta,sK26(dB,X1,X0,X2,beta),X1) | ~step1(dB,beta,X2,cons(dB,X0,X1)) | pp(aa(type,bool,typing(X3,X0),X4)) | ~pp(aa(type,bool,typing(X3,sK27(dB,X1,X0,X2,beta)),X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_450])])).
% 11.66/2.03 tff(f2017,plain,(
% 11.66/2.03 spl32_155 <=> ! [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),sK27(X0,X1,X2,X3,X4))) | step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_155])])).
% 11.66/2.03 tff(f2024,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : list(dB),X4 : type] : (step1(dB,beta,sK26(dB,X1,X0,X2,beta),X1) | ~step1(dB,beta,X2,cons(dB,X0,X1)) | pp(aa(type,bool,typing(X3,X0),X4)) | ~pp(aa(type,bool,typing(X3,sK27(dB,X1,X0,X2,beta)),X4))) ) | (~spl32_129 | ~spl32_155)),
% 11.66/2.03 inference(resolution,[],[f2018,f1695])).
% 11.66/2.03 tff(f2018,plain,(
% 11.66/2.03 ( ! [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),sK27(X0,X1,X2,X3,X4))) | step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | ~spl32_155),
% 11.66/2.03 inference(avatar_component_clause,[],[f2017])).
% 11.66/2.03 tff(f12103,plain,(
% 11.66/2.03 spl32_449 | ~spl32_89 | ~spl32_119),
% 11.66/2.03 inference(avatar_split_clause,[],[f1542,f1527,f1039,f12101])).
% 11.66/2.03 tff(f12101,plain,(
% 11.66/2.03 spl32_449 <=> ! [X1 : $tType,X0 : $tType,X5 : fun(nat,fun(X0,X1)),X3 : type,X4 : type,X6 : X0,X2 : fun(type,fun(type,fun(X0,X1)))] : aa(type,X1,combc(type,X0,X1,aa(type,fun(type,fun(X0,X1)),X2,X3),X6),X4) = aa(X0,X1,type_case(fun(X0,X1),X5,X2,aa(type,type,combc(type,type,type,fun1,X4),X3)),X6)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_449])])).
% 11.66/2.03 tff(f1542,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(type,fun(type,fun(X0,X1))),X3 : type,X6 : X0,X4 : type,X5 : fun(nat,fun(X0,X1))] : (aa(type,X1,combc(type,X0,X1,aa(type,fun(type,fun(X0,X1)),X2,X3),X6),X4) = aa(X0,X1,type_case(fun(X0,X1),X5,X2,aa(type,type,combc(type,type,type,fun1,X4),X3)),X6)) ) | (~spl32_89 | ~spl32_119)),
% 11.66/2.03 inference(superposition,[],[f1040,f1528])).
% 11.66/2.03 tff(f11619,plain,(
% 11.66/2.03 spl32_448 | ~spl32_89 | ~spl32_275 | ~spl32_444),
% 11.66/2.03 inference(avatar_split_clause,[],[f11603,f11599,f3812,f1039,f11617])).
% 11.66/2.03 tff(f11617,plain,(
% 11.66/2.03 spl32_448 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (member(dB,foldr(dB,dB,app,insert(dB,X1,nil(dB)),X2),combc(dB,dB,bool,beta,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X2))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_448])])).
% 11.66/2.03 tff(f11599,plain,(
% 11.66/2.03 spl32_444 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,aa(dB,dB,combc(dB,dB,dB,app,X2),X1),combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X2),X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_444])])).
% 11.66/2.03 tff(f11603,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (member(dB,foldr(dB,dB,app,insert(dB,X1,nil(dB)),X2),combc(dB,dB,bool,beta,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X2))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_444)),
% 11.66/2.03 inference(forward_demodulation,[],[f11602,f3939])).
% 11.66/2.03 tff(f11602,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (member(dB,aa(dB,dB,combc(dB,dB,dB,app,X2),X1),combc(dB,dB,bool,beta,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X2))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_444)),
% 11.66/2.03 inference(forward_demodulation,[],[f11600,f3939])).
% 11.66/2.03 tff(f11600,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,aa(dB,dB,combc(dB,dB,dB,app,X2),X1),combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X2),X0)))) ) | ~spl32_444),
% 11.66/2.03 inference(avatar_component_clause,[],[f11599])).
% 11.66/2.03 tff(f11615,plain,(
% 11.66/2.03 spl32_447 | ~spl32_89 | ~spl32_275 | ~spl32_443),
% 11.66/2.03 inference(avatar_split_clause,[],[f11597,f11593,f3812,f1039,f11613])).
% 11.66/2.03 tff(f11613,plain,(
% 11.66/2.03 spl32_447 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (member(dB,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1),combc(dB,dB,bool,beta,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X0))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_447])])).
% 11.66/2.03 tff(f11593,plain,(
% 11.66/2.03 spl32_443 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X0),X2))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_443])])).
% 11.66/2.03 tff(f11597,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (member(dB,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1),combc(dB,dB,bool,beta,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X0))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_443)),
% 11.66/2.03 inference(forward_demodulation,[],[f11596,f3939])).
% 11.66/2.03 tff(f11596,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (member(dB,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),combc(dB,dB,bool,beta,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X0))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_443)),
% 11.66/2.03 inference(forward_demodulation,[],[f11594,f3939])).
% 11.66/2.03 tff(f11594,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X0),X2)))) ) | ~spl32_443),
% 11.66/2.03 inference(avatar_component_clause,[],[f11593])).
% 11.66/2.03 tff(f11611,plain,(
% 11.66/2.03 spl32_446 | ~spl32_89 | ~spl32_275 | ~spl32_441),
% 11.66/2.03 inference(avatar_split_clause,[],[f11587,f11584,f3812,f1039,f11609])).
% 11.66/2.03 tff(f11609,plain,(
% 11.66/2.03 spl32_446 <=> ! [X4 : type,X0 : dB,X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (pp(aa(list(type),bool,typings(X3,X2),sK22(X4,X2,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_446])])).
% 11.66/2.03 tff(f11584,plain,(
% 11.66/2.03 spl32_441 <=> ! [X4 : type,X0 : dB,X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (pp(aa(list(type),bool,typings(X3,X2),sK22(X4,X2,aa(dB,dB,combc(dB,dB,dB,app,X1),X0),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_441])])).
% 11.66/2.03 tff(f11587,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : dB,X4 : type] : (pp(aa(list(type),bool,typings(X3,X2),sK22(X4,X2,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4))) ) | (~spl32_89 | ~spl32_275 | ~spl32_441)),
% 11.66/2.03 inference(forward_demodulation,[],[f11585,f3939])).
% 11.66/2.03 tff(f11585,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : dB,X4 : type] : (pp(aa(list(type),bool,typings(X3,X2),sK22(X4,X2,aa(dB,dB,combc(dB,dB,dB,app,X1),X0),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4))) ) | ~spl32_441),
% 11.66/2.03 inference(avatar_component_clause,[],[f11584])).
% 11.66/2.03 tff(f11607,plain,(
% 11.66/2.03 spl32_445 | ~spl32_89 | ~spl32_275 | ~spl32_440),
% 11.66/2.03 inference(avatar_split_clause,[],[f11582,f11579,f3812,f1039,f11605])).
% 11.66/2.03 tff(f11605,plain,(
% 11.66/2.03 spl32_445 <=> ! [X4 : type,X0 : dB,X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (pp(aa(list(type),bool,typings(X3,X2),sK21(X4,X2,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_445])])).
% 11.66/2.03 tff(f11579,plain,(
% 11.66/2.03 spl32_440 <=> ! [X4 : type,X0 : dB,X3 : fun(nat,type),X2 : list(dB),X1 : dB] : (pp(aa(list(type),bool,typings(X3,X2),sK21(X4,X2,aa(dB,dB,combc(dB,dB,dB,app,X1),X0),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_440])])).
% 11.66/2.03 tff(f11582,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : dB,X4 : type] : (pp(aa(list(type),bool,typings(X3,X2),sK21(X4,X2,foldr(dB,dB,app,insert(dB,X0,nil(dB)),X1),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4))) ) | (~spl32_89 | ~spl32_275 | ~spl32_440)),
% 11.66/2.03 inference(forward_demodulation,[],[f11580,f3939])).
% 11.66/2.03 tff(f11580,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : dB,X4 : type] : (pp(aa(list(type),bool,typings(X3,X2),sK21(X4,X2,aa(dB,dB,combc(dB,dB,dB,app,X1),X0),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4))) ) | ~spl32_440),
% 11.66/2.03 inference(avatar_component_clause,[],[f11579])).
% 11.66/2.03 tff(f11601,plain,(
% 11.66/2.03 spl32_444 | ~spl32_34 | ~spl32_172),
% 11.66/2.03 inference(avatar_split_clause,[],[f2257,f2252,f708,f11599])).
% 11.66/2.03 tff(f708,plain,(
% 11.66/2.03 spl32_34 <=> ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (member(X0,X2,X1) | ~pp(aa(X0,bool,X1,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_34])])).
% 11.66/2.03 tff(f2252,plain,(
% 11.66/2.03 spl32_172 <=> ! [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))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_172])])).
% 11.66/2.03 tff(f2257,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,aa(dB,dB,combc(dB,dB,dB,app,X2),X1),combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X2),X0)))) ) | (~spl32_34 | ~spl32_172)),
% 11.66/2.03 inference(resolution,[],[f2253,f709])).
% 11.66/2.03 tff(f709,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (~pp(aa(X0,bool,X1,X2)) | member(X0,X2,X1)) ) | ~spl32_34),
% 11.66/2.03 inference(avatar_component_clause,[],[f708])).
% 11.66/2.03 tff(f2253,plain,(
% 11.66/2.03 ( ! [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,combc(dB,dB,bool,beta,X1),X2))) ) | ~spl32_172),
% 11.66/2.03 inference(avatar_component_clause,[],[f2252])).
% 11.66/2.03 tff(f11595,plain,(
% 11.66/2.03 spl32_443 | ~spl32_34 | ~spl32_170),
% 11.66/2.03 inference(avatar_split_clause,[],[f2235,f2230,f708,f11593])).
% 11.66/2.03 tff(f2230,plain,(
% 11.66/2.03 spl32_170 <=> ! [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))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_170])])).
% 11.66/2.03 tff(f2235,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),combc(dB,dB,bool,beta,aa(dB,dB,combc(dB,dB,dB,app,X0),X2)))) ) | (~spl32_34 | ~spl32_170)),
% 11.66/2.03 inference(resolution,[],[f2231,f709])).
% 11.66/2.03 tff(f2231,plain,(
% 11.66/2.03 ( ! [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,combc(dB,dB,bool,beta,X1),X2))) ) | ~spl32_170),
% 11.66/2.03 inference(avatar_component_clause,[],[f2230])).
% 11.66/2.03 tff(f11591,plain,(
% 11.66/2.03 spl32_442 | ~spl32_91 | ~spl32_261),
% 11.66/2.03 inference(avatar_split_clause,[],[f3454,f3388,f1060,f11589])).
% 11.66/2.03 tff(f11589,plain,(
% 11.66/2.03 spl32_442 <=> ! [X4 : bool,X0 : fun(bool,fun(list(bool),bool)),X3 : bool,X2 : list(bool),X1 : bool] : (list_case(bool,bool,X3,X0,cons(bool,X1,X2)) = X4 | fTrue = foldl(bool,list(bool),X0,X1,insert(list(bool),X2,nil(list(bool)))) | fTrue = X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_442])])).
% 11.66/2.03 tff(f3388,plain,(
% 11.66/2.03 spl32_261 <=> ! [X3 : $tType,X5 : bool,X4 : fun(bool,fun(X3,bool)),X6 : X3,X2 : bool] : (fTrue = X2 | fTrue = foldl(bool,X3,X4,X5,insert(X3,X6,nil(X3))) | aa(X3,bool,aa(bool,fun(X3,bool),X4,X5),X6) = X2)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_261])])).
% 11.66/2.03 tff(f3454,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X3 : bool,X0 : fun(bool,fun(list(bool),bool)),X1 : bool,X4 : bool] : (list_case(bool,bool,X3,X0,cons(bool,X1,X2)) = X4 | fTrue = foldl(bool,list(bool),X0,X1,insert(list(bool),X2,nil(list(bool)))) | fTrue = X4) ) | (~spl32_91 | ~spl32_261)),
% 11.66/2.03 inference(superposition,[],[f3389,f1061])).
% 11.66/2.03 tff(f3389,plain,(
% 11.66/2.03 ( ! [X3 : $tType,X2 : bool,X6 : X3,X4 : fun(bool,fun(X3,bool)),X5 : bool] : (aa(X3,bool,aa(bool,fun(X3,bool),X4,X5),X6) = X2 | fTrue = foldl(bool,X3,X4,X5,insert(X3,X6,nil(X3))) | fTrue = X2) ) | ~spl32_261),
% 11.66/2.03 inference(avatar_component_clause,[],[f3388])).
% 11.66/2.03 tff(f11586,plain,(
% 11.66/2.03 spl32_441 | ~spl32_89 | ~spl32_101 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1444,f1325,f1297,f1039,f11584])).
% 11.66/2.03 tff(f1297,plain,(
% 11.66/2.03 spl32_101 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK22(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_101])])).
% 11.66/2.03 tff(f1444,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : dB,X4 : type] : (pp(aa(list(type),bool,typings(X3,X2),sK22(X4,X2,aa(dB,dB,combc(dB,dB,dB,app,X1),X0),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4))) ) | (~spl32_89 | ~spl32_101 | ~spl32_108)),
% 11.66/2.03 inference(forward_demodulation,[],[f1435,f1040])).
% 11.66/2.03 tff(f1435,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : dB,X4 : type] : (~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4)) | pp(aa(list(type),bool,typings(X3,X2),sK22(X4,X2,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1),X3)))) ) | (~spl32_101 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f1298,f1326])).
% 11.66/2.03 tff(f1298,plain,(
% 11.66/2.03 ( ! [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),sK22(X0,X1,X2,X3)))) ) | ~spl32_101),
% 11.66/2.03 inference(avatar_component_clause,[],[f1297])).
% 11.66/2.03 tff(f11581,plain,(
% 11.66/2.03 spl32_440 | ~spl32_89 | ~spl32_100 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1443,f1325,f1293,f1039,f11579])).
% 11.66/2.03 tff(f1293,plain,(
% 11.66/2.03 spl32_100 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_100])])).
% 11.66/2.03 tff(f1443,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : dB,X4 : type] : (pp(aa(list(type),bool,typings(X3,X2),sK21(X4,X2,aa(dB,dB,combc(dB,dB,dB,app,X1),X0),X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4))) ) | (~spl32_89 | ~spl32_100 | ~spl32_108)),
% 11.66/2.03 inference(forward_demodulation,[],[f1434,f1040])).
% 11.66/2.03 tff(f1434,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : fun(nat,type),X0 : dB,X1 : dB,X4 : type] : (~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X0,cons(dB,X1,X2))),X4)) | pp(aa(list(type),bool,typings(X3,X2),sK21(X4,X2,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1),X3)))) ) | (~spl32_100 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f1294,f1326])).
% 11.66/2.03 tff(f1294,plain,(
% 11.66/2.03 ( ! [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),sK21(X0,X1,X2,X3)))) ) | ~spl32_100),
% 11.66/2.03 inference(avatar_component_clause,[],[f1293])).
% 11.66/2.03 tff(f10781,plain,(
% 11.66/2.03 spl32_439 | ~spl32_12 | ~spl32_89 | ~spl32_155 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f5970,f3812,f2017,f1039,f599,f10779])).
% 11.66/2.03 tff(f10779,plain,(
% 11.66/2.03 spl32_439 <=> ! [X0 : list(bool),X3 : fun(bool,fun(bool,bool)),X2 : list(bool),X1 : bool] : (pp(foldr(bool,bool,X3,insert(bool,fFalse,nil(bool)),X1)) | step1(bool,X3,sK26(bool,X0,X1,X2,X3),X0) | ~step1(bool,X3,X2,cons(bool,X1,X0)) | fTrue = sK27(bool,X0,X1,X2,X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_439])])).
% 11.66/2.03 tff(f5970,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X3 : fun(bool,fun(bool,bool)),X0 : list(bool),X1 : bool] : (pp(foldr(bool,bool,X3,insert(bool,fFalse,nil(bool)),X1)) | step1(bool,X3,sK26(bool,X0,X1,X2,X3),X0) | ~step1(bool,X3,X2,cons(bool,X1,X0)) | fTrue = sK27(bool,X0,X1,X2,X3)) ) | (~spl32_12 | ~spl32_89 | ~spl32_155 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f2033,f3939])).
% 11.66/2.03 tff(f2033,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X3 : fun(bool,fun(bool,bool)),X0 : list(bool),X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,X3,X1),fFalse)) | step1(bool,X3,sK26(bool,X0,X1,X2,X3),X0) | ~step1(bool,X3,X2,cons(bool,X1,X0)) | fTrue = sK27(bool,X0,X1,X2,X3)) ) | (~spl32_12 | ~spl32_155)),
% 11.66/2.03 inference(superposition,[],[f2018,f600])).
% 11.66/2.03 tff(f10762,plain,(
% 11.66/2.03 spl32_438 | ~spl32_33 | ~spl32_162),
% 11.66/2.03 inference(avatar_split_clause,[],[f2134,f2128,f704,f10760])).
% 11.66/2.03 tff(f10760,plain,(
% 11.66/2.03 spl32_438 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~member(dB,foldl(dB,dB,app,X2,X1),combc(dB,dB,bool,beta,X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_438])])).
% 11.66/2.03 tff(f2128,plain,(
% 11.66/2.03 spl32_162 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_162])])).
% 11.66/2.03 tff(f2134,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~member(dB,foldl(dB,dB,app,X2,X1),combc(dB,dB,bool,beta,X0))) ) | (~spl32_33 | ~spl32_162)),
% 11.66/2.03 inference(resolution,[],[f2129,f705])).
% 11.66/2.03 tff(f2129,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0) ) | ~spl32_162),
% 11.66/2.03 inference(avatar_component_clause,[],[f2128])).
% 11.66/2.03 tff(f10758,plain,(
% 11.66/2.03 spl32_437 | ~spl32_89 | ~spl32_159),
% 11.66/2.03 inference(avatar_split_clause,[],[f2093,f2084,f1039,f10756])).
% 11.66/2.03 tff(f10756,plain,(
% 11.66/2.03 spl32_437 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : fun(X0,X1),X5 : X0,X3 : fun(X1,X2)] : aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),combc(fun(X1,X2),fun(X0,X1),fun(X0,X2),combb(X1,X2,X0),X4),X3),X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_437])])).
% 11.66/2.03 tff(f2093,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : fun(X1,X2),X4 : fun(X0,X1),X5 : X0] : (aa(X1,X2,X3,aa(X0,X1,X4,X5)) = aa(X0,X2,aa(fun(X1,X2),fun(X0,X2),combc(fun(X1,X2),fun(X0,X1),fun(X0,X2),combb(X1,X2,X0),X4),X3),X5)) ) | (~spl32_89 | ~spl32_159)),
% 11.66/2.03 inference(superposition,[],[f2085,f1040])).
% 11.66/2.03 tff(f10754,plain,(
% 11.66/2.03 spl32_436 | ~spl32_129 | ~spl32_152),
% 11.66/2.03 inference(avatar_split_clause,[],[f1993,f1983,f1694,f10752])).
% 11.66/2.03 tff(f10752,plain,(
% 11.66/2.03 spl32_436 <=> ! [X2 : fun(nat,type),X4 : type,X0 : dB,X3 : list(dB),X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | pp(aa(type,bool,typing(X2,foldl(dB,dB,app,X0,X3)),X4)) | ~pp(aa(type,bool,typing(X2,foldl(dB,dB,app,X1,X3)),X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_436])])).
% 11.66/2.03 tff(f1993,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X3 : list(dB),X0 : dB,X1 : dB,X4 : type] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | pp(aa(type,bool,typing(X2,foldl(dB,dB,app,X0,X3)),X4)) | ~pp(aa(type,bool,typing(X2,foldl(dB,dB,app,X1,X3)),X4))) ) | (~spl32_129 | ~spl32_152)),
% 11.66/2.03 inference(resolution,[],[f1984,f1695])).
% 11.66/2.03 tff(f10750,plain,(
% 11.66/2.03 spl32_435 | ~spl32_89 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1081,f1060,f1039,f10748])).
% 11.66/2.03 tff(f10748,plain,(
% 11.66/2.03 spl32_435 <=> ! [X0 : $tType,X1 : $tType,X2 : $tType,X6 : fun(X1,X2),X4 : X0,X5 : list(X0),X3 : fun(X0,fun(list(X0),fun(X1,X2))),X7 : X1] : aa(list(X0),X2,combc(list(X0),X1,X2,aa(X0,fun(list(X0),fun(X1,X2)),X3,X4),X7),X5) = aa(X1,X2,list_case(fun(X1,X2),X0,X6,X3,cons(X0,X4,X5)),X7)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_435])])).
% 11.66/2.03 tff(f1081,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : fun(X0,fun(list(X0),fun(X1,X2))),X6 : fun(X1,X2),X7 : X1,X4 : X0,X5 : list(X0)] : (aa(list(X0),X2,combc(list(X0),X1,X2,aa(X0,fun(list(X0),fun(X1,X2)),X3,X4),X7),X5) = aa(X1,X2,list_case(fun(X1,X2),X0,X6,X3,cons(X0,X4,X5)),X7)) ) | (~spl32_89 | ~spl32_91)),
% 11.66/2.03 inference(superposition,[],[f1040,f1061])).
% 11.66/2.03 tff(f10746,plain,(
% 11.66/2.03 spl32_434 | ~spl32_89),
% 11.66/2.03 inference(avatar_split_clause,[],[f1049,f1039,f10744])).
% 11.66/2.03 tff(f10744,plain,(
% 11.66/2.03 spl32_434 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : $tType,X5 : X3,X4 : fun(X3,fun(X0,fun(X1,X2))),X7 : X1,X6 : X0] : aa(X0,X2,combc(X0,X1,X2,aa(X3,fun(X0,fun(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),X7)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_434])])).
% 11.66/2.03 tff(f1049,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : X0,X7 : X1,X4 : fun(X3,fun(X0,fun(X1,X2))),X5 : X3] : (aa(X0,X2,combc(X0,X1,X2,aa(X3,fun(X0,fun(X1,X2)),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),combc(X3,X0,fun(X1,X2),X4,X6),X5),X7)) ) | ~spl32_89),
% 11.66/2.03 inference(superposition,[],[f1040,f1040])).
% 11.66/2.03 tff(f10742,plain,(
% 11.66/2.03 spl32_433 | ~spl32_89),
% 11.66/2.03 inference(avatar_split_clause,[],[f1048,f1039,f10740])).
% 11.66/2.03 tff(f10740,plain,(
% 11.66/2.03 spl32_433 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : $tType,X5 : X3,X4 : fun(X0,fun(X3,fun(X1,X2))),X7 : X1,X6 : X0] : aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_433])])).
% 11.66/2.03 tff(f1048,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : X0,X7 : X1,X4 : fun(X0,fun(X3,fun(X1,X2))),X5 : X3] : (aa(X0,X2,combc(X0,X1,X2,combc(X0,X3,fun(X1,X2),X4,X5),X7),X6) = aa(X1,X2,aa(X3,fun(X1,X2),aa(X0,fun(X3,fun(X1,X2)),X4,X6),X5),X7)) ) | ~spl32_89),
% 11.66/2.03 inference(superposition,[],[f1040,f1040])).
% 11.66/2.03 tff(f10706,plain,(
% 11.66/2.03 spl32_432 | ~spl32_40 | ~spl32_310),
% 11.66/2.03 inference(avatar_split_clause,[],[f4606,f4498,f747,f10704])).
% 11.66/2.03 tff(f10704,plain,(
% 11.66/2.03 spl32_432 <=> ! [X2 : fun(bool,fun(list(bool),bool)),X0 : bool,X1 : bool] : (fTrue != list_case(bool,bool,X1,X2,insert(bool,X0,nil(bool))) | fTrue = foldl(bool,list(bool),X2,X0,insert(list(bool),nil(bool),nil(list(bool)))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_432])])).
% 11.66/2.03 tff(f747,plain,(
% 11.66/2.03 spl32_40 <=> ! [X0 : $tType,X1 : X0] : insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_40])])).
% 11.66/2.03 tff(f4498,plain,(
% 11.66/2.03 spl32_310 <=> ! [X0 : fun(bool,fun(list(bool),bool)),X3 : bool,X2 : list(bool),X1 : bool] : (fTrue != list_case(bool,bool,X3,X0,cons(bool,X1,X2)) | fTrue = foldl(bool,list(bool),X0,X1,insert(list(bool),X2,nil(list(bool)))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_310])])).
% 11.66/2.03 tff(f4606,plain,(
% 11.66/2.03 ( ! [X2 : fun(bool,fun(list(bool),bool)),X0 : bool,X1 : bool] : (fTrue != list_case(bool,bool,X1,X2,insert(bool,X0,nil(bool))) | fTrue = foldl(bool,list(bool),X2,X0,insert(list(bool),nil(bool),nil(list(bool))))) ) | (~spl32_40 | ~spl32_310)),
% 11.66/2.03 inference(superposition,[],[f4499,f748])).
% 11.66/2.03 tff(f748,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X1 : X0] : (insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0))) ) | ~spl32_40),
% 11.66/2.03 inference(avatar_component_clause,[],[f747])).
% 11.66/2.03 tff(f4499,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X3 : bool,X0 : fun(bool,fun(list(bool),bool)),X1 : bool] : (fTrue != list_case(bool,bool,X3,X0,cons(bool,X1,X2)) | fTrue = foldl(bool,list(bool),X0,X1,insert(list(bool),X2,nil(list(bool))))) ) | ~spl32_310),
% 11.66/2.03 inference(avatar_component_clause,[],[f4498])).
% 11.66/2.03 tff(f10702,plain,(
% 11.66/2.03 spl32_431 | ~spl32_89 | ~spl32_275 | ~spl32_427),
% 11.66/2.03 inference(avatar_split_clause,[],[f10675,f10671,f3812,f1039,f10700])).
% 11.66/2.03 tff(f10700,plain,(
% 11.66/2.03 spl32_431 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (sP2(dB,X2,X2,beta,foldr(dB,dB,app,insert(dB,X1,nil(dB)),X3),foldr(dB,dB,app,insert(dB,X0,nil(dB)),X3)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_431])])).
% 11.66/2.03 tff(f10671,plain,(
% 11.66/2.03 spl32_427 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),aa(dB,dB,combc(dB,dB,dB,app,X3),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_427])])).
% 11.66/2.03 tff(f10675,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (sP2(dB,X2,X2,beta,foldr(dB,dB,app,insert(dB,X1,nil(dB)),X3),foldr(dB,dB,app,insert(dB,X0,nil(dB)),X3)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_427)),
% 11.66/2.03 inference(forward_demodulation,[],[f10674,f3939])).
% 11.66/2.03 tff(f10674,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (sP2(dB,X2,X2,beta,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),foldr(dB,dB,app,insert(dB,X0,nil(dB)),X3)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_427)),
% 11.66/2.03 inference(forward_demodulation,[],[f10672,f3939])).
% 11.66/2.03 tff(f10672,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),aa(dB,dB,combc(dB,dB,dB,app,X3),X0))) ) | ~spl32_427),
% 11.66/2.03 inference(avatar_component_clause,[],[f10671])).
% 11.66/2.03 tff(f10698,plain,(
% 11.66/2.03 spl32_430 | ~spl32_89 | ~spl32_275 | ~spl32_426),
% 11.66/2.03 inference(avatar_split_clause,[],[f10669,f10665,f3812,f1039,f10696])).
% 11.66/2.03 tff(f10696,plain,(
% 11.66/2.03 spl32_430 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (sP2(dB,X2,X2,beta,foldr(dB,dB,app,insert(dB,X3,nil(dB)),X1),foldr(dB,dB,app,insert(dB,X3,nil(dB)),X0)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_430])])).
% 11.66/2.03 tff(f10665,plain,(
% 11.66/2.03 spl32_426 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),X3),aa(dB,dB,combc(dB,dB,dB,app,X0),X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_426])])).
% 11.66/2.03 tff(f10669,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (sP2(dB,X2,X2,beta,foldr(dB,dB,app,insert(dB,X3,nil(dB)),X1),foldr(dB,dB,app,insert(dB,X3,nil(dB)),X0)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_426)),
% 11.66/2.03 inference(forward_demodulation,[],[f10668,f3939])).
% 11.66/2.03 tff(f10668,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (sP2(dB,X2,X2,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),X3),foldr(dB,dB,app,insert(dB,X3,nil(dB)),X0)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_426)),
% 11.66/2.03 inference(forward_demodulation,[],[f10666,f3939])).
% 11.66/2.03 tff(f10666,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),X3),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) ) | ~spl32_426),
% 11.66/2.03 inference(avatar_component_clause,[],[f10665])).
% 11.66/2.03 tff(f10694,plain,(
% 11.66/2.03 spl32_429 | ~spl32_89 | ~spl32_275 | ~spl32_425),
% 11.66/2.03 inference(avatar_split_clause,[],[f10663,f10659,f3812,f1039,f10692])).
% 11.66/2.03 tff(f10692,plain,(
% 11.66/2.03 spl32_429 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (member(type,foldr(type,type,fun1,insert(type,sK24(X3,X1,X2,X0),nil(type)),X3),typing(X0,X2)) | ~pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_429])])).
% 11.66/2.03 tff(f10659,plain,(
% 11.66/2.03 spl32_425 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X3)) | member(type,aa(type,type,combc(type,type,type,fun1,X3),sK24(X3,X1,X2,X0)),typing(X0,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_425])])).
% 11.66/2.03 tff(f10663,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (member(type,foldr(type,type,fun1,insert(type,sK24(X3,X1,X2,X0),nil(type)),X3),typing(X0,X2)) | ~pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X3))) ) | (~spl32_89 | ~spl32_275 | ~spl32_425)),
% 11.66/2.03 inference(forward_demodulation,[],[f10662,f3939])).
% 11.66/2.03 tff(f10662,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,X2,nil(dB)),X1)),X3)) | member(type,aa(type,type,combc(type,type,type,fun1,X3),sK24(X3,X1,X2,X0)),typing(X0,X2))) ) | (~spl32_89 | ~spl32_275 | ~spl32_425)),
% 11.66/2.03 inference(forward_demodulation,[],[f10660,f3939])).
% 11.66/2.03 tff(f10660,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X3)) | member(type,aa(type,type,combc(type,type,type,fun1,X3),sK24(X3,X1,X2,X0)),typing(X0,X2))) ) | ~spl32_425),
% 11.66/2.03 inference(avatar_component_clause,[],[f10659])).
% 11.66/2.03 tff(f10690,plain,(
% 11.66/2.03 spl32_428 | ~spl32_89 | ~spl32_275 | ~spl32_424),
% 11.66/2.03 inference(avatar_split_clause,[],[f10657,f10654,f3812,f1039,f10688])).
% 11.66/2.03 tff(f10688,plain,(
% 11.66/2.03 spl32_428 <=> ! [X4 : dB,X0 : fun(nat,type),X3 : type,X2 : dB,X1 : nat] : (~pp(aa(type,bool,typing(shift(type,X0,X1,t),foldr(dB,dB,app,insert(dB,a,nil(dB)),X2)),X3)) | ~pp(aa(type,bool,typing(X0,X4),t)) | ~it(X4) | it(subst(a,X4,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_428])])).
% 11.66/2.03 tff(f10654,plain,(
% 11.66/2.03 spl32_424 <=> ! [X4 : dB,X0 : fun(nat,type),X3 : type,X2 : dB,X1 : nat] : (~pp(aa(type,bool,typing(shift(type,X0,X1,t),aa(dB,dB,combc(dB,dB,dB,app,X2),a)),X3)) | ~pp(aa(type,bool,typing(X0,X4),t)) | ~it(X4) | it(subst(a,X4,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_424])])).
% 11.66/2.03 tff(f10657,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : nat,X4 : dB] : (~pp(aa(type,bool,typing(shift(type,X0,X1,t),foldr(dB,dB,app,insert(dB,a,nil(dB)),X2)),X3)) | ~pp(aa(type,bool,typing(X0,X4),t)) | ~it(X4) | it(subst(a,X4,X1))) ) | (~spl32_89 | ~spl32_275 | ~spl32_424)),
% 11.66/2.03 inference(forward_demodulation,[],[f10655,f3939])).
% 11.66/2.03 tff(f10655,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : nat,X4 : dB] : (~pp(aa(type,bool,typing(shift(type,X0,X1,t),aa(dB,dB,combc(dB,dB,dB,app,X2),a)),X3)) | ~pp(aa(type,bool,typing(X0,X4),t)) | ~it(X4) | it(subst(a,X4,X1))) ) | ~spl32_424),
% 11.66/2.03 inference(avatar_component_clause,[],[f10654])).
% 11.66/2.03 tff(f10673,plain,(
% 11.66/2.03 spl32_427 | ~spl32_80 | ~spl32_172),
% 11.66/2.03 inference(avatar_split_clause,[],[f2256,f2252,f969,f10671])).
% 11.66/2.03 tff(f969,plain,(
% 11.66/2.03 spl32_80 <=> ! [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)) | sP2(X3,X1,X1,X2,X4,X5))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_80])])).
% 11.66/2.03 tff(f2256,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),aa(dB,dB,combc(dB,dB,dB,app,X3),X0))) ) | (~spl32_80 | ~spl32_172)),
% 11.66/2.03 inference(resolution,[],[f2253,f970])).
% 11.66/2.03 tff(f970,plain,(
% 11.66/2.03 ( ! [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)) | sP2(X3,X1,X1,X2,X4,X5)) ) | ~spl32_80),
% 11.66/2.03 inference(avatar_component_clause,[],[f969])).
% 11.66/2.03 tff(f10667,plain,(
% 11.66/2.03 spl32_426 | ~spl32_80 | ~spl32_170),
% 11.66/2.03 inference(avatar_split_clause,[],[f2234,f2230,f969,f10665])).
% 11.66/2.03 tff(f2234,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),X3),aa(dB,dB,combc(dB,dB,dB,app,X0),X3))) ) | (~spl32_80 | ~spl32_170)),
% 11.66/2.03 inference(resolution,[],[f2231,f970])).
% 11.66/2.03 tff(f10661,plain,(
% 11.66/2.03 spl32_425 | ~spl32_34 | ~spl32_164),
% 11.66/2.03 inference(avatar_split_clause,[],[f2169,f2156,f708,f10659])).
% 11.66/2.03 tff(f2169,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X2)),X3)) | member(type,aa(type,type,combc(type,type,type,fun1,X3),sK24(X3,X1,X2,X0)),typing(X0,X2))) ) | (~spl32_34 | ~spl32_164)),
% 11.66/2.03 inference(resolution,[],[f2157,f709])).
% 11.66/2.03 tff(f10656,plain,(
% 11.66/2.03 spl32_424 | ~spl32_116 | ~spl32_164),
% 11.66/2.03 inference(avatar_split_clause,[],[f2167,f2156,f1514,f10654])).
% 11.66/2.03 tff(f1514,plain,(
% 11.66/2.03 spl32_116 <=> ! [X0 : dB,X3 : fun(nat,type),X2 : nat,X1 : type] : (it(subst(a,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),t)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,t),a),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_116])])).
% 11.66/2.03 tff(f2167,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : nat,X4 : dB] : (~pp(aa(type,bool,typing(shift(type,X0,X1,t),aa(dB,dB,combc(dB,dB,dB,app,X2),a)),X3)) | ~pp(aa(type,bool,typing(X0,X4),t)) | ~it(X4) | it(subst(a,X4,X1))) ) | (~spl32_116 | ~spl32_164)),
% 11.66/2.03 inference(resolution,[],[f2157,f1515])).
% 11.66/2.03 tff(f1515,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type] : (~pp(aa(type,bool,typing(shift(type,X3,X2,t),a),X1)) | ~pp(aa(type,bool,typing(X3,X0),t)) | ~it(X0) | it(subst(a,X0,X2))) ) | ~spl32_116),
% 11.66/2.03 inference(avatar_component_clause,[],[f1514])).
% 11.66/2.03 tff(f10633,plain,(
% 11.66/2.03 spl32_423 | ~spl32_33 | ~spl32_89 | ~spl32_159),
% 11.66/2.03 inference(avatar_split_clause,[],[f2120,f2084,f1039,f704,f10631])).
% 11.66/2.03 tff(f10631,plain,(
% 11.66/2.03 spl32_423 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : fun(X0,X1),X2 : fun(X1,bool)] : (~member(X0,X4,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2)) | pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_423])])).
% 11.66/2.03 tff(f2120,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,bool),X3 : fun(X0,X1),X4 : X0] : (~member(X0,X4,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2)) | pp(aa(X1,bool,X2,aa(X0,X1,X3,X4)))) ) | (~spl32_33 | ~spl32_89 | ~spl32_159)),
% 11.66/2.03 inference(forward_demodulation,[],[f2106,f1040])).
% 11.66/2.03 tff(f2106,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,bool),X3 : fun(X0,X1),X4 : X0] : (pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))) | ~member(X0,X4,aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3))) ) | (~spl32_33 | ~spl32_159)),
% 11.66/2.03 inference(superposition,[],[f705,f2085])).
% 11.66/2.03 tff(f10629,plain,(
% 11.66/2.03 spl32_422 | ~spl32_34 | ~spl32_89 | ~spl32_159),
% 11.66/2.03 inference(avatar_split_clause,[],[f2119,f2084,f1039,f708,f10627])).
% 11.66/2.03 tff(f10627,plain,(
% 11.66/2.03 spl32_422 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : fun(X0,X1),X2 : fun(X1,bool)] : (member(X0,X4,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2)) | ~pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_422])])).
% 11.66/2.03 tff(f2119,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,bool),X3 : fun(X0,X1),X4 : X0] : (member(X0,X4,aa(fun(X1,bool),fun(X0,bool),combc(fun(X1,bool),fun(X0,X1),fun(X0,bool),combb(X1,bool,X0),X3),X2)) | ~pp(aa(X1,bool,X2,aa(X0,X1,X3,X4)))) ) | (~spl32_34 | ~spl32_89 | ~spl32_159)),
% 11.66/2.03 inference(forward_demodulation,[],[f2105,f1040])).
% 11.66/2.03 tff(f2105,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,bool),X3 : fun(X0,X1),X4 : X0] : (~pp(aa(X1,bool,X2,aa(X0,X1,X3,X4))) | member(X0,X4,aa(fun(X0,X1),fun(X0,bool),aa(fun(X1,bool),fun(fun(X0,X1),fun(X0,bool)),combb(X1,bool,X0),X2),X3))) ) | (~spl32_34 | ~spl32_159)),
% 11.66/2.03 inference(superposition,[],[f709,f2085])).
% 11.66/2.03 tff(f10562,plain,(
% 11.66/2.03 spl32_421 | ~spl32_89 | ~spl32_275 | ~spl32_419),
% 11.66/2.03 inference(avatar_split_clause,[],[f10534,f10531,f3812,f1039,f10560])).
% 11.66/2.03 tff(f10560,plain,(
% 11.66/2.03 spl32_421 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (~pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,abs(X2),nil(dB)),X1)),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X2,X0)),X2),sK9(X2,X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_421])])).
% 11.66/2.03 tff(f10531,plain,(
% 11.66/2.03 spl32_419 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2))),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X2,X0)),X2),sK9(X2,X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_419])])).
% 11.66/2.03 tff(f10534,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,foldr(dB,dB,app,insert(dB,abs(X2),nil(dB)),X1)),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X2,X0)),X2),sK9(X2,X0)))) ) | (~spl32_89 | ~spl32_275 | ~spl32_419)),
% 11.66/2.03 inference(forward_demodulation,[],[f10532,f3939])).
% 11.66/2.03 tff(f10532,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2))),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X2,X0)),X2),sK9(X2,X0)))) ) | ~spl32_419),
% 11.66/2.03 inference(avatar_component_clause,[],[f10531])).
% 11.66/2.03 tff(f10538,plain,(
% 11.66/2.03 spl32_420 | ~spl32_28 | ~spl32_168),
% 11.66/2.03 inference(avatar_split_clause,[],[f2216,f2199,f676,f10536])).
% 11.66/2.03 tff(f10536,plain,(
% 11.66/2.03 spl32_420 <=> ! [X0 : dB,X1 : dB] : (sK16(X1,nil(dB),X0) = X1 | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | sP0(X1,nil(dB),X0) | foldl(dB,dB,app,X0,sK15(X1,nil(dB),X0)) = X1)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_420])])).
% 11.66/2.03 tff(f2216,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (sK16(X1,nil(dB),X0) = X1 | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | sP0(X1,nil(dB),X0) | foldl(dB,dB,app,X0,sK15(X1,nil(dB),X0)) = X1) ) | (~spl32_28 | ~spl32_168)),
% 11.66/2.03 inference(forward_demodulation,[],[f2207,f677])).
% 11.66/2.03 tff(f2207,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | sP0(X1,nil(dB),X0) | foldl(dB,dB,app,X0,sK15(X1,nil(dB),X0)) = X1 | foldl(dB,dB,app,sK16(X1,nil(dB),X0),nil(dB)) = X1) ) | (~spl32_28 | ~spl32_168)),
% 11.66/2.03 inference(superposition,[],[f2200,f677])).
% 11.66/2.03 tff(f10533,plain,(
% 11.66/2.03 spl32_419 | ~spl32_97 | ~spl32_164),
% 11.66/2.03 inference(avatar_split_clause,[],[f2161,f2156,f1273,f10531])).
% 11.66/2.03 tff(f1273,plain,(
% 11.66/2.03 spl32_97 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK8(X1,X2)),X1),sK9(X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_97])])).
% 11.66/2.03 tff(f2161,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2))),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X2,X0)),X2),sK9(X2,X0)))) ) | (~spl32_97 | ~spl32_164)),
% 11.66/2.03 inference(resolution,[],[f2157,f1274])).
% 11.66/2.03 tff(f1274,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (~pp(aa(type,bool,typing(X2,abs(X1)),X0)) | pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK8(X1,X2)),X1),sK9(X1,X2)))) ) | ~spl32_97),
% 11.66/2.03 inference(avatar_component_clause,[],[f1273])).
% 11.66/2.03 tff(f10529,plain,(
% 11.66/2.03 spl32_418 | ~spl32_126 | ~spl32_142),
% 11.66/2.03 inference(avatar_split_clause,[],[f1879,f1859,f1680,f10527])).
% 11.66/2.03 tff(f10527,plain,(
% 11.66/2.03 spl32_418 <=> ! [X0 : fun(nat,type),X3 : dB,X2 : type,X1 : dB] : (~pp(aa(type,bool,typing(X0,X1),sK10(X2,X3,X0))) | pp(aa(type,bool,typing(X0,subst(X3,X1,zero_zero(nat))),sK11(X2,X3,X0))) | ~pp(aa(type,bool,typing(X0,abs(X3)),X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_418])])).
% 11.66/2.03 tff(f1680,plain,(
% 11.66/2.03 spl32_126 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X0,X1,X2)),X1),sK11(X0,X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_126])])).
% 11.66/2.03 tff(f1859,plain,(
% 11.66/2.03 spl32_142 <=> ! [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)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_142])])).
% 11.66/2.03 tff(f1879,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,X1),sK10(X2,X3,X0))) | pp(aa(type,bool,typing(X0,subst(X3,X1,zero_zero(nat))),sK11(X2,X3,X0))) | ~pp(aa(type,bool,typing(X0,abs(X3)),X2))) ) | (~spl32_126 | ~spl32_142)),
% 11.66/2.03 inference(resolution,[],[f1860,f1681])).
% 11.66/2.03 tff(f1681,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X0,X1,X2)),X1),sK11(X0,X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) ) | ~spl32_126),
% 11.66/2.03 inference(avatar_component_clause,[],[f1680])).
% 11.66/2.03 tff(f1860,plain,(
% 11.66/2.03 ( ! [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))) ) | ~spl32_142),
% 11.66/2.03 inference(avatar_component_clause,[],[f1859])).
% 11.66/2.03 tff(f10507,plain,(
% 11.66/2.03 spl32_417 | ~spl32_107 | ~spl32_273),
% 11.66/2.03 inference(avatar_split_clause,[],[f3916,f3804,f1321,f10505])).
% 11.66/2.03 tff(f10505,plain,(
% 11.66/2.03 spl32_417 <=> ! [X0 : fun(bool,fun(bool,bool)),X3 : bool,X2 : list(bool),X1 : bool] : (fTrue != foldr(bool,bool,X0,cons(bool,X1,X2),X3) | fTrue = foldl(bool,bool,X0,X1,insert(bool,foldr(bool,bool,X0,X2,X3),nil(bool))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_417])])).
% 11.66/2.03 tff(f3804,plain,(
% 11.66/2.03 spl32_273 <=> ! [X0 : $tType,X3 : X0,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (fTrue != aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_273])])).
% 11.66/2.03 tff(f3916,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X3 : bool,X0 : fun(bool,fun(bool,bool)),X1 : bool] : (fTrue != foldr(bool,bool,X0,cons(bool,X1,X2),X3) | fTrue = foldl(bool,bool,X0,X1,insert(bool,foldr(bool,bool,X0,X2,X3),nil(bool)))) ) | (~spl32_107 | ~spl32_273)),
% 11.66/2.03 inference(superposition,[],[f3805,f1322])).
% 11.66/2.03 tff(f3805,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool))] : (fTrue != aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0)))) ) | ~spl32_273),
% 11.66/2.03 inference(avatar_component_clause,[],[f3804])).
% 11.66/2.03 tff(f10487,plain,(
% 11.66/2.03 spl32_416 | ~spl32_34 | ~spl32_158),
% 11.66/2.03 inference(avatar_split_clause,[],[f2066,f2062,f708,f10485])).
% 11.66/2.03 tff(f10485,plain,(
% 11.66/2.03 spl32_416 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : list(X0),X1 : X0] : (cons(X0,X1,sK26(X0,X2,X1,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X1,X2)) | member(X0,sK27(X0,X2,X1,X3,X4),combc(X0,X0,bool,X4,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_416])])).
% 11.66/2.03 tff(f2066,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : X0,X4 : fun(X0,fun(X0,bool))] : (cons(X0,X1,sK26(X0,X2,X1,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X1,X2)) | member(X0,sK27(X0,X2,X1,X3,X4),combc(X0,X0,bool,X4,X1))) ) | (~spl32_34 | ~spl32_158)),
% 11.66/2.03 inference(resolution,[],[f2063,f709])).
% 11.66/2.03 tff(f10482,plain,(
% 11.66/2.03 spl32_415 | ~spl32_108 | ~spl32_146),
% 11.66/2.03 inference(avatar_split_clause,[],[f1931,f1918,f1325,f10480])).
% 11.66/2.03 tff(f10480,plain,(
% 11.66/2.03 spl32_415 <=> ! [X4 : list(dB),X0 : dB,X3 : dB,X2 : nat,X1 : dB] : foldl(dB,dB,app,subst(X0,X1,X2),cons(dB,subst(X3,X1,X2),X4)) = foldl(dB,dB,app,subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2),X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_415])])).
% 11.66/2.03 tff(f1918,plain,(
% 11.66/2.03 spl32_146 <=> ! [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)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_146])])).
% 11.66/2.03 tff(f1931,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : dB,X1 : dB,X4 : list(dB)] : (foldl(dB,dB,app,subst(X0,X1,X2),cons(dB,subst(X3,X1,X2),X4)) = foldl(dB,dB,app,subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2),X4)) ) | (~spl32_108 | ~spl32_146)),
% 11.66/2.03 inference(superposition,[],[f1326,f1919])).
% 11.66/2.03 tff(f1919,plain,(
% 11.66/2.03 ( ! [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)) ) | ~spl32_146),
% 11.66/2.03 inference(avatar_component_clause,[],[f1918])).
% 11.66/2.03 tff(f10477,plain,(
% 11.66/2.03 spl32_414 | ~spl32_108 | ~spl32_144),
% 11.66/2.03 inference(avatar_split_clause,[],[f1907,f1894,f1325,f10475])).
% 11.66/2.03 tff(f10475,plain,(
% 11.66/2.03 spl32_414 <=> ! [X4 : list(dB),X0 : nat,X3 : dB,X2 : nat,X1 : dB] : foldl(dB,dB,app,liftn(X0,X1,X2),cons(dB,liftn(X0,X3,X2),X4)) = foldl(dB,dB,app,liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2),X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_414])])).
% 11.66/2.03 tff(f1894,plain,(
% 11.66/2.03 spl32_144 <=> ! [X0 : nat,X3 : nat,X2 : dB,X1 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) = liftn(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_144])])).
% 11.66/2.03 tff(f1907,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : nat,X1 : dB,X4 : list(dB)] : (foldl(dB,dB,app,liftn(X0,X1,X2),cons(dB,liftn(X0,X3,X2),X4)) = foldl(dB,dB,app,liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2),X4)) ) | (~spl32_108 | ~spl32_144)),
% 11.66/2.03 inference(superposition,[],[f1326,f1895])).
% 11.66/2.03 tff(f1895,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : nat,X0 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) = liftn(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)) ) | ~spl32_144),
% 11.66/2.03 inference(avatar_component_clause,[],[f1894])).
% 11.66/2.03 tff(f10473,plain,(
% 11.66/2.03 spl32_413 | ~spl32_99 | ~spl32_112),
% 11.66/2.03 inference(avatar_split_clause,[],[f1474,f1471,f1282,f10471])).
% 11.66/2.03 tff(f10471,plain,(
% 11.66/2.03 spl32_413 <=> ! [X2 : list(dB),X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(foldl(dB,dB,app,var(X1),X2)))) | step1(dB,beta,X2,sK17(sK5(X0,foldl(dB,dB,app,var(X1),X2)),X2,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_413])])).
% 11.66/2.03 tff(f1282,plain,(
% 11.66/2.03 spl32_99 <=> ! [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,sK17(X0,X1,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_99])])).
% 11.66/2.03 tff(f1471,plain,(
% 11.66/2.03 spl32_112 <=> ! [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,sK5(X0,X1)),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_112])])).
% 11.66/2.03 tff(f1474,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(foldl(dB,dB,app,var(X1),X2)))) | step1(dB,beta,X2,sK17(sK5(X0,foldl(dB,dB,app,var(X1),X2)),X2,X1))) ) | (~spl32_99 | ~spl32_112)),
% 11.66/2.03 inference(resolution,[],[f1472,f1283])).
% 11.66/2.03 tff(f1283,plain,(
% 11.66/2.03 ( ! [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,sK17(X0,X1,X2))) ) | ~spl32_99),
% 11.66/2.03 inference(avatar_component_clause,[],[f1282])).
% 11.66/2.03 tff(f1472,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK5(X0,X1)),X1)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1)))) ) | ~spl32_112),
% 11.66/2.03 inference(avatar_component_clause,[],[f1471])).
% 11.66/2.03 tff(f10396,plain,(
% 11.66/2.03 spl32_412 | ~spl32_28 | ~spl32_162),
% 11.66/2.03 inference(avatar_split_clause,[],[f2145,f2128,f676,f10394])).
% 11.66/2.03 tff(f10394,plain,(
% 11.66/2.03 spl32_412 <=> ! [X0 : dB,X1 : dB] : (sK16(X1,nil(dB),X0) = X1 | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | sP0(X1,nil(dB),X0) | step1(dB,beta,nil(dB),sK15(X1,nil(dB),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_412])])).
% 11.66/2.03 tff(f2145,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (sK16(X1,nil(dB),X0) = X1 | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | sP0(X1,nil(dB),X0) | step1(dB,beta,nil(dB),sK15(X1,nil(dB),X0))) ) | (~spl32_28 | ~spl32_162)),
% 11.66/2.03 inference(forward_demodulation,[],[f2136,f677])).
% 11.66/2.03 tff(f2136,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X0)) | sP0(X1,nil(dB),X0) | step1(dB,beta,nil(dB),sK15(X1,nil(dB),X0)) | foldl(dB,dB,app,sK16(X1,nil(dB),X0),nil(dB)) = X1) ) | (~spl32_28 | ~spl32_162)),
% 11.66/2.03 inference(superposition,[],[f2129,f677])).
% 11.66/2.03 tff(f10392,plain,(
% 11.66/2.03 spl32_411 | ~spl32_33 | ~spl32_156),
% 11.66/2.03 inference(avatar_split_clause,[],[f2047,f2041,f704,f10390])).
% 11.66/2.03 tff(f10390,plain,(
% 11.66/2.03 spl32_411 <=> ! [X4 : type,X0 : fun(nat,type),X3 : dB,X2 : list(type),X1 : list(dB)] : (~pp(aa(list(type),bool,typings(X0,X1),X2)) | pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X3,X1)),X4)) | ~member(type,foldr(type,type,fun1,X2,X4),typing(X0,X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_411])])).
% 11.66/2.03 tff(f2047,plain,(
% 11.66/2.03 ( ! [X2 : list(type),X3 : dB,X0 : fun(nat,type),X1 : list(dB),X4 : type] : (~pp(aa(list(type),bool,typings(X0,X1),X2)) | pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X3,X1)),X4)) | ~member(type,foldr(type,type,fun1,X2,X4),typing(X0,X3))) ) | (~spl32_33 | ~spl32_156)),
% 11.66/2.03 inference(resolution,[],[f2042,f705])).
% 11.66/2.03 tff(f9936,plain,(
% 11.66/2.03 spl32_410 | ~spl32_129 | ~spl32_133),
% 11.66/2.03 inference(avatar_split_clause,[],[f1754,f1751,f1694,f9934])).
% 11.66/2.03 tff(f9934,plain,(
% 11.66/2.03 spl32_410 <=> ! [X2 : fun(nat,type),X3 : dB,X4 : nat,X0 : dB,X5 : type,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | pp(aa(type,bool,typing(X2,subst(X0,X3,X4)),X5)) | ~pp(aa(type,bool,typing(X2,subst(X1,X3,X4)),X5)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_410])])).
