TSTP Solution File: ITP125^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP125^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n005.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 : Mon May 20 22:52:33 EDT 2024

% Result   : Theorem 6.25s 1.25s
% Output   : Refutation 6.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :  819
% Syntax   : Number of formulae    : 2602 ( 440 unt; 173 typ;   0 def)
%            Number of atoms       : 31036 (4555 equ;   0 cnn)
%            Maximal formula atoms :   12 (  12 avg)
%            Number of connectives : 8025 (3141   ~;3176   |; 390   &;   0   @)
%                                         ( 410 <=>; 908  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :  972 ( 971   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  578 ( 575 usr; 428 con; 0-6 aty)
%            Number of variables   : 5341 (  70   ^4876   !; 381   ?;5341   :)
%                                         (  14  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    nat: $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_7,type,
    formula_a: $tType ).

thf(type_def_8,type,
    i: $tType ).

thf(type_def_9,type,
    trace_1367752404list_a: $tType ).

thf(type_def_10,type,
    list_a: $tType ).

thf(type_def_11,type,
    prefix1027212443list_a: $tType ).

thf(func_def_0,type,
    prefix1027212443list_a: $tType ).

thf(func_def_1,type,
    trace_1367752404list_a: $tType ).

thf(func_def_2,type,
    i: $tType ).

thf(func_def_3,type,
    formula_a: $tType ).

thf(func_def_4,type,
    list_a: $tType ).

thf(func_def_5,type,
    nat: $tType ).

thf(func_def_6,type,
    one_one_nat: nat ).

thf(func_def_7,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_8,type,
    until_a: formula_a > i > formula_a > formula_a ).

thf(func_def_9,type,
    sat_a: trace_1367752404list_a > list_a > nat > formula_a > $o ).

thf(func_def_10,type,
    monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat ).

thf(func_def_11,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_12,type,
    ord_le887097159list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).

thf(func_def_13,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_14,type,
    ord_le699472955list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).

thf(func_def_15,type,
    tau_Pr257024512list_a: trace_1367752404list_a > nat > nat ).

thf(func_def_16,type,
    plen_P694648887list_a: prefix1027212443list_a > nat ).

thf(func_def_17,type,
    prefix1041802747list_a: prefix1027212443list_a > trace_1367752404list_a > $o ).

thf(func_def_18,type,
    i2: i ).

thf(func_def_19,type,
    phi: formula_a ).

thf(func_def_20,type,
    phi_1: formula_a ).

thf(func_def_21,type,
    phi_2: formula_a ).

thf(func_def_22,type,
    pi: prefix1027212443list_a ).

thf(func_def_23,type,
    sigma: trace_1367752404list_a ).

thf(func_def_24,type,
    sigma2: trace_1367752404list_a ).

thf(func_def_25,type,
    b: nat ).

thf(func_def_26,type,
    i3: nat ).

thf(func_def_27,type,
    ia: nat ).

thf(func_def_28,type,
    j: nat ).

thf(func_def_29,type,
    ja: nat ).

thf(func_def_30,type,
    k: nat ).

thf(func_def_34,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_35,type,
    vAND: $o > $o > $o ).

thf(func_def_36,type,
    vIMP: $o > $o > $o ).

thf(func_def_37,type,
    vNOT: $o > $o ).

thf(func_def_38,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_39,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_40,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_41,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_42,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_43,type,
    vOR: $o > $o > $o ).

thf(func_def_44,type,
    sP0: nat > nat > nat > $o ).

thf(func_def_45,type,
    sP1: nat > nat > nat > $o ).

thf(func_def_46,type,
    sP2: nat > nat > nat > $o ).

thf(func_def_47,type,
    sP3: nat > nat > nat > $o ).

thf(func_def_48,type,
    sP4: nat > ( nat > $o ) > $o ).

thf(func_def_49,type,
    sP5: nat > ( nat > $o ) > nat > $o ).

thf(func_def_50,type,
    sK6: nat ).

thf(func_def_51,type,
    sK7: nat ).

thf(func_def_52,type,
    sK8: nat > nat ).

thf(func_def_53,type,
    sK9: nat > nat ).

thf(func_def_54,type,
    sK10: nat > nat ).

thf(func_def_55,type,
    sK11: nat > nat ).

thf(func_def_56,type,
    sK12: nat > nat ).

thf(func_def_57,type,
    sK13: nat > nat ).

thf(func_def_58,type,
    sK14: nat > nat ).

thf(func_def_59,type,
    sK15: nat > nat ).

thf(func_def_60,type,
    sK16: nat > nat ).

thf(func_def_61,type,
    sK17: nat > nat ).

thf(func_def_62,type,
    sK18: nat > nat ).

thf(func_def_63,type,
    sK19: nat > nat ).

thf(func_def_64,type,
    sK20: prefix1027212443list_a > trace_1367752404list_a ).

thf(func_def_65,type,
    sK21: nat > nat ).

thf(func_def_66,type,
    sK22: ( nat > $o ) > nat ).

thf(func_def_67,type,
    sK23: ( nat > $o ) > nat ).

thf(func_def_68,type,
    sK24: ( nat > $o ) > nat ).

thf(func_def_69,type,
    sK25: nat > nat > nat ).

thf(func_def_70,type,
    sK26: nat > nat > nat ).

thf(func_def_71,type,
    sK27: nat > ( nat > $o ) > nat ).

thf(func_def_72,type,
    sK28: ( nat > $o ) > nat > nat ).

thf(func_def_73,type,
    sK29: ( nat > nat > $o ) > nat ).

thf(func_def_74,type,
    sK30: ( nat > nat > $o ) > nat ).

thf(func_def_75,type,
    sK31: ( nat > nat > $o ) > nat ).

thf(func_def_76,type,
    sK32: ( nat > nat > $o ) > nat ).

thf(func_def_77,type,
    sK33: ( nat > nat > $o ) > nat ).

thf(func_def_78,type,
    sK34: ( nat > nat > $o ) > nat ).

thf(func_def_79,type,
    sK35: ( nat > nat > $o ) > nat ).

thf(func_def_80,type,
    sK36: ( nat > nat > $o ) > nat ).

thf(func_def_81,type,
    sK37: ( nat > nat > $o ) > nat ).

thf(func_def_82,type,
    sK38: ( nat > nat ) > nat ).

thf(func_def_83,type,
    sK39: ( nat > nat ) > nat ).

thf(func_def_84,type,
    sK40: ( nat > nat ) > nat ).

thf(func_def_85,type,
    sK41: ( nat > nat ) > nat ).

thf(func_def_86,type,
    sK42: ( nat > $o ) > nat ).

thf(func_def_87,type,
    sK43: nat > ( nat > $o ) > nat ).

thf(func_def_88,type,
    sK44: nat > nat > ( nat > $o ) > nat ).

thf(func_def_89,type,
    sK45: ( nat > $o ) > nat > nat > nat ).

thf(func_def_90,type,
    sK46: trace_1367752404list_a > nat > nat > nat ).

thf(func_def_91,type,
    sK47: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_92,type,
    sK48: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_93,type,
    sK49: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_94,type,
    sK50: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_95,type,
    sK51: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_96,type,
    sK52: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_97,type,
    sK53: ( nat > nat ) > nat ).

thf(func_def_98,type,
    sK54: ( nat > nat ) > nat ).

thf(func_def_99,type,
    sK55: ( nat > nat ) > nat ).

thf(func_def_100,type,
    sK56: ( nat > nat ) > nat ).

thf(func_def_101,type,
    sK57: trace_1367752404list_a > trace_1367752404list_a > nat > nat ).

thf(func_def_102,type,
    sK58: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_103,type,
    sK59: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_104,type,
    sK60: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_105,type,
    sK61: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_106,type,
    sK62: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_107,type,
    sK63: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_108,type,
    sK64: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_109,type,
    sK65: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_110,type,
    sK66: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_111,type,
    sK67: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_112,type,
    sK68: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_113,type,
    sK69: nat > ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_114,type,
    sK70: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_115,type,
    sK71: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_116,type,
    sK72: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_117,type,
    sK73: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_118,type,
    sK74: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_119,type,
    sK75: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_120,type,
    sK76: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_121,type,
    sK77: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_122,type,
    sK78: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_123,type,
    sK79: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_124,type,
    sK80: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_125,type,
    sK81: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_126,type,
    sK82: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_127,type,
    sK83: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_128,type,
    sK84: ( nat > nat ) > nat ).

thf(func_def_129,type,
    sK85: ( nat > nat ) > nat ).

thf(func_def_130,type,
    sK86: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_131,type,
    sK87: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_132,type,
    sK88: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_133,type,
    sK89: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_134,type,
    sK90: ( nat > nat ) > nat ).

thf(func_def_135,type,
    sK91: ( nat > nat ) > nat ).

thf(func_def_136,type,
    sK92: ( nat > nat ) > nat ).

thf(func_def_137,type,
    sK93: ( nat > nat ) > nat ).

thf(func_def_138,type,
    sK94: ( nat > nat ) > nat ).

thf(func_def_139,type,
    sK95: ( nat > nat ) > nat ).

thf(func_def_140,type,
    sK96: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_141,type,
    sK97: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_142,type,
    sK98: ( nat > nat ) > nat ).

thf(func_def_143,type,
    sK99: ( nat > nat ) > nat ).

thf(func_def_144,type,
    sK100: ( nat > nat ) > nat ).

thf(func_def_145,type,
    sK101: ( nat > nat ) > nat ).

thf(func_def_146,type,
    sK102: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_147,type,
    sK103: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_148,type,
    sK104: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_149,type,
    sK105: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_150,type,
    sK106: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_151,type,
    sK107: ( prefix1027212443list_a > prefix1027212443list_a ) > prefix1027212443list_a ).

thf(func_def_152,type,
    sK108: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_153,type,
    sK109: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_154,type,
    sK110: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_155,type,
    sK111: ( nat > prefix1027212443list_a ) > nat ).

thf(func_def_156,type,
    sK112: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_157,type,
    sK113: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_158,type,
    sK114: ( nat > nat ) > nat ).

thf(func_def_159,type,
    sK115: ( nat > nat ) > nat ).

thf(func_def_160,type,
    sK116: ( nat > nat ) > nat ).

thf(func_def_161,type,
    sK117: ( nat > nat ) > nat ).

thf(func_def_162,type,
    sK118: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_163,type,
    sK119: ( prefix1027212443list_a > nat ) > prefix1027212443list_a ).

thf(func_def_164,type,
    sK120: ( nat > nat ) > nat ).

thf(func_def_165,type,
    sK121: ( nat > nat ) > nat ).

thf(func_def_166,type,
    sK122: ( nat > nat ) > nat ).

thf(func_def_167,type,
    sK123: ( nat > nat ) > nat ).

thf(func_def_169,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(f20808,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2257,f2262,f2266,f2300,f2304,f2308,f2313,f2318,f2325,f2329,f2333,f2337,f2341,f2345,f2349,f2364,f2368,f2372,f2384,f2405,f2409,f2413,f2417,f2421,f2432,f2436,f2440,f2444,f2448,f2452,f2472,f2501,f2505,f2509,f2513,f2529,f2547,f2551,f2555,f2559,f2563,f2567,f2571,f2575,f2613,f2617,f2621,f2637,f2641,f2645,f2658,f2662,f2670,f2674,f2678,f2682,f2686,f2690,f2694,f2720,f2725,f2730,f2735,f2739,f2744,f2749,f2754,f2759,f2764,f2769,f2797,f2833,f2837,f2841,f2845,f2849,f2853,f2857,f2861,f2865,f2869,f3013,f3062,f3074,f3078,f3082,f3086,f3090,f3094,f3098,f3102,f3106,f3163,f3187,f3191,f3265,f3269,f3273,f3278,f3371,f3376,f3382,f3386,f3406,f3410,f3414,f3418,f3422,f3426,f3430,f3434,f3649,f3680,f3684,f3881,f3896,f3909,f3916,f3951,f3956,f3961,f3966,f3971,f3976,f4148,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4677,f4804,f4808,f4812,f4816,f4839,f4893,f4945,f4949,f5037,f5041,f5079,f5083,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5122,f5175,f5179,f5183,f5208,f5314,f5318,f5322,f5326,f5696,f5700,f5704,f5708,f5712,f5716,f5764,f5768,f5772,f5776,f5780,f5784,f5788,f5792,f5796,f5800,f5805,f5809,f5813,f5817,f5821,f5825,f5829,f5833,f6065,f6283,f6287,f6299,f6321,f6325,f6337,f6341,f6345,f6349,f6397,f6401,f6405,f6409,f6413,f6417,f6421,f6425,f6429,f6433,f6437,f6441,f6445,f6449,f6453,f6457,f6461,f6465,f6469,f6473,f6477,f6481,f6485,f6502,f6580,f6656,f6694,f6766,f6771,f6775,f6779,f6783,f7188,f7287,f7292,f7635,f7640,f7645,f7650,f7663,f8011,f8016,f8033,f8038,f8055,f8059,f8063,f8067,f8071,f8207,f8211,f8215,f8219,f8223,f8228,f8233,f8238,f8243,f8469,f8617,f8621,f8625,f8629,f8633,f8637,f8641,f8645,f8649,f8653,f8657,f8661,f9253,f9543,f9547,f9551,f9700,f9776,f9780,f9784,f9788,f9792,f9796,f9800,f9804,f9808,f9872,f10649,f10653,f10657,f10661,f10665,f10669,f10673,f10677,f10681,f10685,f10689,f10693,f11557,f11561,f11585,f11589,f11593,f11597,f11601,f11605,f11609,f11614,f13194,f13198,f13202,f13206,f13210,f13214,f13218,f13222,f13226,f13458,f13723,f13728,f13733,f13738,f13743,f13747,f13752,f13757,f13762,f13767,f13772,f13778,f13783,f13789,f13794,f13799,f14259,f14263,f14267,f14271,f14275,f14279,f14283,f14288,f14292,f14296,f14300,f14304,f14308,f14312,f14316,f14320,f14324,f14328,f14332,f16154,f16158,f16241,f16329,f16335,f16339,f16343,f16347,f16351,f16355,f16359,f16363,f16367,f16371,f16375,f16379,f16383,f16387,f16391,f17100,f17112,f17116,f17120,f17124,f17128,f17132,f17136,f17209,f18496,f18587,f18591,f18595,f18599,f18603,f18608,f18612,f18617,f18621,f18625,f18630,f18634,f18638,f18642,f18647,f18652,f18657,f18662,f20183,f20460,f20464,f20468,f20528,f20761,f20804,f20807]) ).

thf(f20807,plain,
    ( ~ spl124_46
    | ~ spl124_268
    | ~ spl124_291
    | ~ spl124_338 ),
    inference(avatar_contradiction_clause,[],[f20806]) ).

thf(f20806,plain,
    ( $false
    | ~ spl124_46
    | ~ spl124_268
    | ~ spl124_291
    | ~ spl124_338 ),
    inference(trivial_inequality_removal,[],[f20805]) ).

thf(f20805,plain,
    ( ( $true = $false )
    | ~ spl124_46
    | ~ spl124_268
    | ~ spl124_291
    | ~ spl124_338 ),
    inference(forward_demodulation,[],[f20792,f8944]) ).

thf(f8944,plain,
    ( ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) )
    | ~ spl124_46
    | ~ spl124_268 ),
    inference(trivial_inequality_removal,[],[f8718]) ).

thf(f8718,plain,
    ( ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] :
        ( ( $true = $false )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) ) )
    | ~ spl124_46
    | ~ spl124_268 ),
    inference(superposition,[],[f8632,f2616]) ).

thf(f2616,plain,
    ( ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),X2) )
    | ~ spl124_46 ),
    inference(avatar_component_clause,[],[f2615]) ).

thf(f2615,plain,
    ( spl124_46
  <=> ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_46])]) ).

thf(f8632,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_268 ),
    inference(avatar_component_clause,[],[f8631]) ).

thf(f8631,plain,
    ( spl124_268
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_268])]) ).

thf(f20792,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),k)) )
    | ~ spl124_291
    | ~ spl124_338 ),
    inference(superposition,[],[f13793,f10644]) ).

thf(f10644,plain,
    ( ( k = vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi) )
    | ~ spl124_291 ),
    inference(avatar_component_clause,[],[f10642]) ).

thf(f10642,plain,
    ( spl124_291
  <=> ( k = vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_291])]) ).

thf(f13793,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_338 ),
    inference(avatar_component_clause,[],[f13791]) ).

thf(f13791,plain,
    ( spl124_338
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_338])]) ).

thf(f20804,plain,
    ( ~ spl124_46
    | ~ spl124_70
    | ~ spl124_268
    | ~ spl124_291 ),
    inference(avatar_contradiction_clause,[],[f20803]) ).

thf(f20803,plain,
    ( $false
    | ~ spl124_46
    | ~ spl124_70
    | ~ spl124_268
    | ~ spl124_291 ),
    inference(trivial_inequality_removal,[],[f20802]) ).

thf(f20802,plain,
    ( ( $true = $false )
    | ~ spl124_46
    | ~ spl124_70
    | ~ spl124_268
    | ~ spl124_291 ),
    inference(forward_demodulation,[],[f20774,f8944]) ).

thf(f20774,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),k)) )
    | ~ spl124_70
    | ~ spl124_291 ),
    inference(superposition,[],[f2768,f10644]) ).

thf(f2768,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true )
    | ~ spl124_70 ),
    inference(avatar_component_clause,[],[f2766]) ).

thf(f2766,plain,
    ( spl124_70
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_70])]) ).

thf(f20761,plain,
    ( spl124_410
    | ~ spl124_63
    | ~ spl124_74 ),
    inference(avatar_split_clause,[],[f2951,f2839,f2732,f20759]) ).

thf(f20759,plain,
    ( spl124_410
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_410])]) ).

thf(f2732,plain,
    ( spl124_63
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_63])]) ).

thf(f2839,plain,
    ( spl124_74
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_74])]) ).

thf(f2951,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),X0)) )
    | ~ spl124_63
    | ~ spl124_74 ),
    inference(trivial_inequality_removal,[],[f2948]) ).

thf(f2948,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),X0)) ) )
    | ~ spl124_63
    | ~ spl124_74 ),
    inference(superposition,[],[f2840,f2734]) ).

thf(f2734,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_63 ),
    inference(avatar_component_clause,[],[f2732]) ).

thf(f2840,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) )
    | ~ spl124_74 ),
    inference(avatar_component_clause,[],[f2839]) ).

thf(f20528,plain,
    ( ~ spl124_292
    | ~ spl124_335
    | ~ spl124_407 ),
    inference(avatar_contradiction_clause,[],[f20527]) ).

thf(f20527,plain,
    ( $false
    | ~ spl124_292
    | ~ spl124_335
    | ~ spl124_407 ),
    inference(trivial_inequality_removal,[],[f20526]) ).

thf(f20526,plain,
    ( ( $true = $false )
    | ~ spl124_292
    | ~ spl124_335
    | ~ spl124_407 ),
    inference(forward_demodulation,[],[f20516,f10648]) ).

thf(f10648,plain,
    ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ~ spl124_292 ),
    inference(avatar_component_clause,[],[f10646]) ).

thf(f10646,plain,
    ( spl124_292
  <=> ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_292])]) ).

thf(f20516,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ~ spl124_335
    | ~ spl124_407 ),
    inference(trivial_inequality_removal,[],[f20481]) ).

thf(f20481,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ~ spl124_335
    | ~ spl124_407 ),
    inference(superposition,[],[f20459,f13777]) ).

thf(f13777,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_335 ),
    inference(avatar_component_clause,[],[f13775]) ).

thf(f13775,plain,
    ( spl124_335
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_335])]) ).

thf(f20459,plain,
    ( ! [X2: nat,X3: nat,X0: trace_1367752404list_a,X1: formula_a] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
    | ~ spl124_407 ),
    inference(avatar_component_clause,[],[f20458]) ).

thf(f20458,plain,
    ( spl124_407
  <=> ! [X0: trace_1367752404list_a,X3: nat,X2: nat,X1: formula_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_407])]) ).

thf(f20468,plain,
    ( spl124_409
    | ~ spl124_3
    | ~ spl124_100 ),
    inference(avatar_split_clause,[],[f3378,f3369,f2264,f20466]) ).

thf(f20466,plain,
    ( spl124_409
  <=> ! [X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X0),X1)),X0) )
        | ( $false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_409])]) ).

thf(f2264,plain,
    ( spl124_3
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_3])]) ).

thf(f3369,plain,
    ( spl124_100
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X1) )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_100])]) ).

thf(f3378,plain,
    ( ! [X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X0),X1)),X0) )
        | ( $false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_100 ),
    inference(trivial_inequality_removal,[],[f3377]) ).

thf(f3377,plain,
    ( ! [X0: nat,X1: nat > $o] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X0),X1)),X0) )
        | ( $false = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_100 ),
    inference(superposition,[],[f3370,f2265]) ).

thf(f2265,plain,
    ( ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) )
    | ~ spl124_3 ),
    inference(avatar_component_clause,[],[f2264]) ).

thf(f3370,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X1) ) )
    | ~ spl124_100 ),
    inference(avatar_component_clause,[],[f3369]) ).

thf(f20464,plain,
    ( spl124_408
    | ~ spl124_45
    | ~ spl124_89 ),
    inference(avatar_split_clause,[],[f3148,f3092,f2611,f20462]) ).

thf(f20462,plain,
    ( spl124_408
  <=> ! [X0: nat,X3: nat,X2: nat,X1: trace_1367752404list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_408])]) ).

thf(f2611,plain,
    ( spl124_45
  <=> ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_45])]) ).

thf(f3092,plain,
    ( spl124_89
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_89])]) ).