% 11.66/2.03 tff(f1751,plain,(
% 11.66/2.03 spl32_133 <=> ! [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))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_133])])).
% 11.66/2.03 tff(f1754,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X3 : dB,X0 : dB,X1 : dB,X4 : nat,X5 : type] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | pp(aa(type,bool,typing(X2,subst(X0,X3,X4)),X5)) | ~pp(aa(type,bool,typing(X2,subst(X1,X3,X4)),X5))) ) | (~spl32_129 | ~spl32_133)),
% 11.66/2.03 inference(resolution,[],[f1752,f1695])).
% 11.66/2.03 tff(f1752,plain,(
% 11.66/2.03 ( ! [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,combc(dB,dB,bool,beta,X2),X3))) ) | ~spl32_133),
% 11.66/2.03 inference(avatar_component_clause,[],[f1751])).
% 11.66/2.03 tff(f9656,plain,(
% 11.66/2.03 spl32_409 | ~spl32_80 | ~spl32_158),
% 11.66/2.03 inference(avatar_split_clause,[],[f2065,f2062,f969,f9654])).
% 11.66/2.03 tff(f9654,plain,(
% 11.66/2.03 spl32_409 <=> ! [X0 : $tType,X5 : list(X0),X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : list(X0),X1 : X0] : (cons(X0,X1,sK26(X0,X2,X1,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X1,X2)) | sP2(X0,X5,X5,X4,sK27(X0,X2,X1,X3,X4),X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_409])])).
% 11.66/2.03 tff(f2065,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : list(X0),X3 : list(X0),X1 : X0,X4 : fun(X0,fun(X0,bool)),X5 : list(X0)] : (cons(X0,X1,sK26(X0,X2,X1,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X1,X2)) | sP2(X0,X5,X5,X4,sK27(X0,X2,X1,X3,X4),X1)) ) | (~spl32_80 | ~spl32_158)),
% 11.66/2.03 inference(resolution,[],[f2063,f970])).
% 11.66/2.03 tff(f9652,plain,(
% 11.66/2.03 spl32_408 | ~spl32_34 | ~spl32_155),
% 11.66/2.03 inference(avatar_split_clause,[],[f2021,f2017,f708,f9650])).
% 11.66/2.03 tff(f9650,plain,(
% 11.66/2.03 spl32_408 <=> ! [X0 : $tType,X4 : list(X0),X3 : list(X0),X2 : X0,X1 : fun(X0,fun(X0,bool))] : (step1(X0,X1,sK26(X0,X3,X2,X4,X1),X3) | ~step1(X0,X1,X4,cons(X0,X2,X3)) | member(X0,sK27(X0,X3,X2,X4,X1),combc(X0,X0,bool,X1,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_408])])).
% 11.66/2.03 tff(f2021,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(X0,bool)),X4 : list(X0)] : (step1(X0,X1,sK26(X0,X3,X2,X4,X1),X3) | ~step1(X0,X1,X4,cons(X0,X2,X3)) | member(X0,sK27(X0,X3,X2,X4,X1),combc(X0,X0,bool,X1,X2))) ) | (~spl32_34 | ~spl32_155)),
% 11.66/2.03 inference(resolution,[],[f2018,f709])).
% 11.66/2.03 tff(f9648,plain,(
% 11.66/2.03 spl32_407 | ~spl32_116 | ~spl32_134),
% 11.66/2.03 inference(avatar_split_clause,[],[f1811,f1767,f1514,f9646])).
% 11.66/2.03 tff(f9646,plain,(
% 11.66/2.03 spl32_407 <=> ! [X4 : dB,X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : nat] : (~pp(aa(type,bool,typing(shift(type,X0,X1,t),foldl(dB,dB,app,a,X2)),X3)) | ~pp(aa(type,bool,typing(X0,X4),t)) | ~it(X4) | it(subst(a,X4,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_407])])).
% 11.66/2.03 tff(f1811,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : nat,X4 : dB] : (~pp(aa(type,bool,typing(shift(type,X0,X1,t),foldl(dB,dB,app,a,X2)),X3)) | ~pp(aa(type,bool,typing(X0,X4),t)) | ~it(X4) | it(subst(a,X4,X1))) ) | (~spl32_116 | ~spl32_134)),
% 11.66/2.03 inference(resolution,[],[f1768,f1515])).
% 11.66/2.03 tff(f9269,plain,(
% 11.66/2.03 spl32_406 | ~spl32_108 | ~spl32_115),
% 11.66/2.03 inference(avatar_split_clause,[],[f1511,f1495,f1325,f9267])).
% 11.66/2.03 tff(f9267,plain,(
% 11.66/2.03 spl32_406 <=> ! [X0 : dB,X3 : list(dB),X2 : list(dB),X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,cons(dB,X1,X2))),foldl(dB,dB,app,X0,cons(dB,X1,X3)))) | ~step1(dB,beta,X3,X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_406])])).
% 11.66/2.03 tff(f1495,plain,(
% 11.66/2.03 spl32_115 <=> ! [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))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_115])])).
% 11.66/2.03 tff(f1511,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : list(dB),X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,cons(dB,X1,X2))),foldl(dB,dB,app,X0,cons(dB,X1,X3)))) | ~step1(dB,beta,X3,X2)) ) | (~spl32_108 | ~spl32_115)),
% 11.66/2.03 inference(forward_demodulation,[],[f1503,f1326])).
% 11.66/2.03 tff(f1503,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : list(dB),X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,cons(dB,X1,X2))),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1),X3))) | ~step1(dB,beta,X3,X2)) ) | (~spl32_108 | ~spl32_115)),
% 11.66/2.03 inference(superposition,[],[f1496,f1326])).
% 11.66/2.03 tff(f1496,plain,(
% 11.66/2.03 ( ! [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)) ) | ~spl32_115),
% 11.66/2.03 inference(avatar_component_clause,[],[f1495])).
% 11.66/2.03 tff(f9265,plain,(
% 11.66/2.03 spl32_405 | ~spl32_39 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1409,f1325,f737,f9263])).
% 11.66/2.03 tff(f9263,plain,(
% 11.66/2.03 spl32_405 <=> ! [X0 : $tType,X2 : nat,X4 : X0,X5 : list(X0),X3 : fun(X0,nat),X1 : fun(nat,fun(X0,nat))] : foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),X2,cons(X0,X4,X5)) = foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),aa(X0,nat,X3,X4),X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_405])])).
% 11.66/2.03 tff(f737,plain,(
% 11.66/2.03 spl32_39 <=> ! [X0 : $tType,X2 : fun(nat,X0),X4 : nat,X1 : X0] : aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_39])])).
% 11.66/2.03 tff(f1409,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : nat,X3 : fun(X0,nat),X1 : fun(nat,fun(X0,nat)),X4 : X0,X5 : list(X0)] : (foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),X2,cons(X0,X4,X5)) = foldl(nat,X0,shift(fun(X0,nat),X1,X2,X3),aa(X0,nat,X3,X4),X5)) ) | (~spl32_39 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f1326,f738])).
% 11.66/2.03 tff(f738,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : fun(nat,X0),X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1) ) | ~spl32_39),
% 11.66/2.03 inference(avatar_component_clause,[],[f737])).
% 11.66/2.03 tff(f9261,plain,(
% 11.66/2.03 spl32_404 | ~spl32_39 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1375,f1321,f737,f9259])).
% 11.66/2.03 tff(f9259,plain,(
% 11.66/2.03 spl32_404 <=> ! [X0 : $tType,X3 : fun(X0,X0),X4 : list(nat),X5 : X0,X2 : nat,X1 : fun(nat,fun(X0,X0))] : foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),cons(nat,X2,X4),X5) = aa(X0,X0,X3,foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),X4,X5))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_404])])).
% 11.66/2.03 tff(f1375,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : nat,X3 : fun(X0,X0),X1 : fun(nat,fun(X0,X0)),X4 : list(nat),X5 : X0] : (foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),cons(nat,X2,X4),X5) = aa(X0,X0,X3,foldr(nat,X0,shift(fun(X0,X0),X1,X2,X3),X4,X5))) ) | (~spl32_39 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f1322,f738])).
% 11.66/2.03 tff(f9158,plain,(
% 11.66/2.03 spl32_403 | ~spl32_27 | ~spl32_156),
% 11.66/2.03 inference(avatar_split_clause,[],[f2049,f2041,f672,f9156])).
% 11.66/2.03 tff(f9156,plain,(
% 11.66/2.03 spl32_403 <=> ! [X0 : type,X3 : list(dB),X2 : dB,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,X2),X0)) | ~pp(aa(list(type),bool,typings(X1,X3),nil(type))) | pp(aa(type,bool,typing(X1,foldl(dB,dB,app,X2,X3)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_403])])).
% 11.66/2.03 tff(f672,plain,(
% 11.66/2.03 spl32_27 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X0,fun(X1,X1)),X2 : X1] : foldr(X0,X1,X3,nil(X0),X2) = X2),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_27])])).
% 11.66/2.03 tff(f2049,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : list(dB),X0 : type,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,X2),X0)) | ~pp(aa(list(type),bool,typings(X1,X3),nil(type))) | pp(aa(type,bool,typing(X1,foldl(dB,dB,app,X2,X3)),X0))) ) | (~spl32_27 | ~spl32_156)),
% 11.66/2.03 inference(superposition,[],[f2042,f673])).
% 11.66/2.03 tff(f673,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X3,nil(X0),X2) = X2) ) | ~spl32_27),
% 11.66/2.03 inference(avatar_component_clause,[],[f672])).
% 11.66/2.03 tff(f9153,plain,(
% 11.66/2.03 spl32_402 | ~spl32_105 | ~spl32_146),
% 11.66/2.03 inference(avatar_split_clause,[],[f1926,f1918,f1313,f9151])).
% 11.66/2.03 tff(f9151,plain,(
% 11.66/2.03 spl32_402 <=> ! [X5 : dB,X4 : dB,X0 : dB,X3 : dB,X2 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) != subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2) | subst(X0,X1,X2) = X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_402])])).
% 11.66/2.03 tff(f1313,plain,(
% 11.66/2.03 spl32_105 <=> ! [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))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_105])])).
% 11.66/2.03 tff(f1926,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : dB,X1 : dB,X4 : dB,X5 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) != subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2) | subst(X0,X1,X2) = X4) ) | (~spl32_105 | ~spl32_146)),
% 11.66/2.03 inference(superposition,[],[f1314,f1919])).
% 11.66/2.03 tff(f1314,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X2) | X1 = X3) ) | ~spl32_105),
% 11.66/2.03 inference(avatar_component_clause,[],[f1313])).
% 11.66/2.03 tff(f8851,plain,(
% 11.66/2.03 spl32_401 | ~spl32_106 | ~spl32_146),
% 11.66/2.03 inference(avatar_split_clause,[],[f1924,f1918,f1317,f8849])).
% 11.66/2.03 tff(f8849,plain,(
% 11.66/2.03 spl32_401 <=> ! [X5 : dB,X4 : dB,X0 : dB,X3 : dB,X2 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) != subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2) | subst(X3,X1,X2) = X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_401])])).
% 11.66/2.03 tff(f1317,plain,(
% 11.66/2.03 spl32_106 <=> ! [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))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_106])])).
% 11.66/2.03 tff(f1924,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : dB,X1 : dB,X4 : dB,X5 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) != subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2) | subst(X3,X1,X2) = X5) ) | (~spl32_106 | ~spl32_146)),
% 11.66/2.03 inference(superposition,[],[f1318,f1919])).
% 11.66/2.03 tff(f1318,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : 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) ) | ~spl32_106),
% 11.66/2.03 inference(avatar_component_clause,[],[f1317])).
% 11.66/2.03 tff(f8846,plain,(
% 11.66/2.03 spl32_400 | ~spl32_105 | ~spl32_144),
% 11.66/2.03 inference(avatar_split_clause,[],[f1902,f1894,f1313,f8844])).
% 11.66/2.03 tff(f8844,plain,(
% 11.66/2.03 spl32_400 <=> ! [X3 : dB,X4 : dB,X0 : nat,X5 : dB,X2 : nat,X1 : dB] : (liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) | liftn(X0,X1,X2) = X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_400])])).
% 11.66/2.03 tff(f1902,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : nat,X1 : dB,X4 : dB,X5 : dB] : (liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) | liftn(X0,X1,X2) = X4) ) | (~spl32_105 | ~spl32_144)),
% 11.66/2.03 inference(superposition,[],[f1314,f1895])).
% 11.66/2.03 tff(f8841,plain,(
% 11.66/2.03 spl32_399 | ~spl32_106 | ~spl32_144),
% 11.66/2.03 inference(avatar_split_clause,[],[f1900,f1894,f1317,f8839])).
% 11.66/2.03 tff(f8839,plain,(
% 11.66/2.03 spl32_399 <=> ! [X3 : dB,X4 : dB,X0 : nat,X5 : dB,X2 : nat,X1 : dB] : (liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) | liftn(X0,X3,X2) = X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_399])])).
% 11.66/2.03 tff(f1900,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : nat,X1 : dB,X4 : dB,X5 : dB] : (liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X5) | liftn(X0,X3,X2) = X5) ) | (~spl32_106 | ~spl32_144)),
% 11.66/2.03 inference(superposition,[],[f1318,f1895])).
% 11.66/2.03 tff(f8837,plain,(
% 11.66/2.03 spl32_398 | ~spl32_70 | ~spl32_135),
% 11.66/2.03 inference(avatar_split_clause,[],[f1821,f1779,f908,f8835])).
% 11.66/2.03 tff(f8835,plain,(
% 11.66/2.03 spl32_398 <=> ! [X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | aa(nat,type,X0,X1) = foldr(type,type,fun1,sK22(X3,X2,var(X1),X0),X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_398])])).
% 11.66/2.03 tff(f1821,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | aa(nat,type,X0,X1) = foldr(type,type,fun1,sK22(X3,X2,var(X1),X0),X3)) ) | (~spl32_70 | ~spl32_135)),
% 11.66/2.03 inference(resolution,[],[f1780,f909])).
% 11.66/2.03 tff(f8833,plain,(
% 11.66/2.03 spl32_397 | ~spl32_97 | ~spl32_134),
% 11.66/2.03 inference(avatar_split_clause,[],[f1806,f1767,f1273,f8831])).
% 11.66/2.03 tff(f8831,plain,(
% 11.66/2.03 spl32_397 <=> ! [X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : dB] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,abs(X1),X2)),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X1,X0)),X1),sK9(X1,X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_397])])).
% 11.66/2.03 tff(f1806,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,abs(X1),X2)),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X1,X0)),X1),sK9(X1,X0)))) ) | (~spl32_97 | ~spl32_134)),
% 11.66/2.03 inference(resolution,[],[f1768,f1274])).
% 11.66/2.03 tff(f8829,plain,(
% 11.66/2.03 spl32_396 | ~spl32_70 | ~spl32_134),
% 11.66/2.03 inference(avatar_split_clause,[],[f1804,f1767,f908,f8827])).
% 11.66/2.03 tff(f8827,plain,(
% 11.66/2.03 spl32_396 <=> ! [X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | aa(nat,type,X0,X1) = foldr(type,type,fun1,sK21(X3,X2,var(X1),X0),X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_396])])).
% 11.66/2.03 tff(f1804,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | aa(nat,type,X0,X1) = foldr(type,type,fun1,sK21(X3,X2,var(X1),X0),X3)) ) | (~spl32_70 | ~spl32_134)),
% 11.66/2.03 inference(resolution,[],[f1768,f909])).
% 11.66/2.03 tff(f8825,plain,(
% 11.66/2.03 spl32_395 | ~spl32_115 | ~spl32_129),
% 11.66/2.03 inference(avatar_split_clause,[],[f1699,f1694,f1495,f8823])).
% 11.66/2.03 tff(f8823,plain,(
% 11.66/2.03 spl32_395 <=> ! [X4 : list(dB),X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : dB] : (pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X1,X2)),X3)) | ~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X1,X4)),X3)) | ~step1(dB,beta,X4,X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_395])])).
% 11.66/2.03 tff(f1699,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : dB,X4 : list(dB)] : (pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X1,X2)),X3)) | ~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X1,X4)),X3)) | ~step1(dB,beta,X4,X2)) ) | (~spl32_115 | ~spl32_129)),
% 11.66/2.03 inference(resolution,[],[f1695,f1496])).
% 11.66/2.03 tff(f8674,plain,(
% 11.66/2.03 spl32_394 | ~spl32_89 | ~spl32_275 | ~spl32_386),
% 11.66/2.03 inference(avatar_split_clause,[],[f8618,f8615,f3812,f1039,f8672])).
% 11.66/2.03 tff(f8672,plain,(
% 11.66/2.03 spl32_394 <=> ! [X0 : dB,X3 : dB,X2 : nat,X1 : dB] : aa(dB,dB,combc(dB,dB,dB,app,subst(X3,X1,X2)),subst(X0,X1,X2)) = subst(foldr(dB,dB,app,insert(dB,X0,nil(dB)),X3),X1,X2)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_394])])).
% 11.66/2.03 tff(f8615,plain,(
% 11.66/2.03 spl32_386 <=> ! [X0 : dB,X3 : dB,X2 : nat,X1 : dB] : subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2) = aa(dB,dB,combc(dB,dB,dB,app,subst(X3,X1,X2)),subst(X0,X1,X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_386])])).
% 11.66/2.03 tff(f8618,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,subst(X3,X1,X2)),subst(X0,X1,X2)) = subst(foldr(dB,dB,app,insert(dB,X0,nil(dB)),X3),X1,X2)) ) | (~spl32_89 | ~spl32_275 | ~spl32_386)),
% 11.66/2.03 inference(forward_demodulation,[],[f8616,f3939])).
% 11.66/2.03 tff(f8616,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : dB,X1 : dB] : (subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2) = aa(dB,dB,combc(dB,dB,dB,app,subst(X3,X1,X2)),subst(X0,X1,X2))) ) | ~spl32_386),
% 11.66/2.03 inference(avatar_component_clause,[],[f8615])).
% 11.66/2.03 tff(f8670,plain,(
% 11.66/2.03 spl32_393 | ~spl32_89 | ~spl32_275 | ~spl32_385),
% 11.66/2.03 inference(avatar_split_clause,[],[f8613,f8610,f3812,f1039,f8668])).
% 11.66/2.03 tff(f8668,plain,(
% 11.66/2.03 spl32_393 <=> ! [X0 : nat,X3 : dB,X2 : nat,X1 : dB] : aa(dB,dB,combc(dB,dB,dB,app,liftn(X0,X3,X2)),liftn(X0,X1,X2)) = liftn(X0,foldr(dB,dB,app,insert(dB,X1,nil(dB)),X3),X2)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_393])])).
% 11.66/2.03 tff(f8610,plain,(
% 11.66/2.03 spl32_385 <=> ! [X0 : nat,X3 : dB,X2 : nat,X1 : dB] : liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2) = aa(dB,dB,combc(dB,dB,dB,app,liftn(X0,X3,X2)),liftn(X0,X1,X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_385])])).
% 11.66/2.03 tff(f8613,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : nat,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,liftn(X0,X3,X2)),liftn(X0,X1,X2)) = liftn(X0,foldr(dB,dB,app,insert(dB,X1,nil(dB)),X3),X2)) ) | (~spl32_89 | ~spl32_275 | ~spl32_385)),
% 11.66/2.03 inference(forward_demodulation,[],[f8611,f3939])).
% 11.66/2.03 tff(f8611,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : nat,X1 : dB] : (liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2) = aa(dB,dB,combc(dB,dB,dB,app,liftn(X0,X3,X2)),liftn(X0,X1,X2))) ) | ~spl32_385),
% 11.66/2.03 inference(avatar_component_clause,[],[f8610])).
% 11.66/2.03 tff(f8642,plain,(
% 11.66/2.03 spl32_392 | ~spl32_80 | ~spl32_155),
% 11.66/2.03 inference(avatar_split_clause,[],[f2020,f2017,f969,f8640])).
% 11.66/2.03 tff(f8640,plain,(
% 11.66/2.03 spl32_392 <=> ! [X0 : $tType,X5 : list(X0),X4 : list(X0),X3 : list(X0),X2 : X0,X1 : fun(X0,fun(X0,bool))] : (step1(X0,X1,sK26(X0,X3,X2,X4,X1),X3) | ~step1(X0,X1,X4,cons(X0,X2,X3)) | sP2(X0,X5,X5,X1,sK27(X0,X3,X2,X4,X1),X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_392])])).
% 11.66/2.03 tff(f2020,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(X0,bool)),X4 : list(X0),X5 : list(X0)] : (step1(X0,X1,sK26(X0,X3,X2,X4,X1),X3) | ~step1(X0,X1,X4,cons(X0,X2,X3)) | sP2(X0,X5,X5,X1,sK27(X0,X3,X2,X4,X1),X2)) ) | (~spl32_80 | ~spl32_155)),
% 11.66/2.03 inference(resolution,[],[f2018,f970])).
% 11.66/2.03 tff(f8638,plain,(
% 11.66/2.03 spl32_391 | ~spl32_34 | ~spl32_152),
% 11.66/2.03 inference(avatar_split_clause,[],[f1995,f1983,f708,f8636])).
% 11.66/2.03 tff(f8636,plain,(
% 11.66/2.03 spl32_391 <=> ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,foldl(dB,dB,app,X1,X2),combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,X2))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_391])])).
% 11.66/2.03 tff(f1995,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,foldl(dB,dB,app,X1,X2),combc(dB,dB,bool,beta,foldl(dB,dB,app,X0,X2)))) ) | (~spl32_34 | ~spl32_152)),
% 11.66/2.03 inference(resolution,[],[f1984,f709])).
% 11.66/2.03 tff(f8634,plain,(
% 11.66/2.03 spl32_390 | spl32_253 | ~spl32_33 | ~spl32_322),
% 11.66/2.03 inference(avatar_split_clause,[],[f5338,f4663,f704,f3233,f8632])).
% 11.66/2.03 tff(f8632,plain,(
% 11.66/2.03 spl32_390 <=> ! [X0 : $tType,X3 : bool,X2 : X0,X1 : fun(bool,fun(X0,bool))] : (~member(bool,X3,combc(bool,X0,bool,X1,X2)) | fTrue = foldl(bool,X0,X1,X3,insert(X0,X2,nil(X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_390])])).
% 11.66/2.03 tff(f4663,plain,(
% 11.66/2.03 spl32_322 <=> ! [X0 : $tType,X4 : bool,X3 : X0,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) = X4 | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))) | fTrue = X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_322])])).
% 11.66/2.03 tff(f5338,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : bool,X1 : fun(bool,fun(X0,bool)),X4 : bool] : (pp(X4) | ~member(bool,X3,combc(bool,X0,bool,X1,X2)) | fTrue = foldl(bool,X0,X1,X3,insert(X0,X2,nil(X0))) | fTrue = X4) ) | (~spl32_33 | ~spl32_322)),
% 11.66/2.03 inference(superposition,[],[f705,f4664])).
% 11.66/2.03 tff(f4664,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X4 : bool] : (fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))) | aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) = X4 | fTrue = X4) ) | ~spl32_322),
% 11.66/2.03 inference(avatar_component_clause,[],[f4663])).
% 11.66/2.03 tff(f8630,plain,(
% 11.66/2.03 spl32_389 | ~spl32_34 | ~spl32_149),
% 11.66/2.03 inference(avatar_split_clause,[],[f1962,f1953,f708,f8628])).
% 11.66/2.03 tff(f8628,plain,(
% 11.66/2.03 spl32_389 <=> ! [X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | member(type,foldr(type,type,fun1,sK23(X3,X2,X1,X0),X3),typing(X0,var(X1))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_389])])).
% 11.66/2.03 tff(f1962,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | member(type,foldr(type,type,fun1,sK23(X3,X2,X1,X0),X3),typing(X0,var(X1)))) ) | (~spl32_34 | ~spl32_149)),
% 11.66/2.03 inference(resolution,[],[f1954,f709])).
% 11.66/2.03 tff(f8626,plain,(
% 11.66/2.03 spl32_388 | ~spl32_70 | ~spl32_149),
% 11.66/2.03 inference(avatar_split_clause,[],[f1960,f1953,f908,f8624])).
% 11.66/2.03 tff(f8624,plain,(
% 11.66/2.03 spl32_388 <=> ! [X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | aa(nat,type,X0,X1) = foldr(type,type,fun1,sK23(X3,X2,X1,X0),X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_388])])).
% 11.66/2.03 tff(f1960,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | aa(nat,type,X0,X1) = foldr(type,type,fun1,sK23(X3,X2,X1,X0),X3)) ) | (~spl32_70 | ~spl32_149)),
% 11.66/2.03 inference(resolution,[],[f1954,f909])).
% 11.66/2.03 tff(f8622,plain,(
% 11.66/2.03 spl32_387 | ~spl32_97 | ~spl32_148),
% 11.66/2.03 inference(avatar_split_clause,[],[f1942,f1938,f1273,f8620])).
% 11.66/2.03 tff(f8620,plain,(
% 11.66/2.03 spl32_387 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : type] : (~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X1),X2),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X2,X0)),X2),sK9(X2,X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_387])])).
% 11.66/2.03 tff(f1942,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : type] : (~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X1),X2),X3)) | pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X2,X0)),X2),sK9(X2,X0)))) ) | (~spl32_97 | ~spl32_148)),
% 11.66/2.03 inference(resolution,[],[f1939,f1274])).
% 11.66/2.03 tff(f8617,plain,(
% 11.66/2.03 spl32_386 | ~spl32_89 | ~spl32_146),
% 11.66/2.03 inference(avatar_split_clause,[],[f1923,f1918,f1039,f8615])).
% 11.66/2.03 tff(f1923,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : dB,X1 : dB] : (subst(aa(dB,dB,combc(dB,dB,dB,app,X3),X0),X1,X2) = aa(dB,dB,combc(dB,dB,dB,app,subst(X3,X1,X2)),subst(X0,X1,X2))) ) | (~spl32_89 | ~spl32_146)),
% 11.66/2.03 inference(superposition,[],[f1919,f1040])).
% 11.66/2.03 tff(f8612,plain,(
% 11.66/2.03 spl32_385 | ~spl32_89 | ~spl32_144),
% 11.66/2.03 inference(avatar_split_clause,[],[f1899,f1894,f1039,f8610])).
% 11.66/2.03 tff(f1899,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : dB,X0 : nat,X1 : dB] : (liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2) = aa(dB,dB,combc(dB,dB,dB,app,liftn(X0,X3,X2)),liftn(X0,X1,X2))) ) | (~spl32_89 | ~spl32_144)),
% 11.66/2.03 inference(superposition,[],[f1895,f1040])).
% 11.66/2.03 tff(f8608,plain,(
% 11.66/2.03 spl32_384 | ~spl32_70 | ~spl32_126),
% 11.66/2.03 inference(avatar_split_clause,[],[f1710,f1680,f908,f8606])).
% 11.66/2.03 tff(f8606,plain,(
% 11.66/2.03 spl32_384 <=> ! [X2 : type,X0 : fun(nat,type),X1 : nat] : (~pp(aa(type,bool,typing(X0,abs(var(X1))),X2)) | aa(nat,type,shift(type,X0,zero_zero(nat),sK10(X2,var(X1),X0)),X1) = sK11(X2,var(X1),X0))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_384])])).
% 11.66/2.03 tff(f1710,plain,(
% 11.66/2.03 ( ! [X2 : type,X0 : fun(nat,type),X1 : nat] : (~pp(aa(type,bool,typing(X0,abs(var(X1))),X2)) | aa(nat,type,shift(type,X0,zero_zero(nat),sK10(X2,var(X1),X0)),X1) = sK11(X2,var(X1),X0)) ) | (~spl32_70 | ~spl32_126)),
% 11.66/2.03 inference(resolution,[],[f1681,f909])).
% 11.66/2.03 tff(f8603,plain,(
% 11.66/2.03 spl32_383 | ~spl32_110 | ~spl32_129),
% 11.66/2.03 inference(avatar_split_clause,[],[f1700,f1694,f1452,f8601])).
% 11.66/2.03 tff(f8601,plain,(
% 11.66/2.03 spl32_383 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X0,subst(X1,X2,zero_zero(nat))),X3)) | ~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1))),X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_383])])).
% 11.66/2.03 tff(f1700,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (pp(aa(type,bool,typing(X0,subst(X1,X2,zero_zero(nat))),X3)) | ~pp(aa(type,bool,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X2),abs(X1))),X3))) ) | (~spl32_110 | ~spl32_129)),
% 11.66/2.03 inference(resolution,[],[f1695,f1453])).
% 11.66/2.03 tff(f8599,plain,(
% 11.66/2.03 spl32_382 | ~spl32_112 | ~spl32_129),
% 11.66/2.03 inference(avatar_split_clause,[],[f1697,f1694,f1471,f8597])).
% 11.66/2.03 tff(f8597,plain,(
% 11.66/2.03 spl32_382 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X0,sK5(X1,X2)),X3)) | ~pp(aa(type,bool,typing(X0,X2),X3)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),abs(X2))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_382])])).
% 11.66/2.03 tff(f1697,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : dB] : (pp(aa(type,bool,typing(X0,sK5(X1,X2)),X3)) | ~pp(aa(type,bool,typing(X0,X2),X3)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),abs(X2)))) ) | (~spl32_112 | ~spl32_129)),
% 11.66/2.03 inference(resolution,[],[f1695,f1472])).
% 11.66/2.03 tff(f8416,plain,(
% 11.66/2.03 spl32_381 | ~spl32_89 | ~spl32_275 | ~spl32_378),
% 11.66/2.03 inference(avatar_split_clause,[],[f7832,f7829,f3812,f1039,f8414])).
% 11.66/2.03 tff(f8414,plain,(
% 11.66/2.03 spl32_381 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : type] : (member(type,foldr(type,type,fun1,insert(type,X1,nil(type)),X3),typing(X0,abs(X2))) | ~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X1),X2),X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_381])])).
% 11.66/2.03 tff(f7829,plain,(
% 11.66/2.03 spl32_378 <=> ! [X0 : fun(nat,type),X3 : type,X2 : dB,X1 : type] : (~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X1),X2),X3)) | member(type,aa(type,type,combc(type,type,type,fun1,X3),X1),typing(X0,abs(X2))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_378])])).
% 11.66/2.03 tff(f7832,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : type] : (member(type,foldr(type,type,fun1,insert(type,X1,nil(type)),X3),typing(X0,abs(X2))) | ~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X1),X2),X3))) ) | (~spl32_89 | ~spl32_275 | ~spl32_378)),
% 11.66/2.03 inference(forward_demodulation,[],[f7830,f3939])).
% 11.66/2.03 tff(f7830,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : type] : (~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X1),X2),X3)) | member(type,aa(type,type,combc(type,type,type,fun1,X3),X1),typing(X0,abs(X2)))) ) | ~spl32_378),
% 11.66/2.03 inference(avatar_component_clause,[],[f7829])).
% 11.66/2.03 tff(f8412,plain,(
% 11.66/2.03 spl32_380 | ~spl32_89 | ~spl32_275 | ~spl32_377),
% 11.66/2.03 inference(avatar_split_clause,[],[f7827,f7824,f3812,f1039,f8410])).
% 11.66/2.03 tff(f8410,plain,(
% 11.66/2.03 spl32_380 <=> ! [X2 : dB,X0 : nat,X1 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X2,X1,X0)),X1) = subst(foldr(dB,dB,app,insert(dB,X2,nil(dB)),var(X0)),X1,X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_380])])).
% 11.66/2.03 tff(f7824,plain,(
% 11.66/2.03 spl32_377 <=> ! [X2 : dB,X0 : nat,X1 : dB] : subst(aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X2,X1,X0)),X1)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_377])])).
% 11.66/2.03 tff(f7827,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X2,X1,X0)),X1) = subst(foldr(dB,dB,app,insert(dB,X2,nil(dB)),var(X0)),X1,X0)) ) | (~spl32_89 | ~spl32_275 | ~spl32_377)),
% 11.66/2.03 inference(forward_demodulation,[],[f7825,f3939])).
% 11.66/2.03 tff(f7825,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : nat,X1 : dB] : (subst(aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X2,X1,X0)),X1)) ) | ~spl32_377),
% 11.66/2.03 inference(avatar_component_clause,[],[f7824])).
% 11.66/2.03 tff(f8408,plain,(
% 11.66/2.03 spl32_379 | ~spl32_89 | ~spl32_275 | ~spl32_376),
% 11.66/2.03 inference(avatar_split_clause,[],[f7822,f7819,f3812,f1039,f8406])).
% 11.66/2.03 tff(f8406,plain,(
% 11.66/2.03 spl32_379 <=> ! [X2 : dB,X0 : nat,X1 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,X1),subst(X2,X1,X0)) = subst(foldr(dB,dB,app,insert(dB,var(X0),nil(dB)),X2),X1,X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_379])])).
% 11.66/2.03 tff(f7819,plain,(
% 11.66/2.03 spl32_376 <=> ! [X2 : dB,X0 : nat,X1 : dB] : subst(aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X1),subst(X2,X1,X0))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_376])])).
% 11.66/2.03 tff(f7822,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X1),subst(X2,X1,X0)) = subst(foldr(dB,dB,app,insert(dB,var(X0),nil(dB)),X2),X1,X0)) ) | (~spl32_89 | ~spl32_275 | ~spl32_376)),
% 11.66/2.03 inference(forward_demodulation,[],[f7820,f3939])).
% 11.66/2.03 tff(f7820,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : nat,X1 : dB] : (subst(aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X1),subst(X2,X1,X0))) ) | ~spl32_376),
% 11.66/2.03 inference(avatar_component_clause,[],[f7819])).
% 11.66/2.03 tff(f7831,plain,(
% 11.66/2.03 spl32_378 | ~spl32_34 | ~spl32_148),
% 11.66/2.03 inference(avatar_split_clause,[],[f1944,f1938,f708,f7829])).
% 11.66/2.03 tff(f1944,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : type,X0 : fun(nat,type),X1 : type] : (~pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),X1),X2),X3)) | member(type,aa(type,type,combc(type,type,type,fun1,X3),X1),typing(X0,abs(X2)))) ) | (~spl32_34 | ~spl32_148)),
% 11.66/2.03 inference(resolution,[],[f1939,f709])).
% 11.66/2.03 tff(f7826,plain,(
% 11.66/2.03 spl32_377 | ~spl32_16 | ~spl32_146),
% 11.66/2.03 inference(avatar_split_clause,[],[f1922,f1918,f618,f7824])).
% 11.66/2.03 tff(f618,plain,(
% 11.66/2.03 spl32_16 <=> ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_16])])).
% 11.66/2.03 tff(f1922,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : nat,X1 : dB] : (subst(aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X2),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X2,X1,X0)),X1)) ) | (~spl32_16 | ~spl32_146)),
% 11.66/2.03 inference(superposition,[],[f1919,f619])).
% 11.66/2.03 tff(f619,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : nat] : (subst(var(X1),X0,X1) = X0) ) | ~spl32_16),
% 11.66/2.03 inference(avatar_component_clause,[],[f618])).
% 11.66/2.03 tff(f7821,plain,(
% 11.66/2.03 spl32_376 | ~spl32_16 | ~spl32_146),
% 11.66/2.03 inference(avatar_split_clause,[],[f1921,f1918,f618,f7819])).
% 11.66/2.03 tff(f1921,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : nat,X1 : dB] : (subst(aa(dB,dB,combc(dB,dB,dB,app,X2),var(X0)),X1,X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,X1),subst(X2,X1,X0))) ) | (~spl32_16 | ~spl32_146)),
% 11.66/2.03 inference(superposition,[],[f1919,f619])).
% 11.66/2.03 tff(f7810,plain,(
% 11.66/2.03 spl32_375 | ~spl32_33 | ~spl32_142),
% 11.66/2.03 inference(avatar_split_clause,[],[f1880,f1859,f704,f7808])).
% 11.66/2.03 tff(f7808,plain,(
% 11.66/2.03 spl32_375 <=> ! [X3 : dB,X4 : nat,X0 : fun(nat,type),X5 : type,X2 : type,X1 : dB] : (~pp(aa(type,bool,typing(X0,X1),X2)) | pp(aa(type,bool,typing(X0,subst(X3,X1,X4)),X5)) | ~member(type,X5,typing(shift(type,X0,X4,X2),X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_375])])).
% 11.66/2.03 tff(f1880,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : dB,X4 : nat,X5 : type] : (~pp(aa(type,bool,typing(X0,X1),X2)) | pp(aa(type,bool,typing(X0,subst(X3,X1,X4)),X5)) | ~member(type,X5,typing(shift(type,X0,X4,X2),X3))) ) | (~spl32_33 | ~spl32_142)),
% 11.66/2.03 inference(resolution,[],[f1860,f705])).
% 11.66/2.03 tff(f7806,plain,(
% 11.66/2.03 spl32_374 | ~spl32_33 | ~spl32_141),
% 11.66/2.03 inference(avatar_split_clause,[],[f1865,f1855,f704,f7804])).
% 11.66/2.03 tff(f7804,plain,(
% 11.66/2.03 spl32_374 <=> ! [X4 : type,X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : nat] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | X3 = X4 | ~member(type,X4,typing(X0,foldl(dB,dB,app,var(X1),X2))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_374])])).
% 11.66/2.03 tff(f1855,plain,(
% 11.66/2.03 spl32_141 <=> ! [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)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_141])])).
% 11.66/2.03 tff(f1865,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : nat,X4 : type] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,var(X1),X2)),X3)) | X3 = X4 | ~member(type,X4,typing(X0,foldl(dB,dB,app,var(X1),X2)))) ) | (~spl32_33 | ~spl32_141)),
% 11.66/2.03 inference(resolution,[],[f1856,f705])).
% 11.66/2.03 tff(f1856,plain,(
% 11.66/2.03 ( ! [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) ) | ~spl32_141),
% 11.66/2.03 inference(avatar_component_clause,[],[f1855])).
% 11.66/2.03 tff(f7802,plain,(
% 11.66/2.03 spl32_373 | ~spl32_115 | ~spl32_131),
% 11.66/2.03 inference(avatar_split_clause,[],[f1733,f1730,f1495,f7800])).
% 11.66/2.03 tff(f7800,plain,(
% 11.66/2.03 spl32_373 <=> ! [X2 : list(dB),X0 : nat,X1 : list(dB)] : (foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(X0),sK17(foldl(dB,dB,app,var(X0),X1),X2,X0)) | ~step1(dB,beta,X2,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_373])])).
% 11.66/2.03 tff(f1730,plain,(
% 11.66/2.03 spl32_131 <=> ! [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),sK17(X0,X1,X2)) = X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_131])])).
% 11.66/2.03 tff(f1733,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X0 : nat,X1 : list(dB)] : (foldl(dB,dB,app,var(X0),X1) = foldl(dB,dB,app,var(X0),sK17(foldl(dB,dB,app,var(X0),X1),X2,X0)) | ~step1(dB,beta,X2,X1)) ) | (~spl32_115 | ~spl32_131)),
% 11.66/2.03 inference(resolution,[],[f1731,f1496])).
% 11.66/2.03 tff(f1731,plain,(
% 11.66/2.03 ( ! [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),sK17(X0,X1,X2)) = X0) ) | ~spl32_131),
% 11.66/2.03 inference(avatar_component_clause,[],[f1730])).
% 11.66/2.03 tff(f7798,plain,(
% 11.66/2.03 spl32_372 | ~spl32_96 | ~spl32_129),
% 11.66/2.03 inference(avatar_split_clause,[],[f1698,f1694,f1260,f7796])).
% 11.66/2.03 tff(f7796,plain,(
% 11.66/2.03 spl32_372 <=> ! [X0 : fun(nat,type),X3 : dB,X2 : type,X1 : dB] : (pp(aa(type,bool,typing(X0,abs(X1)),X2)) | ~pp(aa(type,bool,typing(X0,abs(X3)),X2)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_372])])).
% 11.66/2.03 tff(f1260,plain,(
% 11.66/2.03 spl32_96 <=> ! [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))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_96])])).
% 11.66/2.03 tff(f1698,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : dB] : (pp(aa(type,bool,typing(X0,abs(X1)),X2)) | ~pp(aa(type,bool,typing(X0,abs(X3)),X2)) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),X3))) ) | (~spl32_96 | ~spl32_129)),
% 11.66/2.03 inference(resolution,[],[f1695,f1261])).
% 11.66/2.03 tff(f1261,plain,(
% 11.66/2.03 ( ! [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))) ) | ~spl32_96),
% 11.66/2.03 inference(avatar_component_clause,[],[f1260])).
% 11.66/2.03 tff(f7793,plain,(
% 11.66/2.03 spl32_371 | ~spl32_119),
% 11.66/2.03 inference(avatar_split_clause,[],[f1532,f1527,f7791])).
% 11.66/2.03 tff(f7791,plain,(
% 11.66/2.03 spl32_371 <=> ! [X0 : $tType,X3 : type,X4 : fun(nat,X0),X5 : fun(nat,X0),X2 : type,X1 : fun(type,fun(type,X0))] : type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = type_case(X0,X5,X1,aa(type,type,combc(type,type,type,fun1,X3),X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_371])])).
% 11.66/2.03 tff(f1532,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,X0)),X4 : fun(nat,X0),X5 : fun(nat,X0)] : (type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = type_case(X0,X5,X1,aa(type,type,combc(type,type,type,fun1,X3),X2))) ) | ~spl32_119),
% 11.66/2.03 inference(superposition,[],[f1528,f1528])).
% 11.66/2.03 tff(f7789,plain,(
% 11.66/2.03 spl32_370 | ~spl32_71 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1432,f1325,f912,f7787])).
% 11.66/2.03 tff(f7787,plain,(
% 11.66/2.03 spl32_370 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (foldl(dB,dB,app,X0,cons(dB,X1,X2)) != foldl(dB,dB,app,X3,X2) | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1) = X3)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_370])])).
% 11.66/2.03 tff(f912,plain,(
% 11.66/2.03 spl32_71 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (X0 = X2 | foldl(dB,dB,app,X0,X1) != foldl(dB,dB,app,X2,X1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_71])])).
% 11.66/2.03 tff(f1432,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (foldl(dB,dB,app,X0,cons(dB,X1,X2)) != foldl(dB,dB,app,X3,X2) | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1) = X3) ) | (~spl32_71 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f913,f1326])).
% 11.66/2.03 tff(f913,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,X0,X1) != foldl(dB,dB,app,X2,X1) | X0 = X2) ) | ~spl32_71),
% 11.66/2.03 inference(avatar_component_clause,[],[f912])).
% 11.66/2.03 tff(f7785,plain,(
% 11.66/2.03 spl32_369 | ~spl32_12 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1420,f1325,f599,f7783])).
% 11.66/2.03 tff(f7783,plain,(
% 11.66/2.03 spl32_369 <=> ! [X0 : $tType,X2 : bool,X4 : list(X0),X3 : X0,X1 : fun(bool,fun(X0,bool))] : (foldl(bool,X0,X1,X2,cons(X0,X3,X4)) = foldl(bool,X0,X1,fFalse,X4) | fTrue = aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_369])])).
% 11.66/2.03 tff(f1420,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X4 : list(X0)] : (foldl(bool,X0,X1,X2,cons(X0,X3,X4)) = foldl(bool,X0,X1,fFalse,X4) | fTrue = aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3)) ) | (~spl32_12 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f1326,f600])).
% 11.66/2.03 tff(f7781,plain,(
% 11.66/2.03 spl32_368 | ~spl32_107 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1413,f1325,f1321,f7779])).
% 11.66/2.03 tff(f7779,plain,(
% 11.66/2.03 spl32_368 <=> ! [X0 : $tType,X3 : list(X0),X4 : X0,X5 : list(X0),X2 : X0,X1 : fun(X0,fun(X0,X0))] : foldl(X0,X0,X1,X2,cons(X0,foldr(X0,X0,X1,X3,X4),X5)) = foldl(X0,X0,X1,foldr(X0,X0,X1,cons(X0,X2,X3),X4),X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_368])])).
% 11.66/2.03 tff(f1413,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(X0,X0)),X4 : X0,X5 : list(X0)] : (foldl(X0,X0,X1,X2,cons(X0,foldr(X0,X0,X1,X3,X4),X5)) = foldl(X0,X0,X1,foldr(X0,X0,X1,cons(X0,X2,X3),X4),X5)) ) | (~spl32_107 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f1326,f1322])).
% 11.66/2.03 tff(f7777,plain,(
% 11.66/2.03 spl32_367 | ~spl32_103 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1404,f1321,f1305,f7775])).
% 11.66/2.03 tff(f7775,plain,(
% 11.66/2.03 spl32_367 <=> ! [X4 : type,X0 : type,X3 : type,X2 : type,X1 : list(type)] : (aa(type,type,aa(type,fun(type,type),fun1,X3),X4) != foldr(type,type,fun1,cons(type,X0,X1),X2) | foldr(type,type,fun1,X1,X2) = X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_367])])).
% 11.66/2.03 tff(f1305,plain,(
% 11.66/2.03 spl32_103 <=> ! [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))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_103])])).
% 11.66/2.03 tff(f1404,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : type,X0 : type,X1 : list(type),X4 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X3),X4) != foldr(type,type,fun1,cons(type,X0,X1),X2) | foldr(type,type,fun1,X1,X2) = X4) ) | (~spl32_103 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f1306,f1322])).
% 11.66/2.03 tff(f1306,plain,(
% 11.66/2.03 ( ! [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) ) | ~spl32_103),
% 11.66/2.03 inference(avatar_component_clause,[],[f1305])).
% 11.66/2.03 tff(f7773,plain,(
% 11.66/2.03 spl32_366 | ~spl32_106 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1397,f1321,f1317,f7771])).
% 11.66/2.03 tff(f7771,plain,(
% 11.66/2.03 spl32_366 <=> ! [X4 : dB,X0 : dB,X3 : dB,X2 : dB,X1 : list(dB)] : (foldr(dB,dB,app,cons(dB,X0,X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) | foldr(dB,dB,app,X1,X2) = X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_366])])).
% 11.66/2.03 tff(f1397,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : list(dB),X4 : dB] : (foldr(dB,dB,app,cons(dB,X0,X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) | foldr(dB,dB,app,X1,X2) = X4) ) | (~spl32_106 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f1318,f1322])).
% 11.66/2.03 tff(f7758,plain,(
% 11.66/2.03 spl32_365 | ~spl32_12 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1392,f1321,f599,f7756])).
% 11.66/2.03 tff(f7756,plain,(
% 11.66/2.03 spl32_365 <=> ! [X0 : $tType,X4 : bool,X3 : list(X0),X2 : X0,X1 : fun(X0,fun(bool,bool))] : (fFalse = foldr(X0,bool,X1,cons(X0,X2,X3),X4) | fTrue = aa(bool,bool,aa(X0,fun(bool,bool),X1,X2),foldr(X0,bool,X1,X3,X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_365])])).
% 11.66/2.03 tff(f1392,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(bool,bool)),X4 : bool] : (fFalse = foldr(X0,bool,X1,cons(X0,X2,X3),X4) | fTrue = aa(bool,bool,aa(X0,fun(bool,bool),X1,X2),foldr(X0,bool,X1,X3,X4))) ) | (~spl32_12 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f1322,f600])).
% 11.66/2.03 tff(f7754,plain,(
% 11.66/2.03 spl32_364 | ~spl32_12 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1385,f1321,f599,f7752])).
% 11.66/2.03 tff(f7752,plain,(
% 11.66/2.03 spl32_364 <=> ! [X0 : $tType,X2 : list(X0),X4 : X0,X3 : bool,X1 : fun(X0,fun(bool,bool))] : (foldr(X0,bool,X1,cons(X0,X4,X2),X3) = aa(bool,bool,aa(X0,fun(bool,bool),X1,X4),fFalse) | fTrue = foldr(X0,bool,X1,X2,X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_364])])).
% 11.66/2.03 tff(f1385,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : list(X0),X3 : bool,X1 : fun(X0,fun(bool,bool)),X4 : X0] : (foldr(X0,bool,X1,cons(X0,X4,X2),X3) = aa(bool,bool,aa(X0,fun(bool,bool),X1,X4),fFalse) | fTrue = foldr(X0,bool,X1,X2,X3)) ) | (~spl32_12 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f1322,f600])).
% 11.66/2.03 tff(f7750,plain,(
% 11.66/2.03 spl32_363 | ~spl32_69 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1069,f1060,f904,f7748])).
% 11.66/2.03 tff(f7748,plain,(
% 11.66/2.03 spl32_363 <=> ! [X0 : $tType,X2 : $tType,X4 : fun(X0,fun(list(X0),X2)),X3 : X2,X1 : list(X0)] : (list_case(X2,X0,X3,X4,X1) = aa(list(X0),X2,aa(X0,fun(list(X0),X2),X4,sK6(X0,X1)),sK7(X0,X1)) | nil(X0) = X1)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_363])])).
% 11.66/2.03 tff(f904,plain,(
% 11.66/2.03 spl32_69 <=> ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 | nil(X0) = X1)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_69])])).
% 11.66/2.03 tff(f1069,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : $tType,X3 : X2,X1 : list(X0),X4 : fun(X0,fun(list(X0),X2))] : (list_case(X2,X0,X3,X4,X1) = aa(list(X0),X2,aa(X0,fun(list(X0),X2),X4,sK6(X0,X1)),sK7(X0,X1)) | nil(X0) = X1) ) | (~spl32_69 | ~spl32_91)),
% 11.66/2.03 inference(superposition,[],[f1061,f905])).
% 11.66/2.03 tff(f905,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 | nil(X0) = X1) ) | ~spl32_69),
% 11.66/2.03 inference(avatar_component_clause,[],[f904])).
% 11.66/2.03 tff(f7746,plain,(
% 11.66/2.03 spl32_362 | ~spl32_68 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1068,f1060,f900,f7744])).
% 11.66/2.03 tff(f7744,plain,(
% 11.66/2.03 spl32_362 <=> ! [X0 : $tType,X2 : $tType,X4 : fun(X0,fun(list(X0),X2)),X3 : X2,X1 : list(X0)] : (aa(list(X0),X2,aa(X0,fun(list(X0),X2),X4,sK3(X0,X1)),sK4(X0,X1)) = list_case(X2,X0,X3,X4,X1) | nil(X0) = X1)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_362])])).
% 11.66/2.03 tff(f900,plain,(
% 11.66/2.03 spl32_68 <=> ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1 | nil(X0) = X1)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_68])])).
% 11.66/2.03 tff(f1068,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : $tType,X3 : X2,X1 : list(X0),X4 : fun(X0,fun(list(X0),X2))] : (aa(list(X0),X2,aa(X0,fun(list(X0),X2),X4,sK3(X0,X1)),sK4(X0,X1)) = list_case(X2,X0,X3,X4,X1) | nil(X0) = X1) ) | (~spl32_68 | ~spl32_91)),
% 11.66/2.03 inference(superposition,[],[f1061,f901])).
% 11.66/2.03 tff(f901,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1 | nil(X0) = X1) ) | ~spl32_68),
% 11.66/2.03 inference(avatar_component_clause,[],[f900])).
% 11.66/2.03 tff(f7618,plain,(
% 11.66/2.03 spl32_361 | ~spl32_12 | ~spl32_89 | ~spl32_119 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f5959,f3812,f1527,f1039,f599,f7616])).
% 11.66/2.03 tff(f7616,plain,(
% 11.66/2.03 spl32_361 <=> ! [X0 : fun(nat,bool),X3 : type,X2 : type,X1 : fun(type,fun(type,bool))] : (fTrue = type_case(bool,X0,X1,foldr(type,type,fun1,insert(type,X3,nil(type)),X2)) | fFalse = aa(type,bool,combc(type,type,bool,X1,X2),X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_361])])).
% 11.66/2.03 tff(f5959,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : type,X0 : fun(nat,bool),X1 : fun(type,fun(type,bool))] : (fTrue = type_case(bool,X0,X1,foldr(type,type,fun1,insert(type,X3,nil(type)),X2)) | fFalse = aa(type,bool,combc(type,type,bool,X1,X2),X3)) ) | (~spl32_12 | ~spl32_89 | ~spl32_119 | ~spl32_275)),
% 11.66/2.03 inference(forward_demodulation,[],[f1550,f3939])).
% 11.66/2.03 tff(f1550,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : type,X0 : fun(nat,bool),X1 : fun(type,fun(type,bool))] : (fFalse = aa(type,bool,combc(type,type,bool,X1,X2),X3) | fTrue = type_case(bool,X0,X1,aa(type,type,combc(type,type,type,fun1,X2),X3))) ) | (~spl32_12 | ~spl32_89 | ~spl32_119)),
% 11.66/2.03 inference(forward_demodulation,[],[f1538,f1040])).
% 11.66/2.03 tff(f1538,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : type,X0 : fun(nat,bool),X1 : fun(type,fun(type,bool))] : (fFalse = aa(type,bool,aa(type,fun(type,bool),X1,X3),X2) | fTrue = type_case(bool,X0,X1,aa(type,type,combc(type,type,type,fun1,X2),X3))) ) | (~spl32_12 | ~spl32_119)),
% 11.66/2.03 inference(superposition,[],[f1528,f600])).
% 11.66/2.03 tff(f7602,plain,(
% 11.66/2.03 spl32_360 | ~spl32_80 | ~spl32_152),
% 11.66/2.03 inference(avatar_split_clause,[],[f1994,f1983,f969,f7600])).
% 11.66/2.03 tff(f7600,plain,(
% 11.66/2.03 spl32_360 <=> ! [X0 : dB,X3 : list(dB),X2 : list(dB),X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,foldl(dB,dB,app,X1,X3),foldl(dB,dB,app,X0,X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_360])])).
% 11.66/2.03 tff(f1994,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,foldl(dB,dB,app,X1,X3),foldl(dB,dB,app,X0,X3))) ) | (~spl32_80 | ~spl32_152)),
% 11.66/2.03 inference(resolution,[],[f1984,f970])).
% 11.66/2.03 tff(f7598,plain,(
% 11.66/2.03 spl32_359 | ~spl32_123 | ~spl32_142),
% 11.66/2.03 inference(avatar_split_clause,[],[f1878,f1859,f1649,f7596])).
% 11.66/2.03 tff(f7596,plain,(
% 11.66/2.03 spl32_359 <=> ! [X0 : dB] : (~pp(aa(type,bool,typing(ea,X0),t)) | pp(aa(type,bool,typing(ea,subst(foldl(dB,dB,app,abs(r),cons(dB,a,as)),X0,ia)),t_a)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_359])])).
% 11.66/2.03 tff(f1649,plain,(
% 11.66/2.03 spl32_123 <=> pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,abs(r),cons(dB,a,as))),t_a))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_123])])).
% 11.66/2.03 tff(f1878,plain,(
% 11.66/2.03 ( ! [X0 : dB] : (~pp(aa(type,bool,typing(ea,X0),t)) | pp(aa(type,bool,typing(ea,subst(foldl(dB,dB,app,abs(r),cons(dB,a,as)),X0,ia)),t_a))) ) | (~spl32_123 | ~spl32_142)),
% 11.66/2.03 inference(resolution,[],[f1860,f1651])).
% 11.66/2.03 tff(f1651,plain,(
% 11.66/2.03 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,abs(r),cons(dB,a,as))),t_a)) | ~spl32_123),
% 11.66/2.03 inference(avatar_component_clause,[],[f1649])).
% 11.66/2.03 tff(f7550,plain,(
% 11.66/2.03 spl32_358 | ~spl32_121 | ~spl32_142),
% 11.66/2.03 inference(avatar_split_clause,[],[f1877,f1859,f1629,f7548])).
% 11.66/2.03 tff(f7548,plain,(
% 11.66/2.03 spl32_358 <=> ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t)) | pp(aa(type,bool,typing(e,subst(foldl(dB,dB,app,abs(r),cons(dB,a,as)),X0,i)),t1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_358])])).
% 11.66/2.03 tff(f1629,plain,(
% 11.66/2.03 spl32_121 <=> pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,abs(r),cons(dB,a,as))),t1))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_121])])).
% 11.66/2.03 tff(f1877,plain,(
% 11.66/2.03 ( ! [X0 : dB] : (~pp(aa(type,bool,typing(e,X0),t)) | pp(aa(type,bool,typing(e,subst(foldl(dB,dB,app,abs(r),cons(dB,a,as)),X0,i)),t1))) ) | (~spl32_121 | ~spl32_142)),
% 11.66/2.03 inference(resolution,[],[f1860,f1631])).
% 11.66/2.03 tff(f1631,plain,(
% 11.66/2.03 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,abs(r),cons(dB,a,as))),t1)) | ~spl32_121),
% 11.66/2.03 inference(avatar_component_clause,[],[f1629])).
% 11.66/2.03 tff(f7546,plain,(
% 11.66/2.03 spl32_357 | ~spl32_48 | ~spl32_142),
% 11.66/2.03 inference(avatar_split_clause,[],[f1876,f1859,f785,f7544])).
% 11.66/2.03 tff(f7544,plain,(
% 11.66/2.03 spl32_357 <=> ! [X4 : nat,X0 : fun(nat,type),X3 : nat,X2 : type,X1 : dB] : (~pp(aa(type,bool,typing(X0,X1),X2)) | pp(aa(type,bool,typing(X0,subst(var(X3),X1,X4)),aa(nat,type,shift(type,X0,X4,X2),X3))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_357])])).
% 11.66/2.03 tff(f1876,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : nat,X0 : fun(nat,type),X1 : dB,X4 : nat] : (~pp(aa(type,bool,typing(X0,X1),X2)) | pp(aa(type,bool,typing(X0,subst(var(X3),X1,X4)),aa(nat,type,shift(type,X0,X4,X2),X3)))) ) | (~spl32_48 | ~spl32_142)),
% 11.66/2.03 inference(resolution,[],[f1860,f786])).
% 11.66/2.03 tff(f7542,plain,(
% 11.66/2.03 spl32_356 | ~spl32_34 | ~spl32_135),
% 11.66/2.03 inference(avatar_split_clause,[],[f1829,f1779,f708,f7540])).
% 11.66/2.03 tff(f7540,plain,(
% 11.66/2.03 spl32_356 <=> ! [X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : dB] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X1,X2)),X3)) | member(type,foldr(type,type,fun1,sK22(X3,X2,X1,X0),X3),typing(X0,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_356])])).
% 11.66/2.03 tff(f1829,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X1,X2)),X3)) | member(type,foldr(type,type,fun1,sK22(X3,X2,X1,X0),X3),typing(X0,X1))) ) | (~spl32_34 | ~spl32_135)),
% 11.66/2.03 inference(resolution,[],[f1780,f709])).
% 11.66/2.03 tff(f7538,plain,(
% 11.66/2.03 spl32_355 | ~spl32_34 | ~spl32_134),
% 11.66/2.03 inference(avatar_split_clause,[],[f1812,f1767,f708,f7536])).
% 11.66/2.03 tff(f7536,plain,(
% 11.66/2.03 spl32_355 <=> ! [X0 : fun(nat,type),X3 : type,X2 : list(dB),X1 : dB] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X1,X2)),X3)) | member(type,foldr(type,type,fun1,sK21(X3,X2,X1,X0),X3),typing(X0,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_355])])).
% 11.66/2.03 tff(f1812,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,foldl(dB,dB,app,X1,X2)),X3)) | member(type,foldr(type,type,fun1,sK21(X3,X2,X1,X0),X3),typing(X0,X1))) ) | (~spl32_34 | ~spl32_134)),
% 11.66/2.03 inference(resolution,[],[f1768,f709])).
% 11.66/2.03 tff(f7534,plain,(
% 11.66/2.03 spl32_354 | ~spl32_100 | ~spl32_123),
% 11.66/2.03 inference(avatar_split_clause,[],[f1654,f1649,f1293,f7531])).
% 11.66/2.03 tff(f7531,plain,(
% 11.66/2.03 spl32_354 <=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),cons(dB,a,as)),sK21(t_a,cons(dB,a,as),abs(r),shift(type,ea,ia,t))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_354])])).
% 11.66/2.03 tff(f1654,plain,(
% 11.66/2.03 pp(aa(list(type),bool,typings(shift(type,ea,ia,t),cons(dB,a,as)),sK21(t_a,cons(dB,a,as),abs(r),shift(type,ea,ia,t)))) | (~spl32_100 | ~spl32_123)),
% 11.66/2.03 inference(resolution,[],[f1651,f1294])).
% 11.66/2.03 tff(f7529,plain,(
% 11.66/2.03 spl32_353 | ~spl32_101 | ~spl32_123),
% 11.66/2.03 inference(avatar_split_clause,[],[f1653,f1649,f1297,f7526])).
% 11.66/2.03 tff(f7526,plain,(
% 11.66/2.03 spl32_353 <=> pp(aa(list(type),bool,typings(shift(type,ea,ia,t),cons(dB,a,as)),sK22(t_a,cons(dB,a,as),abs(r),shift(type,ea,ia,t))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_353])])).
% 11.66/2.03 tff(f1653,plain,(
% 11.66/2.03 pp(aa(list(type),bool,typings(shift(type,ea,ia,t),cons(dB,a,as)),sK22(t_a,cons(dB,a,as),abs(r),shift(type,ea,ia,t)))) | (~spl32_101 | ~spl32_123)),
% 11.66/2.03 inference(resolution,[],[f1651,f1298])).
% 11.66/2.03 tff(f7524,plain,(
% 11.66/2.03 spl32_352 | ~spl32_100 | ~spl32_121),
% 11.66/2.03 inference(avatar_split_clause,[],[f1634,f1629,f1293,f7521])).
% 11.66/2.03 tff(f7521,plain,(
% 11.66/2.03 spl32_352 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t),cons(dB,a,as)),sK21(t1,cons(dB,a,as),abs(r),shift(type,e,i,t))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_352])])).
% 11.66/2.03 tff(f1634,plain,(
% 11.66/2.03 pp(aa(list(type),bool,typings(shift(type,e,i,t),cons(dB,a,as)),sK21(t1,cons(dB,a,as),abs(r),shift(type,e,i,t)))) | (~spl32_100 | ~spl32_121)),
% 11.66/2.03 inference(resolution,[],[f1631,f1294])).
% 11.66/2.03 tff(f7519,plain,(
% 11.66/2.03 spl32_351 | ~spl32_101 | ~spl32_121),
% 11.66/2.03 inference(avatar_split_clause,[],[f1633,f1629,f1297,f7516])).
% 11.66/2.03 tff(f7516,plain,(
% 11.66/2.03 spl32_351 <=> pp(aa(list(type),bool,typings(shift(type,e,i,t),cons(dB,a,as)),sK22(t1,cons(dB,a,as),abs(r),shift(type,e,i,t))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_351])])).
% 11.66/2.03 tff(f1633,plain,(
% 11.66/2.03 pp(aa(list(type),bool,typings(shift(type,e,i,t),cons(dB,a,as)),sK22(t1,cons(dB,a,as),abs(r),shift(type,e,i,t)))) | (~spl32_101 | ~spl32_121)),
% 11.66/2.03 inference(resolution,[],[f1631,f1298])).
% 11.66/2.03 tff(f7514,plain,(
% 11.66/2.03 spl32_350 | ~spl32_12 | ~spl32_89 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1441,f1325,f1039,f599,f7512])).
% 11.66/2.03 tff(f7512,plain,(
% 11.66/2.03 spl32_350 <=> ! [X0 : $tType,X4 : list(X0),X3 : X0,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) | fFalse = foldl(bool,X0,X1,X2,cons(X0,X3,X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_350])])).
% 11.66/2.03 tff(f1441,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X4 : list(X0)] : (fTrue = foldl(bool,X0,X1,aa(bool,bool,combc(bool,X0,bool,X1,X3),X2),X4) | fFalse = foldl(bool,X0,X1,X2,cons(X0,X3,X4))) ) | (~spl32_12 | ~spl32_89 | ~spl32_108)),
% 11.66/2.03 inference(forward_demodulation,[],[f1426,f1040])).
% 11.66/2.03 tff(f1426,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X4 : list(X0)] : (fFalse = foldl(bool,X0,X1,X2,cons(X0,X3,X4)) | fTrue = foldl(bool,X0,X1,aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3),X4)) ) | (~spl32_12 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f1326,f600])).
% 11.66/2.03 tff(f7446,plain,(
% 11.66/2.03 spl32_349 | ~spl32_89 | ~spl32_275 | ~spl32_344),
% 11.66/2.03 inference(avatar_split_clause,[],[f5920,f5888,f3812,f1039,f7444])).
% 11.66/2.03 tff(f7444,plain,(
% 11.66/2.03 spl32_349 <=> ! [X0 : fun(nat,type),X3 : dB,X2 : type,X1 : dB] : (~member(type,X2,typing(X0,foldr(dB,dB,app,insert(dB,X3,nil(dB)),X1))) | pp(aa(type,bool,typing(X0,X1),sK24(X2,X1,X3,X0))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_349])])).
% 11.66/2.03 tff(f5888,plain,(
% 11.66/2.03 spl32_344 <=> ! [X0 : fun(nat,type),X3 : dB,X2 : type,X1 : dB] : (pp(aa(type,bool,typing(X0,X1),sK24(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X3))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_344])])).
% 11.66/2.03 tff(f5920,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : dB] : (~member(type,X2,typing(X0,foldr(dB,dB,app,insert(dB,X3,nil(dB)),X1))) | pp(aa(type,bool,typing(X0,X1),sK24(X2,X1,X3,X0)))) ) | (~spl32_89 | ~spl32_275 | ~spl32_344)),
% 11.66/2.03 inference(forward_demodulation,[],[f5889,f3939])).
% 11.66/2.03 tff(f5889,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : dB] : (pp(aa(type,bool,typing(X0,X1),sK24(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X3)))) ) | ~spl32_344),
% 11.66/2.03 inference(avatar_component_clause,[],[f5888])).
% 11.66/2.03 tff(f7430,plain,(
% 11.66/2.03 spl32_348 | ~spl32_12 | ~spl32_93),
% 11.66/2.03 inference(avatar_split_clause,[],[f1095,f1084,f599,f7428])).
% 11.66/2.03 tff(f7428,plain,(
% 11.66/2.03 spl32_348 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (fFalse != aa(X0,bool,X2,sK25(bool,X0,X1,X2)) | X1 = X2 | fTrue = aa(X0,bool,X1,sK25(bool,X0,X1,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_348])])).
% 11.66/2.03 tff(f1084,plain,(
% 11.66/2.03 spl32_93 <=> ! [X1 : $tType,X0 : $tType,X3 : fun(X1,X0),X2 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK25(X0,X1,X2,X3)) != aa(X1,X0,X2,sK25(X0,X1,X2,X3)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_93])])).
% 11.66/2.03 tff(f1095,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (fFalse != aa(X0,bool,X2,sK25(bool,X0,X1,X2)) | X1 = X2 | fTrue = aa(X0,bool,X1,sK25(bool,X0,X1,X2))) ) | (~spl32_12 | ~spl32_93)),
% 11.66/2.03 inference(superposition,[],[f1085,f600])).
% 11.66/2.03 tff(f1085,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (aa(X1,X0,X3,sK25(X0,X1,X2,X3)) != aa(X1,X0,X2,sK25(X0,X1,X2,X3)) | X2 = X3) ) | ~spl32_93),
% 11.66/2.03 inference(avatar_component_clause,[],[f1084])).
% 11.66/2.03 tff(f7426,plain,(
% 11.66/2.03 spl32_347 | ~spl32_12 | ~spl32_93),
% 11.66/2.03 inference(avatar_split_clause,[],[f1090,f1084,f599,f7424])).
% 11.66/2.03 tff(f7424,plain,(
% 11.66/2.03 spl32_347 <=> ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (fFalse != aa(X0,bool,X2,sK25(bool,X0,X2,X1)) | X1 = X2 | fTrue = aa(X0,bool,X1,sK25(bool,X0,X2,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_347])])).
% 11.66/2.03 tff(f1090,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : fun(X0,bool),X1 : fun(X0,bool)] : (fFalse != aa(X0,bool,X2,sK25(bool,X0,X2,X1)) | X1 = X2 | fTrue = aa(X0,bool,X1,sK25(bool,X0,X2,X1))) ) | (~spl32_12 | ~spl32_93)),
% 11.66/2.03 inference(superposition,[],[f1085,f600])).
% 11.66/2.03 tff(f5919,plain,(
% 11.66/2.03 spl32_29 | ~spl32_18 | ~spl32_253),
% 11.66/2.03 inference(avatar_split_clause,[],[f5860,f3233,f626,f683])).
% 11.66/2.03 tff(f5918,plain,(
% 11.66/2.03 spl32_346 | ~spl32_91 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1387,f1321,f1060,f5916])).
% 11.66/2.03 tff(f5916,plain,(
% 11.66/2.03 spl32_346 <=> ! [X0 : $tType,X5 : list(X0),X4 : list(X0),X3 : list(X0),X2 : X0,X1 : fun(X0,fun(list(X0),list(X0)))] : list_case(list(X0),X0,X5,X1,cons(X0,X2,foldr(X0,list(X0),X1,X3,X4))) = foldr(X0,list(X0),X1,cons(X0,X2,X3),X4)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_346])])).
% 11.66/2.03 tff(f1387,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(list(X0),list(X0))),X4 : list(X0),X5 : list(X0)] : (list_case(list(X0),X0,X5,X1,cons(X0,X2,foldr(X0,list(X0),X1,X3,X4))) = foldr(X0,list(X0),X1,cons(X0,X2,X3),X4)) ) | (~spl32_91 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f1322,f1061])).
% 11.66/2.03 tff(f5895,plain,(
% 11.66/2.03 spl32_345 | ~spl32_53 | ~spl32_158),
% 11.66/2.03 inference(avatar_split_clause,[],[f2067,f2062,f819,f5893])).
% 11.66/2.03 tff(f5893,plain,(
% 11.66/2.03 spl32_345 <=> ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (cons(bool,X0,sK26(bool,X1,X0,X2,fconj)) = X2 | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(sK27(bool,X1,X0,X2,fconj)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_345])])).
% 11.66/2.03 tff(f2067,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (cons(bool,X0,sK26(bool,X1,X0,X2,fconj)) = X2 | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(sK27(bool,X1,X0,X2,fconj))) ) | (~spl32_53 | ~spl32_158)),
% 11.66/2.03 inference(resolution,[],[f2063,f820])).
% 11.66/2.03 tff(f5890,plain,(
% 11.66/2.03 spl32_344 | ~spl32_33 | ~spl32_137),
% 11.66/2.03 inference(avatar_split_clause,[],[f1792,f1788,f704,f5888])).
% 11.66/2.03 tff(f1792,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : dB] : (pp(aa(type,bool,typing(X0,X1),sK24(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,aa(dB,dB,combc(dB,dB,dB,app,X1),X3)))) ) | (~spl32_33 | ~spl32_137)),
% 11.66/2.03 inference(resolution,[],[f1789,f705])).
% 11.66/2.03 tff(f5886,plain,(
% 11.66/2.03 spl32_343 | ~spl32_33 | ~spl32_131),
% 11.66/2.03 inference(avatar_split_clause,[],[f1735,f1730,f704,f5884])).
% 11.66/2.03 tff(f5884,plain,(
% 11.66/2.03 spl32_343 <=> ! [X2 : list(dB),X0 : nat,X1 : dB] : (foldl(dB,dB,app,var(X0),sK17(X1,X2,X0)) = X1 | ~member(dB,foldl(dB,dB,app,var(X0),X2),combc(dB,dB,bool,beta,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_343])])).
% 11.66/2.03 tff(f1735,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X0 : nat,X1 : dB] : (foldl(dB,dB,app,var(X0),sK17(X1,X2,X0)) = X1 | ~member(dB,foldl(dB,dB,app,var(X0),X2),combc(dB,dB,bool,beta,X1))) ) | (~spl32_33 | ~spl32_131)),
% 11.66/2.03 inference(resolution,[],[f1731,f705])).
% 11.66/2.03 tff(f5882,plain,(
% 11.66/2.03 spl32_342 | ~spl32_91 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1415,f1325,f1060,f5880])).
% 11.66/2.03 tff(f5880,plain,(
% 11.66/2.03 spl32_342 <=> ! [X0 : $tType,X3 : list(X0),X4 : X0,X5 : list(list(X0)),X2 : X0,X1 : fun(X0,fun(list(X0),X0))] : foldl(X0,list(X0),X1,X2,cons(list(X0),X3,X5)) = foldl(X0,list(X0),X1,list_case(X0,X0,X4,X1,cons(X0,X2,X3)),X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_342])])).
% 11.66/2.03 tff(f1415,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(list(X0),X0)),X4 : X0,X5 : list(list(X0))] : (foldl(X0,list(X0),X1,X2,cons(list(X0),X3,X5)) = foldl(X0,list(X0),X1,list_case(X0,X0,X4,X1,cons(X0,X2,X3)),X5)) ) | (~spl32_91 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f1326,f1061])).
% 11.66/2.03 tff(f5878,plain,(
% 11.66/2.03 spl32_341 | ~spl32_74 | ~spl32_87),
% 11.66/2.03 inference(avatar_split_clause,[],[f1032,f1028,f945,f5876])).
% 11.66/2.03 tff(f5876,plain,(
% 11.66/2.03 spl32_341 <=> ! [X3 : $tType,X0 : $tType,X4 : X3,X2 : fun(nat,bool),X1 : X0] : (insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) | nil(X3) = sublist(X3,insert(X3,X4,nil(X3)),X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_341])])).
% 11.66/2.03 tff(f1028,plain,(
% 11.66/2.03 spl32_87 <=> ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_87])])).
% 11.66/2.03 tff(f1032,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X3 : $tType,X2 : fun(nat,bool),X1 : X0,X4 : X3] : (insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) | nil(X3) = sublist(X3,insert(X3,X4,nil(X3)),X2)) ) | (~spl32_74 | ~spl32_87)),
% 11.66/2.03 inference(resolution,[],[f1029,f946])).
% 11.66/2.03 tff(f1029,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (~member(nat,zero_zero(nat),X2) | insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2)) ) | ~spl32_87),
% 11.66/2.03 inference(avatar_component_clause,[],[f1028])).
% 11.66/2.03 tff(f5621,plain,(
% 11.66/2.03 spl32_340 | ~spl32_16 | ~spl32_133),
% 11.66/2.03 inference(avatar_split_clause,[],[f1758,f1751,f618,f5619])).
% 11.66/2.03 tff(f5619,plain,(
% 11.66/2.03 spl32_340 <=> ! [X2 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),subst(X2,X1,X0))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,var(X0)),X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_340])])).
% 11.66/2.03 tff(f1758,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : nat,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,X1),subst(X2,X1,X0))) | ~pp(aa(dB,bool,combc(dB,dB,bool,beta,var(X0)),X2))) ) | (~spl32_16 | ~spl32_133)),
% 11.66/2.03 inference(superposition,[],[f1752,f619])).
% 11.66/2.03 tff(f5617,plain,(
% 11.66/2.03 spl32_339 | ~spl32_34 | ~spl32_133),
% 11.66/2.03 inference(avatar_split_clause,[],[f1756,f1751,f708,f5615])).
% 11.66/2.03 tff(f5615,plain,(
% 11.66/2.03 spl32_339 <=> ! [X0 : dB,X3 : nat,X2 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,subst(X1,X2,X3),combc(dB,dB,bool,beta,subst(X0,X2,X3))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_339])])).
% 11.66/2.03 tff(f1756,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : nat,X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,subst(X1,X2,X3),combc(dB,dB,bool,beta,subst(X0,X2,X3)))) ) | (~spl32_34 | ~spl32_133)),
% 11.66/2.03 inference(resolution,[],[f1752,f709])).
% 11.66/2.03 tff(f5613,plain,(
% 11.66/2.03 spl32_338 | ~spl32_34 | ~spl32_126),
% 11.66/2.03 inference(avatar_split_clause,[],[f1716,f1680,f708,f5611])).
% 11.66/2.03 tff(f5611,plain,(
% 11.66/2.03 spl32_338 <=> ! [X2 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,abs(X1)),X2)) | member(type,sK11(X2,X1,X0),typing(shift(type,X0,zero_zero(nat),sK10(X2,X1,X0)),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_338])])).
% 11.66/2.03 tff(f1716,plain,(
% 11.66/2.03 ( ! [X2 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,abs(X1)),X2)) | member(type,sK11(X2,X1,X0),typing(shift(type,X0,zero_zero(nat),sK10(X2,X1,X0)),X1))) ) | (~spl32_34 | ~spl32_126)),
% 11.66/2.03 inference(resolution,[],[f1681,f709])).
% 11.66/2.03 tff(f5609,plain,(
% 11.66/2.03 spl32_337 | ~spl32_46 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1429,f1325,f777,f5607])).
% 11.66/2.03 tff(f5607,plain,(
% 11.66/2.03 spl32_337 <=> ! [X0 : dB,X3 : nat,X2 : list(dB),X1 : dB] : (var(X3) != foldl(dB,dB,app,X0,cons(dB,X1,X2)) | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1) = var(X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_337])])).
% 11.66/2.03 tff(f777,plain,(
% 11.66/2.03 spl32_46 <=> ! [X2 : nat,X0 : list(dB),X1 : dB] : (var(X2) = X1 | var(X2) != foldl(dB,dB,app,X1,X0))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_46])])).
% 11.66/2.03 tff(f1429,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : nat,X0 : dB,X1 : dB] : (var(X3) != foldl(dB,dB,app,X0,cons(dB,X1,X2)) | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1) = var(X3)) ) | (~spl32_46 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f778,f1326])).
% 11.66/2.03 tff(f778,plain,(
% 11.66/2.03 ( ! [X2 : nat,X0 : list(dB),X1 : dB] : (var(X2) != foldl(dB,dB,app,X1,X0) | var(X2) = X1) ) | ~spl32_46),
% 11.66/2.03 inference(avatar_component_clause,[],[f777])).
% 11.66/2.03 tff(f5605,plain,(
% 11.66/2.03 spl32_253 | spl32_336 | ~spl32_67 | ~spl32_275 | ~spl32_276 | ~spl32_322),
% 11.66/2.03 inference(avatar_split_clause,[],[f5514,f4663,f3816,f3812,f891,f5603,f3233])).
% 11.66/2.03 tff(f5603,plain,(
% 11.66/2.03 spl32_336 <=> ! [X0 : bool,X1 : bool] : (fTrue = foldr(bool,bool,fconj,insert(bool,X1,nil(bool)),X0) | ~pp(X1) | ~pp(X0))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_336])])).
% 11.66/2.03 tff(f3816,plain,(
% 11.66/2.03 spl32_276 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X0,X2 : fun(X0,fun(X1,X0))] : aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4) = foldl(X0,X1,X2,X3,insert(X1,X4,nil(X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_276])])).
% 11.66/2.03 tff(f5514,plain,(
% 11.66/2.03 ( ! [X2 : bool,X0 : bool,X1 : bool] : (fTrue = foldr(bool,bool,fconj,insert(bool,X1,nil(bool)),X0) | pp(X2) | ~pp(X0) | ~pp(X1) | fTrue = X2) ) | (~spl32_67 | ~spl32_275 | ~spl32_276 | ~spl32_322)),
% 11.66/2.03 inference(forward_demodulation,[],[f5327,f4018])).
% 11.66/2.03 tff(f4018,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : fun(X0,fun(X0,X0))] : (foldr(X0,X0,X1,insert(X0,X2,nil(X0)),X3) = foldl(X0,X0,X1,X2,insert(X0,X3,nil(X0)))) ) | (~spl32_275 | ~spl32_276)),
% 11.66/2.03 inference(superposition,[],[f3817,f3813])).
% 11.66/2.03 tff(f3817,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X0)),X3 : X0,X4 : X1] : (aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4) = foldl(X0,X1,X2,X3,insert(X1,X4,nil(X1)))) ) | ~spl32_276),
% 11.66/2.03 inference(avatar_component_clause,[],[f3816])).
% 11.66/2.03 tff(f5327,plain,(
% 11.66/2.03 ( ! [X2 : bool,X0 : bool,X1 : bool] : (pp(X2) | ~pp(X0) | ~pp(X1) | fTrue = foldl(bool,bool,fconj,X1,insert(bool,X0,nil(bool))) | fTrue = X2) ) | (~spl32_67 | ~spl32_322)),
% 11.66/2.03 inference(superposition,[],[f892,f4664])).
% 11.66/2.03 tff(f5601,plain,(
% 11.66/2.03 spl32_335 | ~spl32_45 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1428,f1325,f773,f5599])).
% 11.66/2.03 tff(f5599,plain,(
% 11.66/2.03 spl32_335 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (abs(X3) != foldl(dB,dB,app,X0,cons(dB,X1,X2)) | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1) = abs(X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_335])])).
% 11.66/2.03 tff(f773,plain,(
% 11.66/2.03 spl32_45 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : (abs(X2) = X1 | abs(X2) != foldl(dB,dB,app,X1,X0))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_45])])).
% 11.66/2.03 tff(f1428,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (abs(X3) != foldl(dB,dB,app,X0,cons(dB,X1,X2)) | aa(dB,dB,aa(dB,fun(dB,dB),app,X0),X1) = abs(X3)) ) | (~spl32_45 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f774,f1326])).
% 11.66/2.03 tff(f774,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (abs(X2) != foldl(dB,dB,app,X1,X0) | abs(X2) = X1) ) | ~spl32_45),
% 11.66/2.03 inference(avatar_component_clause,[],[f773])).
% 11.66/2.03 tff(f5597,plain,(
% 11.66/2.03 spl32_334 | ~spl32_12 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1077,f1060,f599,f5595])).
% 11.66/2.03 tff(f5595,plain,(
% 11.66/2.03 spl32_334 <=> ! [X0 : $tType,X4 : bool,X3 : list(X0),X2 : X0,X1 : fun(X0,fun(list(X0),bool))] : (fFalse = list_case(bool,X0,X4,X1,cons(X0,X2,X3)) | fTrue = aa(list(X0),bool,aa(X0,fun(list(X0),bool),X1,X2),X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_334])])).
% 11.66/2.03 tff(f1077,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(list(X0),bool)),X4 : bool] : (fFalse = list_case(bool,X0,X4,X1,cons(X0,X2,X3)) | fTrue = aa(list(X0),bool,aa(X0,fun(list(X0),bool),X1,X2),X3)) ) | (~spl32_12 | ~spl32_91)),
% 11.66/2.03 inference(superposition,[],[f1061,f600])).
% 11.66/2.03 tff(f5593,plain,(
% 11.66/2.03 spl32_333 | ~spl32_12 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1070,f1060,f599,f5591])).
% 11.66/2.03 tff(f5591,plain,(
% 11.66/2.03 spl32_333 <=> ! [X0 : $tType,X4 : list(X0),X3 : X0,X2 : fun(X0,fun(list(X0),bool)),X1 : bool] : (fFalse = aa(list(X0),bool,aa(X0,fun(list(X0),bool),X2,X3),X4) | fTrue = list_case(bool,X0,X1,X2,cons(X0,X3,X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_333])])).
% 11.66/2.03 tff(f1070,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : fun(X0,fun(list(X0),bool)),X3 : X0,X1 : bool,X4 : list(X0)] : (fFalse = aa(list(X0),bool,aa(X0,fun(list(X0),bool),X2,X3),X4) | fTrue = list_case(bool,X0,X1,X2,cons(X0,X3,X4))) ) | (~spl32_12 | ~spl32_91)),
% 11.66/2.03 inference(superposition,[],[f1061,f600])).
% 11.66/2.03 tff(f5550,plain,(
% 11.66/2.03 spl32_332 | ~spl32_89 | ~spl32_275 | ~spl32_327),
% 11.66/2.03 inference(avatar_split_clause,[],[f4687,f4684,f3812,f1039,f5548])).
% 11.66/2.03 tff(f5548,plain,(
% 11.66/2.03 spl32_332 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (foldr(type,type,fun1,insert(type,sK10(X0,X1,X2),nil(type)),sK11(X0,X1,X2)) = X0 | ~member(type,X0,typing(X2,abs(X1))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_332])])).
% 11.66/2.03 tff(f4684,plain,(
% 11.66/2.03 spl32_327 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,combc(type,type,type,fun1,sK11(X0,X1,X2)),sK10(X0,X1,X2)) = X0 | ~member(type,X0,typing(X2,abs(X1))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_327])])).
% 11.66/2.03 tff(f4687,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (foldr(type,type,fun1,insert(type,sK10(X0,X1,X2),nil(type)),sK11(X0,X1,X2)) = X0 | ~member(type,X0,typing(X2,abs(X1)))) ) | (~spl32_89 | ~spl32_275 | ~spl32_327)),
% 11.66/2.03 inference(forward_demodulation,[],[f4685,f3939])).
% 11.66/2.03 tff(f4685,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,combc(type,type,type,fun1,sK11(X0,X1,X2)),sK10(X0,X1,X2)) = X0 | ~member(type,X0,typing(X2,abs(X1)))) ) | ~spl32_327),
% 11.66/2.03 inference(avatar_component_clause,[],[f4684])).
% 11.66/2.03 tff(f5301,plain,(
% 11.66/2.03 spl32_331 | ~spl32_89 | ~spl32_275 | ~spl32_324),
% 11.66/2.03 inference(avatar_split_clause,[],[f4674,f4671,f3812,f1039,f5299])).
% 11.66/2.03 tff(f5299,plain,(
% 11.66/2.03 spl32_331 <=> ! [X0 : $tType,X4 : fun(nat,X0),X3 : type,X2 : type,X1 : fun(type,fun(type,X0))] : aa(type,X0,combc(type,type,X0,X1,X3),X2) = type_case(X0,X4,X1,foldr(type,type,fun1,insert(type,X2,nil(type)),X3))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_331])])).
% 11.66/2.03 tff(f4671,plain,(
% 11.66/2.03 spl32_324 <=> ! [X0 : $tType,X4 : fun(nat,X0),X3 : type,X2 : type,X1 : fun(type,fun(type,X0))] : type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = aa(type,X0,combc(type,type,X0,X1,X3),X2)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_324])])).
% 11.66/2.03 tff(f4674,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,X0)),X4 : fun(nat,X0)] : (aa(type,X0,combc(type,type,X0,X1,X3),X2) = type_case(X0,X4,X1,foldr(type,type,fun1,insert(type,X2,nil(type)),X3))) ) | (~spl32_89 | ~spl32_275 | ~spl32_324)),
% 11.66/2.03 inference(forward_demodulation,[],[f4672,f3939])).
% 11.66/2.03 tff(f4672,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,X0)),X4 : fun(nat,X0)] : (type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = aa(type,X0,combc(type,type,X0,X1,X3),X2)) ) | ~spl32_324),
% 11.66/2.03 inference(avatar_component_clause,[],[f4671])).
% 11.66/2.03 tff(f4989,plain,(
% 11.66/2.03 spl32_330 | ~spl32_261 | ~spl32_275),
% 11.66/2.03 inference(avatar_split_clause,[],[f3942,f3812,f3388,f4987])).
% 11.66/2.03 tff(f4987,plain,(
% 11.66/2.03 spl32_330 <=> ! [X0 : fun(bool,fun(bool,bool)),X3 : bool,X2 : bool,X1 : bool] : (foldr(bool,bool,X0,insert(bool,X1,nil(bool)),X2) = X3 | fTrue = foldl(bool,bool,X0,X1,insert(bool,X2,nil(bool))) | fTrue = X3)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_330])])).
% 11.66/2.03 tff(f3942,plain,(
% 11.66/2.03 ( ! [X2 : bool,X3 : bool,X0 : fun(bool,fun(bool,bool)),X1 : bool] : (foldr(bool,bool,X0,insert(bool,X1,nil(bool)),X2) = X3 | fTrue = foldl(bool,bool,X0,X1,insert(bool,X2,nil(bool))) | fTrue = X3) ) | (~spl32_261 | ~spl32_275)),
% 11.66/2.03 inference(superposition,[],[f3813,f3389])).
% 11.66/2.03 tff(f4695,plain,(
% 11.66/2.03 spl32_329 | ~spl32_53 | ~spl32_155),
% 11.66/2.03 inference(avatar_split_clause,[],[f2022,f2017,f819,f4693])).
% 11.66/2.03 tff(f4693,plain,(
% 11.66/2.03 spl32_329 <=> ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (step1(bool,fconj,sK26(bool,X1,X0,X2,fconj),X1) | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(sK27(bool,X1,X0,X2,fconj)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_329])])).
% 11.66/2.03 tff(f2022,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (step1(bool,fconj,sK26(bool,X1,X0,X2,fconj),X1) | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(sK27(bool,X1,X0,X2,fconj))) ) | (~spl32_53 | ~spl32_155)),
% 11.66/2.03 inference(resolution,[],[f2018,f820])).
% 11.66/2.03 tff(f4691,plain,(
% 11.66/2.03 spl32_328 | ~spl32_33 | ~spl32_129),
% 11.66/2.03 inference(avatar_split_clause,[],[f1701,f1694,f704,f4689])).
% 11.66/2.03 tff(f4689,plain,(
% 11.66/2.03 spl32_328 <=> ! [X0 : fun(nat,type),X3 : dB,X2 : type,X1 : dB] : (pp(aa(type,bool,typing(X0,X1),X2)) | ~pp(aa(type,bool,typing(X0,X3),X2)) | ~member(dB,X3,combc(dB,dB,bool,beta,X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_328])])).
% 11.66/2.03 tff(f1701,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : dB] : (pp(aa(type,bool,typing(X0,X1),X2)) | ~pp(aa(type,bool,typing(X0,X3),X2)) | ~member(dB,X3,combc(dB,dB,bool,beta,X1))) ) | (~spl32_33 | ~spl32_129)),
% 11.66/2.03 inference(resolution,[],[f1695,f705])).
% 11.66/2.03 tff(f4686,plain,(
% 11.66/2.03 spl32_327 | ~spl32_33 | ~spl32_125),
% 11.66/2.03 inference(avatar_split_clause,[],[f1671,f1668,f704,f4684])).
% 11.66/2.03 tff(f1668,plain,(
% 11.66/2.03 spl32_125 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,combc(type,type,type,fun1,sK11(X0,X1,X2)),sK10(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_125])])).
% 11.66/2.03 tff(f1671,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,combc(type,type,type,fun1,sK11(X0,X1,X2)),sK10(X0,X1,X2)) = X0 | ~member(type,X0,typing(X2,abs(X1)))) ) | (~spl32_33 | ~spl32_125)),
% 11.66/2.03 inference(resolution,[],[f1669,f705])).
% 11.66/2.03 tff(f1669,plain,(
% 11.66/2.03 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (~pp(aa(type,bool,typing(X2,abs(X1)),X0)) | aa(type,type,combc(type,type,type,fun1,sK11(X0,X1,X2)),sK10(X0,X1,X2)) = X0) ) | ~spl32_125),
% 11.66/2.03 inference(avatar_component_clause,[],[f1668])).
% 11.66/2.03 tff(f4682,plain,(
% 11.66/2.03 spl32_326 | ~spl32_33 | ~spl32_117),
% 11.66/2.03 inference(avatar_split_clause,[],[f1559,f1518,f704,f4680])).
% 11.66/2.03 tff(f4680,plain,(
% 11.66/2.03 spl32_326 <=> ! [X0 : fun(nat,type),X3 : nat,X2 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X0,X1),sK23(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,foldl(dB,dB,app,var(X3),X1))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_326])])).
% 11.66/2.03 tff(f1518,plain,(
% 11.66/2.03 spl32_117 <=> ! [X0 : type,X3 : fun(nat,type),X2 : nat,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK23(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_117])])).
% 11.66/2.03 tff(f1559,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : nat,X0 : fun(nat,type),X1 : list(dB)] : (pp(aa(list(type),bool,typings(X0,X1),sK23(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,foldl(dB,dB,app,var(X3),X1)))) ) | (~spl32_33 | ~spl32_117)),
% 11.66/2.03 inference(resolution,[],[f1519,f705])).
% 11.66/2.03 tff(f1519,plain,(
% 11.66/2.03 ( ! [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),sK23(X0,X1,X2,X3)))) ) | ~spl32_117),
% 11.66/2.03 inference(avatar_component_clause,[],[f1518])).
% 11.66/2.03 tff(f4678,plain,(
% 11.66/2.03 spl32_325 | ~spl32_33 | ~spl32_116),
% 11.66/2.03 inference(avatar_split_clause,[],[f1552,f1514,f704,f4676])).
% 11.66/2.03 tff(f4676,plain,(
% 11.66/2.03 spl32_325 <=> ! [X2 : nat,X0 : fun(nat,type),X1 : dB,X3 : type] : (~pp(aa(type,bool,typing(X0,X1),t)) | ~it(X1) | it(subst(a,X1,X2)) | ~member(type,X3,typing(shift(type,X0,X2,t),a)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_325])])).
% 11.66/2.03 tff(f1552,plain,(
% 11.66/2.03 ( ! [X2 : nat,X3 : type,X0 : fun(nat,type),X1 : dB] : (~pp(aa(type,bool,typing(X0,X1),t)) | ~it(X1) | it(subst(a,X1,X2)) | ~member(type,X3,typing(shift(type,X0,X2,t),a))) ) | (~spl32_33 | ~spl32_116)),
% 11.66/2.03 inference(resolution,[],[f1515,f705])).
% 11.66/2.03 tff(f4673,plain,(
% 11.66/2.03 spl32_324 | ~spl32_89 | ~spl32_119),
% 11.66/2.03 inference(avatar_split_clause,[],[f1533,f1527,f1039,f4671])).
% 11.66/2.03 tff(f1533,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : type,X3 : type,X1 : fun(type,fun(type,X0)),X4 : fun(nat,X0)] : (type_case(X0,X4,X1,aa(type,type,combc(type,type,type,fun1,X3),X2)) = aa(type,X0,combc(type,type,X0,X1,X3),X2)) ) | (~spl32_89 | ~spl32_119)),
% 11.66/2.03 inference(superposition,[],[f1528,f1040])).
% 11.66/2.03 tff(f4669,plain,(
% 11.66/2.03 spl32_323 | ~spl32_82 | ~spl32_112),
% 11.66/2.03 inference(avatar_split_clause,[],[f1476,f1471,f1000,f4667])).
% 11.66/2.03 tff(f4667,plain,(
% 11.66/2.03 spl32_323 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(abs(X1)))) | sK5(X0,abs(X1)) = abs(sK5(sK5(X0,abs(X1)),X1)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_323])])).
% 11.66/2.03 tff(f1000,plain,(
% 11.66/2.03 spl32_82 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK5(X0,X1)) = X0)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_82])])).
% 11.66/2.03 tff(f1476,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(abs(X1)))) | sK5(X0,abs(X1)) = abs(sK5(sK5(X0,abs(X1)),X1))) ) | (~spl32_82 | ~spl32_112)),
% 11.66/2.03 inference(resolution,[],[f1472,f1001])).
% 11.66/2.03 tff(f1001,plain,(
% 11.66/2.03 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK5(X0,X1)) = X0) ) | ~spl32_82),
% 11.66/2.03 inference(avatar_component_clause,[],[f1000])).
% 11.66/2.03 tff(f4665,plain,(
% 11.66/2.03 spl32_322 | ~spl32_89 | ~spl32_261),
% 11.66/2.03 inference(avatar_split_clause,[],[f3453,f3388,f1039,f4663])).
% 11.66/2.03 tff(f3453,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X4 : bool] : (aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) = X4 | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))) | fTrue = X4) ) | (~spl32_89 | ~spl32_261)),
% 11.66/2.03 inference(superposition,[],[f3389,f1040])).
% 11.66/2.03 tff(f4661,plain,(
% 11.66/2.03 spl32_321 | ~spl32_89 | ~spl32_108),
% 11.66/2.03 inference(avatar_split_clause,[],[f1414,f1325,f1039,f4659])).
% 11.66/2.03 tff(f4659,plain,(
% 11.66/2.03 spl32_321 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X0,X5 : list(X0),X2 : fun(X1,fun(X0,X1))] : foldl(X1,X0,X2,X3,cons(X0,X4,X5)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_321])])).
% 11.66/2.03 tff(f1414,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(X0,X1)),X3 : X1,X4 : X0,X5 : list(X0)] : (foldl(X1,X0,X2,X3,cons(X0,X4,X5)) = foldl(X1,X0,X2,aa(X1,X1,combc(X1,X0,X1,X2,X4),X3),X5)) ) | (~spl32_89 | ~spl32_108)),
% 11.66/2.03 inference(superposition,[],[f1326,f1040])).
% 11.66/2.03 tff(f4657,plain,(
% 11.66/2.03 spl32_320 | ~spl32_33 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1396,f1321,f704,f4655])).
% 11.66/2.03 tff(f4655,plain,(
% 11.66/2.03 spl32_320 <=> ! [X0 : $tType,X4 : bool,X3 : list(X0),X2 : X0,X1 : fun(X0,fun(bool,bool))] : (pp(foldr(X0,bool,X1,cons(X0,X2,X3),X4)) | ~member(bool,foldr(X0,bool,X1,X3,X4),aa(X0,fun(bool,bool),X1,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_320])])).
% 11.66/2.03 tff(f1396,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(bool,bool)),X4 : bool] : (pp(foldr(X0,bool,X1,cons(X0,X2,X3),X4)) | ~member(bool,foldr(X0,bool,X1,X3,X4),aa(X0,fun(bool,bool),X1,X2))) ) | (~spl32_33 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f705,f1322])).
% 11.66/2.03 tff(f4653,plain,(
% 11.66/2.03 spl32_319 | ~spl32_34 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1395,f1321,f708,f4651])).
% 11.66/2.03 tff(f4651,plain,(
% 11.66/2.03 spl32_319 <=> ! [X0 : $tType,X4 : bool,X3 : list(X0),X2 : X0,X1 : fun(X0,fun(bool,bool))] : (~pp(foldr(X0,bool,X1,cons(X0,X2,X3),X4)) | member(bool,foldr(X0,bool,X1,X3,X4),aa(X0,fun(bool,bool),X1,X2)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_319])])).
% 11.66/2.03 tff(f1395,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(bool,bool)),X4 : bool] : (~pp(foldr(X0,bool,X1,cons(X0,X2,X3),X4)) | member(bool,foldr(X0,bool,X1,X3,X4),aa(X0,fun(bool,bool),X1,X2))) ) | (~spl32_34 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f709,f1322])).
% 11.66/2.03 tff(f4649,plain,(
% 11.66/2.03 spl32_318 | ~spl32_89 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1386,f1321,f1039,f4647])).
% 11.66/2.03 tff(f4647,plain,(
% 11.66/2.03 spl32_318 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : list(X1),X5 : X0,X2 : fun(X1,fun(X0,X0))] : foldr(X1,X0,X2,cons(X1,X3,X4),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_318])])).
% 11.66/2.03 tff(f1386,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(X0,X0)),X3 : X1,X4 : list(X1),X5 : X0] : (foldr(X1,X0,X2,cons(X1,X3,X4),X5) = aa(X1,X0,combc(X1,X0,X0,X2,foldr(X1,X0,X2,X4,X5)),X3)) ) | (~spl32_89 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f1322,f1040])).
% 11.66/2.03 tff(f4645,plain,(
% 11.66/2.03 spl32_317 | ~spl32_89 | ~spl32_106),
% 11.66/2.03 inference(avatar_split_clause,[],[f1372,f1317,f1039,f4643])).
% 11.66/2.03 tff(f4643,plain,(
% 11.66/2.03 spl32_317 <=> ! [X0 : dB,X3 : dB,X2 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) | X1 = X3)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_317])])).
% 11.66/2.03 tff(f1372,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) | X1 = X3) ) | (~spl32_89 | ~spl32_106)),
% 11.66/2.03 inference(superposition,[],[f1318,f1040])).
% 11.66/2.03 tff(f4641,plain,(
% 11.66/2.03 spl32_316 | ~spl32_89 | ~spl32_105),
% 11.66/2.03 inference(avatar_split_clause,[],[f1354,f1313,f1039,f4639])).
% 11.66/2.03 tff(f4639,plain,(
% 11.66/2.03 spl32_316 <=> ! [X0 : dB,X3 : dB,X2 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) | X0 = X2)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_316])])).
% 11.66/2.03 tff(f1354,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X3) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0) | X0 = X2) ) | (~spl32_89 | ~spl32_105)),
% 11.66/2.03 inference(superposition,[],[f1314,f1040])).
% 11.66/2.03 tff(f4637,plain,(
% 11.66/2.03 spl32_315 | ~spl32_89 | ~spl32_103),
% 11.66/2.03 inference(avatar_split_clause,[],[f1351,f1305,f1039,f4635])).
% 11.66/2.03 tff(f4635,plain,(
% 11.66/2.03 spl32_315 <=> ! [X0 : type,X3 : type,X2 : type,X1 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) | X1 = X3)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_315])])).
% 11.66/2.03 tff(f1351,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : type,X0 : type,X1 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) | X1 = X3) ) | (~spl32_89 | ~spl32_103)),
% 11.66/2.03 inference(superposition,[],[f1306,f1040])).
% 11.66/2.03 tff(f4633,plain,(
% 11.66/2.03 spl32_314 | ~spl32_89 | ~spl32_102),
% 11.66/2.03 inference(avatar_split_clause,[],[f1348,f1301,f1039,f4631])).
% 11.66/2.03 tff(f4631,plain,(
% 11.66/2.03 spl32_314 <=> ! [X0 : type,X3 : type,X2 : type,X1 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) | X0 = X2)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_314])])).
% 11.66/2.03 tff(f1301,plain,(
% 11.66/2.03 spl32_102 <=> ! [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))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_102])])).
% 11.66/2.03 tff(f1348,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : type,X0 : type,X1 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X2),X3) != aa(type,type,combc(type,type,type,fun1,X1),X0) | X0 = X2) ) | (~spl32_89 | ~spl32_102)),
% 11.66/2.03 inference(superposition,[],[f1302,f1040])).
% 11.66/2.03 tff(f1302,plain,(
% 11.66/2.03 ( ! [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) ) | ~spl32_102),
% 11.66/2.03 inference(avatar_component_clause,[],[f1301])).
% 11.66/2.03 tff(f4629,plain,(
% 11.66/2.03 spl32_313 | ~spl32_40 | ~spl32_91),
% 11.66/2.03 inference(avatar_split_clause,[],[f1067,f1060,f747,f4627])).
% 11.66/2.03 tff(f4627,plain,(
% 11.66/2.03 spl32_313 <=> ! [X0 : $tType,X2 : $tType,X4 : fun(X0,fun(list(X0),X2)),X3 : X2,X1 : X0] : aa(list(X0),X2,aa(X0,fun(list(X0),X2),X4,X1),nil(X0)) = list_case(X2,X0,X3,X4,insert(X0,X1,nil(X0)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_313])])).
% 11.66/2.03 tff(f1067,plain,(
% 11.66/2.03 ( ! [X0 : $tType,X2 : $tType,X3 : X2,X1 : X0,X4 : fun(X0,fun(list(X0),X2))] : (aa(list(X0),X2,aa(X0,fun(list(X0),X2),X4,X1),nil(X0)) = list_case(X2,X0,X3,X4,insert(X0,X1,nil(X0)))) ) | (~spl32_40 | ~spl32_91)),
% 11.66/2.03 inference(superposition,[],[f1061,f748])).
% 11.66/2.03 tff(f4625,plain,(
% 11.66/2.03 spl32_312 | ~spl32_12 | ~spl32_89),
% 11.66/2.03 inference(avatar_split_clause,[],[f1050,f1039,f599,f4623])).
% 11.66/2.03 tff(f4623,plain,(
% 11.66/2.03 spl32_312 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X1,X2 : fun(X1,fun(X0,bool))] : (fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) | fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_312])])).
% 11.66/2.03 tff(f1050,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(X0,bool)),X3 : X1,X4 : X0] : (fFalse = aa(X1,bool,combc(X1,X0,bool,X2,X4),X3) | fTrue = aa(X0,bool,aa(X1,fun(X0,bool),X2,X3),X4)) ) | (~spl32_12 | ~spl32_89)),
% 11.66/2.03 inference(superposition,[],[f1040,f600])).
% 11.66/2.03 tff(f4603,plain,(
% 11.66/2.03 spl32_311 | ~spl32_12 | ~spl32_89),
% 11.66/2.03 inference(avatar_split_clause,[],[f1046,f1039,f599,f4601])).
% 11.66/2.03 tff(f4601,plain,(
% 11.66/2.03 spl32_311 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X1,X2 : fun(X0,fun(X1,bool))] : (fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3) | fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_311])])).
% 11.66/2.03 tff(f1046,plain,(
% 11.66/2.03 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,bool)),X3 : X1,X4 : X0] : (fFalse = aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3) | fTrue = aa(X0,bool,combc(X0,X1,bool,X2,X3),X4)) ) | (~spl32_12 | ~spl32_89)),
% 11.66/2.03 inference(superposition,[],[f1040,f600])).
% 11.66/2.03 tff(f4500,plain,(
% 11.66/2.03 spl32_310 | ~spl32_91 | ~spl32_273),
% 11.66/2.03 inference(avatar_split_clause,[],[f3918,f3804,f1060,f4498])).
% 11.66/2.03 tff(f3918,plain,(
% 11.66/2.03 ( ! [X2 : list(bool),X3 : bool,X0 : fun(bool,fun(list(bool),bool)),X1 : bool] : (fTrue != list_case(bool,bool,X3,X0,cons(bool,X1,X2)) | fTrue = foldl(bool,list(bool),X0,X1,insert(list(bool),X2,nil(list(bool))))) ) | (~spl32_91 | ~spl32_273)),
% 11.66/2.03 inference(superposition,[],[f3805,f1061])).
% 11.66/2.03 tff(f4392,plain,(
% 11.66/2.03 spl32_309 | ~spl32_80 | ~spl32_133),
% 11.66/2.03 inference(avatar_split_clause,[],[f1755,f1751,f969,f4390])).
% 11.66/2.03 tff(f4390,plain,(
% 11.66/2.03 spl32_309 <=> ! [X2 : list(dB),X4 : nat,X0 : dB,X3 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,subst(X1,X3,X4),subst(X0,X3,X4)))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_309])])).
% 11.66/2.03 tff(f1755,plain,(
% 11.66/2.03 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB,X4 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,subst(X1,X3,X4),subst(X0,X3,X4))) ) | (~spl32_80 | ~spl32_133)),
% 11.66/2.03 inference(resolution,[],[f1752,f970])).
% 11.66/2.03 tff(f4388,plain,(
% 11.66/2.03 spl32_308 | ~spl32_28 | ~spl32_117),
% 11.66/2.03 inference(avatar_split_clause,[],[f1561,f1518,f676,f4386])).
% 11.66/2.03 tff(f4386,plain,(
% 11.66/2.03 spl32_308 <=> ! [X2 : type,X0 : nat,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,var(X0)),X2)) | pp(aa(list(type),bool,typings(X1,nil(dB)),sK23(X2,nil(dB),X0,X1))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_308])])).
% 11.66/2.03 tff(f1561,plain,(
% 11.66/2.03 ( ! [X2 : type,X0 : nat,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,var(X0)),X2)) | pp(aa(list(type),bool,typings(X1,nil(dB)),sK23(X2,nil(dB),X0,X1)))) ) | (~spl32_28 | ~spl32_117)),
% 11.66/2.03 inference(superposition,[],[f1519,f677])).
% 11.66/2.03 tff(f4375,plain,(
% 11.66/2.03 spl32_307 | ~spl32_34 | ~spl32_115),
% 11.66/2.03 inference(avatar_split_clause,[],[f1500,f1495,f708,f4373])).
% 11.66/2.03 tff(f4373,plain,(
% 11.66/2.03 spl32_307 <=> ! [X2 : dB,X0 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | member(dB,foldl(dB,dB,app,X2,X0),combc(dB,dB,bool,beta,foldl(dB,dB,app,X2,X1))))),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_307])])).
% 11.66/2.03 tff(f1500,plain,(
% 11.66/2.03 ( ! [X2 : dB,X0 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | member(dB,foldl(dB,dB,app,X2,X0),combc(dB,dB,bool,beta,foldl(dB,dB,app,X2,X1)))) ) | (~spl32_34 | ~spl32_115)),
% 11.66/2.03 inference(resolution,[],[f1496,f709])).