thf(f3148,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: trace_1367752404list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) ) )
    | ~ spl124_45
    | ~ spl124_89 ),
    inference(trivial_inequality_removal,[],[f3121]) ).

thf(f3121,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: trace_1367752404list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) ) )
    | ~ spl124_45
    | ~ spl124_89 ),
    inference(superposition,[],[f3093,f2612]) ).

thf(f2612,plain,
    ( ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0)) )
    | ~ spl124_45 ),
    inference(avatar_component_clause,[],[f2611]) ).

thf(f3093,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) )
    | ~ spl124_89 ),
    inference(avatar_component_clause,[],[f3092]) ).

thf(f20460,plain,
    ( spl124_407
    | ~ spl124_46
    | ~ spl124_89 ),
    inference(avatar_split_clause,[],[f3140,f3092,f2615,f20458]) ).

thf(f3140,plain,
    ( ! [X2: nat,X3: nat,X0: trace_1367752404list_a,X1: formula_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) ) )
    | ~ spl124_46
    | ~ spl124_89 ),
    inference(trivial_inequality_removal,[],[f3129]) ).

thf(f3129,plain,
    ( ! [X2: nat,X3: nat,X0: trace_1367752404list_a,X1: formula_a] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) ) )
    | ~ spl124_46
    | ~ spl124_89 ),
    inference(superposition,[],[f3093,f2616]) ).

thf(f20183,plain,
    ( spl124_406
    | ~ spl124_29
    | ~ spl124_252 ),
    inference(avatar_split_clause,[],[f8145,f8065,f2446,f20181]) ).

thf(f20181,plain,
    ( spl124_406
  <=> ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK17,X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_406])]) ).

thf(f2446,plain,
    ( spl124_29
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_29])]) ).

thf(f8065,plain,
    ( spl124_252
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK17,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_252])]) ).

thf(f8145,plain,
    ( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK17,X0))),X0) )
    | ~ spl124_29
    | ~ spl124_252 ),
    inference(trivial_inequality_removal,[],[f8092]) ).

thf(f8092,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK17,X0))),X0) ) )
    | ~ spl124_29
    | ~ spl124_252 ),
    inference(superposition,[],[f2447,f8066]) ).

thf(f8066,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK17,X0))) )
    | ~ spl124_252 ),
    inference(avatar_component_clause,[],[f8065]) ).

thf(f2447,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true ) )
    | ~ spl124_29 ),
    inference(avatar_component_clause,[],[f2446]) ).

thf(f18662,plain,
    ( spl124_405
    | ~ spl124_80
    | ~ spl124_124 ),
    inference(avatar_split_clause,[],[f4141,f3973,f2863,f18659]) ).

thf(f18659,plain,
    ( spl124_405
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_405])]) ).

thf(f2863,plain,
    ( spl124_80
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_80])]) ).

thf(f3973,plain,
    ( spl124_124
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_124])]) ).

thf(f4141,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) )
    | ~ spl124_80
    | ~ spl124_124 ),
    inference(trivial_inequality_removal,[],[f4114]) ).

thf(f4114,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) )
    | ~ spl124_80
    | ~ spl124_124 ),
    inference(superposition,[],[f2864,f3975]) ).

thf(f3975,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) )
    | ~ spl124_124 ),
    inference(avatar_component_clause,[],[f3973]) ).

thf(f2864,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
    | ~ spl124_80 ),
    inference(avatar_component_clause,[],[f2863]) ).

thf(f18657,plain,
    ( spl124_404
    | ~ spl124_80
    | ~ spl124_123 ),
    inference(avatar_split_clause,[],[f4110,f3968,f2863,f18654]) ).

thf(f18654,plain,
    ( spl124_404
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_404])]) ).

thf(f3968,plain,
    ( spl124_123
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_123])]) ).

thf(f4110,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) )
    | ~ spl124_80
    | ~ spl124_123 ),
    inference(trivial_inequality_removal,[],[f4083]) ).

thf(f4083,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) )
    | ~ spl124_80
    | ~ spl124_123 ),
    inference(superposition,[],[f2864,f3970]) ).

thf(f3970,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) )
    | ~ spl124_123 ),
    inference(avatar_component_clause,[],[f3968]) ).

thf(f18652,plain,
    ( spl124_403
    | ~ spl124_80
    | ~ spl124_122 ),
    inference(avatar_split_clause,[],[f4075,f3963,f2863,f18649]) ).

thf(f18649,plain,
    ( spl124_403
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_403])]) ).

thf(f3963,plain,
    ( spl124_122
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_122])]) ).

thf(f4075,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) )
    | ~ spl124_80
    | ~ spl124_122 ),
    inference(trivial_inequality_removal,[],[f4048]) ).

thf(f4048,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) )
    | ~ spl124_80
    | ~ spl124_122 ),
    inference(superposition,[],[f2864,f3965]) ).

thf(f3965,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) )
    | ~ spl124_122 ),
    inference(avatar_component_clause,[],[f3963]) ).

thf(f18647,plain,
    ( spl124_402
    | ~ spl124_80
    | ~ spl124_121 ),
    inference(avatar_split_clause,[],[f4044,f3958,f2863,f18644]) ).

thf(f18644,plain,
    ( spl124_402
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_402])]) ).

thf(f3958,plain,
    ( spl124_121
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_121])]) ).

thf(f4044,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) )
    | ~ spl124_80
    | ~ spl124_121 ),
    inference(trivial_inequality_removal,[],[f4017]) ).

thf(f4017,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) )
    | ~ spl124_80
    | ~ spl124_121 ),
    inference(superposition,[],[f2864,f3960]) ).

thf(f3960,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) )
    | ~ spl124_121 ),
    inference(avatar_component_clause,[],[f3958]) ).

thf(f18642,plain,
    ( spl124_401
    | ~ spl124_10
    | ~ spl124_116 ),
    inference(avatar_split_clause,[],[f3904,f3894,f2327,f18640]) ).

thf(f18640,plain,
    ( spl124_401
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),vAPP(prefix1027212443list_a,trace_1367752404list_a,sK20,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_401])]) ).

thf(f2327,plain,
    ( spl124_10
  <=> ! [X0: prefix1027212443list_a] : ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),vAPP(prefix1027212443list_a,trace_1367752404list_a,sK20,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_10])]) ).

thf(f3894,plain,
    ( spl124_116
  <=> ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: trace_1367752404list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X2),X1) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_116])]) ).

thf(f3904,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),vAPP(prefix1027212443list_a,trace_1367752404list_a,sK20,X0)) ) )
    | ~ spl124_10
    | ~ spl124_116 ),
    inference(trivial_inequality_removal,[],[f3897]) ).

thf(f3897,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),vAPP(prefix1027212443list_a,trace_1367752404list_a,sK20,X0)) ) )
    | ~ spl124_10
    | ~ spl124_116 ),
    inference(superposition,[],[f3895,f2328]) ).

thf(f2328,plain,
    ( ! [X0: prefix1027212443list_a] : ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),vAPP(prefix1027212443list_a,trace_1367752404list_a,sK20,X0)) )
    | ~ spl124_10 ),
    inference(avatar_component_clause,[],[f2327]) ).

thf(f3895,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: trace_1367752404list_a] :
        ( ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X2),X1) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) )
    | ~ spl124_116 ),
    inference(avatar_component_clause,[],[f3894]) ).

thf(f18638,plain,
    ( spl124_400
    | ~ spl124_24
    | ~ spl124_102 ),
    inference(avatar_split_clause,[],[f3469,f3380,f2419,f18636]) ).

thf(f18636,plain,
    ( spl124_400
  <=> ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_400])]) ).

thf(f2419,plain,
    ( spl124_24
  <=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_24])]) ).

thf(f3380,plain,
    ( spl124_102
  <=> ! [X2: trace_1367752404list_a,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_102])]) ).

thf(f3469,plain,
    ( ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0))) )
    | ~ spl124_24
    | ~ spl124_102 ),
    inference(trivial_inequality_removal,[],[f3436]) ).

thf(f3436,plain,
    ( ! [X2: trace_1367752404list_a,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0))) ) )
    | ~ spl124_24
    | ~ spl124_102 ),
    inference(superposition,[],[f3381,f2420]) ).

thf(f2420,plain,
    ( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) )
    | ~ spl124_24 ),
    inference(avatar_component_clause,[],[f2419]) ).

thf(f3381,plain,
    ( ! [X2: trace_1367752404list_a,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X1)) ) )
    | ~ spl124_102 ),
    inference(avatar_component_clause,[],[f3380]) ).

thf(f18634,plain,
    ( spl124_399
    | ~ spl124_23
    | ~ spl124_102 ),
    inference(avatar_split_clause,[],[f3467,f3380,f2415,f18632]) ).

thf(f18632,plain,
    ( spl124_399
  <=> ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_399])]) ).

thf(f2415,plain,
    ( spl124_23
  <=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_23])]) ).

thf(f3467,plain,
    ( ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
    | ~ spl124_23
    | ~ spl124_102 ),
    inference(trivial_inequality_removal,[],[f3438]) ).

thf(f3438,plain,
    ( ! [X2: trace_1367752404list_a,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) )
    | ~ spl124_23
    | ~ spl124_102 ),
    inference(superposition,[],[f3381,f2416]) ).

thf(f2416,plain,
    ( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
    | ~ spl124_23 ),
    inference(avatar_component_clause,[],[f2415]) ).

thf(f18630,plain,
    ( ~ spl124_398
    | ~ spl124_29
    | ~ spl124_99 ),
    inference(avatar_split_clause,[],[f3365,f3275,f2446,f18627]) ).

thf(f18627,plain,
    ( spl124_398
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_398])]) ).

thf(f3275,plain,
    ( spl124_99
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_99])]) ).

thf(f3365,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)) )
    | ~ spl124_29
    | ~ spl124_99 ),
    inference(trivial_inequality_removal,[],[f3348]) ).

thf(f3348,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)) )
    | ~ spl124_29
    | ~ spl124_99 ),
    inference(superposition,[],[f2447,f3277]) ).

thf(f3277,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) = $true )
    | ~ spl124_99 ),
    inference(avatar_component_clause,[],[f3275]) ).

thf(f18625,plain,
    ( spl124_397
    | ~ spl124_269
    | ~ spl124_370 ),
    inference(avatar_split_clause,[],[f18576,f16361,f8635,f18623]) ).

thf(f18623,plain,
    ( spl124_397
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK13,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_397])]) ).

thf(f8635,plain,
    ( spl124_269
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_269])]) ).

thf(f16361,plain,
    ( spl124_370
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_370])]) ).

thf(f18576,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK13,X0)) )
    | ~ spl124_269
    | ~ spl124_370 ),
    inference(trivial_inequality_removal,[],[f18502]) ).

thf(f18502,plain,
    ( ! [X0: nat] :
        ( ( $true = $false )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK13,X0)) ) )
    | ~ spl124_269
    | ~ spl124_370 ),
    inference(superposition,[],[f16362,f8636]) ).

thf(f8636,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) )
    | ~ spl124_269 ),
    inference(avatar_component_clause,[],[f8635]) ).

thf(f16362,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X0) )
    | ~ spl124_370 ),
    inference(avatar_component_clause,[],[f16361]) ).

thf(f18621,plain,
    ( spl124_396
    | ~ spl124_3
    | ~ spl124_98 ),
    inference(avatar_split_clause,[],[f3345,f3271,f2264,f18619]) ).

thf(f18619,plain,
    ( spl124_396
  <=> ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) )
        | ( $true = vAPP(nat,$o,X0,X2) )
        | ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_396])]) ).

thf(f3271,plain,
    ( spl124_98
  <=> ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,X2) )
        | ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) )
        | ( $true != vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_98])]) ).

thf(f3345,plain,
    ( ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) )
        | ( $true = vAPP(nat,$o,X0,X2) )
        | ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X0),X1)) ) )
    | ~ spl124_3
    | ~ spl124_98 ),
    inference(trivial_inequality_removal,[],[f3344]) ).

thf(f3344,plain,
    ( ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) )
        | ( $true = vAPP(nat,$o,X0,X2) )
        | ( $false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X0),X1)) ) )
    | ~ spl124_3
    | ~ spl124_98 ),
    inference(superposition,[],[f3272,f2265]) ).

thf(f3272,plain,
    ( ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true != vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) )
        | ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) )
        | ( $true = vAPP(nat,$o,X1,X2) ) )
    | ~ spl124_98 ),
    inference(avatar_component_clause,[],[f3271]) ).

thf(f18617,plain,
    ( spl124_395
    | ~ spl124_23
    | ~ spl124_97 ),
    inference(avatar_split_clause,[],[f3322,f3267,f2415,f18615]) ).

thf(f18615,plain,
    ( spl124_395
  <=> ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_395])]) ).

thf(f3267,plain,
    ( spl124_97
  <=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_97])]) ).

thf(f3322,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) )
    | ~ spl124_23
    | ~ spl124_97 ),
    inference(superposition,[],[f2416,f3268]) ).

thf(f3268,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
    | ~ spl124_97 ),
    inference(avatar_component_clause,[],[f3267]) ).

thf(f18612,plain,
    ( spl124_394
    | ~ spl124_22
    | ~ spl124_97 ),
    inference(avatar_split_clause,[],[f3321,f3267,f2411,f18610]) ).

thf(f18610,plain,
    ( spl124_394
  <=> ! [X2: nat,X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_394])]) ).

thf(f2411,plain,
    ( spl124_22
  <=> ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_22])]) ).

thf(f3321,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
    | ~ spl124_22
    | ~ spl124_97 ),
    inference(superposition,[],[f2412,f3268]) ).

thf(f2412,plain,
    ( ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) )
    | ~ spl124_22 ),
    inference(avatar_component_clause,[],[f2411]) ).

thf(f18608,plain,
    ( spl124_393
    | ~ spl124_24
    | ~ spl124_96 ),
    inference(avatar_split_clause,[],[f3304,f3263,f2419,f18606]) ).

thf(f18606,plain,
    ( spl124_393
  <=> ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_393])]) ).

thf(f3263,plain,
    ( spl124_96
  <=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_96])]) ).

thf(f3304,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))) )
    | ~ spl124_24
    | ~ spl124_96 ),
    inference(superposition,[],[f2420,f3264]) ).

thf(f3264,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
    | ~ spl124_96 ),
    inference(avatar_component_clause,[],[f3263]) ).

thf(f18603,plain,
    ( spl124_392
    | ~ spl124_21
    | ~ spl124_96 ),
    inference(avatar_split_clause,[],[f3301,f3263,f2407,f18601]) ).

thf(f18601,plain,
    ( spl124_392
  <=> ! [X2: nat,X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_392])]) ).

thf(f2407,plain,
    ( spl124_21
  <=> ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_21])]) ).

thf(f3301,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
    | ~ spl124_21
    | ~ spl124_96 ),
    inference(superposition,[],[f2408,f3264]) ).

thf(f2408,plain,
    ( ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) )
    | ~ spl124_21 ),
    inference(avatar_component_clause,[],[f2407]) ).

thf(f18599,plain,
    ( spl124_391
    | ~ spl124_24
    | ~ spl124_73 ),
    inference(avatar_split_clause,[],[f2932,f2835,f2419,f18597]) ).

thf(f18597,plain,
    ( spl124_391
  <=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_391])]) ).

thf(f2835,plain,
    ( spl124_73
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_73])]) ).

thf(f2932,plain,
    ( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0)) )
    | ~ spl124_24
    | ~ spl124_73 ),
    inference(trivial_inequality_removal,[],[f2903]) ).

thf(f2903,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0)) ) )
    | ~ spl124_24
    | ~ spl124_73 ),
    inference(superposition,[],[f2836,f2420]) ).

thf(f2836,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 ) )
    | ~ spl124_73 ),
    inference(avatar_component_clause,[],[f2835]) ).

thf(f18595,plain,
    ( spl124_390
    | ~ spl124_23
    | ~ spl124_73 ),
    inference(avatar_split_clause,[],[f2930,f2835,f2415,f18593]) ).

thf(f18593,plain,
    ( spl124_390
  <=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_390])]) ).

thf(f2930,plain,
    ( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0)) )
    | ~ spl124_23
    | ~ spl124_73 ),
    inference(trivial_inequality_removal,[],[f2905]) ).

thf(f2905,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0)) ) )
    | ~ spl124_23
    | ~ spl124_73 ),
    inference(superposition,[],[f2836,f2416]) ).

thf(f18591,plain,
    ( spl124_389
    | ~ spl124_24
    | ~ spl124_72 ),
    inference(avatar_split_clause,[],[f2900,f2831,f2419,f18589]) ).

thf(f18589,plain,
    ( spl124_389
  <=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_389])]) ).

thf(f2831,plain,
    ( spl124_72
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_72])]) ).

thf(f2900,plain,
    ( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0)) )
    | ~ spl124_24
    | ~ spl124_72 ),
    inference(trivial_inequality_removal,[],[f2871]) ).

thf(f2871,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0)) ) )
    | ~ spl124_24
    | ~ spl124_72 ),
    inference(superposition,[],[f2832,f2420]) ).

thf(f2832,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 ) )
    | ~ spl124_72 ),
    inference(avatar_component_clause,[],[f2831]) ).

thf(f18587,plain,
    ( spl124_388
    | ~ spl124_23
    | ~ spl124_72 ),
    inference(avatar_split_clause,[],[f2898,f2831,f2415,f18585]) ).

thf(f18585,plain,
    ( spl124_388
  <=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_388])]) ).

thf(f2898,plain,
    ( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0)) )
    | ~ spl124_23
    | ~ spl124_72 ),
    inference(trivial_inequality_removal,[],[f2873]) ).

thf(f2873,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0)) ) )
    | ~ spl124_23
    | ~ spl124_72 ),
    inference(superposition,[],[f2832,f2416]) ).

thf(f18496,plain,
    ( spl124_387
    | ~ spl124_11
    | ~ spl124_115 ),
    inference(avatar_split_clause,[],[f3891,f3879,f2331,f18494]) ).

thf(f18494,plain,
    ( spl124_387
  <=> ! [X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,sK21,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X0),X1))) )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_387])]) ).

thf(f2331,plain,
    ( spl124_11
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_11])]) ).

thf(f3879,plain,
    ( spl124_115
  <=> ! [X0: nat > $o,X1: nat,X3: nat] :
        ( ( $true = vAPP(nat,$o,X0,X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X3) )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_115])]) ).

thf(f3891,plain,
    ( ! [X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,sK21,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X0),X1))) )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) ) )
    | ~ spl124_11
    | ~ spl124_115 ),
    inference(trivial_inequality_removal,[],[f3886]) ).

thf(f3886,plain,
    ( ! [X0: nat,X1: nat > $o] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,X1,vAPP(nat,nat,sK21,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X0),X1))) )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) ) )
    | ~ spl124_11
    | ~ spl124_115 ),
    inference(superposition,[],[f3880,f2332]) ).

thf(f2332,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,X0)) )
    | ~ spl124_11 ),
    inference(avatar_component_clause,[],[f2331]) ).

thf(f3880,plain,
    ( ! [X3: nat,X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X3) )
        | ( $true = vAPP(nat,$o,X0,X3) )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) )
    | ~ spl124_115 ),
    inference(avatar_component_clause,[],[f3879]) ).

thf(f17209,plain,
    ( spl124_386
    | ~ spl124_29
    | ~ spl124_95 ),
    inference(avatar_split_clause,[],[f3261,f3189,f2446,f17207]) ).

thf(f17207,plain,
    ( spl124_386
  <=> ! [X2: nat,X0: nat,X1: trace_1367752404list_a] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X0),X2))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_386])]) ).

thf(f3189,plain,
    ( spl124_95
  <=> ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_95])]) ).

thf(f3261,plain,
    ( ! [X2: nat,X0: nat,X1: trace_1367752404list_a] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X0),X2))),X0) )
    | ~ spl124_29
    | ~ spl124_95 ),
    inference(trivial_inequality_removal,[],[f3240]) ).

thf(f3240,plain,
    ( ! [X2: nat,X0: nat,X1: trace_1367752404list_a] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X0),X2))),X0) ) )
    | ~ spl124_29
    | ~ spl124_95 ),
    inference(superposition,[],[f2447,f3190]) ).

thf(f3190,plain,
    ( ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0))) )
    | ~ spl124_95 ),
    inference(avatar_component_clause,[],[f3189]) ).

thf(f17136,plain,
    ( spl124_385
    | ~ spl124_3
    | ~ spl124_94 ),
    inference(avatar_split_clause,[],[f3217,f3185,f2264,f17134]) ).

thf(f17134,plain,
    ( spl124_385
  <=> ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) )
        | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) )
        | ( $false = vAPP(nat,$o,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_385])]) ).

thf(f3185,plain,
    ( spl124_94
  <=> ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) )
        | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) )
        | ( $true != vAPP(nat,$o,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_94])]) ).

thf(f3217,plain,
    ( ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) )
        | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) )
        | ( $false = vAPP(nat,$o,X0,X1) ) )
    | ~ spl124_3
    | ~ spl124_94 ),
    inference(trivial_inequality_removal,[],[f3216]) ).

thf(f3216,plain,
    ( ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) )
        | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) )
        | ( $false = vAPP(nat,$o,X0,X1) ) )
    | ~ spl124_3
    | ~ spl124_94 ),
    inference(superposition,[],[f3186,f2265]) ).

thf(f3186,plain,
    ( ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,X0,X1) )
        | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) )
        | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) ) )
    | ~ spl124_94 ),
    inference(avatar_component_clause,[],[f3185]) ).

thf(f17132,plain,
    ( spl124_384
    | ~ spl124_45
    | ~ spl124_80 ),
    inference(avatar_split_clause,[],[f3050,f2863,f2611,f17130]) ).

thf(f17130,plain,
    ( spl124_384
  <=> ! [X0: nat,X3: nat,X2: trace_1367752404list_a,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_384])]) ).

thf(f3050,plain,
    ( ! [X2: trace_1367752404list_a,X3: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
    | ~ spl124_45
    | ~ spl124_80 ),
    inference(trivial_inequality_removal,[],[f3041]) ).

thf(f3041,plain,
    ( ! [X2: trace_1367752404list_a,X3: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) )
    | ~ spl124_45
    | ~ spl124_80 ),
    inference(superposition,[],[f2864,f2612]) ).

thf(f17128,plain,
    ( spl124_383
    | ~ spl124_45
    | ~ spl124_79 ),
    inference(avatar_split_clause,[],[f3035,f2859,f2611,f17126]) ).

thf(f17126,plain,
    ( spl124_383
  <=> ! [X0: nat,X3: nat,X2: trace_1367752404list_a,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_383])]) ).

thf(f2859,plain,
    ( spl124_79
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_79])]) ).

thf(f3035,plain,
    ( ! [X2: trace_1367752404list_a,X3: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
    | ~ spl124_45
    | ~ spl124_79 ),
    inference(trivial_inequality_removal,[],[f3026]) ).

thf(f3026,plain,
    ( ! [X2: trace_1367752404list_a,X3: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) )
    | ~ spl124_45
    | ~ spl124_79 ),
    inference(superposition,[],[f2860,f2612]) ).

thf(f2860,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
    | ~ spl124_79 ),
    inference(avatar_component_clause,[],[f2859]) ).

thf(f17124,plain,
    ( spl124_382
    | ~ spl124_45
    | ~ spl124_75 ),
    inference(avatar_split_clause,[],[f2997,f2843,f2611,f17122]) ).

thf(f17122,plain,
    ( spl124_382
  <=> ! [X0: nat,X3: nat,X2: nat,X1: trace_1367752404list_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_382])]) ).

thf(f2843,plain,
    ( spl124_75
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_75])]) ).

thf(f2997,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: trace_1367752404list_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0))) )
    | ~ spl124_45
    | ~ spl124_75 ),
    inference(trivial_inequality_removal,[],[f2970]) ).

thf(f2970,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: trace_1367752404list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0))) ) )
    | ~ spl124_45
    | ~ spl124_75 ),
    inference(superposition,[],[f2844,f2612]) ).

thf(f2844,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) )
    | ~ spl124_75 ),
    inference(avatar_component_clause,[],[f2843]) ).

thf(f17120,plain,
    ( spl124_381
    | ~ spl124_46
    | ~ spl124_75 ),
    inference(avatar_split_clause,[],[f2989,f2843,f2615,f17118]) ).

thf(f17118,plain,
    ( spl124_381
  <=> ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a,X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_381])]) ).

thf(f2989,plain,
    ( ! [X2: nat,X3: nat,X0: trace_1367752404list_a,X1: formula_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) )
    | ~ spl124_46
    | ~ spl124_75 ),
    inference(trivial_inequality_removal,[],[f2978]) ).

thf(f2978,plain,
    ( ! [X2: nat,X3: nat,X0: trace_1367752404list_a,X1: formula_a] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) ) )
    | ~ spl124_46
    | ~ spl124_75 ),
    inference(superposition,[],[f2844,f2616]) ).

thf(f17116,plain,
    ( spl124_380
    | ~ spl124_45
    | ~ spl124_74 ),
    inference(avatar_split_clause,[],[f2963,f2839,f2611,f17114]) ).

thf(f17114,plain,
    ( spl124_380
  <=> ! [X0: nat,X3: nat,X2: nat,X1: trace_1367752404list_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_380])]) ).

thf(f2963,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: trace_1367752404list_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)),X3)) )
    | ~ spl124_45
    | ~ spl124_74 ),
    inference(trivial_inequality_removal,[],[f2936]) ).

thf(f2936,plain,
    ( ! [X2: nat,X3: nat,X0: nat,X1: trace_1367752404list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)),X3)) ) )
    | ~ spl124_45
    | ~ spl124_74 ),
    inference(superposition,[],[f2840,f2612]) ).

thf(f17112,plain,
    ( spl124_379
    | ~ spl124_46
    | ~ spl124_74 ),
    inference(avatar_split_clause,[],[f2955,f2839,f2615,f17110]) ).

thf(f17110,plain,
    ( spl124_379
  <=> ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a,X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_379])]) ).

thf(f2955,plain,
    ( ! [X2: nat,X3: nat,X0: trace_1367752404list_a,X1: formula_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) )
    | ~ spl124_46
    | ~ spl124_74 ),
    inference(trivial_inequality_removal,[],[f2944]) ).

thf(f2944,plain,
    ( ! [X2: nat,X3: nat,X0: trace_1367752404list_a,X1: formula_a] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) ) )
    | ~ spl124_46
    | ~ spl124_74 ),
    inference(superposition,[],[f2840,f2616]) ).

thf(f17100,plain,
    ( spl124_378
    | ~ spl124_94 ),
    inference(avatar_split_clause,[],[f3239,f3185,f17098]) ).

thf(f17098,plain,
    ( spl124_378
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK42,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 )
        | ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_378])]) ).

thf(f3239,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK42,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 )
        | ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 ) )
    | ~ spl124_94 ),
    inference(equality_proxy_clausification,[],[f3192]) ).

thf(f3192,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),vAPP(sTfun(nat,$o),nat,sK42,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1))) )
        | ( vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1 ) )
    | ~ spl124_94 ),
    inference(leibniz_equality_elimination,[],[f3186]) ).

thf(f16391,plain,
    ( spl124_377
    | ~ spl124_7
    | ~ spl124_116 ),
    inference(avatar_split_clause,[],[f3903,f3894,f2310,f16389]) ).

thf(f16389,plain,
    ( spl124_377
  <=> ! [X0: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),pi) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,pi),X0) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),sigma2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_377])]) ).

thf(f2310,plain,
    ( spl124_7
  <=> ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma2) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_7])]) ).

thf(f3903,plain,
    ( ! [X0: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),pi) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,pi),X0) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),sigma2) ) )
    | ~ spl124_7
    | ~ spl124_116 ),
    inference(trivial_inequality_removal,[],[f3898]) ).

thf(f3898,plain,
    ( ! [X0: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),pi) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,pi),X0) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),sigma2) ) )
    | ~ spl124_7
    | ~ spl124_116 ),
    inference(superposition,[],[f3895,f2312]) ).

thf(f2312,plain,
    ( ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma2) = $true )
    | ~ spl124_7 ),
    inference(avatar_component_clause,[],[f2310]) ).

thf(f16387,plain,
    ( spl124_376
    | ~ spl124_8
    | ~ spl124_116 ),
    inference(avatar_split_clause,[],[f3902,f3894,f2315,f16385]) ).

thf(f16385,plain,
    ( spl124_376
  <=> ! [X0: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),pi) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,pi),X0) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),sigma) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_376])]) ).

thf(f2315,plain,
    ( spl124_8
  <=> ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_8])]) ).

thf(f3902,plain,
    ( ! [X0: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),pi) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,pi),X0) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),sigma) ) )
    | ~ spl124_8
    | ~ spl124_116 ),
    inference(trivial_inequality_removal,[],[f3899]) ).

thf(f3899,plain,
    ( ! [X0: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),pi) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,pi),X0) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),sigma) ) )
    | ~ spl124_8
    | ~ spl124_116 ),
    inference(superposition,[],[f3895,f2317]) ).

thf(f2317,plain,
    ( ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma) = $true )
    | ~ spl124_8 ),
    inference(avatar_component_clause,[],[f2315]) ).

thf(f16383,plain,
    ( spl124_375
    | ~ spl124_3
    | ~ spl124_92 ),
    inference(avatar_split_clause,[],[f3180,f3104,f2264,f16381]) ).

thf(f16381,plain,
    ( spl124_375
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_375])]) ).

thf(f3104,plain,
    ( spl124_92
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_92])]) ).

thf(f3180,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_92 ),
    inference(trivial_inequality_removal,[],[f3179]) ).

thf(f3179,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_92 ),
    inference(superposition,[],[f3105,f2265]) ).

thf(f3105,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) )
    | ~ spl124_92 ),
    inference(avatar_component_clause,[],[f3104]) ).

thf(f16379,plain,
    ( spl124_374
    | ~ spl124_3
    | ~ spl124_91 ),
    inference(avatar_split_clause,[],[f3170,f3100,f2264,f16377]) ).

thf(f16377,plain,
    ( spl124_374
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_374])]) ).

thf(f3100,plain,
    ( spl124_91
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_91])]) ).

thf(f3170,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_91 ),
    inference(trivial_inequality_removal,[],[f3169]) ).

thf(f3169,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_91 ),
    inference(superposition,[],[f3101,f2265]) ).

thf(f3101,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) )
    | ~ spl124_91 ),
    inference(avatar_component_clause,[],[f3100]) ).

thf(f16375,plain,
    ( spl124_373
    | ~ spl124_3
    | ~ spl124_90 ),
    inference(avatar_split_clause,[],[f3156,f3096,f2264,f16373]) ).

thf(f16373,plain,
    ( spl124_373
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_373])]) ).

thf(f3096,plain,
    ( spl124_90
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_90])]) ).

thf(f3156,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_90 ),
    inference(trivial_inequality_removal,[],[f3155]) ).

thf(f3155,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_90 ),
    inference(superposition,[],[f3097,f2265]) ).

thf(f3097,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) )
    | ~ spl124_90 ),
    inference(avatar_component_clause,[],[f3096]) ).

thf(f16371,plain,
    ( spl124_372
    | ~ spl124_25
    | ~ spl124_89 ),
    inference(avatar_split_clause,[],[f3146,f3092,f2430,f16369]) ).

thf(f16369,plain,
    ( spl124_372
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_372])]) ).

thf(f2430,plain,
    ( spl124_25
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_25])]) ).

thf(f3146,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_89 ),
    inference(trivial_inequality_removal,[],[f3123]) ).

thf(f3123,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_89 ),
    inference(superposition,[],[f3093,f2431]) ).

thf(f2431,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) )
    | ~ spl124_25 ),
    inference(avatar_component_clause,[],[f2430]) ).

thf(f16367,plain,
    ( spl124_371
    | ~ spl124_3
    | ~ spl124_89 ),
    inference(avatar_split_clause,[],[f3135,f3092,f2264,f16365]) ).

thf(f16365,plain,
    ( spl124_371
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_371])]) ).

thf(f3135,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_89 ),
    inference(trivial_inequality_removal,[],[f3134]) ).

thf(f3134,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_89 ),
    inference(superposition,[],[f3093,f2265]) ).

thf(f16363,plain,
    ( spl124_370
    | ~ spl124_6
    | ~ spl124_294 ),
    inference(avatar_split_clause,[],[f10845,f10655,f2306,f16361]) ).

thf(f2306,plain,
    ( spl124_6
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_6])]) ).

thf(f10655,plain,
    ( spl124_294
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_294])]) ).

thf(f10845,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X0) )
    | ~ spl124_6
    | ~ spl124_294 ),
    inference(trivial_inequality_removal,[],[f10770]) ).

thf(f10770,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X0) ) )
    | ~ spl124_6
    | ~ spl124_294 ),
    inference(superposition,[],[f10656,f2307]) ).

thf(f2307,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) )
    | ~ spl124_6 ),
    inference(avatar_component_clause,[],[f2306]) ).

thf(f10656,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X1) ) )
    | ~ spl124_294 ),
    inference(avatar_component_clause,[],[f10655]) ).

thf(f16359,plain,
    ( spl124_369
    | ~ spl124_3
    | ~ spl124_87 ),
    inference(avatar_split_clause,[],[f3118,f3084,f2264,f16357]) ).

thf(f16357,plain,
    ( spl124_369
  <=> ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_369])]) ).

thf(f3084,plain,
    ( spl124_87
  <=> ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_87])]) ).

thf(f3118,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_87 ),
    inference(trivial_inequality_removal,[],[f3117]) ).

thf(f3117,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_87 ),
    inference(superposition,[],[f3085,f2265]) ).

thf(f3085,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_87 ),
    inference(avatar_component_clause,[],[f3084]) ).

thf(f16355,plain,
    ( spl124_368
    | ~ spl124_3
    | ~ spl124_86 ),
    inference(avatar_split_clause,[],[f3115,f3080,f2264,f16353]) ).

thf(f16353,plain,
    ( spl124_368
  <=> ! [X2: trace_1367752404list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
        | ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_368])]) ).

thf(f3080,plain,
    ( spl124_86
  <=> ! [X2: trace_1367752404list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_86])]) ).

thf(f3115,plain,
    ( ! [X2: trace_1367752404list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
        | ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_86 ),
    inference(trivial_inequality_removal,[],[f3114]) ).

thf(f3114,plain,
    ( ! [X2: trace_1367752404list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
        | ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_86 ),
    inference(superposition,[],[f3081,f2265]) ).

thf(f3081,plain,
    ( ! [X2: trace_1367752404list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
        | ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) ) )
    | ~ spl124_86 ),
    inference(avatar_component_clause,[],[f3080]) ).

thf(f16351,plain,
    ( spl124_367
    | ~ spl124_3
    | ~ spl124_85 ),
    inference(avatar_split_clause,[],[f3112,f3076,f2264,f16349]) ).

thf(f16349,plain,
    ( spl124_367
  <=> ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X0) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_367])]) ).

thf(f3076,plain,
    ( spl124_85
  <=> ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_85])]) ).

thf(f3112,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X0) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_85 ),
    inference(trivial_inequality_removal,[],[f3111]) ).

thf(f3111,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X0) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_85 ),
    inference(superposition,[],[f3077,f2265]) ).

thf(f3077,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_85 ),
    inference(avatar_component_clause,[],[f3076]) ).

thf(f16347,plain,
    ( spl124_366
    | ~ spl124_3
    | ~ spl124_84 ),
    inference(avatar_split_clause,[],[f3109,f3072,f2264,f16345]) ).

thf(f16345,plain,
    ( spl124_366
  <=> ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_366])]) ).

thf(f3072,plain,
    ( spl124_84
  <=> ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_84])]) ).

thf(f3109,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_84 ),
    inference(trivial_inequality_removal,[],[f3108]) ).

thf(f3108,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X2) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_84 ),
    inference(superposition,[],[f3073,f2265]) ).

thf(f3073,plain,
    ( ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_84 ),
    inference(avatar_component_clause,[],[f3072]) ).

thf(f16343,plain,
    ( spl124_365
    | ~ spl124_18 ),
    inference(avatar_split_clause,[],[f2393,f2370,f16341]) ).

thf(f16341,plain,
    ( spl124_365
  <=> ! [X0: nat] : ( vAPP(sTfun(nat,$o),nat,sK24,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_365])]) ).

thf(f2370,plain,
    ( spl124_18
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_18])]) ).

thf(f2393,plain,
    ( ! [X0: nat] : ( vAPP(sTfun(nat,$o),nat,sK24,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 )
    | ~ spl124_18 ),
    inference(leibniz_equality_elimination,[],[f2371]) ).

thf(f2371,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) )
        | ( $true = vAPP(nat,$o,X0,X1) ) )
    | ~ spl124_18 ),
    inference(avatar_component_clause,[],[f2370]) ).

thf(f16339,plain,
    ( spl124_364
    | ~ spl124_17 ),
    inference(avatar_split_clause,[],[f2385,f2366,f16337]) ).

thf(f16337,plain,
    ( spl124_364
  <=> ! [X0: nat] : ( vAPP(sTfun(nat,$o),nat,sK23,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_364])]) ).

thf(f2366,plain,
    ( spl124_17
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK23,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_17])]) ).

thf(f2385,plain,
    ( ! [X0: nat] : ( vAPP(sTfun(nat,$o),nat,sK23,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 )
    | ~ spl124_17 ),
    inference(leibniz_equality_elimination,[],[f2367]) ).

thf(f2367,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK23,X0)) )
        | ( $true = vAPP(nat,$o,X0,X1) ) )
    | ~ spl124_17 ),
    inference(avatar_component_clause,[],[f2366]) ).

thf(f16335,plain,
    ( spl124_363
    | ~ spl124_16 ),
    inference(avatar_split_clause,[],[f2373,f2362,f16333]) ).

thf(f16333,plain,
    ( spl124_363
  <=> ! [X0: nat] : ( vAPP(sTfun(nat,$o),nat,sK22,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_363])]) ).

thf(f2362,plain,
    ( spl124_16
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK22,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_16])]) ).

thf(f2373,plain,
    ( ! [X0: nat] : ( vAPP(sTfun(nat,$o),nat,sK22,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 )
    | ~ spl124_16 ),
    inference(leibniz_equality_elimination,[],[f2363]) ).

thf(f2363,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK22,X0)) )
        | ( $true = vAPP(nat,$o,X0,X1) ) )
    | ~ spl124_16 ),
    inference(avatar_component_clause,[],[f2362]) ).

thf(f16329,plain,
    ( spl124_362
    | ~ spl124_3
    | ~ spl124_83 ),
    inference(avatar_split_clause,[],[f3069,f3060,f2264,f16327]) ).

thf(f16327,plain,
    ( spl124_362
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_362])]) ).

thf(f3060,plain,
    ( spl124_83
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)) )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_83])]) ).

thf(f3069,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)) ) )
    | ~ spl124_3
    | ~ spl124_83 ),
    inference(trivial_inequality_removal,[],[f3068]) ).

thf(f3068,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != $true )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)) ) )
    | ~ spl124_3
    | ~ spl124_83 ),
    inference(superposition,[],[f3061,f2265]) ).

thf(f3061,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)) )
        | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) )
    | ~ spl124_83 ),
    inference(avatar_component_clause,[],[f3060]) ).

thf(f16241,plain,
    ( spl124_361
    | ~ spl124_6
    | ~ spl124_293 ),
    inference(avatar_split_clause,[],[f10769,f10651,f2306,f16239]) ).

thf(f16239,plain,
    ( spl124_361
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK12,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_361])]) ).

thf(f10651,plain,
    ( spl124_293
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK12,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_293])]) ).

thf(f10769,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK12,X0)) )
    | ~ spl124_6
    | ~ spl124_293 ),
    inference(trivial_inequality_removal,[],[f10694]) ).

thf(f10694,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK12,X0)) ) )
    | ~ spl124_6
    | ~ spl124_293 ),
    inference(superposition,[],[f10652,f2307]) ).

thf(f10652,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK12,X1)) ) )
    | ~ spl124_293 ),
    inference(avatar_component_clause,[],[f10651]) ).

thf(f16158,plain,
    ( spl124_360
    | ~ spl124_11
    | ~ spl124_106 ),
    inference(avatar_split_clause,[],[f3588,f3412,f2331,f16156]) ).

thf(f16156,plain,
    ( spl124_360
  <=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,sK21,X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_360])]) ).

thf(f3412,plain,
    ( spl124_106
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_106])]) ).

thf(f3588,plain,
    ( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,sK21,X0)),X1)) )
    | ~ spl124_11
    | ~ spl124_106 ),
    inference(trivial_inequality_removal,[],[f3577]) ).

thf(f3577,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,sK21,X0)),X1)) ) )
    | ~ spl124_11
    | ~ spl124_106 ),
    inference(superposition,[],[f3413,f2332]) ).

thf(f3413,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) )
    | ~ spl124_106 ),
    inference(avatar_component_clause,[],[f3412]) ).

thf(f16154,plain,
    ( spl124_359
    | ~ spl124_11
    | ~ spl124_105 ),
    inference(avatar_split_clause,[],[f3575,f3408,f2331,f16152]) ).

thf(f16152,plain,
    ( spl124_359
  <=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,sK21,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_359])]) ).

thf(f3408,plain,
    ( spl124_105
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_105])]) ).

thf(f3575,plain,
    ( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,sK21,X0))) )
    | ~ spl124_11
    | ~ spl124_105 ),
    inference(trivial_inequality_removal,[],[f3564]) ).

thf(f3564,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,sK21,X0))) ) )
    | ~ spl124_11
    | ~ spl124_105 ),
    inference(superposition,[],[f3409,f2332]) ).

thf(f3409,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) )
    | ~ spl124_105 ),
    inference(avatar_component_clause,[],[f3408]) ).

thf(f14332,plain,
    ( spl124_358
    | ~ spl124_11
    | ~ spl124_274 ),
    inference(avatar_split_clause,[],[f9493,f8655,f2331,f14330]) ).

thf(f14330,plain,
    ( spl124_358
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_358])]) ).

thf(f8655,plain,
    ( spl124_274
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_274])]) ).

thf(f9493,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,X0)),X0) )
    | ~ spl124_11
    | ~ spl124_274 ),
    inference(trivial_inequality_removal,[],[f9453]) ).

thf(f9453,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,X0)),X0) ) )
    | ~ spl124_11
    | ~ spl124_274 ),
    inference(superposition,[],[f8656,f2332]) ).

thf(f8656,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_274 ),
    inference(avatar_component_clause,[],[f8655]) ).

thf(f14328,plain,
    ( spl124_357
    | ~ spl124_3
    | ~ spl124_81 ),
    inference(avatar_split_clause,[],[f3057,f2867,f2264,f14326]) ).

thf(f14326,plain,
    ( spl124_357
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_357])]) ).

thf(f2867,plain,
    ( spl124_81
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_81])]) ).

thf(f3057,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) )
    | ~ spl124_3
    | ~ spl124_81 ),
    inference(trivial_inequality_removal,[],[f3056]) ).

thf(f3056,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) )
    | ~ spl124_3
    | ~ spl124_81 ),
    inference(superposition,[],[f2868,f2265]) ).