% 11.66/2.03 tff(f4371,plain,(
% 11.66/2.03 spl32_306 | ~spl32_102 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1406,f1321,f1301,f4369])).
% 11.66/2.03 tff(f4369,plain,(
% 11.66/2.03 spl32_306 <=> ! [X4 : type,X0 : type,X3 : type,X2 : type,X1 : list(type)] : (aa(type,type,aa(type,fun(type,type),fun1,X3),X4) != foldr(type,type,fun1,cons(type,X0,X1),X2) | X0 = X3)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_306])])).
% 11.66/2.03 tff(f1406,plain,(
% 11.66/2.03 ( ! [X2 : type,X3 : type,X0 : type,X1 : list(type),X4 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X3),X4) != foldr(type,type,fun1,cons(type,X0,X1),X2) | X0 = X3) ) | (~spl32_102 | ~spl32_107)),
% 11.66/2.03 inference(superposition,[],[f1302,f1322])).
% 11.66/2.03 tff(f4367,plain,(
% 11.66/2.03 spl32_305 | ~spl32_105 | ~spl32_107),
% 11.66/2.03 inference(avatar_split_clause,[],[f1399,f1321,f1313,f4365])).
% 11.66/2.03 tff(f4365,plain,(
% 11.66/2.03 spl32_305 <=> ! [X4 : dB,X0 : dB,X3 : dB,X2 : dB,X1 : list(dB)] : (foldr(dB,dB,app,cons(dB,X0,X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) | X0 = X3)),
% 11.66/2.03 introduced(avatar_definition,[new_symbols(naming,[spl32_305])])).
% 11.66/2.03 tff(f1399,plain,(
% 11.66/2.03 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : list(dB),X4 : dB] : (foldr(dB,dB,app,cons(dB,X0,X1),X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X3),X4) | X0 = X3) ) | (~spl32_105 | ~spl32_107)),
% 11.66/2.04 inference(superposition,[],[f1314,f1322])).
% 11.66/2.04 tff(f4363,plain,(
% 11.66/2.04 spl32_304 | ~spl32_33 | ~spl32_101),
% 11.66/2.04 inference(avatar_split_clause,[],[f1341,f1297,f704,f4361])).
% 11.66/2.04 tff(f4361,plain,(
% 11.66/2.04 spl32_304 <=> ! [X0 : fun(nat,type),X3 : dB,X2 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X0,X1),sK22(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,foldl(dB,dB,app,X3,X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_304])])).
% 11.66/2.04 tff(f1341,plain,(
% 11.66/2.04 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : list(dB)] : (pp(aa(list(type),bool,typings(X0,X1),sK22(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,foldl(dB,dB,app,X3,X1)))) ) | (~spl32_33 | ~spl32_101)),
% 11.66/2.04 inference(resolution,[],[f1298,f705])).
% 11.66/2.04 tff(f4359,plain,(
% 11.66/2.04 spl32_303 | ~spl32_33 | ~spl32_100),
% 11.66/2.04 inference(avatar_split_clause,[],[f1334,f1293,f704,f4357])).
% 11.66/2.04 tff(f4357,plain,(
% 11.66/2.04 spl32_303 <=> ! [X0 : fun(nat,type),X3 : dB,X2 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X0,X1),sK21(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,foldl(dB,dB,app,X3,X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_303])])).
% 11.66/2.04 tff(f1334,plain,(
% 11.66/2.04 ( ! [X2 : type,X3 : dB,X0 : fun(nat,type),X1 : list(dB)] : (pp(aa(list(type),bool,typings(X0,X1),sK21(X2,X1,X3,X0))) | ~member(type,X2,typing(X0,foldl(dB,dB,app,X3,X1)))) ) | (~spl32_33 | ~spl32_100)),
% 11.66/2.04 inference(resolution,[],[f1294,f705])).
% 11.66/2.04 tff(f4355,plain,(
% 11.66/2.04 spl32_302 | ~spl32_33 | ~spl32_97),
% 11.66/2.04 inference(avatar_split_clause,[],[f1328,f1273,f704,f4353])).
% 11.66/2.04 tff(f4353,plain,(
% 11.66/2.04 spl32_302 <=> ! [X2 : type,X0 : fun(nat,type),X1 : dB] : (pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X1,X0)),X1),sK9(X1,X0))) | ~member(type,X2,typing(X0,abs(X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_302])])).
% 11.66/2.04 tff(f1328,plain,(
% 11.66/2.04 ( ! [X2 : type,X0 : fun(nat,type),X1 : dB] : (pp(aa(type,bool,typing(shift(type,X0,zero_zero(nat),sK8(X1,X0)),X1),sK9(X1,X0))) | ~member(type,X2,typing(X0,abs(X1)))) ) | (~spl32_33 | ~spl32_97)),
% 11.66/2.04 inference(resolution,[],[f1274,f705])).
% 11.66/2.04 tff(f4351,plain,(
% 11.66/2.04 spl32_301 | ~spl32_48 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1058,f1039,f785,f4349])).
% 11.66/2.04 tff(f4349,plain,(
% 11.66/2.04 spl32_301 <=> ! [X0 : $tType,X3 : nat,X2 : X0,X1 : fun(X0,fun(nat,type))] : pp(aa(type,bool,typing(aa(X0,fun(nat,type),X1,X2),var(X3)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_301])])).
% 11.66/2.04 tff(f1058,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : nat,X1 : fun(X0,fun(nat,type))] : (pp(aa(type,bool,typing(aa(X0,fun(nat,type),X1,X2),var(X3)),aa(X0,type,combc(X0,nat,type,X1,X3),X2)))) ) | (~spl32_48 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f786,f1040])).
% 11.66/2.04 tff(f4347,plain,(
% 11.66/2.04 spl32_300 | ~spl32_69 | ~spl32_78),
% 11.66/2.04 inference(avatar_split_clause,[],[f990,f961,f904,f4345])).
% 11.66/2.04 tff(f4345,plain,(
% 11.66/2.04 spl32_300 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : list(X0)] : (step1(X0,X2,cons(X0,X3,X4),X1) | ~sP2(X0,sK7(X0,X1),X4,X2,X3,sK6(X0,X1)) | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_300])])).
% 11.66/2.04 tff(f990,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : list(X0)] : (step1(X0,X2,cons(X0,X3,X4),X1) | ~sP2(X0,sK7(X0,X1),X4,X2,X3,sK6(X0,X1)) | nil(X0) = X1) ) | (~spl32_69 | ~spl32_78)),
% 11.66/2.04 inference(superposition,[],[f962,f905])).
% 11.66/2.04 tff(f4343,plain,(
% 11.66/2.04 spl32_299 | ~spl32_68 | ~spl32_78),
% 11.66/2.04 inference(avatar_split_clause,[],[f989,f961,f900,f4341])).
% 11.66/2.04 tff(f4341,plain,(
% 11.66/2.04 spl32_299 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : list(X0)] : (step1(X0,X2,cons(X0,X3,X4),X1) | ~sP2(X0,sK4(X0,X1),X4,X2,X3,sK3(X0,X1)) | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_299])])).
% 11.66/2.04 tff(f989,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : list(X0)] : (step1(X0,X2,cons(X0,X3,X4),X1) | ~sP2(X0,sK4(X0,X1),X4,X2,X3,sK3(X0,X1)) | nil(X0) = X1) ) | (~spl32_68 | ~spl32_78)),
% 11.66/2.04 inference(superposition,[],[f962,f901])).
% 11.66/2.04 tff(f4339,plain,(
% 11.66/2.04 spl32_298 | ~spl32_69 | ~spl32_78),
% 11.66/2.04 inference(avatar_split_clause,[],[f987,f961,f904,f4337])).
% 11.66/2.04 tff(f4337,plain,(
% 11.66/2.04 spl32_298 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : list(X0)] : (step1(X0,X2,X1,cons(X0,X3,X4)) | ~sP2(X0,X4,sK7(X0,X1),X2,sK6(X0,X1),X3) | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_298])])).
% 11.66/2.04 tff(f987,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : list(X0)] : (step1(X0,X2,X1,cons(X0,X3,X4)) | ~sP2(X0,X4,sK7(X0,X1),X2,sK6(X0,X1),X3) | nil(X0) = X1) ) | (~spl32_69 | ~spl32_78)),
% 11.66/2.04 inference(superposition,[],[f962,f905])).
% 11.66/2.04 tff(f4325,plain,(
% 11.66/2.04 spl32_297 | ~spl32_68 | ~spl32_78),
% 11.66/2.04 inference(avatar_split_clause,[],[f986,f961,f900,f4323])).
% 11.66/2.04 tff(f4323,plain,(
% 11.66/2.04 spl32_297 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : list(X0)] : (step1(X0,X2,X1,cons(X0,X3,X4)) | ~sP2(X0,X4,sK4(X0,X1),X2,sK3(X0,X1),X3) | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_297])])).
% 11.66/2.04 tff(f986,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : list(X0)] : (step1(X0,X2,X1,cons(X0,X3,X4)) | ~sP2(X0,X4,sK4(X0,X1),X2,sK3(X0,X1),X3) | nil(X0) = X1) ) | (~spl32_68 | ~spl32_78)),
% 11.66/2.04 inference(superposition,[],[f962,f901])).
% 11.66/2.04 tff(f4321,plain,(
% 11.66/2.04 spl32_296 | ~spl32_69 | ~spl32_77),
% 11.66/2.04 inference(avatar_split_clause,[],[f983,f957,f904,f4319])).
% 11.66/2.04 tff(f4319,plain,(
% 11.66/2.04 spl32_296 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : list(X0)] : (~step1(X0,X2,cons(X0,X3,X4),X1) | sP2(X0,sK7(X0,X1),X4,X2,X3,sK6(X0,X1)) | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_296])])).
% 11.66/2.04 tff(f957,plain,(
% 11.66/2.04 spl32_77 <=> ! [X0 : $tType,X3 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool)),X2 : X0,X1 : list(X0)] : (sP2(X0,X1,X3,X5,X4,X2) | ~step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_77])])).
% 11.66/2.04 tff(f983,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : list(X0)] : (~step1(X0,X2,cons(X0,X3,X4),X1) | sP2(X0,sK7(X0,X1),X4,X2,X3,sK6(X0,X1)) | nil(X0) = X1) ) | (~spl32_69 | ~spl32_77)),
% 11.66/2.04 inference(superposition,[],[f958,f905])).
% 11.66/2.04 tff(f958,plain,(
% 11.66/2.04 ( ! [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)) | sP2(X0,X1,X3,X5,X4,X2)) ) | ~spl32_77),
% 11.66/2.04 inference(avatar_component_clause,[],[f957])).
% 11.66/2.04 tff(f4317,plain,(
% 11.66/2.04 spl32_295 | ~spl32_68 | ~spl32_77),
% 11.66/2.04 inference(avatar_split_clause,[],[f982,f957,f900,f4315])).
% 11.66/2.04 tff(f4315,plain,(
% 11.66/2.04 spl32_295 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : list(X0)] : (~step1(X0,X2,cons(X0,X3,X4),X1) | sP2(X0,sK4(X0,X1),X4,X2,X3,sK3(X0,X1)) | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_295])])).
% 11.66/2.04 tff(f982,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : list(X0)] : (~step1(X0,X2,cons(X0,X3,X4),X1) | sP2(X0,sK4(X0,X1),X4,X2,X3,sK3(X0,X1)) | nil(X0) = X1) ) | (~spl32_68 | ~spl32_77)),
% 11.66/2.04 inference(superposition,[],[f958,f901])).
% 11.66/2.04 tff(f4313,plain,(
% 11.66/2.04 spl32_294 | ~spl32_69 | ~spl32_77),
% 11.66/2.04 inference(avatar_split_clause,[],[f980,f957,f904,f4311])).
% 11.66/2.04 tff(f4311,plain,(
% 11.66/2.04 spl32_294 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : list(X0)] : (~step1(X0,X2,X1,cons(X0,X3,X4)) | sP2(X0,X4,sK7(X0,X1),X2,sK6(X0,X1),X3) | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_294])])).
% 11.66/2.04 tff(f980,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : list(X0)] : (~step1(X0,X2,X1,cons(X0,X3,X4)) | sP2(X0,X4,sK7(X0,X1),X2,sK6(X0,X1),X3) | nil(X0) = X1) ) | (~spl32_69 | ~spl32_77)),
% 11.66/2.04 inference(superposition,[],[f958,f905])).
% 11.66/2.04 tff(f4309,plain,(
% 11.66/2.04 spl32_293 | ~spl32_68 | ~spl32_77),
% 11.66/2.04 inference(avatar_split_clause,[],[f979,f957,f900,f4307])).
% 11.66/2.04 tff(f4307,plain,(
% 11.66/2.04 spl32_293 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : list(X0)] : (~step1(X0,X2,X1,cons(X0,X3,X4)) | sP2(X0,X4,sK4(X0,X1),X2,sK3(X0,X1),X3) | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_293])])).
% 11.66/2.04 tff(f979,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : list(X0)] : (~step1(X0,X2,X1,cons(X0,X3,X4)) | sP2(X0,X4,sK4(X0,X1),X2,sK3(X0,X1),X3) | nil(X0) = X1) ) | (~spl32_68 | ~spl32_77)),
% 11.66/2.04 inference(superposition,[],[f958,f901])).
% 11.66/2.04 tff(f4270,plain,(
% 11.66/2.04 spl32_292 | ~spl32_89 | ~spl32_275 | ~spl32_287),
% 11.66/2.04 inference(avatar_split_clause,[],[f4171,f4168,f3812,f1039,f4268])).
% 11.66/2.04 tff(f4268,plain,(
% 11.66/2.04 spl32_292 <=> ! [X0 : dB] : pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,abs(var(zero_zero(nat))),nil(dB)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_292])])).
% 11.66/2.04 tff(f4168,plain,(
% 11.66/2.04 spl32_287 <=> ! [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))))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_287])])).
% 11.66/2.04 tff(f4171,plain,(
% 11.66/2.04 ( ! [X0 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldr(dB,dB,app,insert(dB,abs(var(zero_zero(nat))),nil(dB)),X0)))) ) | (~spl32_89 | ~spl32_275 | ~spl32_287)),
% 11.66/2.04 inference(forward_demodulation,[],[f4169,f3939])).
% 11.66/2.04 tff(f4169,plain,(
% 11.66/2.04 ( ! [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))))))) ) | ~spl32_287),
% 11.66/2.04 inference(avatar_component_clause,[],[f4168])).
% 11.66/2.04 tff(f4266,plain,(
% 11.66/2.04 spl32_291 | ~spl32_273 | ~spl32_275),
% 11.66/2.04 inference(avatar_split_clause,[],[f3969,f3812,f3804,f4264])).
% 11.66/2.04 tff(f4264,plain,(
% 11.66/2.04 spl32_291 <=> ! [X2 : bool,X0 : fun(bool,fun(bool,bool)),X1 : bool] : (fTrue != foldr(bool,bool,X0,insert(bool,X1,nil(bool)),X2) | fTrue = foldl(bool,bool,X0,X1,insert(bool,X2,nil(bool))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_291])])).
% 11.66/2.04 tff(f3969,plain,(
% 11.66/2.04 ( ! [X2 : bool,X0 : fun(bool,fun(bool,bool)),X1 : bool] : (fTrue != foldr(bool,bool,X0,insert(bool,X1,nil(bool)),X2) | fTrue = foldl(bool,bool,X0,X1,insert(bool,X2,nil(bool)))) ) | (~spl32_273 | ~spl32_275)),
% 11.66/2.04 inference(superposition,[],[f3805,f3813])).
% 11.66/2.04 tff(f4262,plain,(
% 11.66/2.04 spl32_290 | ~spl32_89 | ~spl32_275 | ~spl32_286),
% 11.66/2.04 inference(avatar_split_clause,[],[f4166,f4163,f3812,f1039,f4260])).
% 11.66/2.04 tff(f4260,plain,(
% 11.66/2.04 spl32_290 <=> ! [X0 : dB,X1 : dB] : member(dB,foldr(dB,dB,app,insert(dB,abs(X1),nil(dB)),X0),combc(dB,dB,bool,beta,subst(X1,X0,zero_zero(nat))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_290])])).
% 11.66/2.04 tff(f4163,plain,(
% 11.66/2.04 spl32_286 <=> ! [X0 : dB,X1 : dB] : member(dB,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),combc(dB,dB,bool,beta,subst(X1,X0,zero_zero(nat))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_286])])).
% 11.66/2.04 tff(f4166,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (member(dB,foldr(dB,dB,app,insert(dB,abs(X1),nil(dB)),X0),combc(dB,dB,bool,beta,subst(X1,X0,zero_zero(nat))))) ) | (~spl32_89 | ~spl32_275 | ~spl32_286)),
% 11.66/2.04 inference(forward_demodulation,[],[f4164,f3939])).
% 11.66/2.04 tff(f4164,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (member(dB,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),combc(dB,dB,bool,beta,subst(X1,X0,zero_zero(nat))))) ) | ~spl32_286),
% 11.66/2.04 inference(avatar_component_clause,[],[f4163])).
% 11.66/2.04 tff(f4179,plain,(
% 11.66/2.04 spl32_289 | ~spl32_13 | ~spl32_40 | ~spl32_138),
% 11.66/2.04 inference(avatar_split_clause,[],[f1840,f1801,f747,f603,f4177])).
% 11.66/2.04 tff(f4177,plain,(
% 11.66/2.04 spl32_289 <=> ! [X0 : $tType,X3 : fun(X0,fun(X0,bool)),X2 : list(X0),X1 : X0] : (~step1(X0,X3,X2,insert(X0,X1,nil(X0))) | insert(X0,sK27(X0,nil(X0),X1,X2,X3),nil(X0)) = X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_289])])).
% 11.66/2.04 tff(f603,plain,(
% 11.66/2.04 spl32_13 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X1 : list(X0)] : ~step1(X0,X2,X1,nil(X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_13])])).
% 11.66/2.04 tff(f1801,plain,(
% 11.66/2.04 spl32_138 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | cons(X0,sK27(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_138])])).
% 11.66/2.04 tff(f1840,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : list(X0),X3 : fun(X0,fun(X0,bool)),X1 : X0] : (~step1(X0,X3,X2,insert(X0,X1,nil(X0))) | insert(X0,sK27(X0,nil(X0),X1,X2,X3),nil(X0)) = X2) ) | (~spl32_13 | ~spl32_40 | ~spl32_138)),
% 11.66/2.04 inference(forward_demodulation,[],[f1839,f748])).
% 11.66/2.04 tff(f1839,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : list(X0),X3 : fun(X0,fun(X0,bool)),X1 : X0] : (insert(X0,sK27(X0,nil(X0),X1,X2,X3),nil(X0)) = X2 | ~step1(X0,X3,X2,cons(X0,X1,nil(X0)))) ) | (~spl32_13 | ~spl32_40 | ~spl32_138)),
% 11.66/2.04 inference(forward_demodulation,[],[f1838,f748])).
% 11.66/2.04 tff(f1838,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : list(X0),X3 : fun(X0,fun(X0,bool)),X1 : X0] : (cons(X0,sK27(X0,nil(X0),X1,X2,X3),nil(X0)) = X2 | ~step1(X0,X3,X2,cons(X0,X1,nil(X0)))) ) | (~spl32_13 | ~spl32_138)),
% 11.66/2.04 inference(resolution,[],[f1802,f604])).
% 11.66/2.04 tff(f604,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X1 : list(X0)] : (~step1(X0,X2,X1,nil(X0))) ) | ~spl32_13),
% 11.66/2.04 inference(avatar_component_clause,[],[f603])).
% 11.66/2.04 tff(f1802,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | cons(X0,sK27(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | ~spl32_138),
% 11.66/2.04 inference(avatar_component_clause,[],[f1801])).
% 11.66/2.04 tff(f4175,plain,(
% 11.66/2.04 spl32_288 | ~spl32_34 | ~spl32_112),
% 11.66/2.04 inference(avatar_split_clause,[],[f1478,f1471,f708,f4173])).
% 11.66/2.04 tff(f4173,plain,(
% 11.66/2.04 spl32_288 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | member(dB,X1,combc(dB,dB,bool,beta,sK5(X0,X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_288])])).
% 11.66/2.04 tff(f1478,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | member(dB,X1,combc(dB,dB,bool,beta,sK5(X0,X1)))) ) | (~spl32_34 | ~spl32_112)),
% 11.66/2.04 inference(resolution,[],[f1472,f709])).
% 11.66/2.04 tff(f4170,plain,(
% 11.66/2.04 spl32_287 | ~spl32_16 | ~spl32_110),
% 11.66/2.04 inference(avatar_split_clause,[],[f1458,f1452,f618,f4168])).
% 11.66/2.04 tff(f1458,plain,(
% 11.66/2.04 ( ! [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))))))) ) | (~spl32_16 | ~spl32_110)),
% 11.66/2.04 inference(superposition,[],[f1453,f619])).
% 11.66/2.04 tff(f4165,plain,(
% 11.66/2.04 spl32_286 | ~spl32_34 | ~spl32_110),
% 11.66/2.04 inference(avatar_split_clause,[],[f1456,f1452,f708,f4163])).
% 11.66/2.04 tff(f1456,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (member(dB,aa(dB,dB,combc(dB,dB,dB,app,X0),abs(X1)),combc(dB,dB,bool,beta,subst(X1,X0,zero_zero(nat))))) ) | (~spl32_34 | ~spl32_110)),
% 11.66/2.04 inference(resolution,[],[f1453,f709])).
% 11.66/2.04 tff(f4161,plain,(
% 11.66/2.04 spl32_285 | ~spl32_89 | ~spl32_273),
% 11.66/2.04 inference(avatar_split_clause,[],[f3917,f3804,f1039,f4159])).
% 11.66/2.04 tff(f4159,plain,(
% 11.66/2.04 spl32_285 <=> ! [X0 : $tType,X3 : X0,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (fTrue != aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_285])])).
% 11.66/2.04 tff(f3917,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool))] : (fTrue != aa(bool,bool,combc(bool,X0,bool,X1,X3),X2) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0)))) ) | (~spl32_89 | ~spl32_273)),
% 11.66/2.04 inference(superposition,[],[f3805,f1040])).
% 11.66/2.04 tff(f4157,plain,(
% 11.66/2.04 spl32_284 | ~spl32_28 | ~spl32_101),
% 11.66/2.04 inference(avatar_split_clause,[],[f1342,f1297,f676,f4155])).
% 11.66/2.04 tff(f4155,plain,(
% 11.66/2.04 spl32_284 <=> ! [X2 : type,X0 : dB,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,X0),X2)) | pp(aa(list(type),bool,typings(X1,nil(dB)),sK22(X2,nil(dB),X0,X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_284])])).
% 11.66/2.04 tff(f1342,plain,(
% 11.66/2.04 ( ! [X2 : type,X0 : dB,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,X0),X2)) | pp(aa(list(type),bool,typings(X1,nil(dB)),sK22(X2,nil(dB),X0,X1)))) ) | (~spl32_28 | ~spl32_101)),
% 11.66/2.04 inference(superposition,[],[f1298,f677])).
% 11.66/2.04 tff(f4153,plain,(
% 11.66/2.04 spl32_283 | ~spl32_28 | ~spl32_100),
% 11.66/2.04 inference(avatar_split_clause,[],[f1335,f1293,f676,f4151])).
% 11.66/2.04 tff(f4151,plain,(
% 11.66/2.04 spl32_283 <=> ! [X2 : type,X0 : dB,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,X0),X2)) | pp(aa(list(type),bool,typings(X1,nil(dB)),sK21(X2,nil(dB),X0,X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_283])])).
% 11.66/2.04 tff(f1335,plain,(
% 11.66/2.04 ( ! [X2 : type,X0 : dB,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,X0),X2)) | pp(aa(list(type),bool,typings(X1,nil(dB)),sK21(X2,nil(dB),X0,X1)))) ) | (~spl32_28 | ~spl32_100)),
% 11.66/2.04 inference(superposition,[],[f1294,f677])).
% 11.66/2.04 tff(f4149,plain,(
% 11.66/2.04 spl32_282 | ~spl32_33 | ~spl32_99),
% 11.66/2.04 inference(avatar_split_clause,[],[f1285,f1282,f704,f4147])).
% 11.66/2.04 tff(f4147,plain,(
% 11.66/2.04 spl32_282 <=> ! [X2 : nat,X0 : list(dB),X1 : dB] : (step1(dB,beta,X0,sK17(X1,X0,X2)) | ~member(dB,foldl(dB,dB,app,var(X2),X0),combc(dB,dB,bool,beta,X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_282])])).
% 11.66/2.04 tff(f1285,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : list(dB),X1 : dB] : (step1(dB,beta,X0,sK17(X1,X0,X2)) | ~member(dB,foldl(dB,dB,app,var(X2),X0),combc(dB,dB,bool,beta,X1))) ) | (~spl32_33 | ~spl32_99)),
% 11.66/2.04 inference(resolution,[],[f1283,f705])).
% 11.66/2.04 tff(f4145,plain,(
% 11.66/2.04 spl32_281 | ~spl32_12 | ~spl32_93),
% 11.66/2.04 inference(avatar_split_clause,[],[f1091,f1084,f599,f4143])).
% 11.66/2.04 tff(f4143,plain,(
% 11.66/2.04 spl32_281 <=> ! [X0 : $tType,X2 : fun(bool,X0),X1 : fun(bool,X0)] : (aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) | X1 = X2 | fTrue = sK25(X0,bool,X1,X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_281])])).
% 11.66/2.04 tff(f1091,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(bool,X0),X1 : fun(bool,X0)] : (aa(bool,X0,X2,fFalse) != aa(bool,X0,X1,fFalse) | X1 = X2 | fTrue = sK25(X0,bool,X1,X2)) ) | (~spl32_12 | ~spl32_93)),
% 11.66/2.04 inference(superposition,[],[f1085,f600])).
% 11.66/2.04 tff(f4141,plain,(
% 11.66/2.04 spl32_280 | ~spl32_39 | ~spl32_91),
% 11.66/2.04 inference(avatar_split_clause,[],[f1071,f1060,f737,f4139])).
% 11.66/2.04 tff(f4139,plain,(
% 11.66/2.04 spl32_280 <=> ! [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)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_280])])).
% 11.66/2.04 tff(f1071,plain,(
% 11.66/2.04 ( ! [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)) ) | (~spl32_39 | ~spl32_91)),
% 11.66/2.04 inference(superposition,[],[f1061,f738])).
% 11.66/2.04 tff(f3830,plain,(
% 11.66/2.04 spl32_279 | ~spl32_51 | ~spl32_158),
% 11.66/2.04 inference(avatar_split_clause,[],[f2068,f2062,f808,f3828])).
% 11.66/2.04 tff(f3828,plain,(
% 11.66/2.04 spl32_279 <=> ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (cons(bool,X0,sK26(bool,X1,X0,X2,fconj)) = X2 | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_279])])).
% 11.66/2.04 tff(f2068,plain,(
% 11.66/2.04 ( ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (cons(bool,X0,sK26(bool,X1,X0,X2,fconj)) = X2 | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(X0)) ) | (~spl32_51 | ~spl32_158)),
% 11.66/2.04 inference(resolution,[],[f2063,f809])).
% 11.66/2.04 tff(f3826,plain,(
% 11.66/2.04 spl32_278 | ~spl32_16 | ~spl32_140),
% 11.66/2.04 inference(avatar_split_clause,[],[f1851,f1847,f618,f3824])).
% 11.66/2.04 tff(f3824,plain,(
% 11.66/2.04 spl32_278 <=> ! [X0 : dB,X1 : list(dB)] : (~it(foldl(dB,dB,app,X0,X1)) | ~it(X0) | it(foldl(dB,dB,app,abs(var(zero_zero(nat))),cons(dB,X0,X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_278])])).
% 11.66/2.04 tff(f1847,plain,(
% 11.66/2.04 spl32_140 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : (it(foldl(dB,dB,app,abs(X2),cons(dB,X1,X0))) | ~it(X1) | ~it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_140])])).
% 11.66/2.04 tff(f1851,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : list(dB)] : (~it(foldl(dB,dB,app,X0,X1)) | ~it(X0) | it(foldl(dB,dB,app,abs(var(zero_zero(nat))),cons(dB,X0,X1)))) ) | (~spl32_16 | ~spl32_140)),
% 11.66/2.04 inference(superposition,[],[f1848,f619])).
% 11.66/2.04 tff(f1848,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (~it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)) | ~it(X1) | it(foldl(dB,dB,app,abs(X2),cons(dB,X1,X0)))) ) | ~spl32_140),
% 11.66/2.04 inference(avatar_component_clause,[],[f1847])).
% 11.66/2.04 tff(f3822,plain,(
% 11.66/2.04 spl32_277 | ~spl32_80 | ~spl32_115),
% 11.66/2.04 inference(avatar_split_clause,[],[f1499,f1495,f969,f3820])).
% 11.66/2.04 tff(f3820,plain,(
% 11.66/2.04 spl32_277 <=> ! [X0 : list(dB),X3 : dB,X2 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | sP2(dB,X2,X2,beta,foldl(dB,dB,app,X3,X0),foldl(dB,dB,app,X3,X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_277])])).
% 11.66/2.04 tff(f1499,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X3 : dB,X0 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | sP2(dB,X2,X2,beta,foldl(dB,dB,app,X3,X0),foldl(dB,dB,app,X3,X1))) ) | (~spl32_80 | ~spl32_115)),
% 11.66/2.04 inference(resolution,[],[f1496,f970])).
% 11.66/2.04 tff(f3818,plain,(
% 11.66/2.04 spl32_276 | ~spl32_28 | ~spl32_40 | ~spl32_108),
% 11.66/2.04 inference(avatar_split_clause,[],[f1436,f1325,f747,f676,f3816])).
% 11.66/2.04 tff(f1436,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X0)),X3 : X0,X4 : X1] : (aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4) = foldl(X0,X1,X2,X3,insert(X1,X4,nil(X1)))) ) | (~spl32_28 | ~spl32_40 | ~spl32_108)),
% 11.66/2.04 inference(forward_demodulation,[],[f1421,f748])).
% 11.66/2.04 tff(f1421,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X0)),X3 : X0,X4 : X1] : (aa(X1,X0,aa(X0,fun(X1,X0),X2,X3),X4) = foldl(X0,X1,X2,X3,cons(X1,X4,nil(X1)))) ) | (~spl32_28 | ~spl32_108)),
% 11.66/2.04 inference(superposition,[],[f1326,f677])).
% 11.66/2.04 tff(f3814,plain,(
% 11.66/2.04 spl32_275 | ~spl32_27 | ~spl32_40 | ~spl32_107),
% 11.66/2.04 inference(avatar_split_clause,[],[f1408,f1321,f747,f672,f3812])).
% 11.66/2.04 tff(f1408,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X1)),X3 : X1,X4 : X0] : (aa(X1,X1,aa(X0,fun(X1,X1),X2,X4),X3) = foldr(X0,X1,X2,insert(X0,X4,nil(X0)),X3)) ) | (~spl32_27 | ~spl32_40 | ~spl32_107)),
% 11.66/2.04 inference(forward_demodulation,[],[f1380,f748])).
% 11.66/2.04 tff(f1380,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,X1)),X3 : X1,X4 : X0] : (foldr(X0,X1,X2,cons(X0,X4,nil(X0)),X3) = aa(X1,X1,aa(X0,fun(X1,X1),X2,X4),X3)) ) | (~spl32_27 | ~spl32_107)),
% 11.66/2.04 inference(superposition,[],[f1322,f673])).
% 11.66/2.04 tff(f3810,plain,(
% 11.66/2.04 spl32_274 | ~spl32_34 | ~spl32_96),
% 11.66/2.04 inference(avatar_split_clause,[],[f1265,f1260,f708,f3808])).
% 11.66/2.04 tff(f3808,plain,(
% 11.66/2.04 spl32_274 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,abs(X1),combc(dB,dB,bool,beta,abs(X0))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_274])])).
% 11.66/2.04 tff(f1265,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | member(dB,abs(X1),combc(dB,dB,bool,beta,abs(X0)))) ) | (~spl32_34 | ~spl32_96)),
% 11.66/2.04 inference(resolution,[],[f1261,f709])).
% 11.66/2.04 tff(f3806,plain,(
% 11.66/2.04 spl32_273 | ~spl32_261),
% 11.66/2.04 inference(avatar_split_clause,[],[f3590,f3388,f3804])).
% 11.66/2.04 tff(f3590,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool))] : (fTrue != aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0)))) ) | ~spl32_261),
% 11.66/2.04 inference(duplicate_literal_removal,[],[f3586])).
% 11.66/2.04 tff(f3586,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool))] : (fTrue != aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0)))) ) | ~spl32_261),
% 11.66/2.04 inference(equality_factoring,[],[f3389])).
% 11.66/2.04 tff(f3802,plain,(
% 11.66/2.04 spl32_272 | ~spl32_33 | ~spl32_91),
% 11.66/2.04 inference(avatar_split_clause,[],[f1080,f1060,f704,f3800])).
% 11.66/2.04 tff(f3800,plain,(
% 11.66/2.04 spl32_272 <=> ! [X0 : $tType,X4 : bool,X3 : list(X0),X2 : X0,X1 : fun(X0,fun(list(X0),bool))] : (pp(list_case(bool,X0,X4,X1,cons(X0,X2,X3))) | ~member(list(X0),X3,aa(X0,fun(list(X0),bool),X1,X2)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_272])])).
% 11.66/2.04 tff(f1080,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(list(X0),bool)),X4 : bool] : (pp(list_case(bool,X0,X4,X1,cons(X0,X2,X3))) | ~member(list(X0),X3,aa(X0,fun(list(X0),bool),X1,X2))) ) | (~spl32_33 | ~spl32_91)),
% 11.66/2.04 inference(superposition,[],[f705,f1061])).
% 11.66/2.04 tff(f3798,plain,(
% 11.66/2.04 spl32_271 | ~spl32_34 | ~spl32_91),
% 11.66/2.04 inference(avatar_split_clause,[],[f1079,f1060,f708,f3796])).
% 11.66/2.04 tff(f3796,plain,(
% 11.66/2.04 spl32_271 <=> ! [X0 : $tType,X4 : bool,X3 : list(X0),X2 : X0,X1 : fun(X0,fun(list(X0),bool))] : (~pp(list_case(bool,X0,X4,X1,cons(X0,X2,X3))) | member(list(X0),X3,aa(X0,fun(list(X0),bool),X1,X2)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_271])])).
% 11.66/2.04 tff(f1079,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : fun(X0,fun(list(X0),bool)),X4 : bool] : (~pp(list_case(bool,X0,X4,X1,cons(X0,X2,X3))) | member(list(X0),X3,aa(X0,fun(list(X0),bool),X1,X2))) ) | (~spl32_34 | ~spl32_91)),
% 11.66/2.04 inference(superposition,[],[f709,f1061])).
% 11.66/2.04 tff(f3794,plain,(
% 11.66/2.04 spl32_270 | ~spl32_39 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1047,f1039,f737,f3792])).
% 11.66/2.04 tff(f3792,plain,(
% 11.66/2.04 spl32_270 <=> ! [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)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_270])])).
% 11.66/2.04 tff(f1047,plain,(
% 11.66/2.04 ( ! [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)) ) | (~spl32_39 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f1040,f738])).
% 11.66/2.04 tff(f3425,plain,(
% 11.66/2.04 spl32_269 | ~spl32_28 | ~spl32_141),
% 11.66/2.04 inference(avatar_split_clause,[],[f1867,f1855,f676,f3423])).
% 11.66/2.04 tff(f3423,plain,(
% 11.66/2.04 spl32_269 <=> ! [X0 : nat,X3 : type,X2 : type,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,var(X0)),X2)) | ~pp(aa(type,bool,typing(X1,var(X0)),X3)) | X2 = X3)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_269])])).
% 11.66/2.04 tff(f1867,plain,(
% 11.66/2.04 ( ! [X2 : type,X3 : type,X0 : nat,X1 : fun(nat,type)] : (~pp(aa(type,bool,typing(X1,var(X0)),X2)) | ~pp(aa(type,bool,typing(X1,var(X0)),X3)) | X2 = X3) ) | (~spl32_28 | ~spl32_141)),
% 11.66/2.04 inference(superposition,[],[f1856,f677])).
% 11.66/2.04 tff(f3421,plain,(
% 11.66/2.04 spl32_268 | ~spl32_80 | ~spl32_112),
% 11.66/2.04 inference(avatar_split_clause,[],[f1477,f1471,f969,f3419])).
% 11.66/2.04 tff(f3419,plain,(
% 11.66/2.04 spl32_268 <=> ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | sP2(dB,X2,X2,beta,X1,sK5(X0,X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_268])])).
% 11.66/2.04 tff(f1477,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | sP2(dB,X2,X2,beta,X1,sK5(X0,X1))) ) | (~spl32_80 | ~spl32_112)),
% 11.66/2.04 inference(resolution,[],[f1472,f970])).
% 11.66/2.04 tff(f3417,plain,(
% 11.66/2.04 spl32_267 | ~spl32_80 | ~spl32_110),
% 11.66/2.04 inference(avatar_split_clause,[],[f1455,f1452,f969,f3415])).
% 11.66/2.04 tff(f3415,plain,(
% 11.66/2.04 spl32_267 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : sP2(dB,X0,X0,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),subst(X2,X1,zero_zero(nat)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_267])])).
% 11.66/2.04 tff(f1455,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (sP2(dB,X0,X0,beta,aa(dB,dB,combc(dB,dB,dB,app,X1),abs(X2)),subst(X2,X1,zero_zero(nat)))) ) | (~spl32_80 | ~spl32_110)),
% 11.66/2.04 inference(resolution,[],[f1453,f970])).
% 11.66/2.04 tff(f3413,plain,(
% 11.66/2.04 spl32_266 | ~spl32_89 | ~spl32_91),
% 11.66/2.04 inference(avatar_split_clause,[],[f1076,f1060,f1039,f3411])).
% 11.66/2.04 tff(f3411,plain,(
% 11.66/2.04 spl32_266 <=> ! [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)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_266])])).
% 11.66/2.04 tff(f1076,plain,(
% 11.66/2.04 ( ! [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)) ) | (~spl32_89 | ~spl32_91)),
% 11.66/2.04 inference(superposition,[],[f1061,f1040])).
% 11.66/2.04 tff(f3409,plain,(
% 11.66/2.04 spl32_265 | ~spl32_33 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1054,f1039,f704,f3407])).
% 11.66/2.04 tff(f3407,plain,(
% 11.66/2.04 spl32_265 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X1,X2 : fun(X1,fun(X0,bool))] : (pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3)) | ~member(X0,X4,aa(X1,fun(X0,bool),X2,X3)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_265])])).
% 11.66/2.04 tff(f1054,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(X0,bool)),X3 : X1,X4 : X0] : (pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3)) | ~member(X0,X4,aa(X1,fun(X0,bool),X2,X3))) ) | (~spl32_33 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f705,f1040])).
% 11.66/2.04 tff(f3405,plain,(
% 11.66/2.04 spl32_264 | ~spl32_34 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1053,f1039,f708,f3403])).
% 11.66/2.04 tff(f3403,plain,(
% 11.66/2.04 spl32_264 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X1,X2 : fun(X1,fun(X0,bool))] : (~pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3)) | member(X0,X4,aa(X1,fun(X0,bool),X2,X3)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_264])])).
% 11.66/2.04 tff(f1053,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,fun(X0,bool)),X3 : X1,X4 : X0] : (~pp(aa(X1,bool,combc(X1,X0,bool,X2,X4),X3)) | member(X0,X4,aa(X1,fun(X0,bool),X2,X3))) ) | (~spl32_34 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f709,f1040])).
% 11.66/2.04 tff(f3401,plain,(
% 11.66/2.04 spl32_263 | ~spl32_33 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1052,f1039,f704,f3399])).
% 11.66/2.04 tff(f3399,plain,(
% 11.66/2.04 spl32_263 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X1,X2 : fun(X0,fun(X1,bool))] : (pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3)) | ~member(X0,X4,combc(X0,X1,bool,X2,X3)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_263])])).
% 11.66/2.04 tff(f1052,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,bool)),X3 : X1,X4 : X0] : (pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3)) | ~member(X0,X4,combc(X0,X1,bool,X2,X3))) ) | (~spl32_33 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f705,f1040])).
% 11.66/2.04 tff(f3397,plain,(
% 11.66/2.04 spl32_262 | ~spl32_34 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1051,f1039,f708,f3395])).
% 11.66/2.04 tff(f3395,plain,(
% 11.66/2.04 spl32_262 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X1,X2 : fun(X0,fun(X1,bool))] : (~pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3)) | member(X0,X4,combc(X0,X1,bool,X2,X3)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_262])])).
% 11.66/2.04 tff(f1051,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(X1,bool)),X3 : X1,X4 : X0] : (~pp(aa(X1,bool,aa(X0,fun(X1,bool),X2,X4),X3)) | member(X0,X4,combc(X0,X1,bool,X2,X3))) ) | (~spl32_34 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f709,f1040])).
% 11.66/2.04 tff(f3390,plain,(
% 11.66/2.04 spl32_261 | ~spl32_28 | ~spl32_239),
% 11.66/2.04 inference(avatar_split_clause,[],[f3135,f3075,f676,f3388])).
% 11.66/2.04 tff(f3075,plain,(
% 11.66/2.04 spl32_239 <=> ! [X0 : $tType,X5 : $tType,X6 : fun(bool,fun(X5,bool)),X4 : bool,X3 : X0,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))) | aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) = X4 | fTrue = foldl(bool,X5,X6,X4,nil(X5)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_239])])).
% 11.66/2.04 tff(f3135,plain,(
% 11.66/2.04 ( ! [X3 : $tType,X2 : bool,X6 : X3,X4 : fun(bool,fun(X3,bool)),X5 : bool] : (fTrue = X2 | fTrue = foldl(bool,X3,X4,X5,insert(X3,X6,nil(X3))) | aa(X3,bool,aa(bool,fun(X3,bool),X4,X5),X6) = X2) ) | (~spl32_28 | ~spl32_239)),
% 11.66/2.04 inference(superposition,[],[f3076,f677])).
% 11.66/2.04 tff(f3076,plain,(
% 11.66/2.04 ( ! [X5 : $tType,X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X6 : fun(bool,fun(X5,bool)),X4 : bool] : (fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))) | aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) = X4 | fTrue = foldl(bool,X5,X6,X4,nil(X5))) ) | ~spl32_239),
% 11.66/2.04 inference(avatar_component_clause,[],[f3075])).
% 11.66/2.04 tff(f3342,plain,(
% 11.66/2.04 spl32_260 | ~spl32_51 | ~spl32_155),
% 11.66/2.04 inference(avatar_split_clause,[],[f2023,f2017,f808,f3340])).
% 11.66/2.04 tff(f3340,plain,(
% 11.66/2.04 spl32_260 <=> ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (step1(bool,fconj,sK26(bool,X1,X0,X2,fconj),X1) | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_260])])).
% 11.66/2.04 tff(f2023,plain,(
% 11.66/2.04 ( ! [X2 : list(bool),X0 : bool,X1 : list(bool)] : (step1(bool,fconj,sK26(bool,X1,X0,X2,fconj),X1) | ~step1(bool,fconj,X2,cons(bool,X0,X1)) | pp(X0)) ) | (~spl32_51 | ~spl32_155)),
% 11.66/2.04 inference(resolution,[],[f2018,f809])).
% 11.66/2.04 tff(f3338,plain,(
% 11.66/2.04 spl32_259 | ~spl32_28 | ~spl32_40 | ~spl32_140),
% 11.66/2.04 inference(avatar_split_clause,[],[f1853,f1847,f747,f676,f3336])).
% 11.66/2.04 tff(f3336,plain,(
% 11.66/2.04 spl32_259 <=> ! [X0 : dB,X1 : dB] : (it(foldl(dB,dB,app,abs(X0),insert(dB,X1,nil(dB)))) | ~it(subst(X0,X1,zero_zero(nat))) | ~it(X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_259])])).
% 11.66/2.04 tff(f1853,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (it(foldl(dB,dB,app,abs(X0),insert(dB,X1,nil(dB)))) | ~it(subst(X0,X1,zero_zero(nat))) | ~it(X1)) ) | (~spl32_28 | ~spl32_40 | ~spl32_140)),
% 11.66/2.04 inference(forward_demodulation,[],[f1852,f748])).
% 11.66/2.04 tff(f1852,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (~it(subst(X0,X1,zero_zero(nat))) | ~it(X1) | it(foldl(dB,dB,app,abs(X0),cons(dB,X1,nil(dB))))) ) | (~spl32_28 | ~spl32_140)),
% 11.66/2.04 inference(superposition,[],[f1848,f677])).
% 11.66/2.04 tff(f3334,plain,(
% 11.66/2.04 spl32_258 | ~spl32_80 | ~spl32_96),
% 11.66/2.04 inference(avatar_split_clause,[],[f1264,f1260,f969,f3332])).
% 11.66/2.04 tff(f3332,plain,(
% 11.66/2.04 spl32_258 <=> ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,abs(X1),abs(X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_258])])).
% 11.66/2.04 tff(f1264,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | sP2(dB,X2,X2,beta,abs(X1),abs(X0))) ) | (~spl32_80 | ~spl32_96)),
% 11.66/2.04 inference(resolution,[],[f1261,f970])).
% 11.66/2.04 tff(f3330,plain,(
% 11.66/2.04 spl32_257 | ~spl32_40 | ~spl32_78),
% 11.66/2.04 inference(avatar_split_clause,[],[f988,f961,f747,f3328])).
% 11.66/2.04 tff(f3328,plain,(
% 11.66/2.04 spl32_257 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : X0] : (step1(X0,X2,cons(X0,X3,X4),insert(X0,X1,nil(X0))) | ~sP2(X0,nil(X0),X4,X2,X3,X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_257])])).
% 11.66/2.04 tff(f988,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : X0,X4 : list(X0)] : (step1(X0,X2,cons(X0,X3,X4),insert(X0,X1,nil(X0))) | ~sP2(X0,nil(X0),X4,X2,X3,X1)) ) | (~spl32_40 | ~spl32_78)),
% 11.66/2.04 inference(superposition,[],[f962,f748])).
% 11.66/2.04 tff(f3323,plain,(
% 11.66/2.04 spl32_256 | ~spl32_40 | ~spl32_78),
% 11.66/2.04 inference(avatar_split_clause,[],[f985,f961,f747,f3321])).
% 11.66/2.04 tff(f3321,plain,(
% 11.66/2.04 spl32_256 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : X0] : (step1(X0,X2,insert(X0,X1,nil(X0)),cons(X0,X3,X4)) | ~sP2(X0,X4,nil(X0),X2,X1,X3))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_256])])).
% 11.66/2.04 tff(f985,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : X0,X4 : list(X0)] : (step1(X0,X2,insert(X0,X1,nil(X0)),cons(X0,X3,X4)) | ~sP2(X0,X4,nil(X0),X2,X1,X3)) ) | (~spl32_40 | ~spl32_78)),
% 11.66/2.04 inference(superposition,[],[f962,f748])).
% 11.66/2.04 tff(f3319,plain,(
% 11.66/2.04 spl32_255 | ~spl32_40 | ~spl32_77),
% 11.66/2.04 inference(avatar_split_clause,[],[f981,f957,f747,f3317])).
% 11.66/2.04 tff(f3317,plain,(
% 11.66/2.04 spl32_255 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : X0] : (~step1(X0,X2,cons(X0,X3,X4),insert(X0,X1,nil(X0))) | sP2(X0,nil(X0),X4,X2,X3,X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_255])])).
% 11.66/2.04 tff(f981,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : X0,X4 : list(X0)] : (~step1(X0,X2,cons(X0,X3,X4),insert(X0,X1,nil(X0))) | sP2(X0,nil(X0),X4,X2,X3,X1)) ) | (~spl32_40 | ~spl32_77)),
% 11.66/2.04 inference(superposition,[],[f958,f748])).
% 11.66/2.04 tff(f3315,plain,(
% 11.66/2.04 spl32_254 | ~spl32_40 | ~spl32_77),
% 11.66/2.04 inference(avatar_split_clause,[],[f978,f957,f747,f3313])).
% 11.66/2.04 tff(f3313,plain,(
% 11.66/2.04 spl32_254 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X4 : list(X0),X3 : X0,X1 : X0] : (~step1(X0,X2,insert(X0,X1,nil(X0)),cons(X0,X3,X4)) | sP2(X0,X4,nil(X0),X2,X1,X3))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_254])])).
% 11.66/2.04 tff(f978,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : X0,X4 : list(X0)] : (~step1(X0,X2,insert(X0,X1,nil(X0)),cons(X0,X3,X4)) | sP2(X0,X4,nil(X0),X2,X1,X3)) ) | (~spl32_40 | ~spl32_77)),
% 11.66/2.04 inference(superposition,[],[f958,f748])).
% 11.66/2.04 tff(f3235,plain,(
% 11.66/2.04 spl32_252 | spl32_253 | ~spl32_28 | ~spl32_33 | ~spl32_239),
% 11.66/2.04 inference(avatar_split_clause,[],[f3165,f3075,f704,f676,f3233,f3230])).
% 11.66/2.04 tff(f3165,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X4 : bool] : (fTrue = X4 | pp(X4) | ~member(X0,X3,aa(bool,fun(X0,bool),X1,X2)) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0)))) ) | (~spl32_28 | ~spl32_33 | ~spl32_239)),
% 11.66/2.04 inference(forward_demodulation,[],[f3143,f677])).
% 11.66/2.04 tff(f3143,plain,(
% 11.66/2.04 ( ! [X5 : $tType,X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X6 : fun(bool,fun(X5,bool)),X4 : bool] : (pp(X4) | ~member(X0,X3,aa(bool,fun(X0,bool),X1,X2)) | fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))) | fTrue = foldl(bool,X5,X6,X4,nil(X5))) ) | (~spl32_33 | ~spl32_239)),
% 11.66/2.04 inference(superposition,[],[f705,f3076])).
% 11.66/2.04 tff(f3205,plain,(
% 11.66/2.04 spl32_251 | ~spl32_34 | ~spl32_123),
% 11.66/2.04 inference(avatar_split_clause,[],[f1655,f1649,f708,f3202])).
% 11.66/2.04 tff(f3202,plain,(
% 11.66/2.04 spl32_251 <=> member(type,t_a,typing(shift(type,ea,ia,t),foldl(dB,dB,app,abs(r),cons(dB,a,as))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_251])])).
% 11.66/2.04 tff(f1655,plain,(
% 11.66/2.04 member(type,t_a,typing(shift(type,ea,ia,t),foldl(dB,dB,app,abs(r),cons(dB,a,as)))) | (~spl32_34 | ~spl32_123)),
% 11.66/2.04 inference(resolution,[],[f1651,f709])).
% 11.66/2.04 tff(f3200,plain,(
% 11.66/2.04 spl32_250 | ~spl32_34 | ~spl32_121),
% 11.66/2.04 inference(avatar_split_clause,[],[f1635,f1629,f708,f3197])).
% 11.66/2.04 tff(f3197,plain,(
% 11.66/2.04 spl32_250 <=> member(type,t1,typing(shift(type,e,i,t),foldl(dB,dB,app,abs(r),cons(dB,a,as))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_250])])).
% 11.66/2.04 tff(f1635,plain,(
% 11.66/2.04 member(type,t1,typing(shift(type,e,i,t),foldl(dB,dB,app,abs(r),cons(dB,a,as)))) | (~spl32_34 | ~spl32_121)),
% 11.66/2.04 inference(resolution,[],[f1631,f709])).
% 11.66/2.04 tff(f3195,plain,(
% 11.66/2.04 spl32_249 | ~spl32_99 | ~spl32_115),
% 11.66/2.04 inference(avatar_split_clause,[],[f1498,f1495,f1282,f3193])).
% 11.66/2.04 tff(f3193,plain,(
% 11.66/2.04 spl32_249 <=> ! [X2 : nat,X0 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | step1(dB,beta,X0,sK17(foldl(dB,dB,app,var(X2),X1),X0,X2)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_249])])).
% 11.66/2.04 tff(f1498,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : list(dB),X1 : list(dB)] : (~step1(dB,beta,X0,X1) | step1(dB,beta,X0,sK17(foldl(dB,dB,app,var(X2),X1),X0,X2))) ) | (~spl32_99 | ~spl32_115)),
% 11.66/2.04 inference(resolution,[],[f1496,f1283])).
% 11.66/2.04 tff(f3191,plain,(
% 11.66/2.04 spl32_248 | ~spl32_82 | ~spl32_96),
% 11.66/2.04 inference(avatar_split_clause,[],[f1263,f1260,f1000,f3189])).
% 11.66/2.04 tff(f3189,plain,(
% 11.66/2.04 spl32_248 <=> ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | abs(X0) = abs(sK5(abs(X0),X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_248])])).
% 11.66/2.04 tff(f1263,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),X1)) | abs(X0) = abs(sK5(abs(X0),X1))) ) | (~spl32_82 | ~spl32_96)),
% 11.66/2.04 inference(resolution,[],[f1261,f1001])).
% 11.66/2.04 tff(f3187,plain,(
% 11.66/2.04 spl32_247 | ~spl32_91),
% 11.66/2.04 inference(avatar_split_clause,[],[f1075,f1060,f3185])).
% 11.66/2.04 tff(f3185,plain,(
% 11.66/2.04 spl32_247 <=> ! [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))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_247])])).
% 11.66/2.04 tff(f1075,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_91),
% 11.66/2.04 inference(superposition,[],[f1061,f1061])).
% 11.66/2.04 tff(f3183,plain,(
% 11.66/2.04 spl32_246 | ~spl32_86 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1057,f1039,f1024,f3181])).
% 11.66/2.04 tff(f3181,plain,(
% 11.66/2.04 spl32_246 <=> ! [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))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_246])])).
% 11.66/2.04 tff(f1024,plain,(
% 11.66/2.04 spl32_86 <=> ! [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)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_86])])).
% 11.66/2.04 tff(f1057,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_86 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f1025,f1040])).
% 11.66/2.04 tff(f1025,plain,(
% 11.66/2.04 ( ! [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)) ) | ~spl32_86),
% 11.66/2.04 inference(avatar_component_clause,[],[f1024])).
% 11.66/2.04 tff(f3179,plain,(
% 11.66/2.04 spl32_245 | ~spl32_12 | ~spl32_69),
% 11.66/2.04 inference(avatar_split_clause,[],[f926,f904,f599,f3177])).
% 11.66/2.04 tff(f3177,plain,(
% 11.66/2.04 spl32_245 <=> ! [X0 : list(bool)] : (cons(bool,fFalse,sK7(bool,X0)) = X0 | nil(bool) = X0 | fTrue = sK6(bool,X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_245])])).
% 11.66/2.04 tff(f926,plain,(
% 11.66/2.04 ( ! [X0 : list(bool)] : (cons(bool,fFalse,sK7(bool,X0)) = X0 | nil(bool) = X0 | fTrue = sK6(bool,X0)) ) | (~spl32_12 | ~spl32_69)),
% 11.66/2.04 inference(superposition,[],[f905,f600])).
% 11.66/2.04 tff(f3175,plain,(
% 11.66/2.04 spl32_244 | ~spl32_12 | ~spl32_68),
% 11.66/2.04 inference(avatar_split_clause,[],[f919,f900,f599,f3173])).
% 11.66/2.04 tff(f3173,plain,(
% 11.66/2.04 spl32_244 <=> ! [X0 : list(bool)] : (cons(bool,fFalse,sK4(bool,X0)) = X0 | nil(bool) = X0 | fTrue = sK3(bool,X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_244])])).
% 11.66/2.04 tff(f919,plain,(
% 11.66/2.04 ( ! [X0 : list(bool)] : (cons(bool,fFalse,sK4(bool,X0)) = X0 | nil(bool) = X0 | fTrue = sK3(bool,X0)) ) | (~spl32_12 | ~spl32_68)),
% 11.66/2.04 inference(superposition,[],[f901,f600])).
% 11.66/2.04 tff(f3109,plain,(
% 11.66/2.04 spl32_243 | ~spl32_86 | ~spl32_107),
% 11.66/2.04 inference(avatar_split_clause,[],[f1403,f1321,f1024,f3107])).
% 11.66/2.04 tff(f3107,plain,(
% 11.66/2.04 spl32_243 <=> ! [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)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_243])])).
% 11.66/2.04 tff(f1403,plain,(
% 11.66/2.04 ( ! [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)) ) | (~spl32_86 | ~spl32_107)),
% 11.66/2.04 inference(superposition,[],[f1025,f1322])).
% 11.66/2.04 tff(f3105,plain,(
% 11.66/2.04 spl32_242 | ~spl32_59 | ~spl32_69),
% 11.66/2.04 inference(avatar_split_clause,[],[f927,f904,f845,f3103])).
% 11.66/2.04 tff(f3103,plain,(
% 11.66/2.04 spl32_242 <=> ! [X0 : $tType,X3 : list(X0),X2 : X0,X1 : list(X0)] : (cons(X0,X2,X3) != X1 | sK7(X0,X1) = X3 | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_242])])).
% 11.66/2.04 tff(f845,plain,(
% 11.66/2.04 spl32_59 <=> ! [X0 : $tType,X2 : X0,X4 : X0,X3 : list(X0),X1 : list(X0)] : (X1 = X3 | cons(X0,X2,X1) != cons(X0,X4,X3))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_59])])).
% 11.66/2.04 tff(f927,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0)] : (cons(X0,X2,X3) != X1 | sK7(X0,X1) = X3 | nil(X0) = X1) ) | (~spl32_59 | ~spl32_69)),
% 11.66/2.04 inference(superposition,[],[f846,f905])).
% 11.66/2.04 tff(f846,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (cons(X0,X2,X1) != cons(X0,X4,X3) | X1 = X3) ) | ~spl32_59),
% 11.66/2.04 inference(avatar_component_clause,[],[f845])).
% 11.66/2.04 tff(f3101,plain,(
% 11.66/2.04 spl32_241 | ~spl32_59 | ~spl32_68),
% 11.66/2.04 inference(avatar_split_clause,[],[f920,f900,f845,f3099])).
% 11.66/2.04 tff(f3099,plain,(
% 11.66/2.04 spl32_241 <=> ! [X0 : $tType,X3 : list(X0),X2 : X0,X1 : list(X0)] : (cons(X0,X2,X3) != X1 | sK4(X0,X1) = X3 | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_241])])).
% 11.66/2.04 tff(f920,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0)] : (cons(X0,X2,X3) != X1 | sK4(X0,X1) = X3 | nil(X0) = X1) ) | (~spl32_59 | ~spl32_68)),
% 11.66/2.04 inference(superposition,[],[f846,f901])).
% 11.66/2.04 tff(f3081,plain,(
% 11.66/2.04 spl32_240 | ~spl32_58 | ~spl32_108),
% 11.66/2.04 inference(avatar_split_clause,[],[f1431,f1325,f841,f3079])).
% 11.66/2.04 tff(f3079,plain,(
% 11.66/2.04 spl32_240 <=> ! [X0 : dB,X3 : nat,X2 : list(dB),X1 : dB] : (var(X3) != foldl(dB,dB,app,X0,cons(dB,X1,X2)) | nil(dB) = X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_240])])).
% 11.66/2.04 tff(f841,plain,(
% 11.66/2.04 spl32_58 <=> ! [X2 : nat,X0 : list(dB),X1 : dB] : (nil(dB) = X0 | var(X2) != foldl(dB,dB,app,X1,X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_58])])).
% 11.66/2.04 tff(f1431,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X3 : nat,X0 : dB,X1 : dB] : (var(X3) != foldl(dB,dB,app,X0,cons(dB,X1,X2)) | nil(dB) = X2) ) | (~spl32_58 | ~spl32_108)),
% 11.66/2.04 inference(superposition,[],[f842,f1326])).
% 11.66/2.04 tff(f842,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : list(dB),X1 : dB] : (var(X2) != foldl(dB,dB,app,X1,X0) | nil(dB) = X0) ) | ~spl32_58),
% 11.66/2.04 inference(avatar_component_clause,[],[f841])).
% 11.66/2.04 tff(f3077,plain,(
% 11.66/2.04 spl32_239 | ~spl32_40 | ~spl32_108 | ~spl32_227),
% 11.66/2.04 inference(avatar_split_clause,[],[f3051,f2978,f1325,f747,f3075])).
% 11.66/2.04 tff(f2978,plain,(
% 11.66/2.04 spl32_227 <=> ! [X2 : $tType,X4 : $tType,X5 : fun(bool,fun(X4,bool)),X0 : bool,X3 : fun(bool,fun(X2,bool)),X1 : bool] : (X0 = X1 | fTrue = foldl(bool,X2,X3,X1,nil(X2)) | fTrue = foldl(bool,X4,X5,X0,nil(X4)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_227])])).
% 11.66/2.04 tff(f3051,plain,(
% 11.66/2.04 ( ! [X5 : $tType,X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X6 : fun(bool,fun(X5,bool)),X4 : bool] : (fTrue = foldl(bool,X0,X1,X2,insert(X0,X3,nil(X0))) | aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) = X4 | fTrue = foldl(bool,X5,X6,X4,nil(X5))) ) | (~spl32_40 | ~spl32_108 | ~spl32_227)),
% 11.66/2.04 inference(forward_demodulation,[],[f3026,f748])).
% 11.66/2.04 tff(f3026,plain,(
% 11.66/2.04 ( ! [X5 : $tType,X0 : $tType,X2 : bool,X3 : X0,X1 : fun(bool,fun(X0,bool)),X6 : fun(bool,fun(X5,bool)),X4 : bool] : (fTrue = foldl(bool,X0,X1,X2,cons(X0,X3,nil(X0))) | aa(X0,bool,aa(bool,fun(X0,bool),X1,X2),X3) = X4 | fTrue = foldl(bool,X5,X6,X4,nil(X5))) ) | (~spl32_108 | ~spl32_227)),
% 11.66/2.04 inference(superposition,[],[f2979,f1326])).
% 11.66/2.04 tff(f2979,plain,(
% 11.66/2.04 ( ! [X4 : $tType,X2 : $tType,X3 : fun(bool,fun(X2,bool)),X0 : bool,X1 : bool,X5 : fun(bool,fun(X4,bool))] : (X0 = X1 | fTrue = foldl(bool,X2,X3,X1,nil(X2)) | fTrue = foldl(bool,X4,X5,X0,nil(X4))) ) | ~spl32_227),
% 11.66/2.04 inference(avatar_component_clause,[],[f2978])).
% 11.66/2.04 tff(f3073,plain,(
% 11.66/2.04 spl32_238 | ~spl32_57 | ~spl32_108),
% 11.66/2.04 inference(avatar_split_clause,[],[f1430,f1325,f837,f3071])).
% 11.66/2.04 tff(f3071,plain,(
% 11.66/2.04 spl32_238 <=> ! [X0 : dB,X3 : dB,X2 : list(dB),X1 : dB] : (abs(X3) != foldl(dB,dB,app,X0,cons(dB,X1,X2)) | nil(dB) = X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_238])])).
% 11.66/2.04 tff(f837,plain,(
% 11.66/2.04 spl32_57 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : (nil(dB) = X0 | abs(X2) != foldl(dB,dB,app,X1,X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_57])])).
% 11.66/2.04 tff(f1430,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X3 : dB,X0 : dB,X1 : dB] : (abs(X3) != foldl(dB,dB,app,X0,cons(dB,X1,X2)) | nil(dB) = X2) ) | (~spl32_57 | ~spl32_108)),
% 11.66/2.04 inference(superposition,[],[f838,f1326])).
% 11.66/2.04 tff(f838,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (abs(X2) != foldl(dB,dB,app,X1,X0) | nil(dB) = X0) ) | ~spl32_57),
% 11.66/2.04 inference(avatar_component_clause,[],[f837])).
% 11.66/2.04 tff(f3069,plain,(
% 11.66/2.04 spl32_237 | ~spl32_47 | ~spl32_69),
% 11.66/2.04 inference(avatar_split_clause,[],[f929,f904,f781,f3067])).
% 11.66/2.04 tff(f3067,plain,(
% 11.66/2.04 spl32_237 <=> ! [X0 : $tType,X3 : list(X0),X2 : X0,X1 : list(X0)] : (cons(X0,X2,X3) != X1 | sK6(X0,X1) = X2 | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_237])])).
% 11.66/2.04 tff(f781,plain,(
% 11.66/2.04 spl32_47 <=> ! [X0 : $tType,X4 : X0,X3 : list(X0),X2 : X0,X1 : list(X0)] : (X2 = X4 | cons(X0,X2,X1) != cons(X0,X4,X3))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_47])])).
% 11.66/2.04 tff(f929,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0)] : (cons(X0,X2,X3) != X1 | sK6(X0,X1) = X2 | nil(X0) = X1) ) | (~spl32_47 | ~spl32_69)),
% 11.66/2.04 inference(superposition,[],[f782,f905])).
% 11.66/2.04 tff(f782,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (cons(X0,X2,X1) != cons(X0,X4,X3) | X2 = X4) ) | ~spl32_47),
% 11.66/2.04 inference(avatar_component_clause,[],[f781])).
% 11.66/2.04 tff(f3065,plain,(
% 11.66/2.04 spl32_236 | ~spl32_47 | ~spl32_68),
% 11.66/2.04 inference(avatar_split_clause,[],[f922,f900,f781,f3063])).
% 11.66/2.04 tff(f3063,plain,(
% 11.66/2.04 spl32_236 <=> ! [X0 : $tType,X3 : list(X0),X2 : X0,X1 : list(X0)] : (cons(X0,X2,X3) != X1 | sK3(X0,X1) = X2 | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_236])])).
% 11.66/2.04 tff(f922,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0)] : (cons(X0,X2,X3) != X1 | sK3(X0,X1) = X2 | nil(X0) = X1) ) | (~spl32_47 | ~spl32_68)),
% 11.66/2.04 inference(superposition,[],[f782,f901])).
% 11.66/2.04 tff(f3024,plain,(
% 11.66/2.04 spl32_235 | ~spl32_54 | ~spl32_146),
% 11.66/2.04 inference(avatar_split_clause,[],[f1929,f1918,f825,f3022])).
% 11.66/2.04 tff(f3022,plain,(
% 11.66/2.04 spl32_235 <=> ! [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)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_235])])).
% 11.66/2.04 tff(f825,plain,(
% 11.66/2.04 spl32_54 <=> ! [X2 : dB,X0 : nat,X1 : dB] : var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_54])])).
% 11.66/2.04 tff(f1929,plain,(
% 11.66/2.04 ( ! [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)) ) | (~spl32_54 | ~spl32_146)),
% 11.66/2.04 inference(superposition,[],[f826,f1919])).
% 11.66/2.04 tff(f826,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : nat,X1 : dB] : (var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) ) | ~spl32_54),
% 11.66/2.04 inference(avatar_component_clause,[],[f825])).
% 11.66/2.04 tff(f3020,plain,(
% 11.66/2.04 spl32_234 | ~spl32_55 | ~spl32_146),
% 11.66/2.04 inference(avatar_split_clause,[],[f1928,f1918,f829,f3018])).
% 11.66/2.04 tff(f3018,plain,(
% 11.66/2.04 spl32_234 <=> ! [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)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_234])])).
% 11.66/2.04 tff(f829,plain,(
% 11.66/2.04 spl32_55 <=> ! [X2 : dB,X0 : dB,X1 : dB] : abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_55])])).
% 11.66/2.04 tff(f1928,plain,(
% 11.66/2.04 ( ! [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)) ) | (~spl32_55 | ~spl32_146)),
% 11.66/2.04 inference(superposition,[],[f830,f1919])).
% 11.66/2.04 tff(f830,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) ) | ~spl32_55),
% 11.66/2.04 inference(avatar_component_clause,[],[f829])).
% 11.66/2.04 tff(f3016,plain,(
% 11.66/2.04 spl32_233 | ~spl32_54 | ~spl32_144),
% 11.66/2.04 inference(avatar_split_clause,[],[f1905,f1894,f825,f3014])).
% 11.66/2.04 tff(f3014,plain,(
% 11.66/2.04 spl32_233 <=> ! [X4 : nat,X0 : nat,X3 : dB,X2 : nat,X1 : dB] : var(X4) != liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_233])])).
% 11.66/2.04 tff(f1905,plain,(
% 11.66/2.04 ( ! [X2 : nat,X3 : dB,X0 : nat,X1 : dB,X4 : nat] : (var(X4) != liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2)) ) | (~spl32_54 | ~spl32_144)),
% 11.66/2.04 inference(superposition,[],[f826,f1895])).
% 11.66/2.04 tff(f3012,plain,(
% 11.66/2.04 spl32_232 | ~spl32_55 | ~spl32_144),
% 11.66/2.04 inference(avatar_split_clause,[],[f1904,f1894,f829,f3010])).
% 11.66/2.04 tff(f3010,plain,(
% 11.66/2.04 spl32_232 <=> ! [X4 : dB,X0 : nat,X3 : dB,X2 : nat,X1 : dB] : abs(X4) != liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_232])])).
% 11.66/2.04 tff(f1904,plain,(
% 11.66/2.04 ( ! [X2 : nat,X3 : dB,X0 : nat,X1 : dB,X4 : dB] : (abs(X4) != liftn(X0,aa(dB,dB,combc(dB,dB,dB,app,X3),X1),X2)) ) | (~spl32_55 | ~spl32_144)),
% 11.66/2.04 inference(superposition,[],[f830,f1895])).
% 11.66/2.04 tff(f3008,plain,(
% 11.66/2.04 spl32_231 | ~spl32_33 | ~spl32_82),
% 11.66/2.04 inference(avatar_split_clause,[],[f1003,f1000,f704,f3006])).
% 11.66/2.04 tff(f3006,plain,(
% 11.66/2.04 spl32_231 <=> ! [X0 : dB,X1 : dB] : (abs(sK5(X0,X1)) = X0 | ~member(dB,abs(X1),combc(dB,dB,bool,beta,X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_231])])).
% 11.66/2.04 tff(f1003,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (abs(sK5(X0,X1)) = X0 | ~member(dB,abs(X1),combc(dB,dB,bool,beta,X0))) ) | (~spl32_33 | ~spl32_82)),
% 11.66/2.04 inference(resolution,[],[f1001,f705])).
% 11.66/2.04 tff(f3004,plain,(
% 11.66/2.04 spl32_230 | ~spl32_33 | ~spl32_80),
% 11.66/2.04 inference(avatar_split_clause,[],[f992,f969,f704,f3002])).
% 11.66/2.04 tff(f3002,plain,(
% 11.66/2.04 spl32_230 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : fun(X0,fun(X0,bool)),X1 : list(X0)] : (sP2(X0,X1,X1,X2,X3,X4) | ~member(X0,X3,combc(X0,X0,bool,X2,X4)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_230])])).
% 11.66/2.04 tff(f992,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X3 : X0,X1 : list(X0),X4 : X0] : (sP2(X0,X1,X1,X2,X3,X4) | ~member(X0,X3,combc(X0,X0,bool,X2,X4))) ) | (~spl32_33 | ~spl32_80)),
% 11.66/2.04 inference(resolution,[],[f970,f705])).
% 11.66/2.04 tff(f3000,plain,(
% 11.66/2.04 spl32_229 | ~spl32_40 | ~spl32_59),
% 11.66/2.04 inference(avatar_split_clause,[],[f854,f845,f747,f2998])).
% 11.66/2.04 tff(f2998,plain,(
% 11.66/2.04 spl32_229 <=> ! [X0 : $tType,X3 : list(X0),X2 : X0,X1 : X0] : (insert(X0,X1,nil(X0)) != cons(X0,X2,X3) | nil(X0) = X3)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_229])])).
% 11.66/2.04 tff(f854,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : X0] : (insert(X0,X1,nil(X0)) != cons(X0,X2,X3) | nil(X0) = X3) ) | (~spl32_40 | ~spl32_59)),
% 11.66/2.04 inference(superposition,[],[f846,f748])).
% 11.66/2.04 tff(f2985,plain,(
% 11.66/2.04 spl32_228 | spl32_1 | ~spl32_26 | ~spl32_193),
% 11.66/2.04 inference(avatar_split_clause,[],[f2691,f2674,f668,f548,f2983])).
% 11.66/2.04 tff(f2983,plain,(
% 11.66/2.04 spl32_228 <=> ! [X2 : list(dB),X0 : fun(nat,type),X1 : dB] : ~pp(aa(list(type),bool,typings(X0,cons(dB,X1,X2)),nil(type)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_228])])).
% 11.66/2.04 tff(f548,plain,(
% 11.66/2.04 spl32_1 <=> pp(fFalse)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_1])])).
% 11.66/2.04 tff(f668,plain,(
% 11.66/2.04 spl32_26 <=> ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : list_case(X1,X0,X3,X2,nil(X0)) = X3),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_26])])).
% 11.66/2.04 tff(f2674,plain,(
% 11.66/2.04 spl32_193 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_193])])).
% 11.66/2.04 tff(f2691,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X0 : fun(nat,type),X1 : dB] : (pp(fFalse) | ~pp(aa(list(type),bool,typings(X0,cons(dB,X1,X2)),nil(type)))) ) | (~spl32_26 | ~spl32_193)),
% 11.66/2.04 inference(superposition,[],[f2675,f669])).
% 11.66/2.04 tff(f669,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : (list_case(X1,X0,X3,X2,nil(X0)) = X3) ) | ~spl32_26),
% 11.66/2.04 inference(avatar_component_clause,[],[f668])).
% 11.66/2.04 tff(f2675,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_193),
% 11.66/2.04 inference(avatar_component_clause,[],[f2674])).
% 11.66/2.04 tff(f2980,plain,(
% 11.66/2.04 spl32_227 | ~spl32_180),
% 11.66/2.04 inference(avatar_split_clause,[],[f2735,f2346,f2978])).
% 11.66/2.04 tff(f2346,plain,(
% 11.66/2.04 spl32_180 <=> ! [X0 : $tType,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X2 | fTrue = foldl(bool,X0,X1,X2,nil(X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_180])])).
% 11.66/2.04 tff(f2735,plain,(
% 11.66/2.04 ( ! [X4 : $tType,X2 : $tType,X3 : fun(bool,fun(X2,bool)),X0 : bool,X1 : bool,X5 : fun(bool,fun(X4,bool))] : (X0 = X1 | fTrue = foldl(bool,X2,X3,X1,nil(X2)) | fTrue = foldl(bool,X4,X5,X0,nil(X4))) ) | ~spl32_180),
% 11.66/2.04 inference(superposition,[],[f2347,f2347])).
% 11.66/2.04 tff(f2347,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X2 | fTrue = foldl(bool,X0,X1,X2,nil(X0))) ) | ~spl32_180),
% 11.66/2.04 inference(avatar_component_clause,[],[f2346])).
% 11.66/2.04 tff(f2963,plain,(
% 11.66/2.04 spl32_226 | ~spl32_33 | ~spl32_70),
% 11.66/2.04 inference(avatar_split_clause,[],[f934,f908,f704,f2961])).
% 11.66/2.04 tff(f2961,plain,(
% 11.66/2.04 spl32_226 <=> ! [X2 : type,X0 : fun(nat,type),X1 : nat] : (aa(nat,type,X0,X1) = X2 | ~member(type,X2,typing(X0,var(X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_226])])).
% 11.66/2.04 tff(f934,plain,(
% 11.66/2.04 ( ! [X2 : type,X0 : fun(nat,type),X1 : nat] : (aa(nat,type,X0,X1) = X2 | ~member(type,X2,typing(X0,var(X1)))) ) | (~spl32_33 | ~spl32_70)),
% 11.66/2.04 inference(resolution,[],[f909,f705])).
% 11.66/2.04 tff(f2959,plain,(
% 11.66/2.04 spl32_225 | ~spl32_40 | ~spl32_47),
% 11.66/2.04 inference(avatar_split_clause,[],[f795,f781,f747,f2957])).
% 11.66/2.04 tff(f2957,plain,(
% 11.66/2.04 spl32_225 <=> ! [X0 : $tType,X3 : list(X0),X2 : X0,X1 : X0] : (insert(X0,X1,nil(X0)) != cons(X0,X2,X3) | X1 = X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_225])])).
% 11.66/2.04 tff(f795,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : X0] : (insert(X0,X1,nil(X0)) != cons(X0,X2,X3) | X1 = X2) ) | (~spl32_40 | ~spl32_47)),
% 11.66/2.04 inference(superposition,[],[f782,f748])).
% 11.66/2.04 tff(f2955,plain,(
% 11.66/2.04 spl32_224 | ~spl32_12 | ~spl32_39),
% 11.66/2.04 inference(avatar_split_clause,[],[f743,f737,f599,f2953])).
% 11.66/2.04 tff(f2953,plain,(
% 11.66/2.04 spl32_224 <=> ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (fFalse = X2 | fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_224])])).
% 11.66/2.04 tff(f743,plain,(
% 11.66/2.04 ( ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (fFalse = X2 | fTrue = aa(nat,bool,shift(bool,X0,X1,X2),X1)) ) | (~spl32_12 | ~spl32_39)),
% 11.66/2.04 inference(superposition,[],[f738,f600])).
% 11.66/2.04 tff(f2922,plain,(
% 11.66/2.04 spl32_223 | ~spl32_6 | ~spl32_35 | ~spl32_140),
% 11.66/2.04 inference(avatar_split_clause,[],[f1850,f1847,f719,f573,f2919])).
% 11.66/2.04 tff(f2919,plain,(
% 11.66/2.04 spl32_223 <=> it(foldl(dB,dB,app,abs(r),cons(dB,a,as)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_223])])).
% 11.66/2.04 tff(f573,plain,(
% 11.66/2.04 spl32_6 <=> it(a)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_6])])).
% 11.66/2.04 tff(f719,plain,(
% 11.66/2.04 spl32_35 <=> it(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_35])])).
% 11.66/2.04 tff(f1850,plain,(
% 11.66/2.04 ~it(a) | it(foldl(dB,dB,app,abs(r),cons(dB,a,as))) | (~spl32_35 | ~spl32_140)),
% 11.66/2.04 inference(resolution,[],[f1848,f721])).
% 11.66/2.04 tff(f721,plain,(
% 11.66/2.04 it(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)) | ~spl32_35),
% 11.66/2.04 inference(avatar_component_clause,[],[f719])).
% 11.66/2.04 tff(f2917,plain,(
% 11.66/2.04 spl32_222 | ~spl32_44 | ~spl32_112),
% 11.66/2.04 inference(avatar_split_clause,[],[f1475,f1471,f767,f2915])).
% 11.66/2.04 tff(f2915,plain,(
% 11.66/2.04 spl32_222 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(var(X1))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_222])])).
% 11.66/2.04 tff(f767,plain,(
% 11.66/2.04 spl32_44 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_44])])).
% 11.66/2.04 tff(f1475,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(var(X1))))) ) | (~spl32_44 | ~spl32_112)),
% 11.66/2.04 inference(resolution,[],[f1472,f768])).
% 11.66/2.04 tff(f768,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))) ) | ~spl32_44),
% 11.66/2.04 inference(avatar_component_clause,[],[f767])).
% 11.66/2.04 tff(f2913,plain,(
% 11.66/2.04 spl32_221 | ~spl32_54 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1056,f1039,f825,f2911])).
% 11.66/2.04 tff(f2911,plain,(
% 11.66/2.04 spl32_221 <=> ! [X2 : nat,X0 : dB,X1 : dB] : var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_221])])).
% 11.66/2.04 tff(f1056,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : dB,X1 : dB] : (var(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)) ) | (~spl32_54 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f826,f1040])).
% 11.66/2.04 tff(f2909,plain,(
% 11.66/2.04 spl32_220 | ~spl32_55 | ~spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f1055,f1039,f829,f2907])).
% 11.66/2.04 tff(f2907,plain,(
% 11.66/2.04 spl32_220 <=> ! [X2 : dB,X0 : dB,X1 : dB] : abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_220])])).
% 11.66/2.04 tff(f1055,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X2) != aa(dB,dB,combc(dB,dB,dB,app,X1),X0)) ) | (~spl32_55 | ~spl32_89)),
% 11.66/2.04 inference(superposition,[],[f830,f1040])).
% 11.66/2.04 tff(f2905,plain,(
% 11.66/2.04 spl32_219 | ~spl32_28 | ~spl32_76),
% 11.66/2.04 inference(avatar_split_clause,[],[f975,f953,f676,f2903])).
% 11.66/2.04 tff(f2903,plain,(
% 11.66/2.04 spl32_219 <=> ! [X2 : list(dB),X0 : dB,X1 : dB] : (abs(X0) != foldl(dB,dB,app,abs(X1),X2) | X0 = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_219])])).
% 11.66/2.04 tff(f953,plain,(
% 11.66/2.04 spl32_76 <=> ! [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))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_76])])).
% 11.66/2.04 tff(f975,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X0 : dB,X1 : dB] : (abs(X0) != foldl(dB,dB,app,abs(X1),X2) | X0 = X1) ) | (~spl32_28 | ~spl32_76)),
% 11.66/2.04 inference(superposition,[],[f954,f677])).
% 11.66/2.04 tff(f954,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X3 : dB,X0 : list(dB),X1 : dB] : (foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) | X1 = X3) ) | ~spl32_76),
% 11.66/2.04 inference(avatar_component_clause,[],[f953])).
% 11.66/2.04 tff(f2901,plain,(
% 11.66/2.04 spl32_218 | ~spl32_28 | ~spl32_75),
% 11.66/2.04 inference(avatar_split_clause,[],[f972,f949,f676,f2899])).
% 11.66/2.04 tff(f2899,plain,(
% 11.66/2.04 spl32_218 <=> ! [X2 : list(dB),X0 : nat,X1 : nat] : (var(X0) != foldl(dB,dB,app,var(X1),X2) | X0 = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_218])])).
% 11.66/2.04 tff(f949,plain,(
% 11.66/2.04 spl32_75 <=> ! [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))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_75])])).
% 11.66/2.04 tff(f972,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X0 : nat,X1 : nat] : (var(X0) != foldl(dB,dB,app,var(X1),X2) | X0 = X1) ) | (~spl32_28 | ~spl32_75)),
% 11.66/2.04 inference(superposition,[],[f950,f677])).
% 11.66/2.04 tff(f950,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : nat] : (foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,var(X1),X0) | X1 = X3) ) | ~spl32_75),
% 11.66/2.04 inference(avatar_component_clause,[],[f949])).
% 11.66/2.04 tff(f2897,plain,(
% 11.66/2.04 spl32_217 | ~spl32_79 | ~spl32_207),
% 11.66/2.04 inference(avatar_split_clause,[],[f2831,f2804,f965,f2895])).
% 11.66/2.04 tff(f2895,plain,(
% 11.66/2.04 spl32_217 <=> ! [X2 : $tType,X4 : bool,X0 : bool,X3 : fun(bool,fun(X2,bool)),X1 : bool] : (X0 != X1 | foldl(bool,X2,X3,X1,nil(X2)) = X0 | X0 = X4 | fTrue = X4)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_217])])).
% 11.66/2.04 tff(f965,plain,(
% 11.66/2.04 spl32_79 <=> ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_79])])).
% 11.66/2.04 tff(f2804,plain,(
% 11.66/2.04 spl32_207 <=> ! [X1 : $tType,X2 : fun(bool,fun(X1,bool)),X0 : bool] : (fTrue != X0 | fTrue = foldl(bool,X1,X2,X0,nil(X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_207])])).
% 11.66/2.04 tff(f2831,plain,(
% 11.66/2.04 ( ! [X2 : $tType,X3 : fun(bool,fun(X2,bool)),X0 : bool,X1 : bool,X4 : bool] : (X0 != X1 | foldl(bool,X2,X3,X1,nil(X2)) = X0 | X0 = X4 | fTrue = X4) ) | (~spl32_79 | ~spl32_207)),
% 11.66/2.04 inference(superposition,[],[f2805,f966])).
% 11.66/2.04 tff(f966,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl32_79),
% 11.66/2.04 inference(avatar_component_clause,[],[f965])).
% 11.66/2.04 tff(f2805,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X2 : fun(bool,fun(X1,bool)),X0 : bool] : (fTrue != X0 | fTrue = foldl(bool,X1,X2,X0,nil(X1))) ) | ~spl32_207),
% 11.66/2.04 inference(avatar_component_clause,[],[f2804])).
% 11.66/2.04 tff(f2893,plain,(
% 11.66/2.04 spl32_216 | ~spl32_34 | ~spl32_67),
% 11.66/2.04 inference(avatar_split_clause,[],[f896,f891,f708,f2891])).
% 11.66/2.04 tff(f2891,plain,(
% 11.66/2.04 spl32_216 <=> ! [X0 : bool,X1 : bool] : (~pp(X0) | ~pp(X1) | member(bool,X1,combc(bool,bool,bool,fconj,X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_216])])).
% 11.66/2.04 tff(f896,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (~pp(X0) | ~pp(X1) | member(bool,X1,combc(bool,bool,bool,fconj,X0))) ) | (~spl32_34 | ~spl32_67)),
% 11.66/2.04 inference(resolution,[],[f892,f709])).
% 11.66/2.04 tff(f2889,plain,(
% 11.66/2.04 spl32_215 | ~spl32_33 | ~spl32_63),
% 11.66/2.04 inference(avatar_split_clause,[],[f876,f868,f704,f2887])).
% 11.66/2.04 tff(f2887,plain,(
% 11.66/2.04 spl32_215 <=> ! [X0 : list(type),X1 : fun(nat,type)] : (nil(type) = X0 | ~member(list(type),X0,typings(X1,nil(dB))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_215])])).
% 11.66/2.04 tff(f868,plain,(
% 11.66/2.04 spl32_63 <=> ! [X0 : list(type),X1 : fun(nat,type)] : (nil(type) = X0 | ~pp(aa(list(type),bool,typings(X1,nil(dB)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_63])])).
% 11.66/2.04 tff(f876,plain,(
% 11.66/2.04 ( ! [X0 : list(type),X1 : fun(nat,type)] : (nil(type) = X0 | ~member(list(type),X0,typings(X1,nil(dB)))) ) | (~spl32_33 | ~spl32_63)),
% 11.66/2.04 inference(resolution,[],[f869,f705])).
% 11.66/2.04 tff(f869,plain,(
% 11.66/2.04 ( ! [X0 : list(type),X1 : fun(nat,type)] : (~pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) | nil(type) = X0) ) | ~spl32_63),
% 11.66/2.04 inference(avatar_component_clause,[],[f868])).
% 11.66/2.04 tff(f2885,plain,(
% 11.66/2.04 spl32_214 | ~spl32_39 | ~spl32_48),
% 11.66/2.04 inference(avatar_split_clause,[],[f800,f785,f737,f2883])).
% 11.66/2.04 tff(f2883,plain,(
% 11.66/2.04 spl32_214 <=> ! [X2 : type,X0 : fun(nat,type),X1 : nat] : pp(aa(type,bool,typing(shift(type,X0,X1,X2),var(X1)),X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_214])])).
% 11.66/2.04 tff(f800,plain,(
% 11.66/2.04 ( ! [X2 : type,X0 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(shift(type,X0,X1,X2),var(X1)),X2))) ) | (~spl32_39 | ~spl32_48)),
% 11.66/2.04 inference(superposition,[],[f786,f738])).
% 11.66/2.04 tff(f2839,plain,(
% 11.66/2.04 spl32_213 | ~spl32_54 | ~spl32_107),
% 11.66/2.04 inference(avatar_split_clause,[],[f1402,f1321,f825,f2837])).
% 11.66/2.04 tff(f2837,plain,(
% 11.66/2.04 spl32_213 <=> ! [X2 : dB,X0 : dB,X1 : list(dB),X3 : nat] : var(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_213])])).
% 11.66/2.04 tff(f1402,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : nat,X0 : dB,X1 : list(dB)] : (var(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)) ) | (~spl32_54 | ~spl32_107)),
% 11.66/2.04 inference(superposition,[],[f826,f1322])).
% 11.66/2.04 tff(f2830,plain,(
% 11.66/2.04 spl32_212 | ~spl32_55 | ~spl32_107),
% 11.66/2.04 inference(avatar_split_clause,[],[f1401,f1321,f829,f2828])).
% 11.66/2.04 tff(f2828,plain,(
% 11.66/2.04 spl32_212 <=> ! [X2 : dB,X0 : dB,X1 : list(dB),X3 : dB] : abs(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_212])])).
% 11.66/2.04 tff(f1401,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : dB,X0 : dB,X1 : list(dB)] : (abs(X3) != foldr(dB,dB,app,cons(dB,X0,X1),X2)) ) | (~spl32_55 | ~spl32_107)),
% 11.66/2.04 inference(superposition,[],[f830,f1322])).
% 11.66/2.04 tff(f2826,plain,(
% 11.66/2.04 spl32_211 | ~spl32_28 | ~spl32_71),
% 11.66/2.04 inference(avatar_split_clause,[],[f936,f912,f676,f2824])).
% 11.66/2.04 tff(f2824,plain,(
% 11.66/2.04 spl32_211 <=> ! [X0 : dB,X1 : dB] : (foldl(dB,dB,app,X1,nil(dB)) != X0 | X0 = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_211])])).
% 11.66/2.04 tff(f936,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (foldl(dB,dB,app,X1,nil(dB)) != X0 | X0 = X1) ) | (~spl32_28 | ~spl32_71)),
% 11.66/2.04 inference(superposition,[],[f913,f677])).
% 11.66/2.04 tff(f2822,plain,(
% 11.66/2.04 spl32_210 | ~spl32_12 | ~spl32_28),
% 11.66/2.04 inference(avatar_split_clause,[],[f681,f676,f599,f2820])).
% 11.66/2.04 tff(f2820,plain,(
% 11.66/2.04 spl32_210 <=> ! [X0 : $tType,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (fFalse = X2 | fTrue = foldl(bool,X0,X1,X2,nil(X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_210])])).
% 11.66/2.04 tff(f681,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (fFalse = X2 | fTrue = foldl(bool,X0,X1,X2,nil(X0))) ) | (~spl32_12 | ~spl32_28)),
% 11.66/2.04 inference(superposition,[],[f677,f600])).
% 11.66/2.04 tff(f2818,plain,(
% 11.66/2.04 spl32_209 | ~spl32_12 | ~spl32_27),
% 11.66/2.04 inference(avatar_split_clause,[],[f680,f672,f599,f2816])).
% 11.66/2.04 tff(f2816,plain,(
% 11.66/2.04 spl32_209 <=> ! [X0 : $tType,X2 : bool,X1 : fun(X0,fun(bool,bool))] : (fFalse = X2 | fTrue = foldr(X0,bool,X1,nil(X0),X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_209])])).
% 11.66/2.04 tff(f680,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X1 : fun(X0,fun(bool,bool))] : (fFalse = X2 | fTrue = foldr(X0,bool,X1,nil(X0),X2)) ) | (~spl32_12 | ~spl32_27)),
% 11.66/2.04 inference(superposition,[],[f673,f600])).
% 11.66/2.04 tff(f2814,plain,(
% 11.66/2.04 spl32_208 | ~spl32_12 | ~spl32_26),
% 11.66/2.04 inference(avatar_split_clause,[],[f679,f668,f599,f2812])).
% 11.66/2.04 tff(f2812,plain,(
% 11.66/2.04 spl32_208 <=> ! [X0 : $tType,X2 : fun(X0,fun(list(X0),bool)),X1 : bool] : (fFalse = X1 | fTrue = list_case(bool,X0,X1,X2,nil(X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_208])])).
% 11.66/2.04 tff(f679,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(list(X0),bool)),X1 : bool] : (fFalse = X1 | fTrue = list_case(bool,X0,X1,X2,nil(X0))) ) | (~spl32_12 | ~spl32_26)),
% 11.66/2.04 inference(superposition,[],[f669,f600])).
% 11.66/2.04 tff(f2806,plain,(
% 11.66/2.04 spl32_207 | spl32_128 | ~spl32_180),
% 11.66/2.04 inference(avatar_split_clause,[],[f2748,f2346,f1689,f2804])).
% 11.66/2.04 tff(f2748,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X2 : fun(bool,fun(X1,bool)),X0 : bool] : (fTrue != X0 | fTrue = foldl(bool,X1,X2,X0,nil(X1))) ) | (spl32_128 | ~spl32_180)),
% 11.66/2.04 inference(superposition,[],[f1691,f2347])).
% 11.66/2.04 tff(f2798,plain,(
% 11.66/2.04 spl32_206 | ~spl32_67 | ~spl32_80),
% 11.66/2.04 inference(avatar_split_clause,[],[f991,f969,f891,f2796])).
% 11.66/2.04 tff(f2796,plain,(
% 11.66/2.04 spl32_206 <=> ! [X2 : bool,X0 : list(bool),X1 : bool] : (sP2(bool,X0,X0,fconj,X1,X2) | ~pp(X2) | ~pp(X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_206])])).
% 11.66/2.04 tff(f991,plain,(
% 11.66/2.04 ( ! [X2 : bool,X0 : list(bool),X1 : bool] : (sP2(bool,X0,X0,fconj,X1,X2) | ~pp(X2) | ~pp(X1)) ) | (~spl32_67 | ~spl32_80)),
% 11.66/2.04 inference(resolution,[],[f970,f892])).
% 11.66/2.04 tff(f2794,plain,(
% 11.66/2.04 spl32_205 | ~spl32_17 | ~spl32_69),
% 11.66/2.04 inference(avatar_split_clause,[],[f932,f904,f622,f2792])).
% 11.66/2.04 tff(f2792,plain,(
% 11.66/2.04 spl32_205 <=> ! [X0 : $tType,X1 : list(X0)] : (sK7(X0,X1) != X1 | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_205])])).
% 11.66/2.04 tff(f622,plain,(
% 11.66/2.04 spl32_17 <=> ! [X0 : $tType,X2 : list(X0),X1 : X0] : cons(X0,X1,X2) != X2),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_17])])).
% 11.66/2.04 tff(f932,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X1 : list(X0)] : (sK7(X0,X1) != X1 | nil(X0) = X1) ) | (~spl32_17 | ~spl32_69)),
% 11.66/2.04 inference(superposition,[],[f623,f905])).
% 11.66/2.04 tff(f623,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : list(X0),X1 : X0] : (cons(X0,X1,X2) != X2) ) | ~spl32_17),
% 11.66/2.04 inference(avatar_component_clause,[],[f622])).
% 11.66/2.04 tff(f2790,plain,(
% 11.66/2.04 spl32_204 | ~spl32_17 | ~spl32_68),
% 11.66/2.04 inference(avatar_split_clause,[],[f925,f900,f622,f2788])).
% 11.66/2.04 tff(f2788,plain,(
% 11.66/2.04 spl32_204 <=> ! [X0 : $tType,X1 : list(X0)] : (sK4(X0,X1) != X1 | nil(X0) = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_204])])).
% 11.66/2.04 tff(f925,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X1 : list(X0)] : (sK4(X0,X1) != X1 | nil(X0) = X1) ) | (~spl32_17 | ~spl32_68)),
% 11.66/2.04 inference(superposition,[],[f623,f901])).
% 11.66/2.04 tff(f2786,plain,(
% 11.66/2.04 spl32_203 | ~spl32_33 | ~spl32_53),
% 11.66/2.04 inference(avatar_split_clause,[],[f822,f819,f704,f2784])).
% 11.66/2.04 tff(f2784,plain,(
% 11.66/2.04 spl32_203 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~member(bool,X0,combc(bool,bool,bool,fconj,X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_203])])).
% 11.66/2.04 tff(f822,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~member(bool,X0,combc(bool,bool,bool,fconj,X1))) ) | (~spl32_33 | ~spl32_53)),
% 11.66/2.04 inference(resolution,[],[f820,f705])).
% 11.66/2.04 tff(f2782,plain,(
% 11.66/2.04 spl32_202 | ~spl32_33 | ~spl32_51),
% 11.66/2.04 inference(avatar_split_clause,[],[f811,f808,f704,f2780])).
% 11.66/2.04 tff(f2780,plain,(
% 11.66/2.04 spl32_202 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~member(bool,X1,combc(bool,bool,bool,fconj,X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_202])])).
% 11.66/2.04 tff(f811,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~member(bool,X1,combc(bool,bool,bool,fconj,X0))) ) | (~spl32_33 | ~spl32_51)),
% 11.66/2.04 inference(resolution,[],[f809,f705])).
% 11.66/2.04 tff(f2778,plain,(
% 11.66/2.04 spl32_201 | ~spl32_34 | ~spl32_48),
% 11.66/2.04 inference(avatar_split_clause,[],[f798,f785,f708,f2776])).
% 11.66/2.04 tff(f2776,plain,(
% 11.66/2.04 spl32_201 <=> ! [X0 : fun(nat,type),X1 : nat] : member(type,aa(nat,type,X0,X1),typing(X0,var(X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_201])])).
% 11.66/2.04 tff(f798,plain,(
% 11.66/2.04 ( ! [X0 : fun(nat,type),X1 : nat] : (member(type,aa(nat,type,X0,X1),typing(X0,var(X1)))) ) | (~spl32_34 | ~spl32_48)),
% 11.66/2.04 inference(resolution,[],[f786,f709])).
% 11.66/2.04 tff(f2731,plain,(
% 11.66/2.04 spl32_200 | ~spl32_28 | ~spl32_64),
% 11.66/2.04 inference(avatar_split_clause,[],[f879,f872,f676,f2729])).
% 11.66/2.04 tff(f2729,plain,(
% 11.66/2.04 spl32_200 <=> ! [X2 : list(dB),X0 : dB,X1 : nat] : abs(X0) != foldl(dB,dB,app,var(X1),X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_200])])).
% 11.66/2.04 tff(f872,plain,(
% 11.66/2.04 spl32_64 <=> ! [X2 : list(dB),X0 : list(dB),X1 : dB,X3 : nat] : foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_64])])).
% 11.66/2.04 tff(f879,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X0 : dB,X1 : nat] : (abs(X0) != foldl(dB,dB,app,var(X1),X2)) ) | (~spl32_28 | ~spl32_64)),
% 11.66/2.04 inference(superposition,[],[f873,f677])).
% 11.66/2.04 tff(f873,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : dB] : (foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)) ) | ~spl32_64),
% 11.66/2.04 inference(avatar_component_clause,[],[f872])).
% 11.66/2.04 tff(f2727,plain,(
% 11.66/2.04 spl32_199 | ~spl32_28 | ~spl32_64),
% 11.66/2.04 inference(avatar_split_clause,[],[f878,f872,f676,f2725])).
% 11.66/2.04 tff(f2725,plain,(
% 11.66/2.04 spl32_199 <=> ! [X2 : list(dB),X0 : nat,X1 : dB] : var(X0) != foldl(dB,dB,app,abs(X1),X2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_199])])).
% 11.66/2.04 tff(f878,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X0 : nat,X1 : dB] : (var(X0) != foldl(dB,dB,app,abs(X1),X2)) ) | (~spl32_28 | ~spl32_64)),
% 11.66/2.04 inference(superposition,[],[f873,f677])).
% 11.66/2.04 tff(f2723,plain,(
% 11.66/2.04 spl32_198 | ~spl32_33 | ~spl32_44),
% 11.66/2.04 inference(avatar_split_clause,[],[f770,f767,f704,f2721])).
% 11.66/2.04 tff(f2721,plain,(
% 11.66/2.04 spl32_198 <=> ! [X0 : nat,X1 : dB] : ~member(dB,var(X0),combc(dB,dB,bool,beta,X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_198])])).
% 11.66/2.04 tff(f770,plain,(
% 11.66/2.04 ( ! [X0 : nat,X1 : dB] : (~member(dB,var(X0),combc(dB,dB,bool,beta,X1))) ) | (~spl32_33 | ~spl32_44)),
% 11.66/2.04 inference(resolution,[],[f768,f705])).
% 11.66/2.04 tff(f2719,plain,(
% 11.66/2.04 spl32_197 | ~spl32_33 | ~spl32_39),
% 11.66/2.04 inference(avatar_split_clause,[],[f745,f737,f704,f2717])).
% 11.66/2.04 tff(f2717,plain,(
% 11.66/2.04 spl32_197 <=> ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (pp(X2) | ~member(nat,X1,shift(bool,X0,X1,X2)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_197])])).
% 11.66/2.04 tff(f745,plain,(
% 11.66/2.04 ( ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (pp(X2) | ~member(nat,X1,shift(bool,X0,X1,X2))) ) | (~spl32_33 | ~spl32_39)),
% 11.66/2.04 inference(superposition,[],[f705,f738])).
% 11.66/2.04 tff(f2715,plain,(
% 11.66/2.04 spl32_196 | ~spl32_34 | ~spl32_39),
% 11.66/2.04 inference(avatar_split_clause,[],[f744,f737,f708,f2713])).
% 11.66/2.04 tff(f2713,plain,(
% 11.66/2.04 spl32_196 <=> ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (~pp(X2) | member(nat,X1,shift(bool,X0,X1,X2)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_196])])).
% 11.66/2.04 tff(f744,plain,(
% 11.66/2.04 ( ! [X2 : bool,X0 : fun(nat,bool),X1 : nat] : (~pp(X2) | member(nat,X1,shift(bool,X0,X1,X2))) ) | (~spl32_34 | ~spl32_39)),
% 11.66/2.04 inference(superposition,[],[f709,f738])).
% 11.66/2.04 tff(f2684,plain,(
% 11.66/2.04 spl32_195),
% 11.66/2.04 inference(avatar_split_clause,[],[f465,f2682])).
% 11.66/2.04 tff(f2682,plain,(
% 11.66/2.04 spl32_195 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_195])])).
% 11.66/2.04 tff(f465,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f322])).
% 11.66/2.04 tff(f322,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(nnf_transformation,[],[f186])).
% 11.66/2.04 tff(f186,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(rectify,[],[f69])).
% 11.66/2.04 tff(f69,axiom,(
% 11.66/2.04 ! [X75 : list(type),X12 : list(dB),X31 : dB,X30 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X30,cons(dB,X31,X12)),X75)) <=> 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(X30,X31))),typings(X30,X12)),X75)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_typings_Osimps_I2_J)).
% 11.66/2.04 tff(f2680,plain,(
% 11.66/2.04 spl32_194 | ~spl32_26 | ~spl32_114),
% 11.66/2.04 inference(avatar_split_clause,[],[f1587,f1491,f668,f2678])).
% 11.66/2.04 tff(f2678,plain,(
% 11.66/2.04 spl32_194 <=> ! [X0 : $tType,X2 : fun(X0,fun(list(X0),bool)),X1 : bool] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X1 | fTrue = list_case(bool,X0,X1,X2,nil(X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_194])])).
% 11.66/2.04 tff(f1491,plain,(
% 11.66/2.04 spl32_114 <=> ! [X0 : bool] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X0 | fTrue = X0)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_114])])).
% 11.66/2.04 tff(f1587,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(list(X0),bool)),X1 : bool] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X1 | fTrue = list_case(bool,X0,X1,X2,nil(X0))) ) | (~spl32_26 | ~spl32_114)),
% 11.66/2.04 inference(superposition,[],[f669,f1492])).
% 11.66/2.04 tff(f1492,plain,(
% 11.66/2.04 ( ! [X0 : bool] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X0 | fTrue = X0) ) | ~spl32_114),
% 11.66/2.04 inference(avatar_component_clause,[],[f1491])).
% 11.66/2.04 tff(f2676,plain,(
% 11.66/2.04 spl32_193),
% 11.66/2.04 inference(avatar_split_clause,[],[f464,f2674])).
% 11.66/2.04 tff(f464,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f322])).
% 11.66/2.04 tff(f2506,plain,(
% 11.66/2.04 spl32_192),
% 11.66/2.04 inference(avatar_split_clause,[],[f541,f2504])).
% 11.66/2.04 tff(f2504,plain,(
% 11.66/2.04 spl32_192 <=> ! [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,sK30(X0,X1,X5)),sK28(X0,X1,X5))),sK29(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK30(X0,X1,X5)),sK29(X0,X1,X5))),sK28(X0,X1,X5)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_192])])).
% 11.66/2.04 tff(f541,plain,(
% 11.66/2.04 ( ! [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,sK30(X0,X1,X5)),sK28(X0,X1,X5))),sK29(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK30(X0,X1,X5)),sK29(X0,X1,X5))),sK28(X0,X1,X5))) )),
% 11.66/2.04 inference(forward_demodulation,[],[f495,f493])).
% 11.66/2.04 tff(f493,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f201])).
% 11.66/2.04 tff(f201,plain,(
% 11.66/2.04 ! [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)),
% 11.66/2.04 inference(rectify,[],[f58])).
% 11.66/2.04 tff(f58,axiom,(
% 11.66/2.04 ! [X0 : $tType,X1 : $tType,X48 : list(X1),X21 : X1,X49 : X0,X50 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X50,X49,cons(X1,X21,X48)) = foldl(X0,X1,X50,aa(X1,X0,aa(X0,fun(X1,X0),X50,X49),X21),X48)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_foldl__Cons)).
% 11.66/2.04 tff(f495,plain,(
% 11.66/2.04 ( ! [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,sK30(X0,X1,X5)),sK28(X0,X1,X5))),sK29(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK30(X0,X1,X5)),sK29(X0,X1,X5))),sK28(X0,X1,X5))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f338])).
% 11.66/2.04 tff(f338,plain,(
% 11.66/2.04 ! [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,sK30(X0,X1,X5)),sK28(X0,X1,X5))),sK29(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK30(X0,X1,X5)),sK29(X0,X1,X5))),sK28(X0,X1,X5)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30])],[f254,f337])).
% 11.66/2.04 tff(f337,plain,(
% 11.66/2.04 ! [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,sK30(X0,X1,X5)),sK28(X0,X1,X5))),sK29(X0,X1,X5)) != aa(X1,X0,aa(X0,fun(X1,X0),X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,sK30(X0,X1,X5)),sK29(X0,X1,X5))),sK28(X0,X1,X5)))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f254,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(ennf_transformation,[],[f203])).
% 11.66/2.04 tff(f203,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f53])).
% 11.66/2.04 tff(f53,axiom,(
% 11.66/2.04 ! [X1 : $tType,X0 : $tType,X21 : X0,X48 : list(X0),X7 : X1,X50 : fun(X1,fun(X0,X1))] : (! [X53 : X0,X54 : X0,X26 : X1] : aa(X0,X1,aa(X1,fun(X0,X1),X50,aa(X0,X1,aa(X1,fun(X0,X1),X50,X26),X53)),X54) = aa(X0,X1,aa(X1,fun(X0,X1),X50,aa(X0,X1,aa(X1,fun(X0,X1),X50,X26),X54)),X53) => aa(X0,X1,aa(X1,fun(X0,X1),X50,foldl(X1,X0,X50,X7,X48)),X21) = foldl(X1,X0,X50,aa(X0,X1,aa(X1,fun(X0,X1),X50,X7),X21),X48))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_foldl__fun__comm)).
% 11.66/2.04 tff(f2490,plain,(
% 11.66/2.04 spl32_191 | ~spl32_89 | ~spl32_190),
% 11.66/2.04 inference(avatar_split_clause,[],[f2486,f2480,f1039,f2488])).
% 11.66/2.04 tff(f2488,plain,(
% 11.66/2.04 spl32_191 <=> ! [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),sK20(X0,X1,X2)) = X0 | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(X2,X0,X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_191])])).
% 11.66/2.04 tff(f2480,plain,(
% 11.66/2.04 spl32_190 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK19(X0,X1,X2)) = X0 | aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0 | sP1(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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_190])])).
% 11.66/2.04 tff(f2486,plain,(
% 11.66/2.04 ( ! [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),sK20(X0,X1,X2)) = X0 | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_190)),
% 11.66/2.04 inference(forward_demodulation,[],[f2485,f1040])).
% 11.66/2.04 tff(f2485,plain,(
% 11.66/2.04 ( ! [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),sK20(X0,X1,X2)) = X0 | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_190)),
% 11.66/2.04 inference(forward_demodulation,[],[f2484,f1040])).