thf(f2868,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
    | ~ spl124_81 ),
    inference(avatar_component_clause,[],[f2867]) ).

thf(f14324,plain,
    ( spl124_356
    | ~ spl124_3
    | ~ spl124_80 ),
    inference(avatar_split_clause,[],[f3046,f2863,f2264,f14322]) ).

thf(f14322,plain,
    ( spl124_356
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_356])]) ).

thf(f3046,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) )
    | ~ spl124_3
    | ~ spl124_80 ),
    inference(trivial_inequality_removal,[],[f3045]) ).

thf(f3045,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) )
    | ~ spl124_3
    | ~ spl124_80 ),
    inference(superposition,[],[f2864,f2265]) ).

thf(f14320,plain,
    ( spl124_355
    | ~ spl124_3
    | ~ spl124_79 ),
    inference(avatar_split_clause,[],[f3031,f2859,f2264,f14318]) ).

thf(f14318,plain,
    ( spl124_355
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_355])]) ).

thf(f3031,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) )
    | ~ spl124_3
    | ~ spl124_79 ),
    inference(trivial_inequality_removal,[],[f3030]) ).

thf(f3030,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) )
    | ~ spl124_3
    | ~ spl124_79 ),
    inference(superposition,[],[f2860,f2265]) ).

thf(f14316,plain,
    ( spl124_354
    | ~ spl124_3
    | ~ spl124_78 ),
    inference(avatar_split_clause,[],[f3020,f2855,f2264,f14314]) ).

thf(f14314,plain,
    ( spl124_354
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_354])]) ).

thf(f2855,plain,
    ( spl124_78
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_78])]) ).

thf(f3020,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_78 ),
    inference(trivial_inequality_removal,[],[f3019]) ).

thf(f3019,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_78 ),
    inference(superposition,[],[f2856,f2265]) ).

thf(f2856,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) )
    | ~ spl124_78 ),
    inference(avatar_component_clause,[],[f2855]) ).

thf(f14312,plain,
    ( spl124_353
    | ~ spl124_3
    | ~ spl124_77 ),
    inference(avatar_split_clause,[],[f3006,f2851,f2264,f14310]) ).

thf(f14310,plain,
    ( spl124_353
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_353])]) ).

thf(f2851,plain,
    ( spl124_77
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_77])]) ).

thf(f3006,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_77 ),
    inference(trivial_inequality_removal,[],[f3005]) ).

thf(f3005,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_77 ),
    inference(superposition,[],[f2852,f2265]) ).

thf(f2852,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) )
    | ~ spl124_77 ),
    inference(avatar_component_clause,[],[f2851]) ).

thf(f14308,plain,
    ( spl124_352
    | ~ spl124_25
    | ~ spl124_75 ),
    inference(avatar_split_clause,[],[f2995,f2843,f2430,f14306]) ).

thf(f14306,plain,
    ( spl124_352
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_352])]) ).

thf(f2995,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_75 ),
    inference(trivial_inequality_removal,[],[f2972]) ).

thf(f2972,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_75 ),
    inference(superposition,[],[f2844,f2431]) ).

thf(f14304,plain,
    ( spl124_351
    | ~ spl124_3
    | ~ spl124_75 ),
    inference(avatar_split_clause,[],[f2984,f2843,f2264,f14302]) ).

thf(f14302,plain,
    ( spl124_351
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_351])]) ).

thf(f2984,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_75 ),
    inference(trivial_inequality_removal,[],[f2983]) ).

thf(f2983,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_75 ),
    inference(superposition,[],[f2844,f2265]) ).

thf(f14300,plain,
    ( spl124_350
    | ~ spl124_25
    | ~ spl124_74 ),
    inference(avatar_split_clause,[],[f2961,f2839,f2430,f14298]) ).

thf(f14298,plain,
    ( spl124_350
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_350])]) ).

thf(f2961,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_74 ),
    inference(trivial_inequality_removal,[],[f2938]) ).

thf(f2938,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_74 ),
    inference(superposition,[],[f2840,f2431]) ).

thf(f14296,plain,
    ( spl124_349
    | ~ spl124_3
    | ~ spl124_74 ),
    inference(avatar_split_clause,[],[f2950,f2839,f2264,f14294]) ).

thf(f14294,plain,
    ( spl124_349
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_349])]) ).

thf(f2950,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_74 ),
    inference(trivial_inequality_removal,[],[f2949]) ).

thf(f2949,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_74 ),
    inference(superposition,[],[f2840,f2265]) ).

thf(f14292,plain,
    ( spl124_348
    | ~ spl124_25
    | ~ spl124_73 ),
    inference(avatar_split_clause,[],[f2929,f2835,f2430,f14290]) ).

thf(f14290,plain,
    ( spl124_348
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_348])]) ).

thf(f2929,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_73 ),
    inference(trivial_inequality_removal,[],[f2906]) ).

thf(f2906,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_73 ),
    inference(superposition,[],[f2836,f2431]) ).

thf(f14288,plain,
    ( spl124_347
    | ~ spl124_147
    | ~ spl124_274 ),
    inference(avatar_split_clause,[],[f9486,f8655,f4836,f14285]) ).

thf(f14285,plain,
    ( spl124_347
  <=> ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_347])]) ).

thf(f4836,plain,
    ( spl124_147
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_147])]) ).

thf(f9486,plain,
    ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) )
    | ~ spl124_147
    | ~ spl124_274 ),
    inference(trivial_inequality_removal,[],[f9461]) ).

thf(f9461,plain,
    ( ( $true != $true )
    | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) )
    | ~ spl124_147
    | ~ spl124_274 ),
    inference(superposition,[],[f8656,f4838]) ).

thf(f4838,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ~ spl124_147 ),
    inference(avatar_component_clause,[],[f4836]) ).

thf(f14283,plain,
    ( spl124_346
    | ~ spl124_3
    | ~ spl124_73 ),
    inference(avatar_split_clause,[],[f2918,f2835,f2264,f14281]) ).

thf(f14281,plain,
    ( spl124_346
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_346])]) ).

thf(f2918,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_73 ),
    inference(trivial_inequality_removal,[],[f2917]) ).

thf(f2917,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_73 ),
    inference(superposition,[],[f2836,f2265]) ).

thf(f14279,plain,
    ( spl124_345
    | ~ spl124_25
    | ~ spl124_72 ),
    inference(avatar_split_clause,[],[f2897,f2831,f2430,f14277]) ).

thf(f14277,plain,
    ( spl124_345
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_345])]) ).

thf(f2897,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_72 ),
    inference(trivial_inequality_removal,[],[f2874]) ).

thf(f2874,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_72 ),
    inference(superposition,[],[f2832,f2431]) ).

thf(f14275,plain,
    ( spl124_344
    | ~ spl124_3
    | ~ spl124_72 ),
    inference(avatar_split_clause,[],[f2886,f2831,f2264,f14273]) ).

thf(f14273,plain,
    ( spl124_344
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_344])]) ).

thf(f2886,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_72 ),
    inference(trivial_inequality_removal,[],[f2885]) ).

thf(f2885,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_72 ),
    inference(superposition,[],[f2832,f2265]) ).

thf(f14271,plain,
    ( spl124_343
    | ~ spl124_24
    | ~ spl124_34 ),
    inference(avatar_split_clause,[],[f2540,f2507,f2419,f14269]) ).

thf(f14269,plain,
    ( spl124_343
  <=> ! [X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_343])]) ).

thf(f2507,plain,
    ( spl124_34
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_34])]) ).

thf(f2540,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 ) )
    | ~ spl124_24
    | ~ spl124_34 ),
    inference(trivial_inequality_removal,[],[f2531]) ).

thf(f2531,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 ) )
    | ~ spl124_24
    | ~ spl124_34 ),
    inference(superposition,[],[f2508,f2420]) ).

thf(f2508,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( X0 = X1 ) )
    | ~ spl124_34 ),
    inference(avatar_component_clause,[],[f2507]) ).

thf(f14267,plain,
    ( spl124_342
    | ~ spl124_23
    | ~ spl124_34 ),
    inference(avatar_split_clause,[],[f2539,f2507,f2415,f14265]) ).

thf(f14265,plain,
    ( spl124_342
  <=> ! [X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_342])]) ).

thf(f2539,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 ) )
    | ~ spl124_23
    | ~ spl124_34 ),
    inference(trivial_inequality_removal,[],[f2532]) ).

thf(f2532,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 ) )
    | ~ spl124_23
    | ~ spl124_34 ),
    inference(superposition,[],[f2508,f2416]) ).

thf(f14263,plain,
    ( spl124_341
    | ~ spl124_24
    | ~ spl124_32 ),
    inference(avatar_split_clause,[],[f2522,f2499,f2419,f14261]) ).

thf(f14261,plain,
    ( spl124_341
  <=> ! [X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_341])]) ).

thf(f2499,plain,
    ( spl124_32
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_32])]) ).

thf(f2522,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 ) )
    | ~ spl124_24
    | ~ spl124_32 ),
    inference(trivial_inequality_removal,[],[f2515]) ).

thf(f2515,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X0) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) = X0 ) )
    | ~ spl124_24
    | ~ spl124_32 ),
    inference(superposition,[],[f2500,f2420]) ).

thf(f2500,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( X0 = X1 ) )
    | ~ spl124_32 ),
    inference(avatar_component_clause,[],[f2499]) ).

thf(f14259,plain,
    ( spl124_340
    | ~ spl124_23
    | ~ spl124_32 ),
    inference(avatar_split_clause,[],[f2521,f2499,f2415,f14257]) ).

thf(f14257,plain,
    ( spl124_340
  <=> ! [X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_340])]) ).

thf(f2521,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 ) )
    | ~ spl124_23
    | ~ spl124_32 ),
    inference(trivial_inequality_removal,[],[f2516]) ).

thf(f2516,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = X0 ) )
    | ~ spl124_23
    | ~ spl124_32 ),
    inference(superposition,[],[f2500,f2416]) ).

thf(f13799,plain,
    ( spl124_339
    | ~ spl124_23
    | ~ spl124_202 ),
    inference(avatar_split_clause,[],[f6372,f6339,f2415,f13796]) ).

thf(f13796,plain,
    ( spl124_339
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_339])]) ).

thf(f6339,plain,
    ( spl124_202
  <=> ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_202])]) ).

thf(f6372,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_23
    | ~ spl124_202 ),
    inference(trivial_inequality_removal,[],[f6363]) ).

thf(f6363,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_23
    | ~ spl124_202 ),
    inference(superposition,[],[f6340,f2416]) ).

thf(f6340,plain,
    ( ! [X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) )
    | ~ spl124_202 ),
    inference(avatar_component_clause,[],[f6339]) ).

thf(f13794,plain,
    ( spl124_338
    | ~ spl124_99
    | ~ spl124_201 ),
    inference(avatar_split_clause,[],[f6361,f6335,f3275,f13791]) ).

thf(f6335,plain,
    ( spl124_201
  <=> ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_201])]) ).

thf(f6361,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_99
    | ~ spl124_201 ),
    inference(trivial_inequality_removal,[],[f6350]) ).

thf(f6350,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_99
    | ~ spl124_201 ),
    inference(superposition,[],[f6336,f3277]) ).

thf(f6336,plain,
    ( ! [X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) )
    | ~ spl124_201 ),
    inference(avatar_component_clause,[],[f6335]) ).

thf(f13789,plain,
    ( spl124_337
    | ~ spl124_23
    | ~ spl124_201 ),
    inference(avatar_split_clause,[],[f6360,f6335,f2415,f13786]) ).

thf(f13786,plain,
    ( spl124_337
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_337])]) ).

thf(f6360,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_23
    | ~ spl124_201 ),
    inference(trivial_inequality_removal,[],[f6351]) ).

thf(f6351,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_23
    | ~ spl124_201 ),
    inference(superposition,[],[f6336,f2416]) ).

thf(f13783,plain,
    ( ~ spl124_336
    | ~ spl124_30
    | ~ spl124_70 ),
    inference(avatar_split_clause,[],[f2829,f2766,f2450,f13780]) ).

thf(f13780,plain,
    ( spl124_336
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),k) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_336])]) ).

thf(f2450,plain,
    ( spl124_30
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_30])]) ).

thf(f2829,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),k) )
    | ~ spl124_30
    | ~ spl124_70 ),
    inference(trivial_inequality_removal,[],[f2826]) ).

thf(f2826,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),k) )
    | ~ spl124_30
    | ~ spl124_70 ),
    inference(superposition,[],[f2451,f2768]) ).

thf(f2451,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) )
    | ~ spl124_30 ),
    inference(avatar_component_clause,[],[f2450]) ).

thf(f13778,plain,
    ( spl124_335
    | ~ spl124_26
    | ~ spl124_70 ),
    inference(avatar_split_clause,[],[f2828,f2766,f2434,f13775]) ).

thf(f2434,plain,
    ( spl124_26
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_26])]) ).

thf(f2828,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_26
    | ~ spl124_70 ),
    inference(trivial_inequality_removal,[],[f2827]) ).

thf(f2827,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_26
    | ~ spl124_70 ),
    inference(superposition,[],[f2435,f2768]) ).

thf(f2435,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) )
    | ~ spl124_26 ),
    inference(avatar_component_clause,[],[f2434]) ).

thf(f13772,plain,
    ( ~ spl124_334
    | ~ spl124_30
    | ~ spl124_69 ),
    inference(avatar_split_clause,[],[f2825,f2761,f2450,f13769]) ).

thf(f13769,plain,
    ( spl124_334
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),i3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_334])]) ).

thf(f2761,plain,
    ( spl124_69
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_69])]) ).

thf(f2825,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),i3) )
    | ~ spl124_30
    | ~ spl124_69 ),
    inference(trivial_inequality_removal,[],[f2822]) ).

thf(f2822,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),i3) )
    | ~ spl124_30
    | ~ spl124_69 ),
    inference(superposition,[],[f2451,f2763]) ).

thf(f2763,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true )
    | ~ spl124_69 ),
    inference(avatar_component_clause,[],[f2761]) ).

thf(f13767,plain,
    ( spl124_333
    | ~ spl124_26
    | ~ spl124_69 ),
    inference(avatar_split_clause,[],[f2824,f2761,f2434,f13764]) ).

thf(f13764,plain,
    ( spl124_333
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_333])]) ).

thf(f2824,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_26
    | ~ spl124_69 ),
    inference(trivial_inequality_removal,[],[f2823]) ).

thf(f2823,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_26
    | ~ spl124_69 ),
    inference(superposition,[],[f2435,f2763]) ).

thf(f13762,plain,
    ( ~ spl124_332
    | ~ spl124_29
    | ~ spl124_68 ),
    inference(avatar_split_clause,[],[f2819,f2756,f2446,f13759]) ).

thf(f13759,plain,
    ( spl124_332
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),j) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_332])]) ).

thf(f2756,plain,
    ( spl124_68
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_68])]) ).

thf(f2819,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),j) )
    | ~ spl124_29
    | ~ spl124_68 ),
    inference(trivial_inequality_removal,[],[f2818]) ).

thf(f2818,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),j) )
    | ~ spl124_29
    | ~ spl124_68 ),
    inference(superposition,[],[f2447,f2758]) ).

thf(f2758,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true )
    | ~ spl124_68 ),
    inference(avatar_component_clause,[],[f2756]) ).

thf(f13757,plain,
    ( ~ spl124_331
    | ~ spl124_29
    | ~ spl124_67 ),
    inference(avatar_split_clause,[],[f2813,f2751,f2446,f13754]) ).

thf(f13754,plain,
    ( spl124_331
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),j) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_331])]) ).

thf(f2751,plain,
    ( spl124_67
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_67])]) ).

thf(f2813,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),j) )
    | ~ spl124_29
    | ~ spl124_67 ),
    inference(trivial_inequality_removal,[],[f2812]) ).

thf(f2812,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),j) )
    | ~ spl124_29
    | ~ spl124_67 ),
    inference(superposition,[],[f2447,f2753]) ).

thf(f2753,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true )
    | ~ spl124_67 ),
    inference(avatar_component_clause,[],[f2751]) ).

thf(f13752,plain,
    ( ~ spl124_330
    | ~ spl124_29
    | ~ spl124_66 ),
    inference(avatar_split_clause,[],[f2807,f2746,f2446,f13749]) ).

thf(f13749,plain,
    ( spl124_330
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),ja) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_330])]) ).

thf(f2746,plain,
    ( spl124_66
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_66])]) ).

thf(f2807,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),ja) )
    | ~ spl124_29
    | ~ spl124_66 ),
    inference(trivial_inequality_removal,[],[f2806]) ).

thf(f2806,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),ja) )
    | ~ spl124_29
    | ~ spl124_66 ),
    inference(superposition,[],[f2447,f2748]) ).

thf(f2748,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true )
    | ~ spl124_66 ),
    inference(avatar_component_clause,[],[f2746]) ).

thf(f13747,plain,
    ( spl124_329
    | ~ spl124_272
    | ~ spl124_285 ),
    inference(avatar_split_clause,[],[f10048,f9790,f8647,f13745]) ).

thf(f13745,plain,
    ( spl124_329
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( X0 != X1 )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_329])]) ).

thf(f8647,plain,
    ( spl124_272
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_272])]) ).

thf(f9790,plain,
    ( spl124_285
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( X0 != X1 )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_285])]) ).

thf(f10048,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( X0 != X1 )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_272
    | ~ spl124_285 ),
    inference(trivial_inequality_removal,[],[f10047]) ).

thf(f10047,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( X0 != X1 )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_272
    | ~ spl124_285 ),
    inference(duplicate_literal_removal,[],[f10044]) ).

thf(f10044,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( X0 != X1 )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_272
    | ~ spl124_285 ),
    inference(superposition,[],[f9791,f8648]) ).

thf(f8648,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_272 ),
    inference(avatar_component_clause,[],[f8647]) ).

thf(f9791,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( X0 != X1 )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_285 ),
    inference(avatar_component_clause,[],[f9790]) ).

thf(f13743,plain,
    ( ~ spl124_328
    | ~ spl124_29
    | ~ spl124_65 ),
    inference(avatar_split_clause,[],[f2801,f2741,f2446,f13740]) ).

thf(f13740,plain,
    ( spl124_328
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),ja) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_328])]) ).

thf(f2741,plain,
    ( spl124_65
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_65])]) ).

thf(f2801,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),ja) )
    | ~ spl124_29
    | ~ spl124_65 ),
    inference(trivial_inequality_removal,[],[f2800]) ).

thf(f2800,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),ja) )
    | ~ spl124_29
    | ~ spl124_65 ),
    inference(superposition,[],[f2447,f2743]) ).

thf(f2743,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true )
    | ~ spl124_65 ),
    inference(avatar_component_clause,[],[f2741]) ).

thf(f13738,plain,
    ( ~ spl124_327
    | ~ spl124_29
    | ~ spl124_63 ),
    inference(avatar_split_clause,[],[f2791,f2732,f2446,f13735]) ).

thf(f13735,plain,
    ( spl124_327
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_327])]) ).

thf(f2791,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK7) )
    | ~ spl124_29
    | ~ spl124_63 ),
    inference(trivial_inequality_removal,[],[f2790]) ).

thf(f2790,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK7) )
    | ~ spl124_29
    | ~ spl124_63 ),
    inference(superposition,[],[f2447,f2734]) ).

thf(f13733,plain,
    ( ~ spl124_326
    | ~ spl124_29
    | ~ spl124_62 ),
    inference(avatar_split_clause,[],[f2785,f2727,f2446,f13730]) ).

thf(f13730,plain,
    ( spl124_326
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_326])]) ).

thf(f2727,plain,
    ( spl124_62
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_62])]) ).

thf(f2785,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK7) )
    | ~ spl124_29
    | ~ spl124_62 ),
    inference(trivial_inequality_removal,[],[f2784]) ).

thf(f2784,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK7) )
    | ~ spl124_29
    | ~ spl124_62 ),
    inference(superposition,[],[f2447,f2729]) ).

thf(f2729,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_62 ),
    inference(avatar_component_clause,[],[f2727]) ).

thf(f13728,plain,
    ( ~ spl124_325
    | ~ spl124_29
    | ~ spl124_61 ),
    inference(avatar_split_clause,[],[f2779,f2722,f2446,f13725]) ).

thf(f13725,plain,
    ( spl124_325
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_325])]) ).

thf(f2722,plain,
    ( spl124_61
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_61])]) ).

thf(f2779,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK6) )
    | ~ spl124_29
    | ~ spl124_61 ),
    inference(trivial_inequality_removal,[],[f2778]) ).

thf(f2778,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK6) )
    | ~ spl124_29
    | ~ spl124_61 ),
    inference(superposition,[],[f2447,f2724]) ).

thf(f2724,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_61 ),
    inference(avatar_component_clause,[],[f2722]) ).

thf(f13723,plain,
    ( ~ spl124_324
    | ~ spl124_29
    | ~ spl124_60 ),
    inference(avatar_split_clause,[],[f2773,f2717,f2446,f13720]) ).

thf(f13720,plain,
    ( spl124_324
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_324])]) ).

thf(f2717,plain,
    ( spl124_60
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_60])]) ).

thf(f2773,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK6) )
    | ~ spl124_29
    | ~ spl124_60 ),
    inference(trivial_inequality_removal,[],[f2772]) ).

thf(f2772,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),sK6) )
    | ~ spl124_29
    | ~ spl124_60 ),
    inference(superposition,[],[f2447,f2719]) ).

thf(f2719,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    | ~ spl124_60 ),
    inference(avatar_component_clause,[],[f2717]) ).

thf(f13458,plain,
    ( spl124_323
    | ~ spl124_25
    | ~ spl124_282 ),
    inference(avatar_split_clause,[],[f10016,f9778,f2430,f13456]) ).