% 11.66/2.04 tff(f2484,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,X1),sK20(X0,X1,X2)) = X0 | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(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))) ) | (~spl32_89 | ~spl32_190)),
% 11.66/2.04 inference(forward_demodulation,[],[f2483,f1040])).
% 11.66/2.04 tff(f2483,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0 | sP1(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))) ) | (~spl32_89 | ~spl32_190)),
% 11.66/2.04 inference(forward_demodulation,[],[f2481,f1040])).
% 11.66/2.04 tff(f2481,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK19(X0,X1,X2)) = X0 | aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0 | sP1(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))) ) | ~spl32_190),
% 11.66/2.04 inference(avatar_component_clause,[],[f2480])).
% 11.66/2.04 tff(f2482,plain,(
% 11.66/2.04 spl32_190),
% 11.66/2.04 inference(avatar_split_clause,[],[f425,f2480])).
% 11.66/2.04 tff(f425,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK19(X0,X1,X2)) = X0 | aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0 | sP1(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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f303])).
% 11.66/2.04 tff(f303,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : dB,X2 : dB] : ((pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK19(X0,X1,X2))) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK19(X0,X1,X2)) = X0) | (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) & aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0) | sP1(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)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f300,f302,f301])).
% 11.66/2.04 tff(f301,plain,(
% 11.66/2.04 ! [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),sK19(X0,X1,X2))) & aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK19(X0,X1,X2)) = X0))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f302,plain,(
% 11.66/2.04 ! [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),sK20(X0,X1,X2))) & aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f300,plain,(
% 11.66/2.04 ! [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) | sP1(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)))),
% 11.66/2.04 inference(rectify,[],[f266])).
% 11.66/2.04 tff(f266,plain,(
% 11.66/2.04 ! [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) | sP1(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)))),
% 11.66/2.04 inference(definition_folding,[],[f231,f265])).
% 11.66/2.04 tff(f265,plain,(
% 11.66/2.04 ! [X2 : dB,X0 : dB,X1 : dB] : (? [X3 : dB] : (abs(X3) = X2 & subst(X3,X1,zero_zero(nat)) = X0) | ~sP1(X2,X0,X1))),
% 11.66/2.04 introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).
% 11.66/2.04 tff(f231,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f230])).
% 11.66/2.04 tff(f230,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f162])).
% 11.66/2.04 tff(f162,plain,(
% 11.66/2.04 ! [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))))))),
% 11.66/2.04 inference(rectify,[],[f23])).
% 11.66/2.04 tff(f23,axiom,(
% 11.66/2.04 ! [X11 : dB,X4 : dB,X5 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X5),X4)),X11)) => (! [X26 : dB] : (subst(X26,X4,zero_zero(nat)) = X11 => abs(X26) != X5) => (! [X25 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X25),X4) = X11 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X5),X25))) => ~! [X25 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X5),X25) = X11 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X4),X25))))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_beta__cases_I3_J)).
% 11.66/2.04 tff(f2466,plain,(
% 11.66/2.04 spl32_189 | ~spl32_89 | ~spl32_188),
% 11.66/2.04 inference(avatar_split_clause,[],[f2462,f2456,f1039,f2464])).
% 11.66/2.04 tff(f2456,plain,(
% 11.66/2.04 spl32_188 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK19(X0,X1,X2))) | aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0 | sP1(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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_188])])).
% 11.66/2.04 tff(f2462,plain,(
% 11.66/2.04 ( ! [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),sK20(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_188)),
% 11.66/2.04 inference(forward_demodulation,[],[f2461,f1040])).
% 11.66/2.04 tff(f2461,plain,(
% 11.66/2.04 ( ! [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),sK20(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_188)),
% 11.66/2.04 inference(forward_demodulation,[],[f2460,f1040])).
% 11.66/2.04 tff(f2460,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,X1),sK20(X0,X1,X2)) = X0 | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(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))) ) | (~spl32_89 | ~spl32_188)),
% 11.66/2.04 inference(forward_demodulation,[],[f2459,f1040])).
% 11.66/2.04 tff(f2459,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0 | sP1(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))) ) | (~spl32_89 | ~spl32_188)),
% 11.66/2.04 inference(forward_demodulation,[],[f2457,f1040])).
% 11.66/2.04 tff(f2457,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK19(X0,X1,X2))) | aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0 | sP1(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))) ) | ~spl32_188),
% 11.66/2.04 inference(avatar_component_clause,[],[f2456])).
% 11.66/2.04 tff(f2458,plain,(
% 11.66/2.04 spl32_188),
% 11.66/2.04 inference(avatar_split_clause,[],[f427,f2456])).
% 11.66/2.04 tff(f427,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK19(X0,X1,X2))) | aa(dB,dB,aa(dB,fun(dB,dB),app,sK20(X0,X1,X2)),X1) = X0 | sP1(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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f303])).
% 11.66/2.04 tff(f2442,plain,(
% 11.66/2.04 spl32_187 | ~spl32_27 | ~spl32_114),
% 11.66/2.04 inference(avatar_split_clause,[],[f1585,f1491,f672,f2440])).
% 11.66/2.04 tff(f2440,plain,(
% 11.66/2.04 spl32_187 <=> ! [X0 : $tType,X2 : bool,X1 : fun(X0,fun(bool,bool))] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X2 | fTrue = foldr(X0,bool,X1,nil(X0),X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_187])])).
% 11.66/2.04 tff(f1585,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X1 : fun(X0,fun(bool,bool))] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X2 | fTrue = foldr(X0,bool,X1,nil(X0),X2)) ) | (~spl32_27 | ~spl32_114)),
% 11.66/2.04 inference(superposition,[],[f673,f1492])).
% 11.66/2.04 tff(f2438,plain,(
% 11.66/2.04 spl32_186 | ~spl32_89 | ~spl32_185),
% 11.66/2.04 inference(avatar_split_clause,[],[f2434,f2428,f1039,f2436])).
% 11.66/2.04 tff(f2428,plain,(
% 11.66/2.04 spl32_185 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK19(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) | sP1(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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_185])])).
% 11.66/2.04 tff(f2434,plain,(
% 11.66/2.04 ( ! [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,sK20(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_185)),
% 11.66/2.04 inference(forward_demodulation,[],[f2433,f1040])).
% 11.66/2.04 tff(f2433,plain,(
% 11.66/2.04 ( ! [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,sK20(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_185)),
% 11.66/2.04 inference(forward_demodulation,[],[f2432,f1040])).
% 11.66/2.04 tff(f2432,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK20(X0,X1,X2)),X2)) | aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | sP1(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))) ) | (~spl32_89 | ~spl32_185)),
% 11.66/2.04 inference(forward_demodulation,[],[f2431,f1040])).
% 11.66/2.04 tff(f2431,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,combc(dB,dB,dB,app,sK19(X0,X1,X2)),X2) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) | sP1(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))) ) | (~spl32_89 | ~spl32_185)),
% 11.66/2.04 inference(forward_demodulation,[],[f2429,f1040])).
% 11.66/2.04 tff(f2429,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK19(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) | sP1(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))) ) | ~spl32_185),
% 11.66/2.04 inference(avatar_component_clause,[],[f2428])).
% 11.66/2.04 tff(f2430,plain,(
% 11.66/2.04 spl32_185),
% 11.66/2.04 inference(avatar_split_clause,[],[f426,f2428])).
% 11.66/2.04 tff(f426,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X2),sK19(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) | sP1(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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f303])).
% 11.66/2.04 tff(f2414,plain,(
% 11.66/2.04 spl32_184 | ~spl32_89 | ~spl32_183),
% 11.66/2.04 inference(avatar_split_clause,[],[f2410,f2404,f1039,f2412])).
% 11.66/2.04 tff(f2404,plain,(
% 11.66/2.04 spl32_183 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK19(X0,X1,X2))) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) | sP1(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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_183])])).
% 11.66/2.04 tff(f2410,plain,(
% 11.66/2.04 ( ! [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,sK20(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_183)),
% 11.66/2.04 inference(forward_demodulation,[],[f2409,f1040])).
% 11.66/2.04 tff(f2409,plain,(
% 11.66/2.04 ( ! [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,sK20(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(X2,X0,X1)) ) | (~spl32_89 | ~spl32_183)),
% 11.66/2.04 inference(forward_demodulation,[],[f2408,f1040])).
% 11.66/2.04 tff(f2408,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK20(X0,X1,X2)),X2)) | pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | sP1(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))) ) | (~spl32_89 | ~spl32_183)),
% 11.66/2.04 inference(forward_demodulation,[],[f2407,f1040])).
% 11.66/2.04 tff(f2407,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK19(X0,X1,X2)),X1)) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) | sP1(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))) ) | (~spl32_89 | ~spl32_183)),
% 11.66/2.04 inference(forward_demodulation,[],[f2405,f1040])).
% 11.66/2.04 tff(f2405,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK19(X0,X1,X2))) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) | sP1(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))) ) | ~spl32_183),
% 11.66/2.04 inference(avatar_component_clause,[],[f2404])).
% 11.66/2.04 tff(f2406,plain,(
% 11.66/2.04 spl32_183),
% 11.66/2.04 inference(avatar_split_clause,[],[f428,f2404])).
% 11.66/2.04 tff(f428,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK19(X0,X1,X2))) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK20(X0,X1,X2))) | sP1(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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f303])).
% 11.66/2.04 tff(f2388,plain,(
% 11.66/2.04 spl32_182),
% 11.66/2.04 inference(avatar_split_clause,[],[f508,f2386])).
% 11.66/2.04 tff(f2386,plain,(
% 11.66/2.04 spl32_182 <=> ! [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),sK31(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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_182])])).
% 11.66/2.04 tff(f508,plain,(
% 11.66/2.04 ( ! [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),sK31(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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f344])).
% 11.66/2.04 tff(f344,plain,(
% 11.66/2.04 ! [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),sK31(X0,X2,X3,X6))) & foldr(type,type,fun1,sK31(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)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f262,f343])).
% 11.66/2.04 tff(f343,plain,(
% 11.66/2.04 ! [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),sK31(X0,X2,X3,X6))) & foldr(type,type,fun1,sK31(X0,X2,X3,X6),X2) = X0))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f262,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f261])).
% 11.66/2.04 tff(f261,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f208])).
% 11.66/2.04 tff(f208,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f79])).
% 11.66/2.04 tff(f79,axiom,(
% 11.66/2.04 ! [X34 : type,X75 : list(type),X28 : type,X78 : list(dB),X12 : list(dB),X29 : nat,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,foldl(dB,dB,app,foldl(dB,dB,app,var(X29),X12),X78)),X28)) => (pp(aa(list(type),bool,typings(X30,X12),X75)) => (pp(aa(type,bool,typing(X30,foldl(dB,dB,app,var(X29),X12)),X34)) => ? [X79 : list(type)] : (pp(aa(list(type),bool,typings(X30,X78),X79)) & foldr(type,type,fun1,X79,X28) = X34))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_var__app__types)).
% 11.66/2.04 tff(f2370,plain,(
% 11.66/2.04 spl32_181),
% 11.66/2.04 inference(avatar_split_clause,[],[f507,f2368])).
% 11.66/2.04 tff(f2368,plain,(
% 11.66/2.04 spl32_181 <=> ! [X5 : nat,X3 : list(dB),X4 : list(dB),X0 : type,X6 : fun(nat,type),X2 : type,X1 : list(type)] : (foldr(type,type,fun1,sK31(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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_181])])).
% 11.66/2.04 tff(f507,plain,(
% 11.66/2.04 ( ! [X2 : type,X3 : list(dB),X0 : type,X1 : list(type),X6 : fun(nat,type),X4 : list(dB),X5 : nat] : (foldr(type,type,fun1,sK31(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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f344])).
% 11.66/2.04 tff(f2348,plain,(
% 11.66/2.04 spl32_180 | ~spl32_28 | ~spl32_114),
% 11.66/2.04 inference(avatar_split_clause,[],[f1583,f1491,f676,f2346])).
% 11.66/2.04 tff(f1583,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : bool,X1 : fun(bool,fun(X0,bool))] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X2 | fTrue = foldl(bool,X0,X1,X2,nil(X0))) ) | (~spl32_28 | ~spl32_114)),
% 11.66/2.04 inference(superposition,[],[f677,f1492])).
% 11.66/2.04 tff(f2344,plain,(
% 11.66/2.04 spl32_179 | ~spl32_89 | ~spl32_178),
% 11.66/2.04 inference(avatar_split_clause,[],[f2340,f2336,f1039,f2342])).
% 11.66/2.04 tff(f2336,plain,(
% 11.66/2.04 spl32_178 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK16(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_178])])).
% 11.66/2.04 tff(f2340,plain,(
% 11.66/2.04 ( ! [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,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0) ) | (~spl32_89 | ~spl32_178)),
% 11.66/2.04 inference(forward_demodulation,[],[f2339,f1040])).
% 11.66/2.04 tff(f2339,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | (~spl32_89 | ~spl32_178)),
% 11.66/2.04 inference(forward_demodulation,[],[f2337,f1040])).
% 11.66/2.04 tff(f2337,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK16(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl32_178),
% 11.66/2.04 inference(avatar_component_clause,[],[f2336])).
% 11.66/2.04 tff(f2338,plain,(
% 11.66/2.04 spl32_178),
% 11.66/2.04 inference(avatar_split_clause,[],[f419,f2336])).
% 11.66/2.04 tff(f419,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK16(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f293])).
% 11.66/2.04 tff(f293,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : list(dB),X2 : dB] : (sP0(X0,X1,X2) | (foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 & step1(dB,beta,X1,sK15(X0,X1,X2))) | (foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK16(X0,X1,X2)))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f290,f292,f291])).
% 11.66/2.04 tff(f291,plain,(
% 11.66/2.04 ! [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,sK15(X0,X1,X2)) = X0 & step1(dB,beta,X1,sK15(X0,X1,X2))))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f292,plain,(
% 11.66/2.04 ! [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,sK16(X0,X1,X2),X1) = X0 & pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK16(X0,X1,X2)))))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f290,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : list(dB),X2 : dB] : (sP0(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)))),
% 11.66/2.04 inference(rectify,[],[f264])).
% 11.66/2.04 tff(f264,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : list(dB),X2 : dB] : (sP0(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)))),
% 11.66/2.04 inference(definition_folding,[],[f228,f263])).
% 11.66/2.04 tff(f263,plain,(
% 11.66/2.04 ! [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) | ~sP0(X0,X1,X2))),
% 11.66/2.04 introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).
% 11.66/2.04 tff(f228,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f227])).
% 11.66/2.04 tff(f227,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f160])).
% 11.66/2.04 tff(f160,plain,(
% 11.66/2.04 ! [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)))))),
% 11.66/2.04 inference(rectify,[],[f54])).
% 11.66/2.04 tff(f54,axiom,(
% 11.66/2.04 ! [X7 : dB,X8 : list(dB),X9 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X9,X8)),X7)) => (! [X55 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X9),X55)) => foldl(dB,dB,app,X55,X8) != X7) => (! [X56 : list(dB)] : (step1(dB,beta,X8,X56) => foldl(dB,dB,app,X9,X56) != X7) => ~! [X25 : dB] : (abs(X25) = X9 => ! [X57 : dB,X58 : list(dB)] : (cons(dB,X57,X58) = X8 => foldl(dB,dB,app,subst(X25,X57,zero_zero(nat)),X58) != X7)))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_apps__betasE)).
% 11.66/2.04 tff(f2323,plain,(
% 11.66/2.04 spl32_177),
% 11.66/2.04 inference(avatar_split_clause,[],[f462,f2321])).
% 11.66/2.04 tff(f462,plain,(
% 11.66/2.04 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type] : (it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),t)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),X1))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f243])).
% 11.66/2.04 tff(f243,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type)] : (it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),t)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),X1)))),
% 11.66/2.04 inference(flattening,[],[f242])).
% 11.66/2.04 tff(f242,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type)] : (((it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),t))) | ~it(X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),X1)))),
% 11.66/2.04 inference(ennf_transformation,[],[f184])).
% 11.66/2.04 tff(f184,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X3,X2,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),X1)) => (it(X0) => (pp(aa(type,bool,typing(X3,X0),t)) => it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X0,X2)))))),
% 11.66/2.04 inference(rectify,[],[f34])).
% 11.66/2.04 tff(f34,axiom,(
% 11.66/2.04 ! [X27 : dB,X36 : type,X29 : nat,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X30,X29,t),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),X36)) => (it(X27) => (pp(aa(type,bool,typing(X30,X27),t)) => it(subst(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as),X27,X29)))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_SI1)).
% 11.66/2.04 tff(f2309,plain,(
% 11.66/2.04 spl32_176 | ~spl32_89 | ~spl32_175),
% 11.66/2.04 inference(avatar_split_clause,[],[f2305,f2301,f1039,f2307])).
% 11.66/2.04 tff(f2301,plain,(
% 11.66/2.04 spl32_175 <=> ! [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))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_175])])).
% 11.66/2.04 tff(f2305,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_175)),
% 11.66/2.04 inference(forward_demodulation,[],[f2304,f1040])).
% 11.66/2.04 tff(f2304,plain,(
% 11.66/2.04 ( ! [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)))) ) | (~spl32_89 | ~spl32_175)),
% 11.66/2.04 inference(forward_demodulation,[],[f2302,f1040])).
% 11.66/2.04 tff(f2302,plain,(
% 11.66/2.04 ( ! [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)))) ) | ~spl32_175),
% 11.66/2.04 inference(avatar_component_clause,[],[f2301])).
% 11.66/2.04 tff(f2303,plain,(
% 11.66/2.04 spl32_175),
% 11.66/2.04 inference(avatar_split_clause,[],[f486,f2301])).
% 11.66/2.04 tff(f486,plain,(
% 11.66/2.04 ( ! [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)))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f253])).
% 11.66/2.04 tff(f253,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(flattening,[],[f252])).
% 11.66/2.04 tff(f252,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(ennf_transformation,[],[f196])).
% 11.66/2.04 tff(f196,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f41])).
% 11.66/2.04 tff(f41,axiom,(
% 11.66/2.04 ! [X31 : dB,X34 : type,X28 : type,X7 : dB,X44 : fun(nat,type)] : (pp(aa(type,bool,typing(X44,X7),aa(type,type,aa(type,fun(type,type),fun1,X28),X34))) => (pp(aa(type,bool,typing(X44,X31),X28)) => pp(aa(type,bool,typing(X44,aa(dB,dB,aa(dB,fun(dB,dB),app,X7),X31)),X34))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_App)).
% 11.66/2.04 tff(f2282,plain,(
% 11.66/2.04 spl32_174 | ~spl32_89 | ~spl32_173),
% 11.66/2.04 inference(avatar_split_clause,[],[f2278,f2274,f1039,f2280])).
% 11.66/2.04 tff(f2274,plain,(
% 11.66/2.04 spl32_173 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK16(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_173])])).
% 11.66/2.04 tff(f2278,plain,(
% 11.66/2.04 ( ! [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,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2))) ) | (~spl32_89 | ~spl32_173)),
% 11.66/2.04 inference(forward_demodulation,[],[f2277,f1040])).
% 11.66/2.04 tff(f2277,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK16(X0,X1,X2)),X2)) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | (~spl32_89 | ~spl32_173)),
% 11.66/2.04 inference(forward_demodulation,[],[f2275,f1040])).
% 11.66/2.04 tff(f2275,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK16(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl32_173),
% 11.66/2.04 inference(avatar_component_clause,[],[f2274])).
% 11.66/2.04 tff(f2276,plain,(
% 11.66/2.04 spl32_173),
% 11.66/2.04 inference(avatar_split_clause,[],[f417,f2274])).
% 11.66/2.04 tff(f417,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),sK16(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f293])).
% 11.66/2.04 tff(f2254,plain,(
% 11.66/2.04 spl32_172 | ~spl32_89 | ~spl32_171),
% 11.66/2.04 inference(avatar_split_clause,[],[f2250,f2244,f1039,f2252])).
% 11.66/2.04 tff(f2244,plain,(
% 11.66/2.04 spl32_171 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_171])])).
% 11.66/2.04 tff(f2250,plain,(
% 11.66/2.04 ( ! [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)))) ) | (~spl32_89 | ~spl32_171)),
% 11.66/2.04 inference(forward_demodulation,[],[f2249,f1040])).
% 11.66/2.04 tff(f2249,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_171)),
% 11.66/2.04 inference(forward_demodulation,[],[f2248,f1040])).
% 11.66/2.04 tff(f2248,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_171)),
% 11.66/2.04 inference(forward_demodulation,[],[f2247,f1040])).
% 11.66/2.04 tff(f2247,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_171)),
% 11.66/2.04 inference(forward_demodulation,[],[f2245,f1040])).
% 11.66/2.04 tff(f2245,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_171),
% 11.66/2.04 inference(avatar_component_clause,[],[f2244])).
% 11.66/2.04 tff(f2246,plain,(
% 11.66/2.04 spl32_171),
% 11.66/2.04 inference(avatar_split_clause,[],[f413,f2244])).
% 11.66/2.04 tff(f413,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f226])).
% 11.66/2.04 tff(f226,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f159])).
% 11.66/2.04 tff(f159,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f8])).
% 11.66/2.04 tff(f8,axiom,(
% 11.66/2.04 ! [X11 : dB,X4 : dB,X5 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X5),X4)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X5),X11)),aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X11))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_appL)).
% 11.66/2.04 tff(f2232,plain,(
% 11.66/2.04 spl32_170 | ~spl32_89 | ~spl32_169),
% 11.66/2.04 inference(avatar_split_clause,[],[f2228,f2222,f1039,f2230])).
% 11.66/2.04 tff(f2222,plain,(
% 11.66/2.04 spl32_169 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_169])])).
% 11.66/2.04 tff(f2228,plain,(
% 11.66/2.04 ( ! [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)))) ) | (~spl32_89 | ~spl32_169)),
% 11.66/2.04 inference(forward_demodulation,[],[f2227,f1040])).
% 11.66/2.04 tff(f2227,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_169)),
% 11.66/2.04 inference(forward_demodulation,[],[f2226,f1040])).
% 11.66/2.04 tff(f2226,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_169)),
% 11.66/2.04 inference(forward_demodulation,[],[f2225,f1040])).
% 11.66/2.04 tff(f2225,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_169)),
% 11.66/2.04 inference(forward_demodulation,[],[f2223,f1040])).
% 11.66/2.04 tff(f2223,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_169),
% 11.66/2.04 inference(avatar_component_clause,[],[f2222])).
% 11.66/2.04 tff(f2224,plain,(
% 11.66/2.04 spl32_169),
% 11.66/2.04 inference(avatar_split_clause,[],[f412,f2222])).
% 11.66/2.04 tff(f412,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f225])).
% 11.66/2.04 tff(f225,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f158])).
% 11.66/2.04 tff(f158,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f9])).
% 11.66/2.04 tff(f9,axiom,(
% 11.66/2.04 ! [X11 : dB,X4 : dB,X5 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X5),X4)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,X11),X5)),aa(dB,dB,aa(dB,fun(dB,dB),app,X11),X4))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_appR)).
% 11.66/2.04 tff(f2201,plain,(
% 11.66/2.04 spl32_168 | ~spl32_89 | ~spl32_167),
% 11.66/2.04 inference(avatar_split_clause,[],[f2197,f2194,f1039,f2199])).
% 11.66/2.04 tff(f2194,plain,(
% 11.66/2.04 spl32_167 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_167])])).
% 11.66/2.04 tff(f2197,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0) ) | (~spl32_89 | ~spl32_167)),
% 11.66/2.04 inference(forward_demodulation,[],[f2195,f1040])).
% 11.66/2.04 tff(f2195,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl32_167),
% 11.66/2.04 inference(avatar_component_clause,[],[f2194])).
% 11.66/2.04 tff(f2196,plain,(
% 11.66/2.04 spl32_167),
% 11.66/2.04 inference(avatar_split_clause,[],[f420,f2194])).
% 11.66/2.04 tff(f420,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | foldl(dB,dB,app,X2,sK15(X0,X1,X2)) = X0 | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f293])).
% 11.66/2.04 tff(f2184,plain,(
% 11.66/2.04 spl32_166),
% 11.66/2.04 inference(avatar_split_clause,[],[f546,f2182])).
% 11.66/2.04 tff(f2182,plain,(
% 11.66/2.04 spl32_166 <=> ! [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) | it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~it(X4))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_166])])).
% 11.66/2.04 tff(f546,plain,(
% 11.66/2.04 ( ! [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) | it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~it(X4)) )),
% 11.66/2.04 inference(forward_demodulation,[],[f506,f490])).
% 11.66/2.04 tff(f490,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f198])).
% 11.66/2.04 tff(f198,plain,(
% 11.66/2.04 ! [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)),
% 11.66/2.04 inference(rectify,[],[f104])).
% 11.66/2.04 tff(f104,axiom,(
% 11.66/2.04 ! [X0 : $tType,X2 : $tType,X1 : $tType,X90 : X0,X91 : X1,X92 : fun(X0,fun(X1,X2))] : aa(X0,X2,combc(X0,X1,X2,X92,X91),X90) = aa(X1,X2,aa(X0,fun(X1,X2),X92,X90),X91)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U)).
% 11.66/2.04 tff(f506,plain,(
% 11.66/2.04 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~it(X4) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f260])).
% 11.66/2.04 tff(f260,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X5)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) | ~it(X4) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 11.66/2.04 inference(flattening,[],[f259])).
% 11.66/2.04 tff(f259,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (((((it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X5))) | ~it(X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1))) | ~it(X4)) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 11.66/2.04 inference(ennf_transformation,[],[f207])).
% 11.66/2.04 tff(f207,plain,(
% 11.66/2.04 ! [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) => (it(X4) => (pp(aa(type,bool,typing(shift(type,X3,X2,X5),X4),X1)) => (it(X0) => (pp(aa(type,bool,typing(X3,X0),X5)) => it(subst(X4,X0,X2)))))))),
% 11.66/2.04 inference(rectify,[],[f31])).
% 11.66/2.04 tff(f31,axiom,(
% 11.66/2.04 ! [X27 : dB,X28 : type,X29 : nat,X30 : fun(nat,type),X31 : dB,X32 : type,X33 : type] : (t = aa(type,type,aa(type,fun(type,type),fun1,X33),X32) => (it(X31) => (pp(aa(type,bool,typing(shift(type,X30,X29,X32),X31),X28)) => (it(X27) => (pp(aa(type,bool,typing(X30,X27),X32)) => it(subst(X31,X27,X29)))))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_MI2)).
% 11.66/2.04 tff(f2180,plain,(
% 11.66/2.04 spl32_165),
% 11.66/2.04 inference(avatar_split_clause,[],[f545,f2178])).
% 11.66/2.04 tff(f2178,plain,(
% 11.66/2.04 spl32_165 <=> ! [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) | it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X6)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) | ~it(X4))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_165])])).
% 11.66/2.04 tff(f545,plain,(
% 11.66/2.04 ( ! [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) | it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X6)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) | ~it(X4)) )),
% 11.66/2.04 inference(forward_demodulation,[],[f505,f490])).
% 11.66/2.04 tff(f505,plain,(
% 11.66/2.04 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type,X6 : type,X4 : dB,X5 : type] : (it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X6)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) | ~it(X4) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f258])).
% 11.66/2.04 tff(f258,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X6)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) | ~it(X4) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 11.66/2.04 inference(flattening,[],[f257])).
% 11.66/2.04 tff(f257,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type),X4 : dB,X5 : type,X6 : type] : (((((it(subst(X4,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),X6))) | ~it(X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1))) | ~it(X4)) | t != aa(type,type,aa(type,fun(type,type),fun1,X6),X5))),
% 11.66/2.04 inference(ennf_transformation,[],[f206])).
% 11.66/2.04 tff(f206,plain,(
% 11.66/2.04 ! [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) => (it(X4) => (pp(aa(type,bool,typing(shift(type,X3,X2,X6),X4),X1)) => (it(X0) => (pp(aa(type,bool,typing(X3,X0),X6)) => it(subst(X4,X0,X2)))))))),
% 11.66/2.04 inference(rectify,[],[f32])).
% 11.66/2.04 tff(f32,axiom,(
% 11.66/2.04 ! [X27 : dB,X28 : type,X29 : nat,X30 : fun(nat,type),X31 : dB,X32 : type,X33 : type] : (t = aa(type,type,aa(type,fun(type,type),fun1,X33),X32) => (it(X31) => (pp(aa(type,bool,typing(shift(type,X30,X29,X33),X31),X28)) => (it(X27) => (pp(aa(type,bool,typing(X30,X27),X33)) => it(subst(X31,X27,X29)))))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_MI1)).
% 11.66/2.04 tff(f2158,plain,(
% 11.66/2.04 spl32_164 | ~spl32_89 | ~spl32_163),
% 11.66/2.04 inference(avatar_split_clause,[],[f2154,f2150,f1039,f2156])).
% 11.66/2.04 tff(f2150,plain,(
% 11.66/2.04 spl32_163 <=> ! [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,sK24(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_163])])).
% 11.66/2.04 tff(f2154,plain,(
% 11.66/2.04 ( ! [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),sK24(X0,X1,X2,X3))))) ) | (~spl32_89 | ~spl32_163)),
% 11.66/2.04 inference(forward_demodulation,[],[f2153,f1040])).
% 11.66/2.04 tff(f2153,plain,(
% 11.66/2.04 ( ! [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),sK24(X0,X1,X2,X3)))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | (~spl32_89 | ~spl32_163)),
% 11.66/2.04 inference(forward_demodulation,[],[f2151,f1040])).
% 11.66/2.04 tff(f2151,plain,(
% 11.66/2.04 ( ! [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,sK24(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl32_163),
% 11.66/2.04 inference(avatar_component_clause,[],[f2150])).
% 11.66/2.04 tff(f2152,plain,(
% 11.66/2.04 spl32_163),
% 11.66/2.04 inference(avatar_split_clause,[],[f460,f2150])).
% 11.66/2.04 tff(f460,plain,(
% 11.66/2.04 ( ! [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,sK24(X0,X1,X2,X3)),X0))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f319])).
% 11.66/2.04 tff(f319,plain,(
% 11.66/2.04 ! [X0 : type,X1 : dB,X2 : dB,X3 : fun(nat,type)] : ((pp(aa(type,bool,typing(X3,X1),sK24(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK24(X0,X1,X2,X3)),X0)))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f241,f318])).
% 11.66/2.04 tff(f318,plain,(
% 11.66/2.04 ! [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),sK24(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),aa(type,type,aa(type,fun(type,type),fun1,sK24(X0,X1,X2,X3)),X0)))))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f241,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f183])).
% 11.66/2.04 tff(f183,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f48])).
% 11.66/2.04 tff(f48,axiom,(
% 11.66/2.04 ! [X28 : type,X27 : dB,X31 : dB,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,aa(dB,dB,aa(dB,fun(dB,dB),app,X31),X27)),X28)) => ~! [X47 : type] : (pp(aa(type,bool,typing(X30,X31),aa(type,type,aa(type,fun(type,type),fun1,X47),X28))) => ~pp(aa(type,bool,typing(X30,X27),X47))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_typing__elims_I2_J)).
% 11.66/2.04 tff(f2130,plain,(
% 11.66/2.04 spl32_162 | ~spl32_89 | ~spl32_161),
% 11.66/2.04 inference(avatar_split_clause,[],[f2126,f2123,f1039,f2128])).
% 11.66/2.04 tff(f2123,plain,(
% 11.66/2.04 spl32_161 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_161])])).
% 11.66/2.04 tff(f2126,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),foldl(dB,dB,app,X2,X1))) | sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0) ) | (~spl32_89 | ~spl32_161)),
% 11.66/2.04 inference(forward_demodulation,[],[f2124,f1040])).
% 11.66/2.04 tff(f2124,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) ) | ~spl32_161),
% 11.66/2.04 inference(avatar_component_clause,[],[f2123])).
% 11.66/2.04 tff(f2125,plain,(
% 11.66/2.04 spl32_161),
% 11.66/2.04 inference(avatar_split_clause,[],[f418,f2123])).
% 11.66/2.04 tff(f418,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (sP0(X0,X1,X2) | step1(dB,beta,X1,sK15(X0,X1,X2)) | foldl(dB,dB,app,sK16(X0,X1,X2),X1) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f293])).
% 11.66/2.04 tff(f2091,plain,(
% 11.66/2.04 spl32_160 | ~spl32_18 | ~spl32_20),
% 11.66/2.04 inference(avatar_split_clause,[],[f661,f635,f626,f2088])).
% 11.66/2.04 tff(f2088,plain,(
% 11.66/2.04 spl32_160 <=> aa(type,bool,typing(ea,ua),t) = fTrue),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_160])])).
% 11.66/2.04 tff(f635,plain,(
% 11.66/2.04 spl32_20 <=> pp(aa(type,bool,typing(ea,ua),t))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_20])])).
% 11.66/2.04 tff(f661,plain,(
% 11.66/2.04 aa(type,bool,typing(ea,ua),t) = fTrue | (~spl32_18 | ~spl32_20)),
% 11.66/2.04 inference(resolution,[],[f627,f637])).
% 11.66/2.04 tff(f637,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(ea,ua),t)) | ~spl32_20),
% 11.66/2.04 inference(avatar_component_clause,[],[f635])).
% 11.66/2.04 tff(f2086,plain,(
% 11.66/2.04 spl32_159),
% 11.66/2.04 inference(avatar_split_clause,[],[f494,f2084])).
% 11.66/2.04 tff(f494,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f202])).
% 11.66/2.04 tff(f202,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f103])).
% 11.66/2.04 tff(f103,axiom,(
% 11.66/2.04 ! [X2 : $tType,X1 : $tType,X0 : $tType,X90 : X0,X91 : fun(X0,X1),X92 : 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),X92),X91),X90) = aa(X1,X2,X92,aa(X0,X1,X91,X90))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U)).
% 11.66/2.04 tff(f2064,plain,(
% 11.66/2.04 spl32_158 | ~spl32_89 | ~spl32_157),
% 11.66/2.04 inference(avatar_split_clause,[],[f2060,f2057,f1039,f2062])).
% 11.66/2.04 tff(f2057,plain,(
% 11.66/2.04 spl32_157 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3 | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK27(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_157])])).
% 11.66/2.04 tff(f2060,plain,(
% 11.66/2.04 ( ! [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),sK27(X0,X1,X2,X3,X4))) | cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | (~spl32_89 | ~spl32_157)),
% 11.66/2.04 inference(forward_demodulation,[],[f2058,f1040])).
% 11.66/2.04 tff(f2058,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3 | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK27(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | ~spl32_157),
% 11.66/2.04 inference(avatar_component_clause,[],[f2057])).
% 11.66/2.04 tff(f2059,plain,(
% 11.66/2.04 spl32_157),
% 11.66/2.04 inference(avatar_split_clause,[],[f481,f2057])).
% 11.66/2.04 tff(f481,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3 | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK27(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f334])).
% 11.66/2.04 tff(f334,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : fun(X0,fun(X0,bool))] : ((step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) & cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3) | (pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK27(X0,X1,X2,X3,X4)),X2)) & cons(X0,sK27(X0,X1,X2,X3,X4),X1) = X3) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f331,f333,f332])).
% 11.66/2.04 tff(f332,plain,(
% 11.66/2.04 ! [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,sK26(X0,X1,X2,X3,X4),X1) & cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f333,plain,(
% 11.66/2.04 ! [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,sK27(X0,X1,X2,X3,X4)),X2)) & cons(X0,sK27(X0,X1,X2,X3,X4),X1) = X3))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f331,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(rectify,[],[f247])).
% 11.66/2.04 tff(f247,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f246])).
% 11.66/2.04 tff(f246,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f193])).
% 11.66/2.04 tff(f193,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f66])).
% 11.66/2.04 tff(f66,axiom,(
% 11.66/2.04 ! [X0 : $tType,X48 : list(X0),X21 : X0,X62 : list(X0),X9 : fun(X0,fun(X0,bool))] : (step1(X0,X9,X62,cons(X0,X21,X48)) => (! [X54 : X0] : (cons(X0,X54,X48) = X62 => ~pp(aa(X0,bool,aa(X0,fun(X0,bool),X9,X54),X21))) => ~! [X73 : list(X0)] : (cons(X0,X21,X73) = X62 => ~step1(X0,X9,X73,X48))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Cons__step1E)).
% 11.66/2.04 tff(f2043,plain,(
% 11.66/2.04 spl32_156),
% 11.66/2.04 inference(avatar_split_clause,[],[f484,f2041])).
% 11.66/2.04 tff(f484,plain,(
% 11.66/2.04 ( ! [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)))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f249])).
% 11.66/2.04 tff(f249,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(flattening,[],[f248])).
% 11.66/2.04 tff(f248,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(ennf_transformation,[],[f194])).
% 11.66/2.04 tff(f194,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f72])).
% 11.66/2.04 tff(f72,axiom,(
% 11.66/2.04 ! [X12 : list(dB),X28 : type,X75 : list(type),X31 : dB,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,X31),foldr(type,type,fun1,X75,X28))) => (pp(aa(list(type),bool,typings(X30,X12),X75)) => pp(aa(type,bool,typing(X30,foldl(dB,dB,app,X31,X12)),X28))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_list__app__typeI)).
% 11.66/2.04 tff(f2019,plain,(
% 11.66/2.04 spl32_155 | ~spl32_89 | ~spl32_154),
% 11.66/2.04 inference(avatar_split_clause,[],[f2015,f2012,f1039,f2017])).
% 11.66/2.04 tff(f2012,plain,(
% 11.66/2.04 spl32_154 <=> ! [X0 : $tType,X4 : fun(X0,fun(X0,bool)),X3 : list(X0),X2 : X0,X1 : list(X0)] : (step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK27(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_154])])).
% 11.66/2.04 tff(f2015,plain,(
% 11.66/2.04 ( ! [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),sK27(X0,X1,X2,X3,X4))) | step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | (~spl32_89 | ~spl32_154)),
% 11.66/2.04 inference(forward_demodulation,[],[f2013,f1040])).
% 11.66/2.04 tff(f2013,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK27(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1))) ) | ~spl32_154),
% 11.66/2.04 inference(avatar_component_clause,[],[f2012])).
% 11.66/2.04 tff(f2014,plain,(
% 11.66/2.04 spl32_154),
% 11.66/2.04 inference(avatar_split_clause,[],[f483,f2012])).
% 11.66/2.04 tff(f483,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | pp(aa(X0,bool,aa(X0,fun(X0,bool),X4,sK27(X0,X1,X2,X3,X4)),X2)) | ~step1(X0,X4,X3,cons(X0,X2,X1))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f334])).
% 11.66/2.04 tff(f1990,plain,(
% 11.66/2.04 spl32_153 | ~spl32_18 | ~spl32_19),
% 11.66/2.04 inference(avatar_split_clause,[],[f660,f630,f626,f1987])).
% 11.66/2.04 tff(f1987,plain,(
% 11.66/2.04 spl32_153 <=> aa(type,bool,typing(e,u),t) = fTrue),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_153])])).
% 11.66/2.04 tff(f630,plain,(
% 11.66/2.04 spl32_19 <=> pp(aa(type,bool,typing(e,u),t))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_19])])).
% 11.66/2.04 tff(f660,plain,(
% 11.66/2.04 aa(type,bool,typing(e,u),t) = fTrue | (~spl32_18 | ~spl32_19)),
% 11.66/2.04 inference(resolution,[],[f627,f632])).
% 11.66/2.04 tff(f632,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(e,u),t)) | ~spl32_19),
% 11.66/2.04 inference(avatar_component_clause,[],[f630])).
% 11.66/2.04 tff(f1985,plain,(
% 11.66/2.04 spl32_152 | ~spl32_89 | ~spl32_151),
% 11.66/2.04 inference(avatar_split_clause,[],[f1981,f1977,f1039,f1983])).
% 11.66/2.04 tff(f1977,plain,(
% 11.66/2.04 spl32_151 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_151])])).
% 11.66/2.04 tff(f1981,plain,(
% 11.66/2.04 ( ! [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)))) ) | (~spl32_89 | ~spl32_151)),
% 11.66/2.04 inference(forward_demodulation,[],[f1980,f1040])).
% 11.66/2.04 tff(f1980,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_151)),
% 11.66/2.04 inference(forward_demodulation,[],[f1978,f1040])).
% 11.66/2.04 tff(f1978,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_151),
% 11.66/2.04 inference(avatar_component_clause,[],[f1977])).
% 11.66/2.04 tff(f1979,plain,(
% 11.66/2.04 spl32_151),
% 11.66/2.04 inference(avatar_split_clause,[],[f411,f1977])).
% 11.66/2.04 tff(f411,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f224])).
% 11.66/2.04 tff(f224,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f157])).
% 11.66/2.04 tff(f157,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f11])).
% 11.66/2.04 tff(f11,axiom,(
% 11.66/2.04 ! [X6 : list(dB),X7 : dB,X9 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X9),X7)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X9,X6)),foldl(dB,dB,app,X7,X6))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_apps__preserves__beta)).
% 11.66/2.04 tff(f1959,plain,(
% 11.66/2.04 spl32_150),
% 11.66/2.04 inference(avatar_split_clause,[],[f480,f1957])).
% 11.66/2.04 tff(f480,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (cons(X0,X2,sK26(X0,X1,X2,X3,X4)) = X3 | cons(X0,sK27(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f334])).
% 11.66/2.04 tff(f1955,plain,(
% 11.66/2.04 spl32_149),
% 11.66/2.04 inference(avatar_split_clause,[],[f458,f1953])).
% 11.66/2.04 tff(f458,plain,(
% 11.66/2.04 ( ! [X2 : nat,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK23(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f317])).
% 11.66/2.04 tff(f317,plain,(
% 11.66/2.04 ! [X0 : type,X1 : list(dB),X2 : nat,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK23(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK23(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f240,f316])).
% 11.66/2.04 tff(f316,plain,(
% 11.66/2.04 ! [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),sK23(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,var(X2)),foldr(type,type,fun1,sK23(X0,X1,X2,X3),X0)))))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f240,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f182])).
% 11.66/2.04 tff(f182,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f80])).
% 11.66/2.04 tff(f80,axiom,(
% 11.66/2.04 ! [X28 : type,X12 : list(dB),X29 : nat,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,foldl(dB,dB,app,var(X29),X12)),X28)) => ~! [X76 : list(type)] : (pp(aa(type,bool,typing(X30,var(X29)),foldr(type,type,fun1,X76,X28))) => ~pp(aa(list(type),bool,typings(X30,X12),X76))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_var__app__typesE)).
% 11.66/2.04 tff(f1940,plain,(
% 11.66/2.04 spl32_148 | ~spl32_89 | ~spl32_147),
% 11.66/2.04 inference(avatar_split_clause,[],[f1936,f1933,f1039,f1938])).
% 11.66/2.04 tff(f1933,plain,(
% 11.66/2.04 spl32_147 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_147])])).
% 11.66/2.04 tff(f1936,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_147)),
% 11.66/2.04 inference(forward_demodulation,[],[f1934,f1040])).
% 11.66/2.04 tff(f1934,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_147),
% 11.66/2.04 inference(avatar_component_clause,[],[f1933])).
% 11.66/2.04 tff(f1935,plain,(
% 11.66/2.04 spl32_147),
% 11.66/2.04 inference(avatar_split_clause,[],[f457,f1933])).
% 11.66/2.04 tff(f457,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f239])).
% 11.66/2.04 tff(f239,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f181])).
% 11.66/2.04 tff(f181,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f42])).
% 11.66/2.04 tff(f42,axiom,(
% 11.66/2.04 ! [X34 : type,X31 : dB,X28 : type,X44 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X44,zero_zero(nat),X28),X31),X34)) => pp(aa(type,bool,typing(X44,abs(X31)),aa(type,type,aa(type,fun(type,type),fun1,X28),X34))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Abs)).
% 11.66/2.04 tff(f1920,plain,(
% 11.66/2.04 spl32_146 | ~spl32_89 | ~spl32_145),
% 11.66/2.04 inference(avatar_split_clause,[],[f1916,f1913,f1039,f1918])).
% 11.66/2.04 tff(f1913,plain,(
% 11.66/2.04 spl32_145 <=> ! [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))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_145])])).
% 11.66/2.04 tff(f1916,plain,(
% 11.66/2.04 ( ! [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)) ) | (~spl32_89 | ~spl32_145)),
% 11.66/2.04 inference(forward_demodulation,[],[f1914,f1040])).
% 11.66/2.04 tff(f1914,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_145),
% 11.66/2.04 inference(avatar_component_clause,[],[f1913])).
% 11.66/2.04 tff(f1915,plain,(
% 11.66/2.04 spl32_145),
% 11.66/2.04 inference(avatar_split_clause,[],[f449,f1913])).
% 11.66/2.04 tff(f449,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f175])).
% 11.66/2.04 tff(f175,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f7])).
% 11.66/2.04 tff(f7,axiom,(
% 11.66/2.04 ! [X10 : nat,X5 : dB,X11 : dB,X4 : dB] : subst(aa(dB,dB,aa(dB,fun(dB,dB),app,X4),X11),X5,X10) = aa(dB,dB,aa(dB,fun(dB,dB),app,subst(X4,X5,X10)),subst(X11,X5,X10))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subst__App)).
% 11.66/2.04 tff(f1896,plain,(
% 11.66/2.04 spl32_144 | ~spl32_89 | ~spl32_143),
% 11.66/2.04 inference(avatar_split_clause,[],[f1892,f1889,f1039,f1894])).
% 11.66/2.04 tff(f1889,plain,(
% 11.66/2.04 spl32_143 <=> ! [X0 : nat,X3 : nat,X2 : dB,X1 : dB] : liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_143])])).
% 11.66/2.04 tff(f1892,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : nat,X0 : nat,X1 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0)) = liftn(X3,aa(dB,dB,combc(dB,dB,dB,app,X1),X2),X0)) ) | (~spl32_89 | ~spl32_143)),
% 11.66/2.04 inference(forward_demodulation,[],[f1890,f1040])).
% 11.66/2.04 tff(f1890,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : nat,X0 : nat,X1 : dB] : (liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0))) ) | ~spl32_143),
% 11.66/2.04 inference(avatar_component_clause,[],[f1889])).
% 11.66/2.04 tff(f1891,plain,(
% 11.66/2.04 spl32_143),
% 11.66/2.04 inference(avatar_split_clause,[],[f447,f1889])).
% 11.66/2.04 tff(f447,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : nat,X0 : nat,X1 : dB] : (liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f173])).
% 11.66/2.04 tff(f173,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : dB,X2 : dB,X3 : nat] : liftn(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X3,X2,X0)),liftn(X3,X1,X0))),
% 11.66/2.04 inference(rectify,[],[f40])).
% 11.66/2.04 tff(f40,axiom,(
% 11.66/2.04 ! [X10 : nat,X4 : dB,X5 : dB,X37 : nat] : liftn(X37,aa(dB,dB,aa(dB,fun(dB,dB),app,X5),X4),X10) = aa(dB,dB,aa(dB,fun(dB,dB),app,liftn(X37,X5,X10)),liftn(X37,X4,X10))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_liftn_Osimps_I2_J)).
% 11.66/2.04 tff(f1861,plain,(
% 11.66/2.04 spl32_142),
% 11.66/2.04 inference(avatar_split_clause,[],[f538,f1859])).
% 11.66/2.04 tff(f538,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(equality_resolution,[],[f504])).
% 11.66/2.04 tff(f504,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f256])).
% 11.66/2.04 tff(f256,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f255])).
% 11.66/2.04 tff(f255,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f205])).
% 11.66/2.04 tff(f205,plain,(
% 11.66/2.04 ! [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)))))),
% 11.66/2.04 inference(rectify,[],[f33])).
% 11.66/2.04 tff(f33,axiom,(
% 11.66/2.04 ! [X29 : nat,X34 : type,X27 : dB,X35 : fun(nat,type),X28 : type,X31 : dB,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,X31),X28)) => (pp(aa(type,bool,typing(X35,X27),X34)) => (shift(type,X35,X29,X34) = X30 => pp(aa(type,bool,typing(X35,subst(X31,X27,X29)),X28)))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_subst__lemma)).
% 11.66/2.04 tff(f1857,plain,(
% 11.66/2.04 spl32_141),
% 11.66/2.04 inference(avatar_split_clause,[],[f485,f1855])).
% 11.66/2.04 tff(f485,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f251])).
% 11.66/2.04 tff(f251,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f250])).
% 11.66/2.04 tff(f250,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f195])).
% 11.66/2.04 tff(f195,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f95])).
% 11.66/2.04 tff(f95,axiom,(
% 11.66/2.04 ! [X34 : type,X28 : type,X12 : list(dB),X29 : nat,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,foldl(dB,dB,app,var(X29),X12)),X28)) => (pp(aa(type,bool,typing(X30,foldl(dB,dB,app,var(X29),X12)),X34)) => X28 = X34))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_var__app__type__eq)).
% 11.66/2.04 tff(f1849,plain,(
% 11.66/2.04 spl32_140 | ~spl32_108 | ~spl32_139),
% 11.66/2.04 inference(avatar_split_clause,[],[f1845,f1842,f1325,f1847])).
% 11.66/2.04 tff(f1842,plain,(
% 11.66/2.04 spl32_139 <=> ! [X2 : dB,X0 : list(dB),X1 : dB] : (it(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)) | ~it(X1) | ~it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_139])])).
% 11.66/2.04 tff(f1845,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (it(foldl(dB,dB,app,abs(X2),cons(dB,X1,X0))) | ~it(X1) | ~it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0))) ) | (~spl32_108 | ~spl32_139)),
% 11.66/2.04 inference(forward_demodulation,[],[f1843,f1326])).
% 11.66/2.04 tff(f1843,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (it(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)) | ~it(X1) | ~it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0))) ) | ~spl32_139),
% 11.66/2.04 inference(avatar_component_clause,[],[f1842])).
% 11.66/2.04 tff(f1844,plain,(
% 11.66/2.04 spl32_139),
% 11.66/2.04 inference(avatar_split_clause,[],[f410,f1842])).
% 11.66/2.04 tff(f410,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (it(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)) | ~it(X1) | ~it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f223])).
% 11.66/2.04 tff(f223,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : dB] : (it(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)) | ~it(X1) | ~it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)))),
% 11.66/2.04 inference(flattening,[],[f222])).
% 11.66/2.04 tff(f222,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : dB] : ((it(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0)) | ~it(X1)) | ~it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)))),
% 11.66/2.04 inference(ennf_transformation,[],[f156])).
% 11.66/2.04 tff(f156,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : dB] : (it(foldl(dB,dB,app,subst(X2,X1,zero_zero(nat)),X0)) => (it(X1) => it(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X2)),X1),X0))))),
% 11.66/2.04 inference(rectify,[],[f20])).
% 11.66/2.04 tff(f20,axiom,(
% 11.66/2.04 ! [X6 : list(dB),X7 : dB,X9 : dB] : (it(foldl(dB,dB,app,subst(X9,X7,zero_zero(nat)),X6)) => (it(X7) => it(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X9)),X7),X6))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_IT_OBeta)).
% 11.66/2.04 tff(f1803,plain,(
% 11.66/2.04 spl32_138),
% 11.66/2.04 inference(avatar_split_clause,[],[f482,f1801])).
% 11.66/2.04 tff(f482,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : fun(X0,fun(X0,bool))] : (step1(X0,X4,sK26(X0,X1,X2,X3,X4),X1) | cons(X0,sK27(X0,X1,X2,X3,X4),X1) = X3 | ~step1(X0,X4,X3,cons(X0,X2,X1))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f334])).
% 11.66/2.04 tff(f1790,plain,(
% 11.66/2.04 spl32_137 | ~spl32_89 | ~spl32_136),
% 11.66/2.04 inference(avatar_split_clause,[],[f1786,f1783,f1039,f1788])).
% 11.66/2.04 tff(f1783,plain,(
% 11.66/2.04 spl32_136 <=> ! [X0 : type,X3 : fun(nat,type),X2 : dB,X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK24(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_136])])).
% 11.66/2.04 tff(f1786,plain,(
% 11.66/2.04 ( ! [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),sK24(X0,X1,X2,X3)))) ) | (~spl32_89 | ~spl32_136)),
% 11.66/2.04 inference(forward_demodulation,[],[f1784,f1040])).
% 11.66/2.04 tff(f1784,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK24(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) ) | ~spl32_136),
% 11.66/2.04 inference(avatar_component_clause,[],[f1783])).
% 11.66/2.04 tff(f1785,plain,(
% 11.66/2.04 spl32_136),
% 11.66/2.04 inference(avatar_split_clause,[],[f461,f1783])).
% 11.66/2.04 tff(f461,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(X3,X1),sK24(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f319])).
% 11.66/2.04 tff(f1781,plain,(
% 11.66/2.04 spl32_135),
% 11.66/2.04 inference(avatar_split_clause,[],[f455,f1779])).
% 11.66/2.04 tff(f455,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK22(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f315])).
% 11.66/2.04 tff(f315,plain,(
% 11.66/2.04 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK22(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK22(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f238,f314])).
% 11.66/2.04 tff(f314,plain,(
% 11.66/2.04 ! [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),sK22(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK22(X0,X1,X2,X3),X0)))))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f238,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f180])).
% 11.66/2.04 tff(f180,plain,(
% 11.66/2.04 ! [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)))))),
% 11.66/2.04 inference(rectify,[],[f73])).
% 11.66/2.04 tff(f73,axiom,(
% 11.66/2.04 ! [X28 : type,X12 : list(dB),X31 : dB,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,foldl(dB,dB,app,X31,X12)),X28)) => ? [X76 : list(type)] : (pp(aa(list(type),bool,typings(X30,X12),X76)) & pp(aa(type,bool,typing(X30,X31),foldr(type,type,fun1,X76,X28)))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_list__app__typeD)).
% 11.66/2.04 tff(f1769,plain,(
% 11.66/2.04 spl32_134),
% 11.66/2.04 inference(avatar_split_clause,[],[f453,f1767])).
% 11.66/2.04 tff(f453,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f313])).
% 11.66/2.04 tff(f313,plain,(
% 11.66/2.04 ! [X0 : type,X1 : list(dB),X2 : dB,X3 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0)))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f237,f312])).
% 11.66/2.04 tff(f312,plain,(
% 11.66/2.04 ! [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),sK21(X0,X1,X2,X3))) & pp(aa(type,bool,typing(X3,X2),foldr(type,type,fun1,sK21(X0,X1,X2,X3),X0)))))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f237,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f179])).
% 11.66/2.04 tff(f179,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f74])).
% 11.66/2.04 tff(f74,axiom,(
% 11.66/2.04 ! [X28 : type,X12 : list(dB),X31 : dB,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,foldl(dB,dB,app,X31,X12)),X28)) => ~! [X76 : list(type)] : (pp(aa(type,bool,typing(X30,X31),foldr(type,type,fun1,X76,X28))) => ~pp(aa(list(type),bool,typings(X30,X12),X76))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_list__app__typeE)).
% 11.66/2.04 tff(f1753,plain,(
% 11.66/2.04 spl32_133 | ~spl32_89 | ~spl32_132),
% 11.66/2.04 inference(avatar_split_clause,[],[f1749,f1745,f1039,f1751])).
% 11.66/2.04 tff(f1745,plain,(
% 11.66/2.04 spl32_132 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_132])])).
% 11.66/2.04 tff(f1749,plain,(
% 11.66/2.04 ( ! [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)))) ) | (~spl32_89 | ~spl32_132)),
% 11.66/2.04 inference(forward_demodulation,[],[f1748,f1040])).
% 11.66/2.04 tff(f1748,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_132)),
% 11.66/2.04 inference(forward_demodulation,[],[f1746,f1040])).
% 11.66/2.04 tff(f1746,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_132),
% 11.66/2.04 inference(avatar_component_clause,[],[f1745])).
% 11.66/2.04 tff(f1747,plain,(
% 11.66/2.04 spl32_132),
% 11.66/2.04 inference(avatar_split_clause,[],[f451,f1745])).
% 11.66/2.04 tff(f451,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f234])).
% 11.66/2.04 tff(f234,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f177])).
% 11.66/2.04 tff(f177,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f14])).
% 11.66/2.04 tff(f14,axiom,(
% 11.66/2.04 ! [X19 : nat,X4 : dB,X5 : dB,X20 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X20),X5)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,subst(X20,X4,X19)),subst(X5,X4,X19))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_subst__preserves__beta)).
% 11.66/2.04 tff(f1732,plain,(
% 11.66/2.04 spl32_131 | ~spl32_89 | ~spl32_130),
% 11.66/2.04 inference(avatar_split_clause,[],[f1728,f1725,f1039,f1730])).
% 11.66/2.04 tff(f1725,plain,(
% 11.66/2.04 spl32_130 <=> ! [X2 : nat,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,var(X2),sK17(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_130])])).
% 11.66/2.04 tff(f1728,plain,(
% 11.66/2.04 ( ! [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),sK17(X0,X1,X2)) = X0) ) | (~spl32_89 | ~spl32_130)),
% 11.66/2.04 inference(forward_demodulation,[],[f1726,f1040])).
% 11.66/2.04 tff(f1726,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,var(X2),sK17(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))) ) | ~spl32_130),
% 11.66/2.04 inference(avatar_component_clause,[],[f1725])).
% 11.66/2.04 tff(f1727,plain,(
% 11.66/2.04 spl32_130),
% 11.66/2.04 inference(avatar_split_clause,[],[f422,f1725])).
% 11.66/2.04 tff(f422,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,var(X2),sK17(X0,X1,X2)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f295])).
% 11.66/2.04 tff(f295,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : list(dB),X2 : nat] : ((foldl(dB,dB,app,var(X2),sK17(X0,X1,X2)) = X0 & step1(dB,beta,X1,sK17(X0,X1,X2))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f229,f294])).
% 11.66/2.04 tff(f294,plain,(
% 11.66/2.04 ! [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),sK17(X0,X1,X2)) = X0 & step1(dB,beta,X1,sK17(X0,X1,X2))))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f229,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f161])).
% 11.66/2.04 tff(f161,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(rectify,[],[f98])).
% 11.66/2.04 tff(f98,axiom,(
% 11.66/2.04 ! [X88 : dB,X8 : list(dB),X82 : nat] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X82),X8)),X88)) => ? [X89 : list(dB)] : (foldl(dB,dB,app,var(X82),X89) = X88 & step1(dB,beta,X8,X89)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_head__Var__reduction)).
% 11.66/2.04 tff(f1696,plain,(
% 11.66/2.04 spl32_129 | ~spl32_89 | ~spl32_127),
% 11.66/2.04 inference(avatar_split_clause,[],[f1687,f1684,f1039,f1694])).
% 11.66/2.04 tff(f1684,plain,(
% 11.66/2.04 spl32_127 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_127])])).
% 11.66/2.04 tff(f1687,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_127)),
% 11.66/2.04 inference(forward_demodulation,[],[f1685,f1040])).
% 11.66/2.04 tff(f1685,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_127),
% 11.66/2.04 inference(avatar_component_clause,[],[f1684])).
% 11.66/2.04 tff(f1692,plain,(
% 11.66/2.04 spl32_29 | ~spl32_128 | ~spl32_114),
% 11.66/2.04 inference(avatar_split_clause,[],[f1623,f1491,f1689,f683])).
% 11.66/2.04 tff(f1623,plain,(
% 11.66/2.04 ( ! [X0 : bool] : (fTrue != aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) | fTrue = X0) ) | ~spl32_114),
% 11.66/2.04 inference(equality_factoring,[],[f1492])).
% 11.66/2.04 tff(f1686,plain,(
% 11.66/2.04 spl32_127),
% 11.66/2.04 inference(avatar_split_clause,[],[f450,f1684])).
% 11.66/2.04 tff(f450,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f233])).
% 11.66/2.04 tff(f233,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f232])).
% 11.66/2.04 tff(f232,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f176])).
% 11.66/2.04 tff(f176,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f46])).
% 11.66/2.04 tff(f46,axiom,(
% 11.66/2.04 ! [X46 : dB,X28 : type,X31 : dB,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,X31),X28)) => (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X31),X46)) => pp(aa(type,bool,typing(X30,X46),X28))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_subject__reduction)).
% 11.66/2.04 tff(f1682,plain,(
% 11.66/2.04 spl32_126),
% 11.66/2.04 inference(avatar_split_clause,[],[f409,f1680])).
% 11.66/2.04 tff(f409,plain,(
% 11.66/2.04 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X0,X1,X2)),X1),sK11(X0,X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f284])).
% 11.66/2.04 tff(f284,plain,(
% 11.66/2.04 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : ((pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK10(X0,X1,X2)),X1),sK11(X0,X1,X2))) & aa(type,type,aa(type,fun(type,type),fun1,sK10(X0,X1,X2)),sK11(X0,X1,X2)) = X0) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f221,f283])).
% 11.66/2.04 tff(f283,plain,(
% 11.66/2.04 ! [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),sK10(X0,X1,X2)),X1),sK11(X0,X1,X2))) & aa(type,type,aa(type,fun(type,type),fun1,sK10(X0,X1,X2)),sK11(X0,X1,X2)) = X0))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f221,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f155])).
% 11.66/2.04 tff(f155,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f47])).
% 11.66/2.04 tff(f47,axiom,(
% 11.66/2.04 ! [X28 : type,X31 : dB,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,abs(X31)),X28)) => ~! [X47 : type,X38 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X47),X38) = X28 => ~pp(aa(type,bool,typing(shift(type,X30,zero_zero(nat),X47),X31),X38))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_typing__elims_I3_J)).
% 11.66/2.04 tff(f1670,plain,(
% 11.66/2.04 spl32_125 | ~spl32_89 | ~spl32_124),
% 11.66/2.04 inference(avatar_split_clause,[],[f1666,f1663,f1039,f1668])).
% 11.66/2.04 tff(f1663,plain,(
% 11.66/2.04 spl32_124 <=> ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,aa(type,fun(type,type),fun1,sK10(X0,X1,X2)),sK11(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_124])])).
% 11.66/2.04 tff(f1666,plain,(
% 11.66/2.04 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,combc(type,type,type,fun1,sK11(X0,X1,X2)),sK10(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) ) | (~spl32_89 | ~spl32_124)),
% 11.66/2.04 inference(forward_demodulation,[],[f1664,f1040])).
% 11.66/2.04 tff(f1664,plain,(
% 11.66/2.04 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,aa(type,fun(type,type),fun1,sK10(X0,X1,X2)),sK11(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) ) | ~spl32_124),
% 11.66/2.04 inference(avatar_component_clause,[],[f1663])).
% 11.66/2.04 tff(f1665,plain,(
% 11.66/2.04 spl32_124),
% 11.66/2.04 inference(avatar_split_clause,[],[f408,f1663])).
% 11.66/2.04 tff(f408,plain,(
% 11.66/2.04 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (aa(type,type,aa(type,fun(type,type),fun1,sK10(X0,X1,X2)),sK11(X0,X1,X2)) = X0 | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f284])).
% 11.66/2.04 tff(f1652,plain,(
% 11.66/2.04 spl32_123 | ~spl32_108 | ~spl32_122),
% 11.66/2.04 inference(avatar_split_clause,[],[f1647,f1643,f1325,f1649])).
% 11.66/2.04 tff(f1643,plain,(
% 11.66/2.04 spl32_122 <=> pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),t_a))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_122])])).
% 11.66/2.04 tff(f1647,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,abs(r),cons(dB,a,as))),t_a)) | (~spl32_108 | ~spl32_122)),
% 11.66/2.04 inference(forward_demodulation,[],[f1645,f1326])).
% 11.66/2.04 tff(f1645,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),t_a)) | ~spl32_122),
% 11.66/2.04 inference(avatar_component_clause,[],[f1643])).
% 11.66/2.04 tff(f1646,plain,(
% 11.66/2.04 spl32_122),
% 11.66/2.04 inference(avatar_split_clause,[],[f358,f1643])).
% 11.66/2.04 tff(f358,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),t_a))),
% 11.66/2.04 inference(cnf_transformation,[],[f43])).
% 11.66/2.04 tff(f43,axiom,(
% 11.66/2.04 pp(aa(type,bool,typing(shift(type,ea,ia,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),t_a))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Beta_I5_J)).
% 11.66/2.04 tff(f1632,plain,(
% 11.66/2.04 spl32_121 | ~spl32_108 | ~spl32_120),
% 11.66/2.04 inference(avatar_split_clause,[],[f1572,f1568,f1325,f1629])).
% 11.66/2.04 tff(f1568,plain,(
% 11.66/2.04 spl32_120 <=> pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),t1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_120])])).
% 11.66/2.04 tff(f1572,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,abs(r),cons(dB,a,as))),t1)) | (~spl32_108 | ~spl32_120)),
% 11.66/2.04 inference(forward_demodulation,[],[f1570,f1326])).
% 11.66/2.04 tff(f1570,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),t1)) | ~spl32_120),
% 11.66/2.04 inference(avatar_component_clause,[],[f1568])).
% 11.66/2.04 tff(f1571,plain,(
% 11.66/2.04 spl32_120),
% 11.66/2.04 inference(avatar_split_clause,[],[f357,f1568])).
% 11.66/2.04 tff(f357,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),t1))),
% 11.66/2.04 inference(cnf_transformation,[],[f26])).
% 11.66/2.04 tff(f26,axiom,(
% 11.66/2.04 pp(aa(type,bool,typing(shift(type,e,i,t),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),t1))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_T)).
% 11.66/2.04 tff(f1529,plain,(
% 11.66/2.04 spl32_119 | ~spl32_89 | ~spl32_118),
% 11.66/2.04 inference(avatar_split_clause,[],[f1525,f1522,f1039,f1527])).
% 11.66/2.04 tff(f1522,plain,(
% 11.66/2.04 spl32_118 <=> ! [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)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_118])])).
% 11.66/2.04 tff(f1525,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_118)),
% 11.66/2.04 inference(forward_demodulation,[],[f1523,f1040])).
% 11.66/2.04 tff(f1523,plain,(
% 11.66/2.04 ( ! [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)) ) | ~spl32_118),
% 11.66/2.04 inference(avatar_component_clause,[],[f1522])).
% 11.66/2.04 tff(f1524,plain,(
% 11.66/2.04 spl32_118),
% 11.66/2.04 inference(avatar_split_clause,[],[f478,f1522])).
% 11.66/2.04 tff(f478,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f191])).
% 11.66/2.04 tff(f191,plain,(
% 11.66/2.04 ! [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)),
% 11.66/2.04 inference(rectify,[],[f52])).
% 11.66/2.04 tff(f52,axiom,(
% 11.66/2.04 ! [X0 : $tType,X42 : type,X43 : type,X51 : fun(type,fun(type,X0)),X52 : fun(nat,X0)] : type_case(X0,X52,X51,aa(type,type,aa(type,fun(type,type),fun1,X43),X42)) = aa(type,X0,aa(type,fun(type,X0),X51,X43),X42)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_type_Osimps_I6_J)).
% 11.66/2.04 tff(f1520,plain,(
% 11.66/2.04 spl32_117),
% 11.66/2.04 inference(avatar_split_clause,[],[f459,f1518])).
% 11.66/2.04 tff(f459,plain,(
% 11.66/2.04 ( ! [X2 : nat,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK23(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f317])).
% 11.66/2.04 tff(f1516,plain,(
% 11.66/2.04 spl32_116),
% 11.66/2.04 inference(avatar_split_clause,[],[f452,f1514])).
% 11.66/2.04 tff(f452,plain,(
% 11.66/2.04 ( ! [X2 : nat,X3 : fun(nat,type),X0 : dB,X1 : type] : (it(subst(a,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),t)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,t),a),X1))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f236])).
% 11.66/2.04 tff(f236,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type)] : (it(subst(a,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),t)) | ~it(X0) | ~pp(aa(type,bool,typing(shift(type,X3,X2,t),a),X1)))),
% 11.66/2.04 inference(flattening,[],[f235])).
% 11.66/2.04 tff(f235,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type)] : (((it(subst(a,X0,X2)) | ~pp(aa(type,bool,typing(X3,X0),t))) | ~it(X0)) | ~pp(aa(type,bool,typing(shift(type,X3,X2,t),a),X1)))),
% 11.66/2.04 inference(ennf_transformation,[],[f178])).
% 11.66/2.04 tff(f178,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : type,X2 : nat,X3 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X3,X2,t),a),X1)) => (it(X0) => (pp(aa(type,bool,typing(X3,X0),t)) => it(subst(a,X0,X2)))))),
% 11.66/2.04 inference(rectify,[],[f39])).
% 11.66/2.04 tff(f39,axiom,(
% 11.66/2.04 ! [X27 : dB,X36 : type,X29 : nat,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X30,X29,t),a),X36)) => (it(X27) => (pp(aa(type,bool,typing(X30,X27),t)) => it(subst(a,X27,X29)))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_SI2)).
% 11.66/2.04 tff(f1497,plain,(
% 11.66/2.04 spl32_115 | ~spl32_89 | ~spl32_113),
% 11.66/2.04 inference(avatar_split_clause,[],[f1489,f1486,f1039,f1495])).
% 11.66/2.04 tff(f1486,plain,(
% 11.66/2.04 spl32_113 <=> ! [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))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_113])])).
% 11.66/2.04 tff(f1489,plain,(
% 11.66/2.04 ( ! [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)) ) | (~spl32_89 | ~spl32_113)),
% 11.66/2.04 inference(forward_demodulation,[],[f1487,f1040])).
% 11.66/2.04 tff(f1487,plain,(
% 11.66/2.04 ( ! [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)) ) | ~spl32_113),
% 11.66/2.04 inference(avatar_component_clause,[],[f1486])).
% 11.66/2.04 tff(f1493,plain,(
% 11.66/2.04 spl32_114 | spl32_32 | ~spl32_104),
% 11.66/2.04 inference(avatar_split_clause,[],[f1363,f1309,f698,f1491])).
% 11.66/2.04 tff(f1309,plain,(
% 11.66/2.04 spl32_104 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | X0 = X1 | fTrue = X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_104])])).
% 11.66/2.04 tff(f1363,plain,(
% 11.66/2.04 ( ! [X0 : bool] : (aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as))) = X0 | fTrue = X0) ) | (spl32_32 | ~spl32_104)),
% 11.66/2.04 inference(resolution,[],[f1310,f700])).
% 11.66/2.04 tff(f1310,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(X0) | X0 = X1 | fTrue = X1) ) | ~spl32_104),
% 11.66/2.04 inference(avatar_component_clause,[],[f1309])).
% 11.66/2.04 tff(f1488,plain,(
% 11.66/2.04 spl32_113),
% 11.66/2.04 inference(avatar_split_clause,[],[f404,f1486])).
% 11.66/2.04 tff(f404,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f217])).
% 11.66/2.04 tff(f217,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(ennf_transformation,[],[f151])).
% 11.66/2.04 tff(f151,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f25])).
% 11.66/2.04 tff(f25,axiom,(
% 11.66/2.04 ! [X9 : dB,X6 : list(dB),X8 : list(dB)] : (step1(dB,beta,X8,X6) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X9,X8)),foldl(dB,dB,app,X9,X6))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_apps__preserves__betas)).
% 11.66/2.04 tff(f1473,plain,(
% 11.66/2.04 spl32_112 | ~spl32_89 | ~spl32_111),
% 11.66/2.04 inference(avatar_split_clause,[],[f1469,f1465,f1039,f1471])).
% 11.66/2.04 tff(f1465,plain,(
% 11.66/2.04 spl32_111 <=> ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK5(X0,X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_111])])).
% 11.66/2.04 tff(f1469,plain,(
% 11.66/2.04 ( ! [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,sK5(X0,X1)),X1))) ) | (~spl32_89 | ~spl32_111)),
% 11.66/2.04 inference(forward_demodulation,[],[f1468,f1040])).
% 11.66/2.04 tff(f1468,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,combc(dB,dB,bool,beta,sK5(X0,X1)),X1)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) ) | (~spl32_89 | ~spl32_111)),
% 11.66/2.04 inference(forward_demodulation,[],[f1466,f1040])).
% 11.66/2.04 tff(f1466,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK5(X0,X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) ) | ~spl32_111),
% 11.66/2.04 inference(avatar_component_clause,[],[f1465])).
% 11.66/2.04 tff(f1467,plain,(
% 11.66/2.04 spl32_111),
% 11.66/2.04 inference(avatar_split_clause,[],[f381,f1465])).
% 11.66/2.04 tff(f381,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK5(X0,X1))) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f273])).
% 11.66/2.04 tff(f273,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : dB] : ((pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X1),sK5(X0,X1))) & abs(sK5(X0,X1)) = X0) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f214,f272])).
% 11.66/2.04 tff(f272,plain,(
% 11.66/2.04 ! [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),sK5(X0,X1))) & abs(sK5(X0,X1)) = X0))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f214,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f133])).
% 11.66/2.04 tff(f133,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f21])).
% 11.66/2.04 tff(f21,axiom,(
% 11.66/2.04 ! [X5 : dB,X20 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X20)),X5)) => ~! [X25 : dB] : (abs(X25) = X5 => ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X20),X25))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_beta__cases_I2_J)).
% 11.66/2.04 tff(f1454,plain,(
% 11.66/2.04 spl32_110 | ~spl32_89 | ~spl32_109),
% 11.66/2.04 inference(avatar_split_clause,[],[f1450,f1446,f1039,f1452])).
% 11.66/2.04 tff(f1446,plain,(
% 11.66/2.04 spl32_109 <=> ! [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))))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_109])])).
% 11.66/2.04 tff(f1450,plain,(
% 11.66/2.04 ( ! [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))))) ) | (~spl32_89 | ~spl32_109)),
% 11.66/2.04 inference(forward_demodulation,[],[f1449,f1040])).
% 11.66/2.04 tff(f1449,plain,(
% 11.66/2.04 ( ! [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)))) ) | (~spl32_89 | ~spl32_109)),
% 11.66/2.04 inference(forward_demodulation,[],[f1447,f1040])).
% 11.66/2.04 tff(f1447,plain,(
% 11.66/2.04 ( ! [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))))) ) | ~spl32_109),
% 11.66/2.04 inference(avatar_component_clause,[],[f1446])).
% 11.66/2.04 tff(f1448,plain,(
% 11.66/2.04 spl32_109),
% 11.66/2.04 inference(avatar_split_clause,[],[f373,f1446])).
% 11.66/2.04 tff(f373,plain,(
% 11.66/2.04 ( ! [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))))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f126])).
% 11.66/2.04 tff(f126,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f4])).
% 11.66/2.04 tff(f4,axiom,(
% 11.66/2.04 ! [X4 : dB,X5 : dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X5)),X4)),subst(X5,X4,zero_zero(nat))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_beta)).
% 11.66/2.04 tff(f1327,plain,(
% 11.66/2.04 spl32_108),
% 11.66/2.04 inference(avatar_split_clause,[],[f493,f1325])).
% 11.66/2.04 tff(f1323,plain,(
% 11.66/2.04 spl32_107),
% 11.66/2.04 inference(avatar_split_clause,[],[f492,f1321])).
% 11.66/2.04 tff(f492,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f200])).
% 11.66/2.04 tff(f200,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f78])).
% 11.66/2.04 tff(f78,axiom,(
% 11.66/2.04 ! [X1 : $tType,X0 : $tType,X49 : X0,X48 : list(X1),X21 : X1,X50 : fun(X1,fun(X0,X0))] : foldr(X1,X0,X50,cons(X1,X21,X48),X49) = aa(X0,X0,aa(X1,fun(X0,X0),X50,X21),foldr(X1,X0,X50,X48,X49))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_foldr_Osimps_I2_J)).
% 11.66/2.04 tff(f1319,plain,(
% 11.66/2.04 spl32_106),
% 11.66/2.04 inference(avatar_split_clause,[],[f476,f1317])).
% 11.66/2.04 tff(f476,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f330])).
% 11.66/2.04 tff(f330,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f329])).
% 11.66/2.04 tff(f329,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(nnf_transformation,[],[f190])).
% 11.66/2.04 tff(f190,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f13])).
% 11.66/2.04 tff(f13,axiom,(
% 11.66/2.04 ! [X15 : dB,X16 : dB,X17 : dB,X18 : dB] : (aa(dB,dB,aa(dB,fun(dB,dB),app,X18),X17) = aa(dB,dB,aa(dB,fun(dB,dB),app,X16),X15) <=> (X15 = X17 & X16 = X18))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_dB_Osimps_I2_J)).
% 11.66/2.04 tff(f1315,plain,(
% 11.66/2.04 spl32_105),
% 11.66/2.04 inference(avatar_split_clause,[],[f475,f1313])).
% 11.66/2.04 tff(f475,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f330])).
% 11.66/2.04 tff(f1311,plain,(
% 11.66/2.04 spl32_104 | ~spl32_7 | ~spl32_79),
% 11.66/2.04 inference(avatar_split_clause,[],[f1179,f965,f578,f1309])).
% 11.66/2.04 tff(f1179,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(X0) | X0 = X1 | fTrue = X1) ) | (~spl32_7 | ~spl32_79)),
% 11.66/2.04 inference(superposition,[],[f580,f966])).
% 11.66/2.04 tff(f580,plain,(
% 11.66/2.04 pp(fTrue) | ~spl32_7),
% 11.66/2.04 inference(avatar_component_clause,[],[f578])).
% 11.66/2.04 tff(f1307,plain,(
% 11.66/2.04 spl32_103),
% 11.66/2.04 inference(avatar_split_clause,[],[f473,f1305])).
% 11.66/2.04 tff(f473,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f328])).
% 11.66/2.04 tff(f328,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f327])).
% 11.66/2.04 tff(f327,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(nnf_transformation,[],[f189])).
% 11.66/2.04 tff(f189,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f38])).
% 11.66/2.04 tff(f38,axiom,(
% 11.66/2.04 ! [X40 : type,X41 : type,X42 : type,X43 : type] : (aa(type,type,aa(type,fun(type,type),fun1,X43),X42) = aa(type,type,aa(type,fun(type,type),fun1,X41),X40) <=> (X40 = X42 & X41 = X43))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_type_Osimps_I2_J)).
% 11.66/2.04 tff(f1303,plain,(
% 11.66/2.04 spl32_102),
% 11.66/2.04 inference(avatar_split_clause,[],[f472,f1301])).
% 11.66/2.04 tff(f472,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f328])).
% 11.66/2.04 tff(f1299,plain,(
% 11.66/2.04 spl32_101),
% 11.66/2.04 inference(avatar_split_clause,[],[f456,f1297])).
% 11.66/2.04 tff(f456,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK22(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f315])).
% 11.66/2.04 tff(f1295,plain,(
% 11.66/2.04 spl32_100),
% 11.66/2.04 inference(avatar_split_clause,[],[f454,f1293])).
% 11.66/2.04 tff(f454,plain,(
% 11.66/2.04 ( ! [X2 : dB,X3 : fun(nat,type),X0 : type,X1 : list(dB)] : (pp(aa(list(type),bool,typings(X3,X1),sK21(X0,X1,X2,X3))) | ~pp(aa(type,bool,typing(X3,foldl(dB,dB,app,X2,X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f313])).
% 11.66/2.04 tff(f1284,plain,(
% 11.66/2.04 spl32_99 | ~spl32_89 | ~spl32_98),
% 11.66/2.04 inference(avatar_split_clause,[],[f1280,f1277,f1039,f1282])).
% 11.66/2.04 tff(f1277,plain,(
% 11.66/2.04 spl32_98 <=> ! [X2 : nat,X0 : dB,X1 : list(dB)] : (step1(dB,beta,X1,sK17(X0,X1,X2)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_98])])).
% 11.66/2.04 tff(f1280,plain,(
% 11.66/2.04 ( ! [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,sK17(X0,X1,X2))) ) | (~spl32_89 | ~spl32_98)),
% 11.66/2.04 inference(forward_demodulation,[],[f1278,f1040])).
% 11.66/2.04 tff(f1278,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (step1(dB,beta,X1,sK17(X0,X1,X2)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))) ) | ~spl32_98),
% 11.66/2.04 inference(avatar_component_clause,[],[f1277])).
% 11.66/2.04 tff(f1279,plain,(
% 11.66/2.04 spl32_98),
% 11.66/2.04 inference(avatar_split_clause,[],[f421,f1277])).
% 11.66/2.04 tff(f421,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : dB,X1 : list(dB)] : (step1(dB,beta,X1,sK17(X0,X1,X2)) | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,var(X2),X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f295])).
% 11.66/2.04 tff(f1275,plain,(
% 11.66/2.04 spl32_97),
% 11.66/2.04 inference(avatar_split_clause,[],[f407,f1273])).
% 11.66/2.04 tff(f407,plain,(
% 11.66/2.04 ( ! [X2 : fun(nat,type),X0 : type,X1 : dB] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK8(X1,X2)),X1),sK9(X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f282])).
% 11.66/2.04 tff(f282,plain,(
% 11.66/2.04 ! [X0 : type,X1 : dB,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(shift(type,X2,zero_zero(nat),sK8(X1,X2)),X1),sK9(X1,X2))) | ~pp(aa(type,bool,typing(X2,abs(X1)),X0)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f220,f281])).
% 11.66/2.04 tff(f281,plain,(
% 11.66/2.04 ! [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),sK8(X1,X2)),X1),sK9(X1,X2))))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f220,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f154])).
% 11.66/2.04 tff(f154,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(rectify,[],[f36])).
% 11.66/2.04 tff(f36,axiom,(
% 11.66/2.04 ! [X28 : type,X31 : dB,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,abs(X31)),X28)) => ~! [X38 : type,X39 : type] : ~pp(aa(type,bool,typing(shift(type,X30,zero_zero(nat),X38),X31),X39)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_abs__typeE)).
% 11.66/2.04 tff(f1262,plain,(
% 11.66/2.04 spl32_96 | ~spl32_89 | ~spl32_95),
% 11.66/2.04 inference(avatar_split_clause,[],[f1106,f1102,f1039,f1260])).
% 11.66/2.04 tff(f1102,plain,(
% 11.66/2.04 spl32_95 <=> ! [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)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_95])])).
% 11.66/2.04 tff(f1106,plain,(
% 11.66/2.04 ( ! [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)))) ) | (~spl32_89 | ~spl32_95)),
% 11.66/2.04 inference(forward_demodulation,[],[f1105,f1040])).
% 11.66/2.04 tff(f1105,plain,(
% 11.66/2.04 ( ! [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))) ) | (~spl32_89 | ~spl32_95)),
% 11.66/2.04 inference(forward_demodulation,[],[f1103,f1040])).
% 11.66/2.04 tff(f1103,plain,(
% 11.66/2.04 ( ! [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))) ) | ~spl32_95),
% 11.66/2.04 inference(avatar_component_clause,[],[f1102])).
% 11.66/2.04 tff(f1104,plain,(
% 11.66/2.04 spl32_95),
% 11.66/2.04 inference(avatar_split_clause,[],[f379,f1102])).
% 11.66/2.04 tff(f379,plain,(
% 11.66/2.04 ( ! [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))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f213])).
% 11.66/2.04 tff(f213,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(ennf_transformation,[],[f132])).
% 11.66/2.04 tff(f132,plain,(
% 11.66/2.04 ! [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))))),
% 11.66/2.04 inference(rectify,[],[f6])).
% 11.66/2.04 tff(f6,axiom,(
% 11.66/2.04 ! [X4 : dB,X5 : dB] : (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X5),X4)) => pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X5)),abs(X4))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_abs)).
% 11.66/2.04 tff(f1100,plain,(
% 11.66/2.04 spl32_94),
% 11.66/2.04 inference(avatar_split_clause,[],[f416,f1098])).
% 11.66/2.04 tff(f1098,plain,(
% 11.66/2.04 spl32_94 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,subst(sK12(X0,X1,X2),sK13(X0,X1,X2),zero_zero(nat)),sK14(X0,X1,X2)) = X0 | ~sP0(X0,X1,X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_94])])).
% 11.66/2.04 tff(f416,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (foldl(dB,dB,app,subst(sK12(X0,X1,X2),sK13(X0,X1,X2),zero_zero(nat)),sK14(X0,X1,X2)) = X0 | ~sP0(X0,X1,X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f289])).
% 11.66/2.04 tff(f289,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : list(dB),X2 : dB] : (((foldl(dB,dB,app,subst(sK12(X0,X1,X2),sK13(X0,X1,X2),zero_zero(nat)),sK14(X0,X1,X2)) = X0 & cons(dB,sK13(X0,X1,X2),sK14(X0,X1,X2)) = X1) & abs(sK12(X0,X1,X2)) = X2) | ~sP0(X0,X1,X2))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f286,f288,f287])).
% 11.66/2.04 tff(f287,plain,(
% 11.66/2.04 ! [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(sK12(X0,X1,X2),X4,zero_zero(nat)),X5) = X0 & cons(dB,X4,X5) = X1) & abs(sK12(X0,X1,X2)) = X2))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f288,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : list(dB),X2 : dB] : (? [X5 : list(dB),X4 : dB] : (foldl(dB,dB,app,subst(sK12(X0,X1,X2),X4,zero_zero(nat)),X5) = X0 & cons(dB,X4,X5) = X1) => (foldl(dB,dB,app,subst(sK12(X0,X1,X2),sK13(X0,X1,X2),zero_zero(nat)),sK14(X0,X1,X2)) = X0 & cons(dB,sK13(X0,X1,X2),sK14(X0,X1,X2)) = X1))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f286,plain,(
% 11.66/2.04 ! [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) | ~sP0(X0,X1,X2))),
% 11.66/2.04 inference(rectify,[],[f285])).
% 11.66/2.04 tff(f285,plain,(
% 11.66/2.04 ! [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) | ~sP0(X0,X1,X2))),
% 11.66/2.04 inference(nnf_transformation,[],[f263])).
% 11.66/2.04 tff(f1086,plain,(
% 11.66/2.04 spl32_93),
% 11.66/2.04 inference(avatar_split_clause,[],[f463,f1084])).
% 11.66/2.04 tff(f463,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK25(X0,X1,X2,X3)) != aa(X1,X0,X2,sK25(X0,X1,X2,X3))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f321])).
% 11.66/2.04 tff(f321,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : $tType,X2 : fun(X1,X0),X3 : fun(X1,X0)] : (X2 = X3 | aa(X1,X0,X3,sK25(X0,X1,X2,X3)) != aa(X1,X0,X2,sK25(X0,X1,X2,X3)))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f244,f320])).
% 11.66/2.04 tff(f320,plain,(
% 11.66/2.04 ! [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,sK25(X0,X1,X2,X3)) != aa(X1,X0,X2,sK25(X0,X1,X2,X3)))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f244,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(ennf_transformation,[],[f185])).
% 11.66/2.04 tff(f185,plain,(
% 11.66/2.04 ! [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)),
% 11.66/2.04 inference(rectify,[],[f75])).
% 11.66/2.04 tff(f75,axiom,(
% 11.66/2.04 ! [X1 : $tType,X0 : $tType,X77 : fun(X0,X1),X50 : fun(X0,X1)] : (! [X53 : X0] : aa(X0,X1,X50,X53) = aa(X0,X1,X77,X53) => X50 = X77)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext)).
% 11.66/2.04 tff(f1066,plain,(
% 11.66/2.04 spl32_92),
% 11.66/2.04 inference(avatar_split_clause,[],[f543,f1064])).
% 11.66/2.04 tff(f1064,plain,(
% 11.66/2.04 spl32_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)) | step1(X3,X2,X1,X0) | ~sP2(X3,X0,X1,X2,X4,X5))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_92])])).
% 11.66/2.04 tff(f543,plain,(
% 11.66/2.04 ( ! [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) | ~sP2(X3,X0,X1,X2,X4,X5)) )),
% 11.66/2.04 inference(forward_demodulation,[],[f498,f490])).
% 11.66/2.04 tff(f498,plain,(
% 11.66/2.04 ( ! [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)) | ~sP2(X3,X0,X1,X2,X4,X5)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f341])).
% 11.66/2.04 tff(f341,plain,(
% 11.66/2.04 ! [X0 : list(X3),X1 : list(X3),X2 : fun(X3,fun(X3,bool)),X3 : $tType,X4 : X3,X5 : X3] : ((sP2(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))) | ~sP2(X3,X0,X1,X2,X4,X5)))),
% 11.66/2.04 inference(rectify,[],[f340])).
% 11.66/2.04 tff(f340,plain,(
% 11.66/2.04 ! [X1 : list(X0),X3 : list(X0),X5 : fun(X0,fun(X0,bool)),X0 : $tType,X4 : X0,X2 : X0] : ((sP2(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))) | ~sP2(X0,X1,X3,X5,X4,X2)))),
% 11.66/2.04 inference(flattening,[],[f339])).
% 11.66/2.04 tff(f339,plain,(
% 11.66/2.04 ! [X1 : list(X0),X3 : list(X0),X5 : fun(X0,fun(X0,bool)),X0 : $tType,X4 : X0,X2 : X0] : ((sP2(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)))) | ~sP2(X0,X1,X3,X5,X4,X2)))),
% 11.66/2.04 inference(nnf_transformation,[],[f267])).
% 11.66/2.04 tff(f267,plain,(
% 11.66/2.04 ! [X1 : list(X0),X3 : list(X0),X5 : fun(X0,fun(X0,bool)),X0 : $tType,X4 : X0,X2 : X0] : (sP2(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)))))),
% 11.66/2.04 introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])])).
% 11.66/2.04 tff(f1062,plain,(
% 11.66/2.04 spl32_91),
% 11.66/2.04 inference(avatar_split_clause,[],[f491,f1060])).
% 11.66/2.04 tff(f491,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f199])).
% 11.66/2.04 tff(f199,plain,(
% 11.66/2.04 ! [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)),
% 11.66/2.04 inference(rectify,[],[f59])).
% 11.66/2.04 tff(f59,axiom,(
% 11.66/2.04 ! [X0 : $tType,X1 : $tType,X61 : list(X1),X49 : X1,X51 : fun(X1,fun(list(X1),X0)),X52 : X0] : list_case(X0,X1,X52,X51,cons(X1,X49,X61)) = aa(list(X1),X0,aa(X1,fun(list(X1),X0),X51,X49),X61)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_list_Osimps_I5_J)).
% 11.66/2.04 tff(f1045,plain,(
% 11.66/2.04 spl32_90 | ~spl32_24 | ~spl32_40),
% 11.66/2.04 inference(avatar_split_clause,[],[f754,f747,f652,f1043])).
% 11.66/2.04 tff(f1043,plain,(
% 11.66/2.04 spl32_90 <=> ! [X0 : $tType,X1 : X0] : nil(X0) != insert(X0,X1,nil(X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_90])])).
% 11.66/2.04 tff(f652,plain,(
% 11.66/2.04 spl32_24 <=> ! [X0 : $tType,X2 : X0,X3 : list(X0)] : nil(X0) != cons(X0,X2,X3)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_24])])).
% 11.66/2.04 tff(f754,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X1 : X0] : (nil(X0) != insert(X0,X1,nil(X0))) ) | (~spl32_24 | ~spl32_40)),
% 11.66/2.04 inference(superposition,[],[f653,f748])).
% 11.66/2.04 tff(f653,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0)] : (nil(X0) != cons(X0,X2,X3)) ) | ~spl32_24),
% 11.66/2.04 inference(avatar_component_clause,[],[f652])).
% 11.66/2.04 tff(f1041,plain,(
% 11.66/2.04 spl32_89),
% 11.66/2.04 inference(avatar_split_clause,[],[f490,f1039])).
% 11.66/2.04 tff(f1036,plain,(
% 11.66/2.04 spl32_88),
% 11.66/2.04 inference(avatar_split_clause,[],[f544,f1034])).
% 11.66/2.04 tff(f1034,plain,(
% 11.66/2.04 spl32_88 <=> ! [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 | ~sP2(X3,X0,X1,X2,X4,X5))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_88])])).
% 11.66/2.04 tff(f544,plain,(
% 11.66/2.04 ( ! [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 | ~sP2(X3,X0,X1,X2,X4,X5)) )),
% 11.66/2.04 inference(forward_demodulation,[],[f496,f490])).
% 11.66/2.04 tff(f496,plain,(
% 11.66/2.04 ( ! [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)) | ~sP2(X3,X0,X1,X2,X4,X5)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f341])).
% 11.66/2.04 tff(f1030,plain,(
% 11.66/2.04 spl32_87),
% 11.66/2.04 inference(avatar_split_clause,[],[f540,f1028])).
% 11.66/2.04 tff(f540,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2)) )),
% 11.66/2.04 inference(forward_demodulation,[],[f401,f371])).
% 11.66/2.04 tff(f371,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X1 : X0] : (insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f124])).
% 11.66/2.04 tff(f124,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : X0] : insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0))),
% 11.66/2.04 inference(rectify,[],[f67])).
% 11.66/2.04 tff(f67,axiom,(
% 11.66/2.04 ! [X0 : $tType,X65 : X0] : insert(X0,X65,nil(X0)) = cons(X0,X65,nil(X0))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_insert__Nil)).
% 11.66/2.04 tff(f401,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f215])).
% 11.66/2.04 tff(f215,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : X0,X2 : fun(nat,bool)] : ((nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2)) & (cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) | ~member(nat,zero_zero(nat),X2)))),
% 11.66/2.04 inference(ennf_transformation,[],[f149])).
% 11.66/2.04 tff(f149,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : X0,X2 : fun(nat,bool)] : ((~member(nat,zero_zero(nat),X2) => nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2)) & (member(nat,zero_zero(nat),X2) => cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2)))),
% 11.66/2.04 inference(rectify,[],[f68])).
% 11.66/2.04 tff(f68,axiom,(
% 11.66/2.04 ! [X0 : $tType,X21 : X0,X74 : fun(nat,bool)] : ((~member(nat,zero_zero(nat),X74) => nil(X0) = sublist(X0,cons(X0,X21,nil(X0)),X74)) & (member(nat,zero_zero(nat),X74) => cons(X0,X21,nil(X0)) = sublist(X0,cons(X0,X21,nil(X0)),X74)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_sublist__singleton)).
% 11.66/2.04 tff(f1026,plain,(
% 11.66/2.04 spl32_86),
% 11.66/2.04 inference(avatar_split_clause,[],[f446,f1024])).
% 11.66/2.04 tff(f446,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f172])).
% 11.66/2.04 tff(f172,plain,(
% 11.66/2.04 ! [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)),
% 11.66/2.04 inference(rectify,[],[f97])).
% 11.66/2.04 tff(f97,axiom,(
% 11.66/2.04 ! [X6 : list(dB),X82 : nat,X31 : dB,X7 : dB] : foldl(dB,dB,app,var(X82),X6) != aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X7)),X31)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Abs__App__neq__Var__apps)).
% 11.66/2.04 tff(f1016,plain,(
% 11.66/2.04 spl32_85),
% 11.66/2.04 inference(avatar_split_clause,[],[f470,f1014])).
% 11.66/2.04 tff(f1014,plain,(
% 11.66/2.04 spl32_85 <=> ! [X2 : list(dB),X0 : list(dB),X1 : dB,X3 : dB] : (X0 = X2 | foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_85])])).
% 11.66/2.04 tff(f470,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f326])).
% 11.66/2.04 tff(f326,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f325])).
% 11.66/2.04 tff(f325,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(nnf_transformation,[],[f188])).
% 11.66/2.04 tff(f188,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f5])).
% 11.66/2.04 tff(f5,axiom,(
% 11.66/2.04 ! [X6 : list(dB),X7 : dB,X8 : list(dB),X9 : dB] : (foldl(dB,dB,app,abs(X9),X8) = foldl(dB,dB,app,abs(X7),X6) <=> (X6 = X8 & X7 = X9))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Abs__apps__eq__Abs__apps__conv)).
% 11.66/2.04 tff(f1012,plain,(
% 11.66/2.04 spl32_84 | ~spl32_34 | ~spl32_38),
% 11.66/2.04 inference(avatar_split_clause,[],[f740,f733,f708,f1010])).
% 11.66/2.04 tff(f1010,plain,(
% 11.66/2.04 spl32_84 <=> ! [X0 : fun(nat,type)] : member(list(type),nil(type),typings(X0,nil(dB)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_84])])).
% 11.66/2.04 tff(f733,plain,(
% 11.66/2.04 spl32_38 <=> ! [X1 : fun(nat,type)] : pp(aa(list(type),bool,typings(X1,nil(dB)),nil(type)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_38])])).
% 11.66/2.04 tff(f740,plain,(
% 11.66/2.04 ( ! [X0 : fun(nat,type)] : (member(list(type),nil(type),typings(X0,nil(dB)))) ) | (~spl32_34 | ~spl32_38)),
% 11.66/2.04 inference(resolution,[],[f734,f709])).
% 11.66/2.04 tff(f734,plain,(
% 11.66/2.04 ( ! [X1 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),nil(type)))) ) | ~spl32_38),
% 11.66/2.04 inference(avatar_component_clause,[],[f733])).
% 11.66/2.04 tff(f1008,plain,(
% 11.66/2.04 spl32_83),
% 11.66/2.04 inference(avatar_split_clause,[],[f467,f1006])).
% 11.66/2.04 tff(f1006,plain,(
% 11.66/2.04 spl32_83 <=> ! [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))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_83])])).
% 11.66/2.04 tff(f467,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f324])).
% 11.66/2.04 tff(f324,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f323])).
% 11.66/2.04 tff(f323,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(nnf_transformation,[],[f187])).
% 11.66/2.04 tff(f187,plain,(
% 11.66/2.04 ! [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))),
% 11.66/2.04 inference(rectify,[],[f85])).
% 11.66/2.04 tff(f85,axiom,(
% 11.66/2.04 ! [X6 : list(dB),X82 : nat,X8 : list(dB),X83 : nat] : (foldl(dB,dB,app,var(X83),X8) = foldl(dB,dB,app,var(X82),X6) <=> (X6 = X8 & X82 = X83))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Var__apps__eq__Var__apps__conv)).
% 11.66/2.04 tff(f1002,plain,(
% 11.66/2.04 spl32_82 | ~spl32_81),
% 11.66/2.04 inference(avatar_split_clause,[],[f998,f995,f1000])).
% 11.66/2.04 tff(f995,plain,(
% 11.66/2.04 spl32_81 <=> ! [X0 : dB,X1 : dB] : (abs(sK5(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_81])])).
% 11.66/2.04 tff(f998,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),abs(X1))) | abs(sK5(X0,X1)) = X0) ) | ~spl32_81),
% 11.66/2.04 inference(forward_demodulation,[],[f996,f490])).
% 11.66/2.04 tff(f996,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (abs(sK5(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) ) | ~spl32_81),
% 11.66/2.04 inference(avatar_component_clause,[],[f995])).
% 11.66/2.04 tff(f997,plain,(
% 11.66/2.04 spl32_81),
% 11.66/2.04 inference(avatar_split_clause,[],[f380,f995])).
% 11.66/2.04 tff(f380,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (abs(sK5(X0,X1)) = X0 | ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,abs(X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f273])).
% 11.66/2.04 tff(f971,plain,(
% 11.66/2.04 spl32_80),
% 11.66/2.04 inference(avatar_split_clause,[],[f542,f969])).
% 11.66/2.04 tff(f542,plain,(
% 11.66/2.04 ( ! [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)) | sP2(X3,X1,X1,X2,X4,X5)) )),
% 11.66/2.04 inference(forward_demodulation,[],[f537,f490])).
% 11.66/2.04 tff(f537,plain,(
% 11.66/2.04 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X1 : list(X3),X4 : X3,X5 : X3] : (sP2(X3,X1,X1,X2,X4,X5) | ~pp(aa(X3,bool,aa(X3,fun(X3,bool),X2,X4),X5))) )),
% 11.66/2.04 inference(equality_resolution,[],[f500])).
% 11.66/2.04 tff(f500,plain,(
% 11.66/2.04 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (sP2(X3,X0,X1,X2,X4,X5) | X0 != X1 | ~pp(aa(X3,bool,aa(X3,fun(X3,bool),X2,X4),X5))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f341])).
% 11.66/2.04 tff(f967,plain,(
% 11.66/2.04 spl32_79 | ~spl32_12),
% 11.66/2.04 inference(avatar_split_clause,[],[f610,f599,f965])).
% 11.66/2.04 tff(f610,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (X0 = X1 | fTrue = X1 | fTrue = X0) ) | ~spl32_12),
% 11.66/2.04 inference(superposition,[],[f600,f600])).
% 11.66/2.04 tff(f963,plain,(
% 11.66/2.04 spl32_78),
% 11.66/2.04 inference(avatar_split_clause,[],[f503,f961])).
% 11.66/2.04 tff(f503,plain,(
% 11.66/2.04 ( ! [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)) | ~sP2(X0,X1,X3,X5,X4,X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f342])).
% 11.66/2.04 tff(f342,plain,(
% 11.66/2.04 ! [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)) | ~sP2(X0,X1,X3,X5,X4,X2)) & (sP2(X0,X1,X3,X5,X4,X2) | ~step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1))))),
% 11.66/2.04 inference(nnf_transformation,[],[f268])).
% 11.66/2.04 tff(f268,plain,(
% 11.66/2.04 ! [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)) <=> sP2(X0,X1,X3,X5,X4,X2))),
% 11.66/2.04 inference(definition_folding,[],[f204,f267])).
% 11.66/2.04 tff(f204,plain,(
% 11.66/2.04 ! [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)))))),
% 11.66/2.04 inference(rectify,[],[f57])).
% 11.66/2.04 tff(f57,axiom,(
% 11.66/2.04 ! [X0 : $tType,X48 : list(X0),X21 : X0,X62 : list(X0),X63 : X0,X9 : fun(X0,fun(X0,bool))] : (step1(X0,X9,cons(X0,X63,X62),cons(X0,X21,X48)) <=> ((step1(X0,X9,X62,X48) & X21 = X63) | (X48 = X62 & pp(aa(X0,bool,aa(X0,fun(X0,bool),X9,X63),X21)))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Cons__step1__Cons)).
% 11.66/2.04 tff(f959,plain,(
% 11.66/2.04 spl32_77),
% 11.66/2.04 inference(avatar_split_clause,[],[f502,f957])).
% 11.66/2.04 tff(f502,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0,X5 : fun(X0,fun(X0,bool))] : (sP2(X0,X1,X3,X5,X4,X2) | ~step1(X0,X5,cons(X0,X4,X3),cons(X0,X2,X1))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f342])).
% 11.66/2.04 tff(f955,plain,(
% 11.66/2.04 spl32_76),
% 11.66/2.04 inference(avatar_split_clause,[],[f469,f953])).
% 11.66/2.04 tff(f469,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f326])).
% 11.66/2.04 tff(f951,plain,(
% 11.66/2.04 spl32_75),
% 11.66/2.04 inference(avatar_split_clause,[],[f466,f949])).
% 11.66/2.04 tff(f466,plain,(
% 11.66/2.04 ( ! [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)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f324])).
% 11.66/2.04 tff(f947,plain,(
% 11.66/2.04 spl32_74),
% 11.66/2.04 inference(avatar_split_clause,[],[f539,f945])).
% 11.66/2.04 tff(f539,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2)) )),
% 11.66/2.04 inference(forward_demodulation,[],[f402,f371])).
% 11.66/2.04 tff(f402,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(nat,bool),X1 : X0] : (nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) | member(nat,zero_zero(nat),X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f215])).
% 11.66/2.04 tff(f943,plain,(
% 11.66/2.04 spl32_73),
% 11.66/2.04 inference(avatar_split_clause,[],[f415,f941])).
% 11.66/2.04 tff(f941,plain,(
% 11.66/2.04 spl32_73 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (cons(dB,sK13(X0,X1,X2),sK14(X0,X1,X2)) = X1 | ~sP0(X0,X1,X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_73])])).
% 11.66/2.04 tff(f415,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (cons(dB,sK13(X0,X1,X2),sK14(X0,X1,X2)) = X1 | ~sP0(X0,X1,X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f289])).
% 11.66/2.04 tff(f918,plain,(
% 11.66/2.04 spl32_72),
% 11.66/2.04 inference(avatar_split_clause,[],[f499,f916])).
% 11.66/2.04 tff(f916,plain,(
% 11.66/2.04 spl32_72 <=> ! [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 | ~sP2(X3,X0,X1,X2,X4,X5))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_72])])).
% 11.66/2.04 tff(f499,plain,(
% 11.66/2.04 ( ! [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 | ~sP2(X3,X0,X1,X2,X4,X5)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f341])).
% 11.66/2.04 tff(f914,plain,(
% 11.66/2.04 spl32_71),
% 11.66/2.04 inference(avatar_split_clause,[],[f440,f912])).
% 11.66/2.04 tff(f440,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (X0 = X2 | foldl(dB,dB,app,X0,X1) != foldl(dB,dB,app,X2,X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f311])).
% 11.66/2.04 tff(f311,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(nnf_transformation,[],[f167])).
% 11.66/2.04 tff(f167,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : list(dB),X2 : dB] : (foldl(dB,dB,app,X0,X1) = foldl(dB,dB,app,X2,X1) <=> X0 = X2)),
% 11.66/2.04 inference(rectify,[],[f10])).
% 11.66/2.04 tff(f10,axiom,(
% 11.66/2.04 ! [X7 : dB,X12 : list(dB),X9 : dB] : (foldl(dB,dB,app,X9,X12) = foldl(dB,dB,app,X7,X12) <=> X7 = X9)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_apps__eq__tail__conv)).
% 11.66/2.04 tff(f910,plain,(
% 11.66/2.04 spl32_70),
% 11.66/2.04 inference(avatar_split_clause,[],[f406,f908])).
% 11.66/2.04 tff(f406,plain,(
% 11.66/2.04 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f219])).
% 11.66/2.04 tff(f219,plain,(
% 11.66/2.04 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (aa(nat,type,X2,X1) = X0 | ~pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 11.66/2.04 inference(ennf_transformation,[],[f153])).
% 11.66/2.04 tff(f153,plain,(
% 11.66/2.04 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) => aa(nat,type,X2,X1) = X0)),
% 11.66/2.04 inference(rectify,[],[f83])).
% 11.66/2.04 tff(f83,axiom,(
% 11.66/2.04 ! [X28 : type,X29 : nat,X30 : fun(nat,type)] : (pp(aa(type,bool,typing(X30,var(X29)),X28)) => aa(nat,type,X30,X29) = X28)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_typing__elims_I1_J)).
% 11.66/2.04 tff(f906,plain,(
% 11.66/2.04 spl32_69),
% 11.66/2.04 inference(avatar_split_clause,[],[f382,f904])).
% 11.66/2.04 tff(f382,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 | nil(X0) = X1) )),
% 11.66/2.04 inference(cnf_transformation,[],[f277])).
% 11.66/2.04 tff(f277,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1) & (cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 | nil(X0) = X1))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f275,f276])).
% 11.66/2.04 tff(f276,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : (? [X4 : X0,X5 : list(X0)] : cons(X0,X4,X5) = X1 => cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1)),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f275,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1) & (? [X4 : X0,X5 : list(X0)] : cons(X0,X4,X5) = X1 | nil(X0) = X1))),
% 11.66/2.04 inference(rectify,[],[f274])).
% 11.66/2.04 tff(f274,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : ((nil(X0) != X1 | ! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1) & (? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1 | nil(X0) = X1))),
% 11.66/2.04 inference(nnf_transformation,[],[f134])).
% 11.66/2.04 tff(f134,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 <=> ? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1)),
% 11.66/2.04 inference(rectify,[],[f64])).
% 11.66/2.04 tff(f64,axiom,(
% 11.66/2.04 ! [X0 : $tType,X48 : list(X0)] : (nil(X0) != X48 <=> ? [X68 : X0,X69 : list(X0)] : cons(X0,X68,X69) = X48)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_neq__Nil__conv)).
% 11.66/2.04 tff(f902,plain,(
% 11.66/2.04 spl32_68),
% 11.66/2.04 inference(avatar_split_clause,[],[f378,f900])).
% 11.66/2.04 tff(f378,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1 | nil(X0) = X1) )),
% 11.66/2.04 inference(cnf_transformation,[],[f271])).
% 11.66/2.04 tff(f271,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : (cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1 | nil(X0) = X1)),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f212,f270])).
% 11.66/2.04 tff(f270,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1 => cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1)),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f212,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : (? [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) = X1 | nil(X0) = X1)),
% 11.66/2.04 inference(ennf_transformation,[],[f131])).