thf(f13456,plain,
    ( spl124_323
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( X0 != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_323])]) ).

thf(f9778,plain,
    ( spl124_282
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( X0 != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_282])]) ).

thf(f10016,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( X0 != X1 ) )
    | ~ spl124_25
    | ~ spl124_282 ),
    inference(trivial_inequality_removal,[],[f10015]) ).

thf(f10015,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( X0 != X1 ) )
    | ~ spl124_25
    | ~ spl124_282 ),
    inference(duplicate_literal_removal,[],[f9958]) ).

thf(f9958,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( X0 != X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_25
    | ~ spl124_282 ),
    inference(superposition,[],[f9779,f2431]) ).

thf(f9779,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( X0 != X1 ) )
    | ~ spl124_282 ),
    inference(avatar_component_clause,[],[f9778]) ).

thf(f13226,plain,
    ( spl124_322
    | ~ spl124_3
    | ~ spl124_59 ),
    inference(avatar_split_clause,[],[f2715,f2692,f2264,f13224]) ).

thf(f13224,plain,
    ( spl124_322
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_322])]) ).

thf(f2692,plain,
    ( spl124_59
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_59])]) ).

thf(f2715,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_59 ),
    inference(trivial_inequality_removal,[],[f2714]) ).

thf(f2714,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_59 ),
    inference(superposition,[],[f2693,f2265]) ).

thf(f2693,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X2),X1),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_59 ),
    inference(avatar_component_clause,[],[f2692]) ).

thf(f13222,plain,
    ( spl124_321
    | ~ spl124_3
    | ~ spl124_58 ),
    inference(avatar_split_clause,[],[f2713,f2688,f2264,f13220]) ).

thf(f13220,plain,
    ( spl124_321
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_321])]) ).

thf(f2688,plain,
    ( spl124_58
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_58])]) ).

thf(f2713,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_58 ),
    inference(trivial_inequality_removal,[],[f2712]) ).

thf(f2712,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_58 ),
    inference(superposition,[],[f2689,f2265]) ).

thf(f2689,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X2),X1),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
    | ~ spl124_58 ),
    inference(avatar_component_clause,[],[f2688]) ).

thf(f13218,plain,
    ( spl124_320
    | ~ spl124_3
    | ~ spl124_57 ),
    inference(avatar_split_clause,[],[f2711,f2684,f2264,f13216]) ).

thf(f13216,plain,
    ( spl124_320
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_320])]) ).

thf(f2684,plain,
    ( spl124_57
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_57])]) ).

thf(f2711,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_57 ),
    inference(trivial_inequality_removal,[],[f2710]) ).

thf(f2710,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_57 ),
    inference(superposition,[],[f2685,f2265]) ).

thf(f2685,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X2),X1),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_57 ),
    inference(avatar_component_clause,[],[f2684]) ).

thf(f13214,plain,
    ( spl124_319
    | ~ spl124_3
    | ~ spl124_56 ),
    inference(avatar_split_clause,[],[f2709,f2680,f2264,f13212]) ).

thf(f13212,plain,
    ( spl124_319
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_319])]) ).

thf(f2680,plain,
    ( spl124_56
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_56])]) ).

thf(f2709,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_56 ),
    inference(trivial_inequality_removal,[],[f2708]) ).

thf(f2708,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_56 ),
    inference(superposition,[],[f2681,f2265]) ).

thf(f2681,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X2),X1),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
    | ~ spl124_56 ),
    inference(avatar_component_clause,[],[f2680]) ).

thf(f13210,plain,
    ( spl124_318
    | ~ spl124_3
    | ~ spl124_55 ),
    inference(avatar_split_clause,[],[f2707,f2676,f2264,f13208]) ).

thf(f13208,plain,
    ( spl124_318
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_318])]) ).

thf(f2676,plain,
    ( spl124_55
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_55])]) ).

thf(f2707,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_55 ),
    inference(trivial_inequality_removal,[],[f2706]) ).

thf(f2706,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_55 ),
    inference(superposition,[],[f2677,f2265]) ).

thf(f2677,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_55 ),
    inference(avatar_component_clause,[],[f2676]) ).

thf(f13206,plain,
    ( spl124_317
    | ~ spl124_3
    | ~ spl124_54 ),
    inference(avatar_split_clause,[],[f2705,f2672,f2264,f13204]) ).

thf(f13204,plain,
    ( spl124_317
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_317])]) ).

thf(f2672,plain,
    ( spl124_54
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_54])]) ).

thf(f2705,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_54 ),
    inference(trivial_inequality_removal,[],[f2704]) ).

thf(f2704,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_54 ),
    inference(superposition,[],[f2673,f2265]) ).

thf(f2673,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
    | ~ spl124_54 ),
    inference(avatar_component_clause,[],[f2672]) ).

thf(f13202,plain,
    ( spl124_316
    | ~ spl124_3
    | ~ spl124_53 ),
    inference(avatar_split_clause,[],[f2702,f2668,f2264,f13200]) ).

thf(f13200,plain,
    ( spl124_316
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_316])]) ).

thf(f2668,plain,
    ( spl124_53
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_53])]) ).

thf(f2702,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_53 ),
    inference(trivial_inequality_removal,[],[f2701]) ).

thf(f2701,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_53 ),
    inference(superposition,[],[f2669,f2265]) ).

thf(f2669,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
    | ~ spl124_53 ),
    inference(avatar_component_clause,[],[f2668]) ).

thf(f13198,plain,
    ( spl124_315
    | ~ spl124_3
    | ~ spl124_52 ),
    inference(avatar_split_clause,[],[f2700,f2660,f2264,f13196]) ).

thf(f13196,plain,
    ( spl124_315
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_315])]) ).

thf(f2660,plain,
    ( spl124_52
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_52])]) ).

thf(f2700,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_52 ),
    inference(trivial_inequality_removal,[],[f2699]) ).

thf(f2699,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X0),X1),X2) ) )
    | ~ spl124_3
    | ~ spl124_52 ),
    inference(superposition,[],[f2661,f2265]) ).

thf(f2661,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
    | ~ spl124_52 ),
    inference(avatar_component_clause,[],[f2660]) ).

thf(f13194,plain,
    ( spl124_314
    | ~ spl124_3
    | ~ spl124_51 ),
    inference(avatar_split_clause,[],[f2697,f2656,f2264,f13192]) ).

thf(f13192,plain,
    ( spl124_314
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_314])]) ).

thf(f2656,plain,
    ( spl124_51
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_51])]) ).

thf(f2697,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_51 ),
    inference(trivial_inequality_removal,[],[f2696]) ).

thf(f2696,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_51 ),
    inference(superposition,[],[f2657,f2265]) ).

thf(f2657,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) ) )
    | ~ spl124_51 ),
    inference(avatar_component_clause,[],[f2656]) ).

thf(f11614,plain,
    ( spl124_313
    | ~ spl124_21
    | ~ spl124_97 ),
    inference(avatar_split_clause,[],[f3320,f3267,f2407,f11612]) ).

thf(f11612,plain,
    ( spl124_313
  <=> ! [X2: nat,X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_313])]) ).

thf(f3320,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X2) )
    | ~ spl124_21
    | ~ spl124_97 ),
    inference(superposition,[],[f2408,f3268]) ).

thf(f11609,plain,
    ( spl124_312
    | ~ spl124_22
    | ~ spl124_96 ),
    inference(avatar_split_clause,[],[f3302,f3263,f2411,f11607]) ).

thf(f11607,plain,
    ( spl124_312
  <=> ! [X2: nat,X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_312])]) ).

thf(f3302,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))),X0) )
    | ~ spl124_22
    | ~ spl124_96 ),
    inference(superposition,[],[f2412,f3264]) ).

thf(f11605,plain,
    ( spl124_311
    | ~ spl124_11
    | ~ spl124_88
    | ~ spl124_274
    | ~ spl124_282 ),
    inference(avatar_split_clause,[],[f10028,f9778,f8655,f3088,f2331,f11603]) ).

thf(f11603,plain,
    ( spl124_311
  <=> ! [X0: nat] : ( vAPP(nat,nat,sK21,X0) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_311])]) ).

thf(f3088,plain,
    ( spl124_88
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_88])]) ).

thf(f10028,plain,
    ( ! [X0: nat] : ( vAPP(nat,nat,sK21,X0) != X0 )
    | ~ spl124_11
    | ~ spl124_88
    | ~ spl124_274
    | ~ spl124_282 ),
    inference(trivial_inequality_removal,[],[f10027]) ).

thf(f10027,plain,
    ( ! [X0: nat] :
        ( ( $true = $false )
        | ( vAPP(nat,nat,sK21,X0) != X0 ) )
    | ~ spl124_11
    | ~ spl124_88
    | ~ spl124_274
    | ~ spl124_282 ),
    inference(forward_demodulation,[],[f10022,f9493]) ).

thf(f10022,plain,
    ( ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,X0)),X0) )
        | ( vAPP(nat,nat,sK21,X0) != X0 ) )
    | ~ spl124_88
    | ~ spl124_282 ),
    inference(trivial_inequality_removal,[],[f9951]) ).

thf(f9951,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,X0)),X0) )
        | ( vAPP(nat,nat,sK21,X0) != X0 ) )
    | ~ spl124_88
    | ~ spl124_282 ),
    inference(superposition,[],[f9779,f3089]) ).

thf(f3089,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,X0)) )
    | ~ spl124_88 ),
    inference(avatar_component_clause,[],[f3088]) ).

thf(f11601,plain,
    ( spl124_310
    | ~ spl124_24
    | ~ spl124_75 ),
    inference(avatar_split_clause,[],[f2998,f2843,f2419,f11599]) ).

thf(f11599,plain,
    ( spl124_310
  <=> ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_310])]) ).

thf(f2998,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0))) )
    | ~ spl124_24
    | ~ spl124_75 ),
    inference(trivial_inequality_removal,[],[f2969]) ).

thf(f2969,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0))) ) )
    | ~ spl124_24
    | ~ spl124_75 ),
    inference(superposition,[],[f2844,f2420]) ).

thf(f11597,plain,
    ( spl124_309
    | ~ spl124_24
    | ~ spl124_74 ),
    inference(avatar_split_clause,[],[f2966,f2839,f2419,f11595]) ).

thf(f11595,plain,
    ( spl124_309
  <=> ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_309])]) ).

thf(f2966,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))) )
    | ~ spl124_24
    | ~ spl124_74 ),
    inference(forward_demodulation,[],[f2964,f1518]) ).

thf(f1518,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ),
    inference(cnf_transformation,[],[f868]) ).

thf(f868,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ),
    inference(rectify,[],[f256]) ).

thf(f256,axiom,
    ! [X35: nat,X12: nat,X42: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X12)),X42) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add_Oassoc) ).

thf(f2964,plain,
    ( ! [X2: nat,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X2)) )
    | ~ spl124_24
    | ~ spl124_74 ),
    inference(trivial_inequality_removal,[],[f2935]) ).

thf(f2935,plain,
    ( ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),X2)) ) )
    | ~ spl124_24
    | ~ spl124_74 ),
    inference(superposition,[],[f2840,f2420]) ).

thf(f11593,plain,
    ( spl124_308
    | ~ spl124_3
    | ~ spl124_50 ),
    inference(avatar_split_clause,[],[f2654,f2643,f2264,f11591]) ).

thf(f11591,plain,
    ( spl124_308
  <=> ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK24,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_308])]) ).

thf(f2643,plain,
    ( spl124_50
  <=> ! [X0: nat > $o,X1: nat,X3: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $true = vAPP(nat,$o,X0,X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK24,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_50])]) ).

thf(f2654,plain,
    ( ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK24,X1)) ) )
    | ~ spl124_3
    | ~ spl124_50 ),
    inference(trivial_inequality_removal,[],[f2653]) ).

thf(f2653,plain,
    ( ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK24,X1)) ) )
    | ~ spl124_3
    | ~ spl124_50 ),
    inference(superposition,[],[f2644,f2265]) ).

thf(f2644,plain,
    ( ! [X3: nat,X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK24,X0)) )
        | ( $true = vAPP(nat,$o,X0,X3) )
        | ( $true = vAPP(nat,$o,X0,X1) ) )
    | ~ spl124_50 ),
    inference(avatar_component_clause,[],[f2643]) ).

thf(f11589,plain,
    ( spl124_307
    | ~ spl124_3
    | ~ spl124_49 ),
    inference(avatar_split_clause,[],[f2651,f2639,f2264,f11587]) ).

thf(f11587,plain,
    ( spl124_307
  <=> ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK23,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_307])]) ).

thf(f2639,plain,
    ( spl124_49
  <=> ! [X0: nat > $o,X1: nat,X3: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $true = vAPP(nat,$o,X0,X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK23,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_49])]) ).

thf(f2651,plain,
    ( ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK23,X1)) ) )
    | ~ spl124_3
    | ~ spl124_49 ),
    inference(trivial_inequality_removal,[],[f2650]) ).

thf(f2650,plain,
    ( ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK23,X1)) ) )
    | ~ spl124_3
    | ~ spl124_49 ),
    inference(superposition,[],[f2640,f2265]) ).

thf(f2640,plain,
    ( ! [X3: nat,X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK23,X0)) )
        | ( $true = vAPP(nat,$o,X0,X3) )
        | ( $true = vAPP(nat,$o,X0,X1) ) )
    | ~ spl124_49 ),
    inference(avatar_component_clause,[],[f2639]) ).

thf(f11585,plain,
    ( spl124_306
    | ~ spl124_3
    | ~ spl124_48 ),
    inference(avatar_split_clause,[],[f2648,f2635,f2264,f11583]) ).

thf(f11583,plain,
    ( spl124_306
  <=> ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK22,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_306])]) ).

thf(f2635,plain,
    ( spl124_48
  <=> ! [X0: nat > $o,X1: nat,X3: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $true = vAPP(nat,$o,X0,X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK22,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_48])]) ).

thf(f2648,plain,
    ( ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK22,X1)) ) )
    | ~ spl124_3
    | ~ spl124_48 ),
    inference(trivial_inequality_removal,[],[f2647]) ).

thf(f2647,plain,
    ( ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,X1,X0) )
        | ( $true = vAPP(nat,$o,X1,X2) )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(sTfun(nat,$o),nat,sK22,X1)) ) )
    | ~ spl124_3
    | ~ spl124_48 ),
    inference(superposition,[],[f2636,f2265]) ).

thf(f2636,plain,
    ( ! [X3: nat,X0: nat > $o,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK22,X0)) )
        | ( $true = vAPP(nat,$o,X0,X3) )
        | ( $true = vAPP(nat,$o,X0,X1) ) )
    | ~ spl124_48 ),
    inference(avatar_component_clause,[],[f2635]) ).

thf(f11561,plain,
    ( spl124_305
    | ~ spl124_29
    | ~ spl124_46 ),
    inference(avatar_split_clause,[],[f2631,f2615,f2446,f11559]) ).

thf(f11559,plain,
    ( spl124_305
  <=> ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_305])]) ).

thf(f2631,plain,
    ( ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) )
    | ~ spl124_29
    | ~ spl124_46 ),
    inference(trivial_inequality_removal,[],[f2630]) ).

thf(f2630,plain,
    ( ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)) ) )
    | ~ spl124_29
    | ~ spl124_46 ),
    inference(superposition,[],[f2447,f2616]) ).

thf(f11557,plain,
    ( spl124_304
    | ~ spl124_29
    | ~ spl124_45 ),
    inference(avatar_split_clause,[],[f2625,f2611,f2446,f11555]) ).

thf(f11555,plain,
    ( spl124_304
  <=> ! [X2: nat,X0: nat,X1: trace_1367752404list_a] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_304])]) ).

thf(f2625,plain,
    ( ! [X2: nat,X0: nat,X1: trace_1367752404list_a] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)),X0) )
    | ~ spl124_29
    | ~ spl124_45 ),
    inference(trivial_inequality_removal,[],[f2624]) ).

thf(f2624,plain,
    ( ! [X2: nat,X0: nat,X1: trace_1367752404list_a] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X1),X2),X0)),X0) ) )
    | ~ spl124_29
    | ~ spl124_45 ),
    inference(superposition,[],[f2447,f2612]) ).

thf(f10693,plain,
    ( spl124_303
    | ~ spl124_11
    | ~ spl124_92 ),
    inference(avatar_split_clause,[],[f3183,f3104,f2331,f10691]) ).

thf(f10691,plain,
    ( spl124_303
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_303])]) ).

thf(f3183,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X1) ) )
    | ~ spl124_11
    | ~ spl124_92 ),
    inference(trivial_inequality_removal,[],[f3175]) ).

thf(f3175,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X1) ) )
    | ~ spl124_11
    | ~ spl124_92 ),
    inference(superposition,[],[f3105,f2332]) ).

thf(f10689,plain,
    ( spl124_302
    | ~ spl124_11
    | ~ spl124_91 ),
    inference(avatar_split_clause,[],[f3173,f3100,f2331,f10687]) ).

thf(f10687,plain,
    ( spl124_302
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_302])]) ).

thf(f3173,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,X0)),X1) ) )
    | ~ spl124_11
    | ~ spl124_91 ),
    inference(trivial_inequality_removal,[],[f3165]) ).

thf(f3165,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,X0)),X1) ) )
    | ~ spl124_11
    | ~ spl124_91 ),
    inference(superposition,[],[f3101,f2332]) ).

thf(f10685,plain,
    ( spl124_301
    | ~ spl124_11
    | ~ spl124_90 ),
    inference(avatar_split_clause,[],[f3159,f3096,f2331,f10683]) ).

thf(f10683,plain,
    ( spl124_301
  <=> ! [X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK21,X0)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_301])]) ).

thf(f3159,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK21,X0)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true ) )
    | ~ spl124_11
    | ~ spl124_90 ),
    inference(trivial_inequality_removal,[],[f3151]) ).

thf(f3151,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),vAPP(nat,nat,sK21,X0)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true ) )
    | ~ spl124_11
    | ~ spl124_90 ),
    inference(superposition,[],[f3097,f2332]) ).

thf(f10681,plain,
    ( spl124_300
    | ~ spl124_3
    | ~ spl124_44 ),
    inference(avatar_split_clause,[],[f2608,f2573,f2264,f10679]) ).

thf(f10679,plain,
    ( spl124_300
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK19,X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_300])]) ).

thf(f2573,plain,
    ( spl124_44
  <=> ! [X2: nat,X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK19,X0)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_44])]) ).

thf(f2608,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK19,X0)),X1) ) )
    | ~ spl124_3
    | ~ spl124_44 ),
    inference(trivial_inequality_removal,[],[f2607]) ).

thf(f2607,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK19,X0)),X1) ) )
    | ~ spl124_3
    | ~ spl124_44 ),
    inference(superposition,[],[f2574,f2265]) ).

thf(f2574,plain,
    ( ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK19,X0)),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
    | ~ spl124_44 ),
    inference(avatar_component_clause,[],[f2573]) ).

thf(f10677,plain,
    ( spl124_299
    | ~ spl124_3
    | ~ spl124_43 ),
    inference(avatar_split_clause,[],[f2604,f2569,f2264,f10675]) ).

thf(f10675,plain,
    ( spl124_299
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK18,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_299])]) ).

thf(f2569,plain,
    ( spl124_43
  <=> ! [X2: nat,X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK18,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_43])]) ).

thf(f2604,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK18,X1)) ) )
    | ~ spl124_3
    | ~ spl124_43 ),
    inference(trivial_inequality_removal,[],[f2603]) ).

thf(f2603,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK18,X1)) ) )
    | ~ spl124_3
    | ~ spl124_43 ),
    inference(superposition,[],[f2570,f2265]) ).

thf(f2570,plain,
    ( ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK18,X0)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) )
    | ~ spl124_43 ),
    inference(avatar_component_clause,[],[f2569]) ).

thf(f10673,plain,
    ( spl124_298
    | ~ spl124_3
    | ~ spl124_42 ),
    inference(avatar_split_clause,[],[f2600,f2565,f2264,f10671]) ).

thf(f10671,plain,
    ( spl124_298
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK17,X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_298])]) ).

thf(f2565,plain,
    ( spl124_42
  <=> ! [X2: nat,X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK17,X0)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_42])]) ).

thf(f2600,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK17,X0)),X1) ) )
    | ~ spl124_3
    | ~ spl124_42 ),
    inference(trivial_inequality_removal,[],[f2599]) ).

thf(f2599,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK17,X0)),X1) ) )
    | ~ spl124_3
    | ~ spl124_42 ),
    inference(superposition,[],[f2566,f2265]) ).

thf(f2566,plain,
    ( ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK17,X0)),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
    | ~ spl124_42 ),
    inference(avatar_component_clause,[],[f2565]) ).

thf(f10669,plain,
    ( spl124_297
    | ~ spl124_3
    | ~ spl124_41 ),
    inference(avatar_split_clause,[],[f2596,f2561,f2264,f10667]) ).

thf(f10667,plain,
    ( spl124_297
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK16,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_297])]) ).

thf(f2561,plain,
    ( spl124_41
  <=> ! [X2: nat,X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK16,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_41])]) ).

thf(f2596,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK16,X1)) ) )
    | ~ spl124_3
    | ~ spl124_41 ),
    inference(trivial_inequality_removal,[],[f2595]) ).

thf(f2595,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK16,X1)) ) )
    | ~ spl124_3
    | ~ spl124_41 ),
    inference(superposition,[],[f2562,f2265]) ).

thf(f2562,plain,
    ( ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK16,X0)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
    | ~ spl124_41 ),
    inference(avatar_component_clause,[],[f2561]) ).

thf(f10665,plain,
    ( spl124_296
    | ~ spl124_3
    | ~ spl124_40 ),
    inference(avatar_split_clause,[],[f2592,f2557,f2264,f10663]) ).

thf(f10663,plain,
    ( spl124_296
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK15,X0)),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_296])]) ).

thf(f2557,plain,
    ( spl124_40
  <=> ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK15,X0)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_40])]) ).

thf(f2592,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK15,X0)),X1) ) )
    | ~ spl124_3
    | ~ spl124_40 ),
    inference(trivial_inequality_removal,[],[f2591]) ).

thf(f2591,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK15,X0)),X1) ) )
    | ~ spl124_3
    | ~ spl124_40 ),
    inference(superposition,[],[f2558,f2265]) ).

thf(f2558,plain,
    ( ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK15,X0)),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) )
    | ~ spl124_40 ),
    inference(avatar_component_clause,[],[f2557]) ).

thf(f10661,plain,
    ( spl124_295
    | ~ spl124_3
    | ~ spl124_39 ),
    inference(avatar_split_clause,[],[f2588,f2553,f2264,f10659]) ).

thf(f10659,plain,
    ( spl124_295
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK14,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_295])]) ).

thf(f2553,plain,
    ( spl124_39
  <=> ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK14,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_39])]) ).

thf(f2588,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK14,X1)) ) )
    | ~ spl124_3
    | ~ spl124_39 ),
    inference(trivial_inequality_removal,[],[f2587]) ).

thf(f2587,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK14,X1)) ) )
    | ~ spl124_3
    | ~ spl124_39 ),
    inference(superposition,[],[f2554,f2265]) ).

thf(f2554,plain,
    ( ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK14,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) )
    | ~ spl124_39 ),
    inference(avatar_component_clause,[],[f2553]) ).

thf(f10657,plain,
    ( spl124_294
    | ~ spl124_3
    | ~ spl124_38 ),
    inference(avatar_split_clause,[],[f2584,f2549,f2264,f10655]) ).

thf(f2549,plain,
    ( spl124_38
  <=> ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_38])]) ).

thf(f2584,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X1) ) )
    | ~ spl124_3
    | ~ spl124_38 ),
    inference(trivial_inequality_removal,[],[f2583]) ).

thf(f2583,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X1) ) )
    | ~ spl124_3
    | ~ spl124_38 ),
    inference(superposition,[],[f2550,f2265]) ).

thf(f2550,plain,
    ( ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
    | ~ spl124_38 ),
    inference(avatar_component_clause,[],[f2549]) ).

thf(f10653,plain,
    ( spl124_293
    | ~ spl124_3
    | ~ spl124_37 ),
    inference(avatar_split_clause,[],[f2580,f2545,f2264,f10651]) ).

thf(f2545,plain,
    ( spl124_37
  <=> ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK12,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_37])]) ).

thf(f2580,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK12,X1)) ) )
    | ~ spl124_3
    | ~ spl124_37 ),
    inference(trivial_inequality_removal,[],[f2579]) ).

thf(f2579,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK12,X1)) ) )
    | ~ spl124_3
    | ~ spl124_37 ),
    inference(superposition,[],[f2546,f2265]) ).

thf(f2546,plain,
    ( ! [X2: nat,X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK12,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
    | ~ spl124_37 ),
    inference(avatar_component_clause,[],[f2545]) ).

thf(f10649,plain,
    ( spl124_291
    | spl124_292
    | ~ spl124_9
    | ~ spl124_286 ),
    inference(avatar_split_clause,[],[f10250,f9794,f2322,f10646,f10642]) ).

thf(f2322,plain,
    ( spl124_9
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_9])]) ).

thf(f9794,plain,
    ( spl124_286
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_286])]) ).

thf(f10250,plain,
    ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ( k = vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi) )
    | ~ spl124_9
    | ~ spl124_286 ),
    inference(trivial_inequality_removal,[],[f10055]) ).

thf(f10055,plain,
    ( ( $true = $false )
    | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ( k = vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi) )
    | ~ spl124_9
    | ~ spl124_286 ),
    inference(superposition,[],[f9795,f2324]) ).

thf(f2324,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) = $false )
    | ~ spl124_9 ),
    inference(avatar_component_clause,[],[f2322]) ).

thf(f9795,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false )
        | ( X0 = X1 ) )
    | ~ spl124_286 ),
    inference(avatar_component_clause,[],[f9794]) ).

thf(f9872,plain,
    spl124_290,
    inference(avatar_split_clause,[],[f2243,f9870]) ).

thf(f9870,plain,
    ( spl124_290
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_290])]) ).

thf(f2243,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ),
    inference(binary_proxy_clausification,[],[f2242]) ).

thf(f2242,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
    inference(equality_proxy_clausification,[],[f2241]) ).

thf(f2241,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
    inference(not_proxy_clausification,[],[f2240]) ).

thf(f2240,plain,
    ! [X0: nat,X1: nat] :
      ( ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) )
      | ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
    inference(binary_proxy_clausification,[],[f1431]) ).

thf(f1431,plain,
    ! [X0: nat,X1: nat] : ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ),
    inference(cnf_transformation,[],[f411]) ).

thf(f411,plain,
    ! [X0: nat,X1: nat] : ( vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ),
    inference(fool_elimination,[],[f410]) ).

thf(f410,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 != X1 )
        = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
      | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 != X1 )
        = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) )
      | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nat__neq__iff) ).

thf(f9808,plain,
    spl124_289,
    inference(avatar_split_clause,[],[f2208,f9806]) ).

thf(f9806,plain,
    ( spl124_289
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( X0 = X1 )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_289])]) ).

thf(f2208,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 = X1 )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
      | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2205]) ).

thf(f2205,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
      | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1451]) ).

thf(f1451,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f911]) ).

thf(f911,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f843]) ).

thf(f843,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f449]) ).

thf(f449,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(fool_elimination,[],[f448]) ).

thf(f448,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ~ vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
        = ( X0 = X1 ) ) ),
    inference(rectify,[],[f168]) ).

thf(f168,axiom,
    ! [X7: prefix1027212443list_a,X8: prefix1027212443list_a] :
      ( ~ vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X7),X8)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X7),X8)
        = ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_antisym__conv1) ).

thf(f9804,plain,
    spl124_288,
    inference(avatar_split_clause,[],[f2207,f9802]) ).

thf(f9802,plain,
    ( spl124_288
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( X0 != X1 )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_288])]) ).

thf(f2207,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 != X1 )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(equality_proxy_clausification,[],[f2206]) ).

thf(f2206,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1451]) ).

thf(f9800,plain,
    spl124_287,
    inference(avatar_split_clause,[],[f2198,f9798]) ).

thf(f9798,plain,
    ( spl124_287
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
        | ( X0 != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_287])]) ).

thf(f2198,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
      | ( X0 != X1 ) ),
    inference(equality_proxy_clausification,[],[f2195]) ).

thf(f2195,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1455]) ).

thf(f1455,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ),
    inference(cnf_transformation,[],[f915]) ).

thf(f915,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ),
    inference(ennf_transformation,[],[f847]) ).

thf(f847,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
    inference(flattening,[],[f457]) ).

thf(f457,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
    inference(fool_elimination,[],[f456]) ).

thf(f456,plain,
    ! [X0: nat,X1: nat] :
      ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
        = ( X0 = X1 ) ) ),
    inference(rectify,[],[f169]) ).

thf(f169,axiom,
    ! [X7: nat,X8: nat] :
      ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X7),X8)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8)
        = ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_antisym__conv1) ).

thf(f9796,plain,
    spl124_286,
    inference(avatar_split_clause,[],[f2197,f9794]) ).

thf(f2197,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
      | ( X0 = X1 ) ),
    inference(equality_proxy_clausification,[],[f2196]) ).

thf(f2196,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1455]) ).

thf(f9792,plain,
    spl124_285,
    inference(avatar_split_clause,[],[f2192,f9790]) ).

thf(f2192,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 != X1 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(not_proxy_clausification,[],[f2191]) ).

thf(f2191,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 != X1 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $true = vAPP($o,$o,vNOT,vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)) ) ),
    inference(equality_proxy_clausification,[],[f2190]) ).

thf(f2190,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $true = vAPP($o,$o,vNOT,vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1467]) ).

thf(f1467,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP($o,$o,vNOT,vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f925]) ).

thf(f925,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP($o,$o,vNOT,vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f475]) ).

thf(f475,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP($o,$o,vNOT,vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)) ) ),
    inference(fool_elimination,[],[f474]) ).

thf(f474,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( ~ vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)
        = ( X0 = X1 ) ) ),
    inference(rectify,[],[f170]) ).

thf(f170,axiom,
    ! [X7: prefix1027212443list_a,X8: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X7),X8)
     => ( ~ vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X7),X8)
        = ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_antisym__conv2) ).

thf(f9788,plain,
    spl124_284,
    inference(avatar_split_clause,[],[f2188,f9786]) ).

thf(f9786,plain,
    ( spl124_284
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( X0 = X1 )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_284])]) ).

thf(f2188,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 = X1 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) ) ),
    inference(equality_proxy_clausification,[],[f2185]) ).

thf(f2185,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) ) ),
    inference(binary_proxy_clausification,[],[f1468]) ).

thf(f1468,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f926]) ).

thf(f926,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f477]) ).

thf(f477,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) ) ),
    inference(fool_elimination,[],[f476]) ).

thf(f476,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0)
        = ( X0 = X1 ) ) ),
    inference(rectify,[],[f83]) ).

thf(f83,axiom,
    ! [X8: prefix1027212443list_a,X7: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X8),X7)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X7),X8)
        = ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_antisym__conv) ).

thf(f9784,plain,
    spl124_283,
    inference(avatar_split_clause,[],[f2187,f9782]) ).

thf(f9782,plain,
    ( spl124_283
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( X0 != X1 )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_283])]) ).

thf(f2187,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 != X1 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) ) ),
    inference(equality_proxy_clausification,[],[f2186]) ).

thf(f2186,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),vEQ(prefix1027212443list_a),X0),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) ) ),
    inference(binary_proxy_clausification,[],[f1468]) ).

thf(f9780,plain,
    spl124_282,
    inference(avatar_split_clause,[],[f2178,f9778]) ).

thf(f2178,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( X0 != X1 ) ),
    inference(equality_proxy_clausification,[],[f2175]) ).

thf(f2175,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1477]) ).

thf(f1477,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f940]) ).

thf(f940,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f495]) ).

thf(f495,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
    inference(fool_elimination,[],[f494]) ).

thf(f494,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
        = ( X0 = X1 ) ) ),
    inference(rectify,[],[f84]) ).

thf(f84,axiom,
    ! [X8: nat,X7: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X8),X7)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8)
        = ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_antisym__conv) ).

thf(f9776,plain,
    spl124_281,
    inference(avatar_split_clause,[],[f2177,f9774]) ).

thf(f9774,plain,
    ( spl124_281
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $false )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_281])]) ).

thf(f2177,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $false )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( X0 = X1 ) ),
    inference(equality_proxy_clausification,[],[f2176]) ).

thf(f2176,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $false )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
    inference(binary_proxy_clausification,[],[f1477]) ).

thf(f9700,plain,
    ( spl124_280
    | ~ spl124_64
    | ~ spl124_269 ),
    inference(avatar_split_clause,[],[f9247,f8635,f2737,f9698]) ).

thf(f9698,plain,
    ( spl124_280
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK8,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_280])]) ).

thf(f2737,plain,
    ( spl124_64
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_64])]) ).

thf(f9247,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK8,X0)) )
    | ~ spl124_64
    | ~ spl124_269 ),
    inference(trivial_inequality_removal,[],[f8958]) ).

thf(f8958,plain,
    ( ! [X0: nat] :
        ( ( $true = $false )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK8,X0)) ) )
    | ~ spl124_64
    | ~ spl124_269 ),
    inference(superposition,[],[f8636,f2738]) ).

thf(f2738,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X0)),X0) )
    | ~ spl124_64 ),
    inference(avatar_component_clause,[],[f2737]) ).

thf(f9551,plain,
    ( spl124_279
    | ~ spl124_11
    | ~ spl124_81 ),
    inference(avatar_split_clause,[],[f3058,f2867,f2331,f9549]) ).

thf(f9549,plain,
    ( spl124_279
  <=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_279])]) ).

thf(f3058,plain,
    ( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
    | ~ spl124_11
    | ~ spl124_81 ),
    inference(trivial_inequality_removal,[],[f3055]) ).

thf(f3055,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) )
    | ~ spl124_11
    | ~ spl124_81 ),
    inference(superposition,[],[f2868,f2332]) ).

thf(f9547,plain,
    ( spl124_278
    | ~ spl124_11
    | ~ spl124_78 ),
    inference(avatar_split_clause,[],[f3023,f2855,f2331,f9545]) ).

thf(f9545,plain,
    ( spl124_278
  <=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,sK21,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_278])]) ).

thf(f3023,plain,
    ( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,sK21,X0))) )
    | ~ spl124_11
    | ~ spl124_78 ),
    inference(trivial_inequality_removal,[],[f3015]) ).

thf(f3015,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,sK21,X0))) ) )
    | ~ spl124_11
    | ~ spl124_78 ),
    inference(superposition,[],[f2856,f2332]) ).

thf(f9543,plain,
    ( spl124_277
    | ~ spl124_11
    | ~ spl124_77 ),
    inference(avatar_split_clause,[],[f3009,f2851,f2331,f9541]) ).

thf(f9541,plain,
    ( spl124_277
  <=> ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,sK21,X0)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_277])]) ).

thf(f3009,plain,
    ( ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,sK21,X0)),X1)) )
    | ~ spl124_11
    | ~ spl124_77 ),
    inference(trivial_inequality_removal,[],[f3001]) ).

thf(f3001,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,sK21,X0)),X1)) ) )
    | ~ spl124_11
    | ~ spl124_77 ),
    inference(superposition,[],[f2852,f2332]) ).

thf(f9253,plain,
    ( spl124_276
    | ~ spl124_82
    | ~ spl124_269 ),
    inference(avatar_split_clause,[],[f9246,f8635,f3011,f9251]) ).

thf(f9251,plain,
    ( spl124_276
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK11,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_276])]) ).

thf(f3011,plain,
    ( spl124_82
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_82])]) ).

thf(f9246,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK11,X0)) )
    | ~ spl124_82
    | ~ spl124_269 ),
    inference(trivial_inequality_removal,[],[f8959]) ).

thf(f8959,plain,
    ( ! [X0: nat] :
        ( ( $true = $false )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK11,X0)) ) )
    | ~ spl124_82
    | ~ spl124_269 ),
    inference(superposition,[],[f8636,f3012]) ).

thf(f3012,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X0)),X0) )
    | ~ spl124_82 ),
    inference(avatar_component_clause,[],[f3011]) ).

thf(f8661,plain,
    ( spl124_275
    | ~ spl124_3
    | ~ spl124_30 ),
    inference(avatar_split_clause,[],[f2495,f2450,f2264,f8659]) ).

thf(f8659,plain,
    ( spl124_275
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_275])]) ).

thf(f2495,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_30 ),
    inference(trivial_inequality_removal,[],[f2494]) ).

thf(f2494,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_30 ),
    inference(superposition,[],[f2451,f2265]) ).

thf(f8657,plain,
    ( spl124_274
    | ~ spl124_3
    | ~ spl124_29 ),
    inference(avatar_split_clause,[],[f2485,f2446,f2264,f8655]) ).

thf(f2485,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_29 ),
    inference(trivial_inequality_removal,[],[f2484]) ).

thf(f2484,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_29 ),
    inference(superposition,[],[f2447,f2265]) ).

thf(f8653,plain,
    ( spl124_273
    | ~ spl124_3
    | ~ spl124_28 ),
    inference(avatar_split_clause,[],[f2477,f2442,f2264,f8651]) ).

thf(f8651,plain,
    ( spl124_273
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_273])]) ).

thf(f2442,plain,
    ( spl124_28
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_28])]) ).

thf(f2477,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_28 ),
    inference(trivial_inequality_removal,[],[f2476]) ).

thf(f2476,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_28 ),
    inference(superposition,[],[f2443,f2265]) ).

thf(f2443,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) ) )
    | ~ spl124_28 ),
    inference(avatar_component_clause,[],[f2442]) ).

thf(f8649,plain,
    ( spl124_272
    | ~ spl124_3
    | ~ spl124_27 ),
    inference(avatar_split_clause,[],[f2474,f2438,f2264,f8647]) ).

thf(f2438,plain,
    ( spl124_27
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_27])]) ).

thf(f2474,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_27 ),
    inference(trivial_inequality_removal,[],[f2473]) ).

thf(f2473,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) )
    | ~ spl124_3
    | ~ spl124_27 ),
    inference(superposition,[],[f2439,f2265]) ).

thf(f2439,plain,
    ( ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) )
    | ~ spl124_27 ),
    inference(avatar_component_clause,[],[f2438]) ).

thf(f8645,plain,
    ( spl124_271
    | ~ spl124_3
    | ~ spl124_251 ),
    inference(avatar_split_clause,[],[f8088,f8061,f2264,f8643]) ).

thf(f8643,plain,
    ( spl124_271
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK15,X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_271])]) ).

thf(f8061,plain,
    ( spl124_251
  <=> ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK15,X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_251])]) ).

thf(f8088,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK15,X0))),X0) )
    | ~ spl124_3
    | ~ spl124_251 ),
    inference(trivial_inequality_removal,[],[f8087]) ).

thf(f8087,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK15,X0))),X0) ) )
    | ~ spl124_3
    | ~ spl124_251 ),
    inference(superposition,[],[f8062,f2265]) ).

thf(f8062,plain,
    ( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK15,X0))),X0) )
    | ~ spl124_251 ),
    inference(avatar_component_clause,[],[f8061]) ).

thf(f8641,plain,
    ( spl124_270
    | ~ spl124_3
    | ~ spl124_26 ),
    inference(avatar_split_clause,[],[f2467,f2434,f2264,f8639]) ).

thf(f8639,plain,
    ( spl124_270
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_270])]) ).

thf(f2467,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_26 ),
    inference(trivial_inequality_removal,[],[f2466]) ).

thf(f2466,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $false ) )
    | ~ spl124_3
    | ~ spl124_26 ),
    inference(superposition,[],[f2435,f2265]) ).

thf(f8637,plain,
    spl124_269,
    inference(avatar_split_clause,[],[f2229,f8635]) ).

thf(f2229,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ),
    inference(not_proxy_clausification,[],[f2226]) ).

thf(f2226,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $true )
      | ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1433]) ).

thf(f1433,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f415]) ).

thf(f415,plain,
    ! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)) ),
    inference(fool_elimination,[],[f414]) ).

thf(f414,plain,
    ! [X0: nat,X1: nat] :
      ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ),
    inference(rectify,[],[f164]) ).

thf(f164,axiom,
    ! [X7: nat,X8: nat] :
      ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X8),X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_not__le) ).

thf(f8633,plain,
    spl124_268,
    inference(avatar_split_clause,[],[f2228,f8631]) ).

thf(f2228,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $false ) ),
    inference(not_proxy_clausification,[],[f2227]) ).

thf(f2227,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false )
      | ( $true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)) ) ),
    inference(binary_proxy_clausification,[],[f1433]) ).

thf(f8629,plain,
    spl124_267,
    inference(avatar_split_clause,[],[f2158,f8627]) ).

thf(f8627,plain,
    ( spl124_267
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) )
        | ( X1 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_267])]) ).

thf(f2158,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) )
      | ( X1 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2157]) ).

thf(f2157,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2153]) ).

thf(f2153,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1520]) ).

thf(f1520,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) ),
    inference(cnf_transformation,[],[f563]) ).

thf(f563,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) ),
    inference(fool_elimination,[],[f562]) ).

thf(f562,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) )
      = ( X1 = X2 ) ),
    inference(rectify,[],[f246]) ).

thf(f246,axiom,
    ! [X35: nat,X12: nat,X42: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X42) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X12) )
      = ( X12 = X42 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add__left__cancel) ).

thf(f8625,plain,
    spl124_266,
    inference(avatar_split_clause,[],[f2156,f8623]) ).

thf(f8623,plain,
    ( spl124_266
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_266])]) ).

thf(f2156,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) )
      | ( X1 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2155]) ).

thf(f2155,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) ) ),
    inference(equality_proxy_clausification,[],[f2154]) ).

thf(f2154,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2) ) ),
    inference(binary_proxy_clausification,[],[f1520]) ).

thf(f8621,plain,
    spl124_265,
    inference(avatar_split_clause,[],[f2152,f8619]) ).

thf(f8619,plain,
    ( spl124_265
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
        | ( X0 != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_265])]) ).

thf(f2152,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
      | ( X0 != X2 ) ),
    inference(equality_proxy_clausification,[],[f2151]) ).

thf(f2151,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2147]) ).

thf(f2147,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1521]) ).

thf(f1521,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ),
    inference(cnf_transformation,[],[f565]) ).

thf(f565,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ),
    inference(fool_elimination,[],[f564]) ).

thf(f564,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
      = ( X0 = X2 ) ),
    inference(rectify,[],[f247]) ).

thf(f247,axiom,
    ! [X12: nat,X35: nat,X42: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),X35) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X35) )
      = ( X12 = X42 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__right__cancel) ).

thf(f8617,plain,
    spl124_264,
    inference(avatar_split_clause,[],[f2150,f8615]) ).

thf(f8615,plain,
    ( spl124_264
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
        | ( X0 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_264])]) ).

thf(f2150,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
      | ( X0 = X2 ) ),
    inference(equality_proxy_clausification,[],[f2149]) ).

thf(f2149,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
    inference(equality_proxy_clausification,[],[f2148]) ).