% 11.66/2.04 tff(f131,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0)] : (nil(X0) != X1 => ~! [X2 : X0,X3 : list(X0)] : cons(X0,X2,X3) != X1)),
% 11.66/2.04 inference(rectify,[],[f65])).
% 11.66/2.04 tff(f65,axiom,(
% 11.66/2.04 ! [X0 : $tType,X70 : list(X0)] : (nil(X0) != X70 => ~! [X71 : X0,X72 : list(X0)] : cons(X0,X71,X72) != X70)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_list_Oexhaust)).
% 11.66/2.04 tff(f893,plain,(
% 11.66/2.04 spl32_67 | ~spl32_65),
% 11.66/2.04 inference(avatar_split_clause,[],[f884,f881,f891])).
% 11.66/2.04 tff(f881,plain,(
% 11.66/2.04 spl32_65 <=> ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_65])])).
% 11.66/2.04 tff(f884,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | ~pp(X0) | ~pp(X1)) ) | ~spl32_65),
% 11.66/2.04 inference(forward_demodulation,[],[f882,f490])).
% 11.66/2.04 tff(f882,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) ) | ~spl32_65),
% 11.66/2.04 inference(avatar_component_clause,[],[f881])).
% 11.66/2.04 tff(f889,plain,(
% 11.66/2.04 ~spl32_66 | spl32_32 | ~spl32_33),
% 11.66/2.04 inference(avatar_split_clause,[],[f711,f704,f698,f886])).
% 11.66/2.04 tff(f886,plain,(
% 11.66/2.04 spl32_66 <=> member(dB,foldl(dB,dB,app,abs(r),cons(dB,a,as)),combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_66])])).
% 11.66/2.04 tff(f711,plain,(
% 11.66/2.04 ~member(dB,foldl(dB,dB,app,abs(r),cons(dB,a,as)),combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))) | (spl32_32 | ~spl32_33)),
% 11.66/2.04 inference(resolution,[],[f705,f700])).
% 11.66/2.04 tff(f883,plain,(
% 11.66/2.04 spl32_65),
% 11.66/2.04 inference(avatar_split_clause,[],[f374,f881])).
% 11.66/2.04 tff(f374,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f127])).
% 11.66/2.04 tff(f127,plain,(
% 11.66/2.04 ! [X0 : bool,X1 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) | ~pp(X0) | ~pp(X1))),
% 11.66/2.04 inference(rectify,[],[f105])).
% 11.66/2.04 tff(f105,axiom,(
% 11.66/2.04 ! [X91 : bool,X92 : bool] : (pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X92),X91)) | ~pp(X91) | ~pp(X92))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U)).
% 11.66/2.04 tff(f874,plain,(
% 11.66/2.04 spl32_64),
% 11.66/2.04 inference(avatar_split_clause,[],[f445,f872])).
% 11.66/2.04 tff(f445,plain,(
% 11.66/2.04 ( ! [X2 : list(dB),X3 : nat,X0 : list(dB),X1 : dB] : (foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f171])).
% 11.66/2.04 tff(f171,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : list(dB),X3 : nat] : foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0)),
% 11.66/2.04 inference(rectify,[],[f96])).
% 11.66/2.04 tff(f96,axiom,(
% 11.66/2.04 ! [X6 : list(dB),X9 : dB,X12 : list(dB),X82 : nat] : foldl(dB,dB,app,var(X82),X12) != foldl(dB,dB,app,abs(X9),X6)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Var__apps__neq__Abs__apps)).
% 11.66/2.04 tff(f870,plain,(
% 11.66/2.04 spl32_63),
% 11.66/2.04 inference(avatar_split_clause,[],[f388,f868])).
% 11.66/2.04 tff(f388,plain,(
% 11.66/2.04 ( ! [X0 : list(type),X1 : fun(nat,type)] : (nil(type) = X0 | ~pp(aa(list(type),bool,typings(X1,nil(dB)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f280])).
% 11.66/2.04 tff(f280,plain,(
% 11.66/2.04 ! [X0 : list(type),X1 : fun(nat,type)] : ((pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) | nil(type) != X0) & (nil(type) = X0 | ~pp(aa(list(type),bool,typings(X1,nil(dB)),X0))))),
% 11.66/2.04 inference(nnf_transformation,[],[f137])).
% 11.66/2.04 tff(f137,plain,(
% 11.66/2.04 ! [X0 : list(type),X1 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) <=> nil(type) = X0)),
% 11.66/2.04 inference(rectify,[],[f71])).
% 11.66/2.04 tff(f71,axiom,(
% 11.66/2.04 ! [X75 : list(type),X30 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X30,nil(dB)),X75)) <=> nil(type) = X75)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_typings_Osimps_I1_J)).
% 11.66/2.04 tff(f866,plain,(
% 11.66/2.04 spl32_62 | ~spl32_61),
% 11.66/2.04 inference(avatar_split_clause,[],[f862,f859,f864])).
% 11.66/2.04 tff(f864,plain,(
% 11.66/2.04 spl32_62 <=> ! [X0 : nat,X1 : dB] : (it(aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)) | ~it(X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_62])])).
% 11.66/2.04 tff(f859,plain,(
% 11.66/2.04 spl32_61 <=> ! [X0 : nat,X1 : dB] : (it(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))) | ~it(X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_61])])).
% 11.66/2.04 tff(f862,plain,(
% 11.66/2.04 ( ! [X0 : nat,X1 : dB] : (it(aa(dB,dB,combc(dB,dB,dB,app,var(X0)),X1)) | ~it(X1)) ) | ~spl32_61),
% 11.66/2.04 inference(forward_demodulation,[],[f860,f490])).
% 11.66/2.04 tff(f860,plain,(
% 11.66/2.04 ( ! [X0 : nat,X1 : dB] : (it(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))) | ~it(X1)) ) | ~spl32_61),
% 11.66/2.04 inference(avatar_component_clause,[],[f859])).
% 11.66/2.04 tff(f861,plain,(
% 11.66/2.04 spl32_61),
% 11.66/2.04 inference(avatar_split_clause,[],[f377,f859])).
% 11.66/2.04 tff(f377,plain,(
% 11.66/2.04 ( ! [X0 : nat,X1 : dB] : (it(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))) | ~it(X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f211])).
% 11.66/2.04 tff(f211,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : dB] : (it(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))) | ~it(X1))),
% 11.66/2.04 inference(ennf_transformation,[],[f130])).
% 11.66/2.04 tff(f130,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : dB] : (it(X1) => it(aa(dB,dB,aa(dB,fun(dB,dB),app,X1),var(X0))))),
% 11.66/2.04 inference(rectify,[],[f93])).
% 11.66/2.04 tff(f93,axiom,(
% 11.66/2.04 ! [X19 : nat,X4 : dB] : (it(X4) => it(aa(dB,dB,aa(dB,fun(dB,dB),app,X4),var(X19))))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_app__Var__IT)).
% 11.66/2.04 tff(f851,plain,(
% 11.66/2.04 spl32_60),
% 11.66/2.04 inference(avatar_split_clause,[],[f497,f849])).
% 11.66/2.04 tff(f849,plain,(
% 11.66/2.04 spl32_60 <=> ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X4 : X3,X0 : list(X3),X5 : X3,X1 : list(X3)] : (X4 = X5 | X0 = X1 | ~sP2(X3,X0,X1,X2,X4,X5))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_60])])).
% 11.66/2.04 tff(f497,plain,(
% 11.66/2.04 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (X4 = X5 | X0 = X1 | ~sP2(X3,X0,X1,X2,X4,X5)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f341])).
% 11.66/2.04 tff(f847,plain,(
% 11.66/2.04 spl32_59),
% 11.66/2.04 inference(avatar_split_clause,[],[f488,f845])).
% 11.66/2.04 tff(f488,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X1 = X3 | cons(X0,X2,X1) != cons(X0,X4,X3)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f336])).
% 11.66/2.04 tff(f336,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(flattening,[],[f335])).
% 11.66/2.04 tff(f335,plain,(
% 11.66/2.04 ! [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)))),
% 11.66/2.04 inference(nnf_transformation,[],[f197])).
% 11.66/2.04 tff(f197,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0),X2 : X0,X3 : list(X0),X4 : X0] : (cons(X0,X2,X1) = cons(X0,X4,X3) <=> (X1 = X3 & X2 = X4))),
% 11.66/2.04 inference(rectify,[],[f56])).
% 11.66/2.04 tff(f56,axiom,(
% 11.66/2.04 ! [X0 : $tType,X59 : list(X0),X60 : X0,X61 : list(X0),X49 : X0] : (cons(X0,X49,X61) = cons(X0,X60,X59) <=> (X59 = X61 & X49 = X60))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_list_Oinject)).
% 11.66/2.04 tff(f843,plain,(
% 11.66/2.04 spl32_58),
% 11.66/2.04 inference(avatar_split_clause,[],[f438,f841])).
% 11.66/2.04 tff(f438,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : list(dB),X1 : dB] : (nil(dB) = X0 | var(X2) != foldl(dB,dB,app,X1,X0)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f310])).
% 11.66/2.04 tff(f310,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : nat] : ((var(X2) = foldl(dB,dB,app,X1,X0) | nil(dB) != X0 | var(X2) != X1) & ((nil(dB) = X0 & var(X2) = X1) | var(X2) != foldl(dB,dB,app,X1,X0)))),
% 11.66/2.04 inference(flattening,[],[f309])).
% 11.66/2.04 tff(f309,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : nat] : ((var(X2) = foldl(dB,dB,app,X1,X0) | (nil(dB) != X0 | var(X2) != X1)) & ((nil(dB) = X0 & var(X2) = X1) | var(X2) != foldl(dB,dB,app,X1,X0)))),
% 11.66/2.04 inference(nnf_transformation,[],[f166])).
% 11.66/2.04 tff(f166,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : nat] : (var(X2) = foldl(dB,dB,app,X1,X0) <=> (nil(dB) = X0 & var(X2) = X1))),
% 11.66/2.04 inference(rectify,[],[f86])).
% 11.66/2.04 tff(f86,axiom,(
% 11.66/2.04 ! [X6 : list(dB),X7 : dB,X83 : nat] : (foldl(dB,dB,app,X7,X6) = var(X83) <=> (nil(dB) = X6 & var(X83) = X7))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Var__eq__apps__conv)).
% 11.66/2.04 tff(f839,plain,(
% 11.66/2.04 spl32_57),
% 11.66/2.04 inference(avatar_split_clause,[],[f432,f837])).
% 11.66/2.04 tff(f432,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (nil(dB) = X0 | abs(X2) != foldl(dB,dB,app,X1,X0)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f306])).
% 11.66/2.04 tff(f306,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : dB] : ((abs(X2) = foldl(dB,dB,app,X1,X0) | nil(dB) != X0 | abs(X2) != X1) & ((nil(dB) = X0 & abs(X2) = X1) | abs(X2) != foldl(dB,dB,app,X1,X0)))),
% 11.66/2.04 inference(flattening,[],[f305])).
% 11.66/2.04 tff(f305,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : dB] : ((abs(X2) = foldl(dB,dB,app,X1,X0) | (nil(dB) != X0 | abs(X2) != X1)) & ((nil(dB) = X0 & abs(X2) = X1) | abs(X2) != foldl(dB,dB,app,X1,X0)))),
% 11.66/2.04 inference(nnf_transformation,[],[f164])).
% 11.66/2.04 tff(f164,plain,(
% 11.66/2.04 ! [X0 : list(dB),X1 : dB,X2 : dB] : (abs(X2) = foldl(dB,dB,app,X1,X0) <=> (nil(dB) = X0 & abs(X2) = X1))),
% 11.66/2.04 inference(rectify,[],[f30])).
% 11.66/2.04 tff(f30,axiom,(
% 11.66/2.04 ! [X6 : list(dB),X7 : dB,X9 : dB] : (abs(X9) = foldl(dB,dB,app,X7,X6) <=> (nil(dB) = X6 & abs(X9) = X7))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Abs__eq__apps__conv)).
% 11.66/2.04 tff(f835,plain,(
% 11.66/2.04 spl32_56),
% 11.66/2.04 inference(avatar_split_clause,[],[f423,f833])).
% 11.66/2.04 tff(f833,plain,(
% 11.66/2.04 spl32_56 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (subst(sK18(X0,X1,X2),X2,zero_zero(nat)) = X1 | ~sP1(X0,X1,X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_56])])).
% 11.66/2.04 tff(f423,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (subst(sK18(X0,X1,X2),X2,zero_zero(nat)) = X1 | ~sP1(X0,X1,X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f299])).
% 11.66/2.04 tff(f299,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : dB,X2 : dB] : ((abs(sK18(X0,X1,X2)) = X0 & subst(sK18(X0,X1,X2),X2,zero_zero(nat)) = X1) | ~sP1(X0,X1,X2))),
% 11.66/2.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f297,f298])).
% 11.66/2.04 tff(f298,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X3 : dB] : (abs(X3) = X0 & subst(X3,X2,zero_zero(nat)) = X1) => (abs(sK18(X0,X1,X2)) = X0 & subst(sK18(X0,X1,X2),X2,zero_zero(nat)) = X1))),
% 11.66/2.04 introduced(choice_axiom,[])).
% 11.66/2.04 tff(f297,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : dB,X2 : dB] : (? [X3 : dB] : (abs(X3) = X0 & subst(X3,X2,zero_zero(nat)) = X1) | ~sP1(X0,X1,X2))),
% 11.66/2.04 inference(rectify,[],[f296])).
% 11.66/2.04 tff(f296,plain,(
% 11.66/2.04 ! [X2 : dB,X0 : dB,X1 : dB] : (? [X3 : dB] : (abs(X3) = X2 & subst(X3,X1,zero_zero(nat)) = X0) | ~sP1(X2,X0,X1))),
% 11.66/2.04 inference(nnf_transformation,[],[f265])).
% 11.66/2.04 tff(f831,plain,(
% 11.66/2.04 spl32_55),
% 11.66/2.04 inference(avatar_split_clause,[],[f399,f829])).
% 11.66/2.04 tff(f399,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f147])).
% 11.66/2.04 tff(f147,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : dB,X2 : dB] : abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),
% 11.66/2.04 inference(rectify,[],[f18])).
% 11.66/2.04 tff(f18,axiom,(
% 11.66/2.04 ! [X22 : dB,X23 : dB,X24 : dB] : aa(dB,dB,aa(dB,fun(dB,dB),app,X24),X23) != abs(X22)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_dB_Osimps_I8_J)).
% 11.66/2.04 tff(f827,plain,(
% 11.66/2.04 spl32_54),
% 11.66/2.04 inference(avatar_split_clause,[],[f397,f825])).
% 11.66/2.04 tff(f397,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : nat,X1 : dB] : (var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f145])).
% 11.66/2.04 tff(f145,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : dB,X2 : dB] : var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1)),
% 11.66/2.04 inference(rectify,[],[f88])).
% 11.66/2.04 tff(f88,axiom,(
% 11.66/2.04 ! [X86 : nat,X84 : dB,X85 : dB] : var(X86) != aa(dB,dB,aa(dB,fun(dB,dB),app,X85),X84)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dB_Osimps_I5_J)).
% 11.66/2.04 tff(f821,plain,(
% 11.66/2.04 spl32_53 | ~spl32_52),
% 11.66/2.04 inference(avatar_split_clause,[],[f817,f814,f819])).
% 11.66/2.04 tff(f814,plain,(
% 11.66/2.04 spl32_52 <=> ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_52])])).
% 11.66/2.04 tff(f817,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X1)) ) | ~spl32_52),
% 11.66/2.04 inference(forward_demodulation,[],[f815,f490])).
% 11.66/2.04 tff(f815,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) ) | ~spl32_52),
% 11.66/2.04 inference(avatar_component_clause,[],[f814])).
% 11.66/2.04 tff(f816,plain,(
% 11.66/2.04 spl32_52),
% 11.66/2.04 inference(avatar_split_clause,[],[f376,f814])).
% 11.66/2.04 tff(f376,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f129])).
% 11.66/2.04 tff(f129,plain,(
% 11.66/2.04 ! [X0 : bool,X1 : bool] : (pp(X1) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 11.66/2.04 inference(rectify,[],[f106])).
% 11.66/2.04 tff(f106,axiom,(
% 11.66/2.04 ! [X91 : bool,X92 : bool] : (pp(X92) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X92),X91)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U)).
% 11.66/2.04 tff(f810,plain,(
% 11.66/2.04 spl32_51 | ~spl32_50),
% 11.66/2.04 inference(avatar_split_clause,[],[f806,f803,f808])).
% 11.66/2.04 tff(f803,plain,(
% 11.66/2.04 spl32_50 <=> ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_50])])).
% 11.66/2.04 tff(f806,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (~pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1)) | pp(X0)) ) | ~spl32_50),
% 11.66/2.04 inference(forward_demodulation,[],[f804,f490])).
% 11.66/2.04 tff(f804,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) ) | ~spl32_50),
% 11.66/2.04 inference(avatar_component_clause,[],[f803])).
% 11.66/2.04 tff(f805,plain,(
% 11.66/2.04 spl32_50),
% 11.66/2.04 inference(avatar_split_clause,[],[f375,f803])).
% 11.66/2.04 tff(f375,plain,(
% 11.66/2.04 ( ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f128])).
% 11.66/2.04 tff(f128,plain,(
% 11.66/2.04 ! [X0 : bool,X1 : bool] : (pp(X0) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)))),
% 11.66/2.04 inference(rectify,[],[f107])).
% 11.66/2.04 tff(f107,axiom,(
% 11.66/2.04 ! [X91 : bool,X92 : bool] : (pp(X91) | ~pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X92),X91)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U)).
% 11.66/2.04 tff(f794,plain,(
% 11.66/2.04 spl32_49 | ~spl32_20 | ~spl32_34),
% 11.66/2.04 inference(avatar_split_clause,[],[f715,f708,f635,f791])).
% 11.66/2.04 tff(f791,plain,(
% 11.66/2.04 spl32_49 <=> member(type,t,typing(ea,ua))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_49])])).
% 11.66/2.04 tff(f715,plain,(
% 11.66/2.04 member(type,t,typing(ea,ua)) | (~spl32_20 | ~spl32_34)),
% 11.66/2.04 inference(resolution,[],[f709,f637])).
% 11.66/2.04 tff(f787,plain,(
% 11.66/2.04 spl32_48),
% 11.66/2.04 inference(avatar_split_clause,[],[f517,f785])).
% 11.66/2.04 tff(f517,plain,(
% 11.66/2.04 ( ! [X2 : fun(nat,type),X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),aa(nat,type,X2,X1)))) )),
% 11.66/2.04 inference(equality_resolution,[],[f405])).
% 11.66/2.04 tff(f405,plain,(
% 11.66/2.04 ( ! [X2 : fun(nat,type),X0 : type,X1 : nat] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) != X0) )),
% 11.66/2.04 inference(cnf_transformation,[],[f218])).
% 11.66/2.04 tff(f218,plain,(
% 11.66/2.04 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (pp(aa(type,bool,typing(X2,var(X1)),X0)) | aa(nat,type,X2,X1) != X0)),
% 11.66/2.04 inference(ennf_transformation,[],[f152])).
% 11.66/2.04 tff(f152,plain,(
% 11.66/2.04 ! [X0 : type,X1 : nat,X2 : fun(nat,type)] : (aa(nat,type,X2,X1) = X0 => pp(aa(type,bool,typing(X2,var(X1)),X0)))),
% 11.66/2.04 inference(rectify,[],[f82])).
% 11.66/2.04 tff(f82,axiom,(
% 11.66/2.04 ! [X28 : type,X21 : nat,X44 : fun(nat,type)] : (aa(nat,type,X44,X21) = X28 => pp(aa(type,bool,typing(X44,var(X21)),X28)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_typing_OVar)).
% 11.66/2.04 tff(f783,plain,(
% 11.66/2.04 spl32_47),
% 11.66/2.04 inference(avatar_split_clause,[],[f487,f781])).
% 11.66/2.04 tff(f487,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0),X4 : X0] : (X2 = X4 | cons(X0,X2,X1) != cons(X0,X4,X3)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f336])).
% 11.66/2.04 tff(f779,plain,(
% 11.66/2.04 spl32_46),
% 11.66/2.04 inference(avatar_split_clause,[],[f437,f777])).
% 11.66/2.04 tff(f437,plain,(
% 11.66/2.04 ( ! [X2 : nat,X0 : list(dB),X1 : dB] : (var(X2) = X1 | var(X2) != foldl(dB,dB,app,X1,X0)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f310])).
% 11.66/2.04 tff(f775,plain,(
% 11.66/2.04 spl32_45),
% 11.66/2.04 inference(avatar_split_clause,[],[f431,f773])).
% 11.66/2.04 tff(f431,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : list(dB),X1 : dB] : (abs(X2) = X1 | abs(X2) != foldl(dB,dB,app,X1,X0)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f306])).
% 11.66/2.04 tff(f769,plain,(
% 11.66/2.04 spl32_44 | ~spl32_43),
% 11.66/2.04 inference(avatar_split_clause,[],[f765,f762,f767])).
% 11.66/2.04 tff(f762,plain,(
% 11.66/2.04 spl32_43 <=> ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_43])])).
% 11.66/2.04 tff(f765,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,combc(dB,dB,bool,beta,X0),var(X1)))) ) | ~spl32_43),
% 11.66/2.04 inference(forward_demodulation,[],[f763,f490])).
% 11.66/2.04 tff(f763,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))) ) | ~spl32_43),
% 11.66/2.04 inference(avatar_component_clause,[],[f762])).
% 11.66/2.04 tff(f764,plain,(
% 11.66/2.04 spl32_43),
% 11.66/2.04 inference(avatar_split_clause,[],[f372,f762])).
% 11.66/2.04 tff(f372,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : nat] : (~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f125])).
% 11.66/2.04 tff(f125,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X1)),X0))),
% 11.66/2.04 inference(rectify,[],[f84])).
% 11.66/2.04 tff(f84,axiom,(
% 11.66/2.04 ! [X4 : dB,X19 : nat] : ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,var(X19)),X4))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_beta__cases_I1_J)).
% 11.66/2.04 tff(f760,plain,(
% 11.66/2.04 spl32_42 | ~spl32_19 | ~spl32_34),
% 11.66/2.04 inference(avatar_split_clause,[],[f714,f708,f630,f757])).
% 11.66/2.04 tff(f757,plain,(
% 11.66/2.04 spl32_42 <=> member(type,t,typing(e,u))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_42])])).
% 11.66/2.04 tff(f714,plain,(
% 11.66/2.04 member(type,t,typing(e,u)) | (~spl32_19 | ~spl32_34)),
% 11.66/2.04 inference(resolution,[],[f709,f632])).
% 11.66/2.04 tff(f753,plain,(
% 11.66/2.04 spl32_41),
% 11.66/2.04 inference(avatar_split_clause,[],[f536,f751])).
% 11.66/2.04 tff(f751,plain,(
% 11.66/2.04 spl32_41 <=> ! [X3 : $tType,X0 : list(X3),X5 : X3,X2 : fun(X3,fun(X3,bool)),X1 : list(X3)] : (sP2(X3,X0,X1,X2,X5,X5) | ~step1(X3,X2,X1,X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_41])])).
% 11.66/2.04 tff(f536,plain,(
% 11.66/2.04 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X5 : X3] : (sP2(X3,X0,X1,X2,X5,X5) | ~step1(X3,X2,X1,X0)) )),
% 11.66/2.04 inference(equality_resolution,[],[f501])).
% 11.66/2.04 tff(f501,plain,(
% 11.66/2.04 ( ! [X3 : $tType,X2 : fun(X3,fun(X3,bool)),X0 : list(X3),X1 : list(X3),X4 : X3,X5 : X3] : (sP2(X3,X0,X1,X2,X4,X5) | ~step1(X3,X2,X1,X0) | X4 != X5) )),
% 11.66/2.04 inference(cnf_transformation,[],[f341])).
% 11.66/2.04 tff(f749,plain,(
% 11.66/2.04 spl32_40),
% 11.66/2.04 inference(avatar_split_clause,[],[f371,f747])).
% 11.66/2.04 tff(f739,plain,(
% 11.66/2.04 spl32_39),
% 11.66/2.04 inference(avatar_split_clause,[],[f533,f737])).
% 11.66/2.04 tff(f533,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(nat,X0),X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X4) = X1) )),
% 11.66/2.04 inference(equality_resolution,[],[f479])).
% 11.66/2.04 tff(f479,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(nat,X0),X3 : nat,X1 : X0,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4) )),
% 11.66/2.04 inference(cnf_transformation,[],[f245])).
% 11.66/2.04 tff(f245,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : X0,X2 : fun(nat,X0),X3 : nat,X4 : nat] : (aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1 | X3 != X4)),
% 11.66/2.04 inference(ennf_transformation,[],[f192])).
% 11.66/2.04 tff(f192,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : X0,X2 : fun(nat,X0),X3 : nat,X4 : nat] : (X3 = X4 => aa(nat,X0,shift(X0,X2,X4,X1),X3) = X1)),
% 11.66/2.04 inference(rectify,[],[f45])).
% 11.66/2.04 tff(f45,axiom,(
% 11.66/2.04 ! [X0 : $tType,X28 : X0,X30 : fun(nat,X0),X45 : nat,X29 : nat] : (X29 = X45 => aa(nat,X0,shift(X0,X30,X29,X28),X45) = X28)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_shift__eq)).
% 11.66/2.04 tff(f735,plain,(
% 11.66/2.04 spl32_38),
% 11.66/2.04 inference(avatar_split_clause,[],[f516,f733])).
% 11.66/2.04 tff(f516,plain,(
% 11.66/2.04 ( ! [X1 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),nil(type)))) )),
% 11.66/2.04 inference(equality_resolution,[],[f389])).
% 11.66/2.04 tff(f389,plain,(
% 11.66/2.04 ( ! [X0 : list(type),X1 : fun(nat,type)] : (pp(aa(list(type),bool,typings(X1,nil(dB)),X0)) | nil(type) != X0) )),
% 11.66/2.04 inference(cnf_transformation,[],[f280])).
% 11.66/2.04 tff(f730,plain,(
% 11.66/2.04 spl32_37),
% 11.66/2.04 inference(avatar_split_clause,[],[f424,f728])).
% 11.66/2.04 tff(f728,plain,(
% 11.66/2.04 spl32_37 <=> ! [X2 : dB,X0 : dB,X1 : dB] : (abs(sK18(X0,X1,X2)) = X0 | ~sP1(X0,X1,X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_37])])).
% 11.66/2.04 tff(f424,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : dB] : (abs(sK18(X0,X1,X2)) = X0 | ~sP1(X0,X1,X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f299])).
% 11.66/2.04 tff(f726,plain,(
% 11.66/2.04 spl32_36),
% 11.66/2.04 inference(avatar_split_clause,[],[f414,f724])).
% 11.66/2.04 tff(f724,plain,(
% 11.66/2.04 spl32_36 <=> ! [X2 : dB,X0 : dB,X1 : list(dB)] : (abs(sK12(X0,X1,X2)) = X2 | ~sP0(X0,X1,X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_36])])).
% 11.66/2.04 tff(f414,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : dB,X1 : list(dB)] : (abs(sK12(X0,X1,X2)) = X2 | ~sP0(X0,X1,X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f289])).
% 11.66/2.04 tff(f722,plain,(
% 11.66/2.04 spl32_35),
% 11.66/2.04 inference(avatar_split_clause,[],[f356,f719])).
% 11.66/2.04 tff(f356,plain,(
% 11.66/2.04 it(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))),
% 11.66/2.04 inference(cnf_transformation,[],[f3])).
% 11.66/2.04 tff(f3,axiom,(
% 11.66/2.04 it(foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Beta_I1_J)).
% 11.66/2.04 tff(f710,plain,(
% 11.66/2.04 spl32_34),
% 11.66/2.04 inference(avatar_split_clause,[],[f430,f708])).
% 11.66/2.04 tff(f430,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (member(X0,X2,X1) | ~pp(aa(X0,bool,X1,X2))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f304])).
% 11.66/2.04 tff(f304,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : ((member(X0,X2,X1) | ~pp(aa(X0,bool,X1,X2))) & (pp(aa(X0,bool,X1,X2)) | ~member(X0,X2,X1)))),
% 11.66/2.04 inference(nnf_transformation,[],[f163])).
% 11.66/2.04 tff(f163,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : fun(X0,bool),X2 : X0] : (member(X0,X2,X1) <=> pp(aa(X0,bool,X1,X2)))),
% 11.66/2.04 inference(rectify,[],[f76])).
% 11.66/2.04 tff(f76,axiom,(
% 11.66/2.04 ! [X0 : $tType,X74 : fun(X0,bool),X21 : X0] : (member(X0,X21,X74) <=> pp(aa(X0,bool,X74,X21)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def)).
% 11.66/2.04 tff(f706,plain,(
% 11.66/2.04 spl32_33),
% 11.66/2.04 inference(avatar_split_clause,[],[f429,f704])).
% 11.66/2.04 tff(f429,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X1 : fun(X0,bool)] : (pp(aa(X0,bool,X1,X2)) | ~member(X0,X2,X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f304])).
% 11.66/2.04 tff(f701,plain,(
% 11.66/2.04 ~spl32_32 | spl32_31),
% 11.66/2.04 inference(avatar_split_clause,[],[f696,f691,f698])).
% 11.66/2.04 tff(f691,plain,(
% 11.66/2.04 spl32_31 <=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_31])])).
% 11.66/2.04 tff(f696,plain,(
% 11.66/2.04 ~pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,abs(r),cons(dB,a,as)))) | spl32_31),
% 11.66/2.04 inference(forward_demodulation,[],[f695,f493])).
% 11.66/2.04 tff(f695,plain,(
% 11.66/2.04 ~pp(aa(dB,bool,combc(dB,dB,bool,beta,foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as))) | spl32_31),
% 11.66/2.04 inference(forward_demodulation,[],[f693,f490])).
% 11.66/2.04 tff(f693,plain,(
% 11.66/2.04 ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))) | spl32_31),
% 11.66/2.04 inference(avatar_component_clause,[],[f691])).
% 11.66/2.04 tff(f694,plain,(
% 11.66/2.04 ~spl32_31),
% 11.66/2.04 inference(avatar_split_clause,[],[f345,f691])).
% 11.66/2.04 tff(f345,plain,(
% 11.66/2.04 ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)))),
% 11.66/2.04 inference(cnf_transformation,[],[f112])).
% 11.66/2.04 tff(f112,plain,(
% 11.66/2.04 ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)))),
% 11.66/2.04 inference(flattening,[],[f111])).
% 11.66/2.04 tff(f111,negated_conjecture,(
% 11.66/2.04 ~pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)))),
% 11.66/2.04 inference(negated_conjecture,[],[f110])).
% 11.66/2.04 tff(f110,conjecture,(
% 11.66/2.04 pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 11.66/2.04 tff(f689,plain,(
% 11.66/2.04 spl32_29 | ~spl32_30 | ~spl32_12),
% 11.66/2.04 inference(avatar_split_clause,[],[f612,f599,f686,f683])).
% 11.66/2.04 tff(f612,plain,(
% 11.66/2.04 ( ! [X0 : bool] : (fFalse != fTrue | fTrue = X0) ) | ~spl32_12),
% 11.66/2.04 inference(equality_factoring,[],[f600])).
% 11.66/2.04 tff(f678,plain,(
% 11.66/2.04 spl32_28),
% 11.66/2.04 inference(avatar_split_clause,[],[f444,f676])).
% 11.66/2.04 tff(f444,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : (foldl(X1,X0,X3,X2,nil(X0)) = X2) )),
% 11.66/2.04 inference(cnf_transformation,[],[f170])).
% 11.66/2.04 tff(f170,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X1,fun(X0,X1))] : foldl(X1,X0,X3,X2,nil(X0)) = X2),
% 11.66/2.04 inference(rectify,[],[f51])).
% 11.66/2.04 tff(f51,axiom,(
% 11.66/2.04 ! [X1 : $tType,X0 : $tType,X49 : X0,X50 : fun(X0,fun(X1,X0))] : foldl(X0,X1,X50,X49,nil(X1)) = X49),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_foldl__Nil)).
% 11.66/2.04 tff(f674,plain,(
% 11.66/2.04 spl32_27),
% 11.66/2.04 inference(avatar_split_clause,[],[f443,f672])).
% 11.66/2.04 tff(f443,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : (foldr(X0,X1,X3,nil(X0),X2) = X2) )),
% 11.66/2.04 inference(cnf_transformation,[],[f169])).
% 11.66/2.04 tff(f169,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : fun(X0,fun(X1,X1))] : foldr(X0,X1,X3,nil(X0),X2) = X2),
% 11.66/2.04 inference(rectify,[],[f77])).
% 11.66/2.04 tff(f77,axiom,(
% 11.66/2.04 ! [X1 : $tType,X0 : $tType,X49 : X0,X50 : fun(X1,fun(X0,X0))] : foldr(X1,X0,X50,nil(X1),X49) = X49),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_foldr_Osimps_I1_J)).
% 11.66/2.04 tff(f670,plain,(
% 11.66/2.04 spl32_26),
% 11.66/2.04 inference(avatar_split_clause,[],[f442,f668])).
% 11.66/2.04 tff(f442,plain,(
% 11.66/2.04 ( ! [X1 : $tType,X0 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : (list_case(X1,X0,X3,X2,nil(X0)) = X3) )),
% 11.66/2.04 inference(cnf_transformation,[],[f168])).
% 11.66/2.04 tff(f168,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : $tType,X2 : fun(X0,fun(list(X0),X1)),X3 : X1] : list_case(X1,X0,X3,X2,nil(X0)) = X3),
% 11.66/2.04 inference(rectify,[],[f55])).
% 11.66/2.04 tff(f55,axiom,(
% 11.66/2.04 ! [X1 : $tType,X0 : $tType,X51 : fun(X1,fun(list(X1),X0)),X52 : X0] : list_case(X0,X1,X52,X51,nil(X1)) = X52),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_list_Osimps_I4_J)).
% 11.66/2.04 tff(f666,plain,(
% 11.66/2.04 spl32_25),
% 11.66/2.04 inference(avatar_split_clause,[],[f369,f664])).
% 11.66/2.04 tff(f664,plain,(
% 11.66/2.04 spl32_25 <=> ! [X0 : $tType,X1 : fun(nat,bool)] : nil(X0) = sublist(X0,nil(X0),X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_25])])).
% 11.66/2.04 tff(f369,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X1 : fun(nat,bool)] : (nil(X0) = sublist(X0,nil(X0),X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f122])).
% 11.66/2.04 tff(f122,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : fun(nat,bool)] : nil(X0) = sublist(X0,nil(X0),X1)),
% 11.66/2.04 inference(rectify,[],[f70])).
% 11.66/2.04 tff(f70,axiom,(
% 11.66/2.04 ! [X0 : $tType,X74 : fun(nat,bool)] : nil(X0) = sublist(X0,nil(X0),X74)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_sublist__nil)).
% 11.66/2.04 tff(f654,plain,(
% 11.66/2.04 spl32_24),
% 11.66/2.04 inference(avatar_split_clause,[],[f513,f652])).
% 11.66/2.04 tff(f513,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0)] : (nil(X0) != cons(X0,X2,X3)) )),
% 11.66/2.04 inference(equality_resolution,[],[f383])).
% 11.66/2.04 tff(f383,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : X0,X3 : list(X0),X1 : list(X0)] : (nil(X0) != X1 | cons(X0,X2,X3) != X1) )),
% 11.66/2.04 inference(cnf_transformation,[],[f277])).
% 11.66/2.04 tff(f650,plain,(
% 11.66/2.04 spl32_23),
% 11.66/2.04 inference(avatar_split_clause,[],[f403,f648])).
% 11.66/2.04 tff(f648,plain,(
% 11.66/2.04 spl32_23 <=> ! [X2 : dB,X0 : nat,X1 : nat] : (it(subst(X2,var(X1),X0)) | ~it(X2))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_23])])).
% 11.66/2.04 tff(f403,plain,(
% 11.66/2.04 ( ! [X2 : dB,X0 : nat,X1 : nat] : (it(subst(X2,var(X1),X0)) | ~it(X2)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f216])).
% 11.66/2.04 tff(f216,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : nat,X2 : dB] : (it(subst(X2,var(X1),X0)) | ~it(X2))),
% 11.66/2.04 inference(ennf_transformation,[],[f150])).
% 11.66/2.04 tff(f150,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : nat,X2 : dB] : (it(X2) => it(subst(X2,var(X1),X0)))),
% 11.66/2.04 inference(rectify,[],[f94])).
% 11.66/2.04 tff(f94,axiom,(
% 11.66/2.04 ! [X87 : nat,X19 : nat,X20 : dB] : (it(X20) => it(subst(X20,var(X19),X87)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_subst__Var__IT)).
% 11.66/2.04 tff(f646,plain,(
% 11.66/2.04 spl32_22),
% 11.66/2.04 inference(avatar_split_clause,[],[f386,f644])).
% 11.66/2.04 tff(f644,plain,(
% 11.66/2.04 spl32_22 <=> ! [X0 : dB,X1 : dB] : (X0 = X1 | abs(X0) != abs(X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_22])])).
% 11.66/2.04 tff(f386,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : dB] : (X0 = X1 | abs(X0) != abs(X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f279])).
% 11.66/2.04 tff(f279,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : dB] : ((abs(X0) = abs(X1) | X0 != X1) & (X0 = X1 | abs(X0) != abs(X1)))),
% 11.66/2.04 inference(nnf_transformation,[],[f136])).
% 11.66/2.04 tff(f136,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : dB] : (abs(X0) = abs(X1) <=> X0 = X1)),
% 11.66/2.04 inference(rectify,[],[f12])).
% 11.66/2.04 tff(f12,axiom,(
% 11.66/2.04 ! [X13 : dB,X14 : dB] : (abs(X14) = abs(X13) <=> X13 = X14)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_dB_Osimps_I3_J)).
% 11.66/2.04 tff(f642,plain,(
% 11.66/2.04 spl32_21),
% 11.66/2.04 inference(avatar_split_clause,[],[f384,f640])).
% 11.66/2.04 tff(f640,plain,(
% 11.66/2.04 spl32_21 <=> ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_21])])).
% 11.66/2.04 tff(f384,plain,(
% 11.66/2.04 ( ! [X0 : nat,X1 : nat] : (X0 = X1 | var(X0) != var(X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f278])).
% 11.66/2.04 tff(f278,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : nat] : ((var(X0) = var(X1) | X0 != X1) & (X0 = X1 | var(X0) != var(X1)))),
% 11.66/2.04 inference(nnf_transformation,[],[f135])).
% 11.66/2.04 tff(f135,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : nat] : (var(X0) = var(X1) <=> X0 = X1)),
% 11.66/2.04 inference(rectify,[],[f81])).
% 11.66/2.04 tff(f81,axiom,(
% 11.66/2.04 ! [X80 : nat,X81 : nat] : (var(X81) = var(X80) <=> X80 = X81)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_dB_Osimps_I1_J)).
% 11.66/2.04 tff(f638,plain,(
% 11.66/2.04 spl32_20),
% 11.66/2.04 inference(avatar_split_clause,[],[f355,f635])).
% 11.66/2.04 tff(f355,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(ea,ua),t))),
% 11.66/2.04 inference(cnf_transformation,[],[f37])).
% 11.66/2.04 tff(f37,axiom,(
% 11.66/2.04 pp(aa(type,bool,typing(ea,ua),t))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Beta_I7_J)).
% 11.66/2.04 tff(f633,plain,(
% 11.66/2.04 spl32_19),
% 11.66/2.04 inference(avatar_split_clause,[],[f354,f630])).
% 11.66/2.04 tff(f354,plain,(
% 11.66/2.04 pp(aa(type,bool,typing(e,u),t))),
% 11.66/2.04 inference(cnf_transformation,[],[f28])).
% 11.66/2.04 tff(f28,axiom,(
% 11.66/2.04 pp(aa(type,bool,typing(e,u),t))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_uT)).
% 11.66/2.04 tff(f628,plain,(
% 11.66/2.04 spl32_18 | spl32_1 | ~spl32_12),
% 11.66/2.04 inference(avatar_split_clause,[],[f611,f599,f548,f626])).
% 11.66/2.04 tff(f611,plain,(
% 11.66/2.04 ( ! [X0 : bool] : (~pp(X0) | fTrue = X0) ) | (spl32_1 | ~spl32_12)),
% 11.66/2.04 inference(superposition,[],[f550,f600])).
% 11.66/2.04 tff(f550,plain,(
% 11.66/2.04 ~pp(fFalse) | spl32_1),
% 11.66/2.04 inference(avatar_component_clause,[],[f548])).
% 11.66/2.04 tff(f624,plain,(
% 11.66/2.04 spl32_17),
% 11.66/2.04 inference(avatar_split_clause,[],[f392,f622])).
% 11.66/2.04 tff(f392,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : list(X0),X1 : X0] : (cons(X0,X1,X2) != X2) )),
% 11.66/2.04 inference(cnf_transformation,[],[f140])).
% 11.66/2.04 tff(f140,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : X0,X2 : list(X0)] : cons(X0,X1,X2) != X2),
% 11.66/2.04 inference(rectify,[],[f61])).
% 11.66/2.04 tff(f61,axiom,(
% 11.66/2.04 ! [X0 : $tType,X65 : X0,X64 : list(X0)] : cons(X0,X65,X64) != X64),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_not__Cons__self)).
% 11.66/2.04 tff(f620,plain,(
% 11.66/2.04 spl32_16),
% 11.66/2.04 inference(avatar_split_clause,[],[f368,f618])).
% 11.66/2.04 tff(f368,plain,(
% 11.66/2.04 ( ! [X0 : dB,X1 : nat] : (subst(var(X1),X0,X1) = X0) )),
% 11.66/2.04 inference(cnf_transformation,[],[f121])).
% 11.66/2.04 tff(f121,plain,(
% 11.66/2.04 ! [X0 : dB,X1 : nat] : subst(var(X1),X0,X1) = X0),
% 11.66/2.04 inference(rectify,[],[f91])).
% 11.66/2.04 tff(f91,axiom,(
% 11.66/2.04 ! [X11 : dB,X10 : nat] : subst(var(X10),X11,X10) = X11),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_subst__eq)).
% 11.66/2.04 tff(f616,plain,(
% 11.66/2.04 spl32_15),
% 11.66/2.04 inference(avatar_split_clause,[],[f367,f614])).
% 11.66/2.04 tff(f614,plain,(
% 11.66/2.04 spl32_15 <=> ! [X0 : nat,X1 : dB] : liftn(zero_zero(nat),X1,X0) = X1),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_15])])).
% 11.66/2.04 tff(f367,plain,(
% 11.66/2.04 ( ! [X0 : nat,X1 : dB] : (liftn(zero_zero(nat),X1,X0) = X1) )),
% 11.66/2.04 inference(cnf_transformation,[],[f120])).
% 11.66/2.04 tff(f120,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : dB] : liftn(zero_zero(nat),X1,X0) = X1),
% 11.66/2.04 inference(rectify,[],[f44])).
% 11.66/2.04 tff(f44,axiom,(
% 11.66/2.04 ! [X10 : nat,X4 : dB] : liftn(zero_zero(nat),X4,X10) = X4),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_liftn__0)).
% 11.66/2.04 tff(f609,plain,(
% 11.66/2.04 spl32_14),
% 11.66/2.04 inference(avatar_split_clause,[],[f391,f607])).
% 11.66/2.04 tff(f607,plain,(
% 11.66/2.04 spl32_14 <=> ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X1 : list(X0)] : ~step1(X0,X2,nil(X0),X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_14])])).
% 11.66/2.04 tff(f391,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X1 : list(X0)] : (~step1(X0,X2,nil(X0),X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f139])).
% 11.66/2.04 tff(f139,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,fun(X0,bool))] : ~step1(X0,X2,nil(X0),X1)),
% 11.66/2.04 inference(rectify,[],[f49])).
% 11.66/2.04 tff(f49,axiom,(
% 11.66/2.04 ! [X0 : $tType,X48 : list(X0),X9 : fun(X0,fun(X0,bool))] : ~step1(X0,X9,nil(X0),X48)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_not__Nil__step1)).
% 11.66/2.04 tff(f605,plain,(
% 11.66/2.04 spl32_13),
% 11.66/2.04 inference(avatar_split_clause,[],[f390,f603])).
% 11.66/2.04 tff(f390,plain,(
% 11.66/2.04 ( ! [X0 : $tType,X2 : fun(X0,fun(X0,bool)),X1 : list(X0)] : (~step1(X0,X2,X1,nil(X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f138])).
% 11.66/2.04 tff(f138,plain,(
% 11.66/2.04 ! [X0 : $tType,X1 : list(X0),X2 : fun(X0,fun(X0,bool))] : ~step1(X0,X2,X1,nil(X0))),
% 11.66/2.04 inference(rectify,[],[f50])).
% 11.66/2.04 tff(f50,axiom,(
% 11.66/2.04 ! [X0 : $tType,X48 : list(X0),X9 : fun(X0,fun(X0,bool))] : ~step1(X0,X9,X48,nil(X0))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_not__step1__Nil)).
% 11.66/2.04 tff(f601,plain,(
% 11.66/2.04 spl32_12),
% 11.66/2.04 inference(avatar_split_clause,[],[f361,f599])).
% 11.66/2.04 tff(f361,plain,(
% 11.66/2.04 ( ! [X0 : bool] : (fFalse = X0 | fTrue = X0) )),
% 11.66/2.04 inference(cnf_transformation,[],[f115])).
% 11.66/2.04 tff(f115,plain,(
% 11.66/2.04 ! [X0 : bool] : (fFalse = X0 | fTrue = X0)),
% 11.66/2.04 inference(rectify,[],[f109])).
% 11.66/2.04 tff(f109,axiom,(
% 11.66/2.04 ! [X92 : bool] : (fFalse = X92 | fTrue = X92)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T)).
% 11.66/2.04 tff(f597,plain,(
% 11.66/2.04 spl32_11),
% 11.66/2.04 inference(avatar_split_clause,[],[f360,f595])).
% 11.66/2.04 tff(f595,plain,(
% 11.66/2.04 spl32_11 <=> ! [X0 : nat] : zero_zero(nat) = dB_size(var(X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_11])])).
% 11.66/2.04 tff(f360,plain,(
% 11.66/2.04 ( ! [X0 : nat] : (zero_zero(nat) = dB_size(var(X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f114])).
% 11.66/2.04 tff(f114,plain,(
% 11.66/2.04 ! [X0 : nat] : zero_zero(nat) = dB_size(var(X0))),
% 11.66/2.04 inference(rectify,[],[f99])).
% 11.66/2.04 tff(f99,axiom,(
% 11.66/2.04 ! [X86 : nat] : zero_zero(nat) = dB_size(var(X86))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_dB_Osize_I1_J)).
% 11.66/2.04 tff(f593,plain,(
% 11.66/2.04 spl32_10),
% 11.66/2.04 inference(avatar_split_clause,[],[f365,f591])).
% 11.66/2.04 tff(f591,plain,(
% 11.66/2.04 spl32_10 <=> ! [X0 : nat,X1 : dB] : var(X0) != abs(X1)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_10])])).
% 11.66/2.04 tff(f365,plain,(
% 11.66/2.04 ( ! [X0 : nat,X1 : dB] : (var(X0) != abs(X1)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f118])).
% 11.66/2.04 tff(f118,plain,(
% 11.66/2.04 ! [X0 : nat,X1 : dB] : var(X0) != abs(X1)),
% 11.66/2.04 inference(rectify,[],[f89])).
% 11.66/2.04 tff(f89,axiom,(
% 11.66/2.04 ! [X86 : nat,X22 : dB] : abs(X22) != var(X86)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dB_Osimps_I7_J)).
% 11.66/2.04 tff(f589,plain,(
% 11.66/2.04 spl32_9),
% 11.66/2.04 inference(avatar_split_clause,[],[f364,f587])).
% 11.66/2.04 tff(f587,plain,(
% 11.66/2.04 spl32_9 <=> ! [X0 : dB] : (it(abs(X0)) | ~it(X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_9])])).
% 11.66/2.04 tff(f364,plain,(
% 11.66/2.04 ( ! [X0 : dB] : (it(abs(X0)) | ~it(X0)) )),
% 11.66/2.04 inference(cnf_transformation,[],[f210])).
% 11.66/2.04 tff(f210,plain,(
% 11.66/2.04 ! [X0 : dB] : (it(abs(X0)) | ~it(X0))),
% 11.66/2.04 inference(ennf_transformation,[],[f117])).
% 11.66/2.04 tff(f117,plain,(
% 11.66/2.04 ! [X0 : dB] : (it(X0) => it(abs(X0)))),
% 11.66/2.04 inference(rectify,[],[f22])).
% 11.66/2.04 tff(f22,axiom,(
% 11.66/2.04 ! [X20 : dB] : (it(X20) => it(abs(X20)))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Lambda)).
% 11.66/2.04 tff(f585,plain,(
% 11.66/2.04 spl32_8),
% 11.66/2.04 inference(avatar_split_clause,[],[f359,f583])).
% 11.66/2.04 tff(f583,plain,(
% 11.66/2.04 spl32_8 <=> ! [X0 : nat] : it(var(X0))),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_8])])).
% 11.66/2.04 tff(f359,plain,(
% 11.66/2.04 ( ! [X0 : nat] : (it(var(X0))) )),
% 11.66/2.04 inference(cnf_transformation,[],[f113])).
% 11.66/2.04 tff(f113,plain,(
% 11.66/2.04 ! [X0 : nat] : it(var(X0))),
% 11.66/2.04 inference(rectify,[],[f92])).
% 11.66/2.04 tff(f92,axiom,(
% 11.66/2.04 ! [X37 : nat] : it(var(X37))),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Var__IT)).
% 11.66/2.04 tff(f581,plain,(
% 11.66/2.04 spl32_7),
% 11.66/2.04 inference(avatar_split_clause,[],[f353,f578])).
% 11.66/2.04 tff(f353,plain,(
% 11.66/2.04 pp(fTrue)),
% 11.66/2.04 inference(cnf_transformation,[],[f102])).
% 11.66/2.04 tff(f102,axiom,(
% 11.66/2.04 pp(fTrue)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U)).
% 11.66/2.04 tff(f576,plain,(
% 11.66/2.04 spl32_6),
% 11.66/2.04 inference(avatar_split_clause,[],[f352,f573])).
% 11.66/2.04 tff(f352,plain,(
% 11.66/2.04 it(a)),
% 11.66/2.04 inference(cnf_transformation,[],[f2])).
% 11.66/2.04 tff(f2,axiom,(
% 11.66/2.04 it(a)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Beta_I3_J)).
% 11.66/2.04 tff(f571,plain,(
% 11.66/2.04 spl32_5),
% 11.66/2.04 inference(avatar_split_clause,[],[f351,f568])).
% 11.66/2.04 tff(f568,plain,(
% 11.66/2.04 spl32_5 <=> it(u)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_5])])).
% 11.66/2.04 tff(f351,plain,(
% 11.66/2.04 it(u)),
% 11.66/2.04 inference(cnf_transformation,[],[f16])).
% 11.66/2.04 tff(f16,axiom,(
% 11.66/2.04 it(u)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_uIT)).
% 11.66/2.04 tff(f566,plain,(
% 11.66/2.04 spl32_4),
% 11.66/2.04 inference(avatar_split_clause,[],[f350,f563])).
% 11.66/2.04 tff(f563,plain,(
% 11.66/2.04 spl32_4 <=> it(ua)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_4])])).
% 11.66/2.04 tff(f350,plain,(
% 11.66/2.04 it(ua)),
% 11.66/2.04 inference(cnf_transformation,[],[f15])).
% 11.66/2.04 tff(f15,axiom,(
% 11.66/2.04 it(ua)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Beta_I6_J)).
% 11.66/2.04 tff(f561,plain,(
% 11.66/2.04 spl32_3),
% 11.66/2.04 inference(avatar_split_clause,[],[f349,f558])).
% 11.66/2.04 tff(f558,plain,(
% 11.66/2.04 spl32_3 <=> it(t2)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_3])])).
% 11.66/2.04 tff(f349,plain,(
% 11.66/2.04 it(t2)),
% 11.66/2.04 inference(cnf_transformation,[],[f1])).
% 11.66/2.04 tff(f1,axiom,(
% 11.66/2.04 it(t2)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096)).
% 11.66/2.04 tff(f556,plain,(
% 11.66/2.04 spl32_2),
% 11.66/2.04 inference(avatar_split_clause,[],[f348,f553])).
% 11.66/2.04 tff(f553,plain,(
% 11.66/2.04 spl32_2 <=> zero(nat)),
% 11.66/2.04 introduced(avatar_definition,[new_symbols(naming,[spl32_2])])).
% 11.66/2.04 tff(f348,plain,(
% 11.66/2.04 zero(nat)),
% 11.66/2.04 inference(cnf_transformation,[],[f100])).
% 11.66/2.04 tff(f100,axiom,(
% 11.66/2.04 zero(nat)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero)).
% 11.66/2.04 tff(f551,plain,(
% 11.66/2.04 ~spl32_1),
% 11.66/2.04 inference(avatar_split_clause,[],[f346,f548])).
% 11.66/2.04 tff(f346,plain,(
% 11.66/2.04 ~pp(fFalse)),
% 11.66/2.04 inference(cnf_transformation,[],[f108])).
% 11.66/2.04 tff(f108,axiom,(
% 11.66/2.04 ~pp(fFalse)),
% 11.66/2.04 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U)).
% 11.66/2.04 % SZS output end Proof for theBenchmark
% 11.66/2.04 % (17287)------------------------------
% 11.66/2.04 % (17287)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 11.66/2.04 % (17287)Termination reason: Refutation
% 11.66/2.04
% 11.66/2.04 % (17287)Memory used [KB]: 12085
% 11.66/2.04 % (17287)Time elapsed: 1.670 s
% 11.66/2.04 % (17287)Instructions burned: 3353 (million)
% 11.66/2.04 % (17282)Success in time 1.719 s
%------------------------------------------------------------------------------