thf(f2148,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X2) ) ),
    inference(binary_proxy_clausification,[],[f1521]) ).

thf(f8469,plain,
    ( spl124_263
    | ~ spl124_25
    | ~ spl124_250 ),
    inference(avatar_split_clause,[],[f8082,f8057,f2430,f8467]) ).

thf(f8467,plain,
    ( spl124_263
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_263])]) ).

thf(f8057,plain,
    ( spl124_250
  <=> ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_250])]) ).

thf(f8082,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))) )
    | ~ spl124_25
    | ~ spl124_250 ),
    inference(trivial_inequality_removal,[],[f8072]) ).

thf(f8072,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))) ) )
    | ~ spl124_25
    | ~ spl124_250 ),
    inference(superposition,[],[f8058,f2431]) ).

thf(f8058,plain,
    ( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))),X0) )
    | ~ spl124_250 ),
    inference(avatar_component_clause,[],[f8057]) ).

thf(f8243,plain,
    ( spl124_262
    | ~ spl124_79
    | ~ spl124_124 ),
    inference(avatar_split_clause,[],[f4140,f3973,f2859,f8240]) ).

thf(f8240,plain,
    ( spl124_262
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_262])]) ).

thf(f4140,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) )
    | ~ spl124_79
    | ~ spl124_124 ),
    inference(trivial_inequality_removal,[],[f4115]) ).

thf(f4115,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) )
    | ~ spl124_79
    | ~ spl124_124 ),
    inference(superposition,[],[f2860,f3975]) ).

thf(f8238,plain,
    ( spl124_261
    | ~ spl124_79
    | ~ spl124_123 ),
    inference(avatar_split_clause,[],[f4109,f3968,f2859,f8235]) ).

thf(f8235,plain,
    ( spl124_261
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_261])]) ).

thf(f4109,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) )
    | ~ spl124_79
    | ~ spl124_123 ),
    inference(trivial_inequality_removal,[],[f4084]) ).

thf(f4084,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) )
    | ~ spl124_79
    | ~ spl124_123 ),
    inference(superposition,[],[f2860,f3970]) ).

thf(f8233,plain,
    ( spl124_260
    | ~ spl124_79
    | ~ spl124_122 ),
    inference(avatar_split_clause,[],[f4074,f3963,f2859,f8230]) ).

thf(f8230,plain,
    ( spl124_260
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_260])]) ).

thf(f4074,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) )
    | ~ spl124_79
    | ~ spl124_122 ),
    inference(trivial_inequality_removal,[],[f4049]) ).

thf(f4049,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) )
    | ~ spl124_79
    | ~ spl124_122 ),
    inference(superposition,[],[f2860,f3965]) ).

thf(f8228,plain,
    ( spl124_259
    | ~ spl124_79
    | ~ spl124_121 ),
    inference(avatar_split_clause,[],[f4043,f3958,f2859,f8225]) ).

thf(f8225,plain,
    ( spl124_259
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_259])]) ).

thf(f4043,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) )
    | ~ spl124_79
    | ~ spl124_121 ),
    inference(trivial_inequality_removal,[],[f4018]) ).

thf(f4018,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,b),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) )
    | ~ spl124_79
    | ~ spl124_121 ),
    inference(superposition,[],[f2860,f3960]) ).

thf(f8223,plain,
    ( spl124_258
    | ~ spl124_6
    | ~ spl124_73 ),
    inference(avatar_split_clause,[],[f2933,f2835,f2306,f8221]) ).

thf(f8221,plain,
    ( spl124_258
  <=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X0),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_258])]) ).

thf(f2933,plain,
    ( ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X0),X0)) = X0 )
    | ~ spl124_6
    | ~ spl124_73 ),
    inference(trivial_inequality_removal,[],[f2902]) ).

thf(f2902,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X0),X0)) = X0 ) )
    | ~ spl124_6
    | ~ spl124_73 ),
    inference(superposition,[],[f2836,f2307]) ).

thf(f8219,plain,
    ( spl124_257
    | ~ spl124_3
    | ~ spl124_250 ),
    inference(avatar_split_clause,[],[f8079,f8057,f2264,f8217]) ).

thf(f8217,plain,
    ( spl124_257
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_257])]) ).

thf(f8079,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))),X0) )
    | ~ spl124_3
    | ~ spl124_250 ),
    inference(trivial_inequality_removal,[],[f8078]) ).

thf(f8078,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))),X0) ) )
    | ~ spl124_3
    | ~ spl124_250 ),
    inference(superposition,[],[f8058,f2265]) ).

thf(f8215,plain,
    ( spl124_256
    | ~ spl124_6
    | ~ spl124_72 ),
    inference(avatar_split_clause,[],[f2901,f2831,f2306,f8213]) ).

thf(f8213,plain,
    ( spl124_256
  <=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X0),X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_256])]) ).

thf(f2901,plain,
    ( ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X0),X0)) = X0 )
    | ~ spl124_6
    | ~ spl124_72 ),
    inference(trivial_inequality_removal,[],[f2870]) ).

thf(f2870,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X0),X0)) = X0 ) )
    | ~ spl124_6
    | ~ spl124_72 ),
    inference(superposition,[],[f2832,f2307]) ).

thf(f8211,plain,
    ( spl124_255
    | ~ spl124_3
    | ~ spl124_22 ),
    inference(avatar_split_clause,[],[f2425,f2411,f2264,f8209]) ).

thf(f8209,plain,
    ( spl124_255
  <=> ! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_255])]) ).

thf(f2425,plain,
    ( ! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) )
    | ~ spl124_3
    | ~ spl124_22 ),
    inference(trivial_inequality_removal,[],[f2424]) ).

thf(f2424,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ) )
    | ~ spl124_3
    | ~ spl124_22 ),
    inference(superposition,[],[f2412,f2265]) ).

thf(f8207,plain,
    ( spl124_254
    | ~ spl124_3
    | ~ spl124_21 ),
    inference(avatar_split_clause,[],[f2423,f2407,f2264,f8205]) ).

thf(f8205,plain,
    ( spl124_254
  <=> ! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_254])]) ).

thf(f2423,plain,
    ( ! [X0: nat,X1: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) )
    | ~ spl124_3
    | ~ spl124_21 ),
    inference(trivial_inequality_removal,[],[f2422]) ).

thf(f2422,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ) )
    | ~ spl124_3
    | ~ spl124_21 ),
    inference(superposition,[],[f2408,f2265]) ).

thf(f8071,plain,
    ( spl124_253
    | ~ spl124_11
    | ~ spl124_44 ),
    inference(avatar_split_clause,[],[f2609,f2573,f2331,f8069]) ).

thf(f8069,plain,
    ( spl124_253
  <=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK19,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_253])]) ).

thf(f2609,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK19,X0))) )
    | ~ spl124_11
    | ~ spl124_44 ),
    inference(trivial_inequality_removal,[],[f2606]) ).

thf(f2606,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK19,X0))) ) )
    | ~ spl124_11
    | ~ spl124_44 ),
    inference(superposition,[],[f2574,f2332]) ).

thf(f8067,plain,
    ( spl124_252
    | ~ spl124_11
    | ~ spl124_42 ),
    inference(avatar_split_clause,[],[f2601,f2565,f2331,f8065]) ).

thf(f2601,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK17,X0))) )
    | ~ spl124_11
    | ~ spl124_42 ),
    inference(trivial_inequality_removal,[],[f2598]) ).

thf(f2598,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,vAPP(nat,nat,sK17,X0))) ) )
    | ~ spl124_11
    | ~ spl124_42 ),
    inference(superposition,[],[f2566,f2332]) ).

thf(f8063,plain,
    ( spl124_251
    | ~ spl124_11
    | ~ spl124_40 ),
    inference(avatar_split_clause,[],[f2593,f2557,f2331,f8061]) ).

thf(f2593,plain,
    ( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK15,X0))),X0) )
    | ~ spl124_11
    | ~ spl124_40 ),
    inference(trivial_inequality_removal,[],[f2590]) ).

thf(f2590,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK15,X0))),X0) ) )
    | ~ spl124_11
    | ~ spl124_40 ),
    inference(superposition,[],[f2558,f2332]) ).

thf(f8059,plain,
    ( spl124_250
    | ~ spl124_11
    | ~ spl124_38 ),
    inference(avatar_split_clause,[],[f2585,f2549,f2331,f8057]) ).

thf(f2585,plain,
    ( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))),X0) )
    | ~ spl124_11
    | ~ spl124_38 ),
    inference(trivial_inequality_removal,[],[f2582]) ).

thf(f2582,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,sK21,vAPP(nat,nat,sK13,X0))),X0) ) )
    | ~ spl124_11
    | ~ spl124_38 ),
    inference(superposition,[],[f2550,f2332]) ).

thf(f8055,plain,
    spl124_249,
    inference(avatar_split_clause,[],[f1367,f8052]) ).

thf(f8052,plain,
    ( spl124_249
  <=> ( vSIGMA(nat) = vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_nat))))),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_249])]) ).

thf(f1367,plain,
    vSIGMA(nat) = vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_nat))))),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT))))),
    inference(cnf_transformation,[],[f291]) ).

thf(f291,plain,
    vSIGMA(nat) = vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),$o),vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),$o)),bCOMB,vSIGMA(nat)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vPI(nat))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,$o),sTfun(nat,sTfun(nat,$o))),cCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_nat))))),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT))))),
    inference(fool_elimination,[],[f290]) ).

thf(f290,plain,
    ( ( ^ [X0: nat > $o] :
        ? [X1: nat] : vAPP(nat,$o,X0,X1) )
    = ( ^ [X2: nat > $o] :
        ? [X3: nat] :
          ( ! [X4: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X3)
             => ~ vAPP(nat,$o,X2,X4) )
          & vAPP(nat,$o,X2,X3) ) ) ),
    inference(rectify,[],[f139]) ).

thf(f139,axiom,
    ( ( ^ [X49: nat > $o] :
        ? [X50: nat] : vAPP(nat,$o,X49,X50) )
    = ( ^ [X51: nat > $o] :
        ? [X25: nat] :
          ( ! [X24: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X24),X25)
             => ~ vAPP(nat,$o,X51,X24) )
          & vAPP(nat,$o,X51,X25) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_exists__least__iff) ).

thf(f8038,plain,
    spl124_248,
    inference(avatar_split_clause,[],[f1394,f8035]) ).

thf(f8035,plain,
    ( spl124_248
  <=> ( ord_less_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_248])]) ).

thf(f1394,plain,
    ord_less_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat))),
    inference(cnf_transformation,[],[f345]) ).

thf(f345,plain,
    ord_less_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat))),
    inference(fool_elimination,[],[f344]) ).

thf(f344,plain,
    ( ord_less_nat
    = ( ^ [X0: nat,X1: nat] :
          ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
          & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
    inference(rectify,[],[f182]) ).

thf(f182,axiom,
    ( ord_less_nat
    = ( ^ [X46: nat,X47: nat] :
          ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X47),X46)
          & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X46),X47) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_less__le__not__le) ).

thf(f8033,plain,
    spl124_247,
    inference(avatar_split_clause,[],[f1377,f8030]) ).

thf(f8030,plain,
    ( spl124_247
  <=> ( ord_le887097159list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),bCOMB,vNOT)),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_247])]) ).

thf(f1377,plain,
    ord_le887097159list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),bCOMB,vNOT)),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a))),
    inference(cnf_transformation,[],[f311]) ).

thf(f311,plain,
    ord_le887097159list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),bCOMB,vNOT)),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a))),
    inference(fool_elimination,[],[f310]) ).

thf(f310,plain,
    ( ord_le887097159list_a
    = ( ^ [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
          ( ~ vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0)
          & vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    inference(rectify,[],[f200]) ).

thf(f200,axiom,
    ( ord_le887097159list_a
    = ( ^ [X46: prefix1027212443list_a,X47: prefix1027212443list_a] :
          ( ~ vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X47),X46)
          & vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X46),X47) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_less__prefix__def) ).

thf(f8016,plain,
    spl124_246,
    inference(avatar_split_clause,[],[f1390,f8013]) ).

thf(f8013,plain,
    ( spl124_246
  <=> ( ord_less_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_246])]) ).

thf(f1390,plain,
    ord_less_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))),
    inference(cnf_transformation,[],[f337]) ).

thf(f337,plain,
    ord_less_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))),
    inference(fool_elimination,[],[f336]) ).

thf(f336,plain,
    ( ord_less_nat
    = ( ^ [X0: nat,X1: nat] :
          ( ( X0 != X1 )
          & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ),
    inference(rectify,[],[f57]) ).

thf(f57,axiom,
    ( ord_less_nat
    = ( ^ [X38: nat,X39: nat] :
          ( ( X38 != X39 )
          & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X38),X39) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dual__order_Ostrict__iff__order) ).

thf(f8011,plain,
    spl124_245,
    inference(avatar_split_clause,[],[f1374,f8008]) ).

thf(f8008,plain,
    ( spl124_245
  <=> ( ord_le887097159list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),bCOMB,vNOT)),vEQ(prefix1027212443list_a))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_245])]) ).

thf(f1374,plain,
    ord_le887097159list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),bCOMB,vNOT)),vEQ(prefix1027212443list_a))),
    inference(cnf_transformation,[],[f305]) ).

thf(f305,plain,
    ord_le887097159list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)),bCOMB,vNOT)),vEQ(prefix1027212443list_a))),
    inference(fool_elimination,[],[f304]) ).

thf(f304,plain,
    ( ord_le887097159list_a
    = ( ^ [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
          ( ( X0 != X1 )
          & vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    inference(rectify,[],[f56]) ).

thf(f56,axiom,
    ( ord_le887097159list_a
    = ( ^ [X38: prefix1027212443list_a,X39: prefix1027212443list_a] :
          ( ( X38 != X39 )
          & vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X38),X39) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_dual__order_Ostrict__iff__order) ).

thf(f7663,plain,
    spl124_244,
    inference(avatar_split_clause,[],[f1387,f7660]) ).

thf(f7660,plain,
    ( spl124_244
  <=> ( ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_244])]) ).

thf(f1387,plain,
    ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus_nat))),
    inference(cnf_transformation,[],[f331]) ).

thf(f331,plain,
    ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus_nat))),
    inference(fool_elimination,[],[f330]) ).

thf(f330,plain,
    ( ord_less_eq_nat
    = ( ^ [X0: nat,X1: nat] :
        ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 ) ) ),
    inference(rectify,[],[f268]) ).

thf(f268,axiom,
    ( ord_less_eq_nat
    = ( ^ [X39: nat,X38: nat] :
        ? [X69: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X39),X69) = X38 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_le__iff__add) ).

thf(f7650,plain,
    spl124_243,
    inference(avatar_split_clause,[],[f1373,f7647]) ).

thf(f7647,plain,
    ( spl124_243
  <=> ( vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)))),ord_less_eq_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_243])]) ).

thf(f1373,plain,
    vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)))),ord_less_eq_nat),
    inference(cnf_transformation,[],[f303]) ).

thf(f303,plain,
    vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)))),ord_less_eq_nat),
    inference(fool_elimination,[],[f302]) ).

thf(f302,plain,
    ( ( ^ [X0: nat,X1: nat] : ( X0 = X1 ) )
    = ( ^ [X2: nat,X3: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
          & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) ) ),
    inference(rectify,[],[f67]) ).

thf(f67,axiom,
    ( ( ^ [X40: nat,X41: nat] : ( X40 = X41 ) )
    = ( ^ [X39: nat,X38: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X39),X38)
          & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X38),X39) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_dual__order_Oeq__iff) ).

thf(f7645,plain,
    spl124_242,
    inference(avatar_split_clause,[],[f1371,f7642]) ).

thf(f7642,plain,
    ( spl124_242
  <=> ( vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_242])]) ).

thf(f1371,plain,
    vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)),
    inference(cnf_transformation,[],[f299]) ).

thf(f299,plain,
    vEQ(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq_nat))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,ord_less_eq_nat)),
    inference(fool_elimination,[],[f298]) ).

thf(f298,plain,
    ( ( ^ [X0: nat,X1: nat] : ( X0 = X1 ) )
    = ( ^ [X2: nat,X3: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2)
          & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ) ),
    inference(rectify,[],[f82]) ).

thf(f82,axiom,
    ( ( ^ [X40: nat,X41: nat] : ( X40 = X41 ) )
    = ( ^ [X39: nat,X38: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X38),X39)
          & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X39),X38) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_order__class_Oorder_Oeq__iff) ).

thf(f7640,plain,
    spl124_241,
    inference(avatar_split_clause,[],[f1369,f7637]) ).

thf(f7637,plain,
    ( spl124_241
  <=> ( vEQ(prefix1027212443list_a) = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_241])]) ).

thf(f1369,plain,
    vEQ(prefix1027212443list_a) = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a)),
    inference(cnf_transformation,[],[f295]) ).

thf(f295,plain,
    vEQ(prefix1027212443list_a) = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),ord_le699472955list_a))),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a)),
    inference(fool_elimination,[],[f294]) ).

thf(f294,plain,
    ( ( ^ [X0: prefix1027212443list_a,X1: prefix1027212443list_a] : ( X0 = X1 ) )
    = ( ^ [X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
          ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X3),X2)
          & vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ) ),
    inference(rectify,[],[f94]) ).

thf(f94,axiom,
    ( ( ^ [X40: prefix1027212443list_a,X41: prefix1027212443list_a] : ( X40 = X41 ) )
    = ( ^ [X46: prefix1027212443list_a,X47: prefix1027212443list_a] :
          ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X47),X46)
          & vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X46),X47) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_eq__iff) ).

thf(f7635,plain,
    spl124_240,
    inference(avatar_split_clause,[],[f1368,f7632]) ).

thf(f7632,plain,
    ( spl124_240
  <=> ( vEQ(prefix1027212443list_a) = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a)))),ord_le699472955list_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_240])]) ).

thf(f1368,plain,
    vEQ(prefix1027212443list_a) = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a)))),ord_le699472955list_a),
    inference(cnf_transformation,[],[f293]) ).

thf(f293,plain,
    vEQ(prefix1027212443list_a) = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),cCOMB,ord_le699472955list_a)))),ord_le699472955list_a),
    inference(fool_elimination,[],[f292]) ).

thf(f292,plain,
    ( ( ^ [X0: prefix1027212443list_a,X1: prefix1027212443list_a] : ( X0 = X1 ) )
    = ( ^ [X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
          ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3)
          & vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X3),X2) ) ) ),
    inference(rectify,[],[f66]) ).

thf(f66,axiom,
    ( ( ^ [X40: prefix1027212443list_a,X41: prefix1027212443list_a] : ( X40 = X41 ) )
    = ( ^ [X39: prefix1027212443list_a,X38: prefix1027212443list_a] :
          ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X39),X38)
          & vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X38),X39) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_dual__order_Oeq__iff) ).

thf(f7292,plain,
    spl124_239,
    inference(avatar_split_clause,[],[f1383,f7289]) ).

thf(f7289,plain,
    ( spl124_239
  <=> ( ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less_nat))),vEQ(nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_239])]) ).

thf(f1383,plain,
    ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less_nat))),vEQ(nat)),
    inference(cnf_transformation,[],[f323]) ).

thf(f323,plain,
    ord_less_eq_nat = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less_nat))),vEQ(nat)),
    inference(fool_elimination,[],[f322]) ).

thf(f322,plain,
    ( ord_less_eq_nat
    = ( ^ [X0: nat,X1: nat] :
          ( ( X0 = X1 )
          | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ) ),
    inference(rectify,[],[f59]) ).

thf(f59,axiom,
    ( ord_less_eq_nat
    = ( ^ [X38: nat,X39: nat] :
          ( ( X38 = X39 )
          | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X38),X39) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_dual__order_Oorder__iff__strict) ).

thf(f7287,plain,
    spl124_238,
    inference(avatar_split_clause,[],[f1379,f7284]) ).

thf(f7284,plain,
    ( spl124_238
  <=> ( ord_le699472955list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vOR)),ord_le887097159list_a))),vEQ(prefix1027212443list_a)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_238])]) ).

thf(f1379,plain,
    ord_le699472955list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vOR)),ord_le887097159list_a))),vEQ(prefix1027212443list_a)),
    inference(cnf_transformation,[],[f315]) ).

thf(f315,plain,
    ord_le699472955list_a = vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),vAPP(sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o))),sCOMB,vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(prefix1027212443list_a,sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,$o)))),bCOMB,sCOMB),vAPP(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o))),vAPP(sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),sTfun(sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o)),sTfun(prefix1027212443list_a,sTfun(prefix1027212443list_a,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(prefix1027212443list_a,$o),sTfun(prefix1027212443list_a,sTfun($o,$o))),bCOMB,vOR)),ord_le887097159list_a))),vEQ(prefix1027212443list_a)),
    inference(fool_elimination,[],[f314]) ).

thf(f314,plain,
    ( ord_le699472955list_a
    = ( ^ [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
          ( ( X0 = X1 )
          | vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ) ),
    inference(rectify,[],[f188]) ).

thf(f188,axiom,
    ( ord_le699472955list_a
    = ( ^ [X39: prefix1027212443list_a,X38: prefix1027212443list_a] :
          ( ( X38 = X39 )
          | vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X39),X38) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_order_Oorder__iff__strict) ).

thf(f7188,plain,
    spl124_237,
    inference(avatar_split_clause,[],[f1537,f7186]) ).

thf(f7186,plain,
    ( spl124_237
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X2),X1) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X1),X0),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_237])]) ).

thf(f1537,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X2),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X1),X0),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1194]) ).

thf(f1194,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X2),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X1),X0),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ),
    inference(definition_folding,[],[f986,f1193,f1192,f1191,f1190]) ).

thf(f1190,plain,
    ! [X2: nat,X1: nat,X0: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1191,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X1),X0),X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1192,plain,
    ! [X1: nat,X2: nat,X0: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X2),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1193,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f986,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
      | ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ) ),
    inference(flattening,[],[f985]) ).

thf(f985,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
      | ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
      | ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ) ),
    inference(ennf_transformation,[],[f872]) ).

thf(f872,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
       => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
     => ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
       => ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
           => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
         => ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
             => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true ) )
           => ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
               => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
             => ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
                 => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ) ) ) ) ),
    inference(flattening,[],[f573]) ).

thf(f573,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
       => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) )
     => ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
       => ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
           => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
         => ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
             => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true ) )
           => ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
               => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) )
             => ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
                 => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f572]) ).

thf(f572,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
       => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
       => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2)
           => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
         => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1)
             => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) )
           => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
               => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
             => ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0)
                 => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ) ) ) ) ) ),
    inference(rectify,[],[f85]) ).

thf(f85,axiom,
    ! [X7: nat,X8: nat,X45: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8)
       => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X8),X45) )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X8),X7)
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X45) )
       => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X45)
           => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X45),X8) )
         => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X45),X8)
             => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X8),X7) )
           => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X8),X45)
               => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X45),X7) )
             => ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X45),X7)
                 => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_le__cases3) ).

thf(f6783,plain,
    spl124_236,
    inference(avatar_split_clause,[],[f1551,f6781]) ).

thf(f6781,plain,
    ( spl124_236
  <=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_236])]) ).

thf(f1551,plain,
    ! [X2: nat,X0: nat > nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ),
    inference(cnf_transformation,[],[f1262]) ).

thf(f1262,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36,sK37])],[f1258,f1261,f1260,f1259]) ).

thf(f1259,plain,
    ! [X0: nat > nat > $o] :
      ( ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X4),X3) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1260,plain,
    ! [X0: nat > nat > $o] :
      ( ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X5) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f1261,plain,
    ! [X0: nat > nat > $o] :
      ( ? [X6: nat,X7: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X7) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X7) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1258,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X4),X3) ) )
      | ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X5) )
      | ? [X6: nat,X7: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X7) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X7) ) ) ),
    inference(rectify,[],[f992]) ).

thf(f992,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ? [X6: nat,X7: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X7) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X7),X6) ) )
      | ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X5) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) ) ),
    inference(flattening,[],[f991]) ).

thf(f991,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ? [X6: nat,X7: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X7) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X7),X6) ) )
      | ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X5) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) ) ),
    inference(ennf_transformation,[],[f579]) ).

thf(f579,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ! [X3: nat,X4: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
     => ( ! [X5: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X5) )
       => ( ! [X6: nat,X7: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X7),X6) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X7) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ) ),
    inference(fool_elimination,[],[f578]) ).

thf(f578,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ! [X3: nat,X4: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4)
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
     => ( ! [X5: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X5)
       => ( ! [X6: nat,X7: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X7),X6)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X7) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ),
    inference(rectify,[],[f140]) ).

thf(f140,axiom,
    ! [X4: nat > nat > $o,X35: nat,X12: nat] :
      ( ! [X43: nat,X44: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X43),X44)
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X43),X44) )
     => ( ! [X43: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X43),X43)
       => ( ! [X43: nat,X44: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X44),X43)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X43),X44) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X35),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_linorder__less__wlog) ).

thf(f6779,plain,
    spl124_235,
    inference(avatar_split_clause,[],[f1550,f6777]) ).

thf(f6777,plain,
    ( spl124_235
  <=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_235])]) ).

thf(f1550,plain,
    ! [X2: nat,X0: nat > nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ),
    inference(cnf_transformation,[],[f1262]) ).

thf(f6775,plain,
    spl124_234,
    inference(avatar_split_clause,[],[f1549,f6773]) ).

thf(f6773,plain,
    ( spl124_234
  <=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_234])]) ).

thf(f1549,plain,
    ! [X2: nat,X0: nat > nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ),
    inference(cnf_transformation,[],[f1262]) ).

thf(f6771,plain,
    spl124_233,
    inference(avatar_split_clause,[],[f1548,f6769]) ).

thf(f6769,plain,
    ( spl124_233
  <=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_233])]) ).

thf(f1548,plain,
    ! [X2: nat,X0: nat > nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK36,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK37,X0)) ) ),
    inference(cnf_transformation,[],[f1262]) ).

thf(f6766,plain,
    spl124_232,
    inference(avatar_split_clause,[],[f1642,f6764]) ).

thf(f6764,plain,
    ( spl124_232
  <=> ! [X0: nat,X3: formula_a,X2: trace_1367752404list_a,X1: trace_1367752404list_a] :
        ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),X0) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0) )
        | ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)) != vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_232])]) ).

thf(f1642,plain,
    ! [X2: trace_1367752404list_a,X3: formula_a,X0: nat,X1: trace_1367752404list_a] :
      ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),X0) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0) )
      | ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)) != vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)) ) ),
    inference(cnf_transformation,[],[f1291]) ).

thf(f1291,plain,
    ! [X0: nat,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: formula_a] :
      ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),X0) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0) )
      | ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)) != vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f1108,f1290]) ).

thf(f1290,plain,
    ! [X0: nat,X1: trace_1367752404list_a,X2: trace_1367752404list_a] :
      ( ? [X4: nat] :
          ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X4) != vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X0) ) )
     => ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)) != vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)),X0) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1108,plain,
    ! [X0: nat,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: formula_a] :
      ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),X0) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0) )
      | ? [X4: nat] :
          ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X4) != vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X0) ) ) ),
    inference(ennf_transformation,[],[f717]) ).

thf(f717,plain,
    ! [X0: nat,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: formula_a] :
      ( ! [X4: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X0) )
         => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X4) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X4) ) )
     => ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),X0) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0) ) ),
    inference(fool_elimination,[],[f716]) ).

thf(f716,plain,
    ! [X0: nat,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: formula_a] :
      ( ! [X4: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X0)
         => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X4) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X4) ) )
     => ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),X0) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0) ) ),
    inference(rectify,[],[f240]) ).

thf(f240,axiom,
    ! [X10: nat,X16: trace_1367752404list_a,X27: trace_1367752404list_a,X17: formula_a] :
      ( ! [X22: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X22),X10)
         => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X16),X22) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X27),X22) ) )
     => ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X16),X17),X10) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X27),X17),X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_progress__time__conv) ).

thf(f6694,plain,
    spl124_231,
    inference(avatar_split_clause,[],[f2146,f6692]) ).

thf(f6692,plain,
    ( spl124_231
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X2),X1) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X1),X0),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_231])]) ).

thf(f2146,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X2),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X1),X0),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ),
    inference(duplicate_literal_removal,[],[f1536]) ).

thf(f1536,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X2),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X1),X0),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ),
    inference(cnf_transformation,[],[f1194]) ).

thf(f6656,plain,
    ( spl124_230
    | ~ spl124_3
    | ~ spl124_18 ),
    inference(avatar_split_clause,[],[f2398,f2370,f2264,f6654]) ).

thf(f6654,plain,
    ( spl124_230
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_230])]) ).

thf(f2398,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) ) )
    | ~ spl124_3
    | ~ spl124_18 ),
    inference(trivial_inequality_removal,[],[f2397]) ).

thf(f2397,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) ) )
    | ~ spl124_3
    | ~ spl124_18 ),
    inference(superposition,[],[f2371,f2265]) ).

thf(f6580,plain,
    ( spl124_229
    | ~ spl124_3
    | ~ spl124_17 ),
    inference(avatar_split_clause,[],[f2390,f2366,f2264,f6578]) ).

thf(f6578,plain,
    ( spl124_229
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK23,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_229])]) ).

thf(f2390,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK23,X0)) ) )
    | ~ spl124_3
    | ~ spl124_17 ),
    inference(trivial_inequality_removal,[],[f2389]) ).

thf(f2389,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK23,X0)) ) )
    | ~ spl124_3
    | ~ spl124_17 ),
    inference(superposition,[],[f2367,f2265]) ).

thf(f6502,plain,
    ( spl124_228
    | ~ spl124_3
    | ~ spl124_16 ),
    inference(avatar_split_clause,[],[f2378,f2362,f2264,f6500]) ).

thf(f6500,plain,
    ( spl124_228
  <=> ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK22,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_228])]) ).

thf(f2378,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK22,X0)) ) )
    | ~ spl124_3
    | ~ spl124_16 ),
    inference(trivial_inequality_removal,[],[f2377]) ).

thf(f2377,plain,
    ( ! [X0: nat > $o,X1: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,X0,X1) )
        | ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK22,X0)) ) )
    | ~ spl124_3
    | ~ spl124_16 ),
    inference(superposition,[],[f2363,f2265]) ).

thf(f6485,plain,
    spl124_227,
    inference(avatar_split_clause,[],[f1722,f6483]) ).

thf(f6483,plain,
    ( spl124_227
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK122,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK123,X1))) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_227])]) ).

thf(f1722,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK122,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK123,X1))) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1365]) ).

thf(f1365,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK122,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK123,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK122,X1)),vAPP(sTfun(nat,nat),nat,sK123,X1)) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK122,sK123])],[f1189,f1364]) ).

thf(f1364,plain,
    ! [X1: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK122,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK123,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK122,X1)),vAPP(sTfun(nat,nat),nat,sK123,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1189,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(flattening,[],[f1188]) ).

thf(f1188,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(ennf_transformation,[],[f799]) ).

thf(f799,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f798]) ).

thf(f798,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f114]) ).

thf(f114,axiom,
    ! [X35: nat,X21: nat > nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),vAPP(nat,nat,X21,X12))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),vAPP(nat,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_order__less__subst1) ).

thf(f6481,plain,
    spl124_226,
    inference(avatar_split_clause,[],[f1720,f6479]) ).

thf(f6479,plain,
    ( spl124_226
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK120,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK121,X1))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_226])]) ).

thf(f1720,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK120,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK121,X1))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1363]) ).

thf(f1363,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK120,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK121,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK120,X1)),vAPP(sTfun(nat,nat),nat,sK121,X1)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK120,sK121])],[f1187,f1362]) ).

thf(f1362,plain,
    ! [X1: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK120,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK121,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK120,X1)),vAPP(sTfun(nat,nat),nat,sK121,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1187,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(flattening,[],[f1186]) ).

thf(f1186,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(ennf_transformation,[],[f797]) ).

thf(f797,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f796]) ).

thf(f796,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f161]) ).

thf(f161,axiom,
    ! [X35: nat,X21: nat > nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),vAPP(nat,nat,X21,X12))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),vAPP(nat,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_order__less__le__subst1) ).

thf(f6477,plain,
    spl124_225,
    inference(avatar_split_clause,[],[f1718,f6475]) ).

thf(f6475,plain,
    ( spl124_225
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: prefix1027212443list_a,X1: prefix1027212443list_a > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK118,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK119,X1))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_225])]) ).

thf(f1718,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: prefix1027212443list_a > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK118,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK119,X1))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1361]) ).

thf(f1361,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK118,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK119,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK118,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK119,X1)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK118,sK119])],[f1185,f1360]) ).

thf(f1360,plain,
    ! [X1: prefix1027212443list_a > nat] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK118,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK119,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK118,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK119,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1185,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(flattening,[],[f1184]) ).

thf(f1184,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(ennf_transformation,[],[f795]) ).

thf(f795,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f794]) ).

thf(f794,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2))
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f159]) ).

thf(f159,axiom,
    ! [X35: nat,X21: prefix1027212443list_a > nat,X12: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),vAPP(prefix1027212443list_a,nat,X21,X12))
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X14)),vAPP(prefix1027212443list_a,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),vAPP(prefix1027212443list_a,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_order__less__le__subst1) ).

thf(f6473,plain,
    spl124_224,
    inference(avatar_split_clause,[],[f1716,f6471]) ).

thf(f6471,plain,
    ( spl124_224
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK116,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK117,X1))) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_224])]) ).

thf(f1716,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK116,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK117,X1))) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1359]) ).

thf(f1359,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK116,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK117,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK116,X1)),vAPP(sTfun(nat,nat),nat,sK117,X1)) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK116,sK117])],[f1183,f1358]) ).

thf(f1358,plain,
    ! [X1: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK116,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK117,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK116,X1)),vAPP(sTfun(nat,nat),nat,sK117,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1183,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(flattening,[],[f1182]) ).

thf(f1182,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(ennf_transformation,[],[f793]) ).

thf(f793,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f792]) ).

thf(f792,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f153]) ).

thf(f153,axiom,
    ! [X35: nat,X21: nat > nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),vAPP(nat,nat,X21,X12))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),vAPP(nat,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_order__le__less__subst1) ).

thf(f6469,plain,
    spl124_223,
    inference(avatar_split_clause,[],[f1714,f6467]) ).

thf(f6467,plain,
    ( spl124_223
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK114,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK115,X1))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_223])]) ).

thf(f1714,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK114,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK115,X1))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1357]) ).

thf(f1357,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK114,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK115,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK114,X1)),vAPP(sTfun(nat,nat),nat,sK115,X1)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK114,sK115])],[f1181,f1356]) ).

thf(f1356,plain,
    ! [X1: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK114,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK115,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK114,X1)),vAPP(sTfun(nat,nat),nat,sK115,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1181,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(flattening,[],[f1180]) ).

thf(f1180,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(ennf_transformation,[],[f791]) ).

thf(f791,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f790]) ).

thf(f790,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f111]) ).

thf(f111,axiom,
    ! [X35: nat,X21: nat > nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),vAPP(nat,nat,X21,X12))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),vAPP(nat,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_order__subst1) ).

thf(f6465,plain,
    spl124_222,
    inference(avatar_split_clause,[],[f1712,f6463]) ).

thf(f6463,plain,
    ( spl124_222
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: prefix1027212443list_a,X1: prefix1027212443list_a > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK112,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK113,X1))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_222])]) ).

thf(f1712,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: prefix1027212443list_a > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK112,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK113,X1))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1355]) ).

thf(f1355,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK112,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK113,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK112,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK113,X1)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113])],[f1179,f1354]) ).

thf(f1354,plain,
    ! [X1: prefix1027212443list_a > nat] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK112,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK113,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK112,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK113,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1179,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(flattening,[],[f1178]) ).

thf(f1178,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(ennf_transformation,[],[f789]) ).

thf(f789,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f788]) ).

thf(f788,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2))
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f108]) ).

thf(f108,axiom,
    ! [X35: nat,X21: prefix1027212443list_a > nat,X12: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),vAPP(prefix1027212443list_a,nat,X21,X12))
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X14)),vAPP(prefix1027212443list_a,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),vAPP(prefix1027212443list_a,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_order__subst1) ).

thf(f6461,plain,
    spl124_221,
    inference(avatar_split_clause,[],[f1710,f6459]) ).

thf(f6459,plain,
    ( spl124_221
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: nat,X1: nat > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK110,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK111,X1))) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_221])]) ).

thf(f1710,plain,
    ! [X2: nat,X3: nat,X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK110,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK111,X1))) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1353]) ).

thf(f1353,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK110,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK111,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK110,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK111,X1)) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111])],[f1177,f1352]) ).

thf(f1352,plain,
    ! [X1: nat > prefix1027212443list_a] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK110,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK111,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK110,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK111,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1177,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(flattening,[],[f1176]) ).

thf(f1176,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(ennf_transformation,[],[f787]) ).

thf(f787,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f786]) ).

thf(f786,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) ) ) ),
    inference(rectify,[],[f152]) ).

thf(f152,axiom,
    ! [X35: prefix1027212443list_a,X21: nat > prefix1027212443list_a,X12: nat,X42: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),vAPP(nat,prefix1027212443list_a,X21,X12))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X21,X14)),vAPP(nat,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X35),vAPP(nat,prefix1027212443list_a,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_order__le__less__subst1) ).

thf(f6457,plain,
    spl124_220,
    inference(avatar_split_clause,[],[f1708,f6455]) ).

thf(f6455,plain,
    ( spl124_220
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: nat,X1: nat > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK108,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK109,X1))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_220])]) ).

thf(f1708,plain,
    ! [X2: nat,X3: nat,X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK108,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK109,X1))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1351]) ).

thf(f1351,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK108,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK109,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK108,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK109,X1)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK108,sK109])],[f1175,f1350]) ).

thf(f1350,plain,
    ! [X1: nat > prefix1027212443list_a] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK108,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK109,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK108,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK109,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1175,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(flattening,[],[f1174]) ).

thf(f1174,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(ennf_transformation,[],[f785]) ).

thf(f785,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f784]) ).

thf(f784,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) ) ) ),
    inference(rectify,[],[f109]) ).

thf(f109,axiom,
    ! [X35: prefix1027212443list_a,X21: nat > prefix1027212443list_a,X12: nat,X42: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),vAPP(nat,prefix1027212443list_a,X21,X12))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X14)),vAPP(nat,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),vAPP(nat,prefix1027212443list_a,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_order__subst1) ).

thf(f6453,plain,
    spl124_219,
    inference(avatar_split_clause,[],[f1706,f6451]) ).

thf(f6451,plain,
    ( spl124_219
  <=> ! [X0: prefix1027212443list_a,X3: prefix1027212443list_a,X2: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK106,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK107,X1))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_219])]) ).

thf(f1706,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK106,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK107,X1))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1349]) ).

thf(f1349,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK106,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK107,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK106,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK107,X1)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107])],[f1173,f1348]) ).

thf(f1348,plain,
    ! [X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK106,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK107,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK106,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK107,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1173,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(flattening,[],[f1172]) ).

thf(f1172,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(ennf_transformation,[],[f783]) ).

thf(f783,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f782]) ).

thf(f782,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2))
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) ) ) ),
    inference(rectify,[],[f110]) ).

thf(f110,axiom,
    ! [X35: prefix1027212443list_a,X21: prefix1027212443list_a > prefix1027212443list_a,X12: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X12))
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X14)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_order__subst1) ).

thf(f6449,plain,
    spl124_218,
    inference(avatar_split_clause,[],[f1704,f6447]) ).

thf(f6447,plain,
    ( spl124_218
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: nat,X1: nat > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK104,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK105,X1))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_218])]) ).

thf(f1704,plain,
    ! [X2: nat,X3: nat,X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK104,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK105,X1))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1347]) ).

thf(f1347,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK104,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK105,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK104,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK105,X1)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK104,sK105])],[f1171,f1346]) ).

thf(f1346,plain,
    ! [X1: nat > prefix1027212443list_a] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK104,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK105,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK104,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK105,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1171,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(flattening,[],[f1170]) ).

thf(f1170,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(ennf_transformation,[],[f781]) ).

thf(f781,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f780]) ).

thf(f780,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) ) ) ),
    inference(rectify,[],[f158]) ).

thf(f158,axiom,
    ! [X35: prefix1027212443list_a,X21: nat > prefix1027212443list_a,X12: nat,X42: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X35),vAPP(nat,prefix1027212443list_a,X21,X12))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X14)),vAPP(nat,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X35),vAPP(nat,prefix1027212443list_a,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_order__less__le__subst1) ).

thf(f6445,plain,
    spl124_217,
    inference(avatar_split_clause,[],[f1702,f6443]) ).

thf(f6443,plain,
    ( spl124_217
  <=> ! [X0: prefix1027212443list_a,X3: prefix1027212443list_a,X2: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK102,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK103,X1))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_217])]) ).

thf(f1702,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK102,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK103,X1))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1345]) ).

thf(f1345,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK102,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK103,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK102,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK103,X1)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK102,sK103])],[f1169,f1344]) ).

thf(f1344,plain,
    ! [X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK102,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK103,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK102,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK103,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1169,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(flattening,[],[f1168]) ).

thf(f1168,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(ennf_transformation,[],[f779]) ).

thf(f779,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f778]) ).

thf(f778,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2))
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) ) ) ),
    inference(rectify,[],[f160]) ).

thf(f160,axiom,
    ! [X35: prefix1027212443list_a,X21: prefix1027212443list_a > prefix1027212443list_a,X12: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X35),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X12))
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X14)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X35),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_order__less__le__subst1) ).

thf(f6441,plain,
    spl124_216,
    inference(avatar_split_clause,[],[f1700,f6439]) ).

thf(f6439,plain,
    ( spl124_216
  <=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK100,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK101,X2))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_216])]) ).

thf(f1700,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK100,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK101,X2))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1343]) ).

thf(f1343,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK100,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK101,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK100,X2)),vAPP(sTfun(nat,nat),nat,sK101,X2)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK100,sK101])],[f1167,f1342]) ).

thf(f1342,plain,
    ! [X2: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK100,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK101,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK100,X2)),vAPP(sTfun(nat,nat),nat,sK101,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1167,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1166]) ).

thf(f1166,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f777]) ).

thf(f777,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f776]) ).

thf(f776,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f115]) ).

thf(f115,axiom,
    ! [X35: nat,X12: nat,X21: nat > nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X12)),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_order__less__subst2) ).

thf(f6437,plain,
    spl124_215,
    inference(avatar_split_clause,[],[f1698,f6435]) ).

thf(f6435,plain,
    ( spl124_215
  <=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK98,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK99,X2))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_215])]) ).

thf(f1698,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK98,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK99,X2))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1341]) ).

thf(f1341,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK98,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK99,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK98,X2)),vAPP(sTfun(nat,nat),nat,sK99,X2)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK98,sK99])],[f1165,f1340]) ).

thf(f1340,plain,
    ! [X2: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK98,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK99,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK98,X2)),vAPP(sTfun(nat,nat),nat,sK99,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1165,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1164]) ).

thf(f1164,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f775]) ).

thf(f775,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f774]) ).

thf(f774,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f163]) ).

thf(f163,axiom,
    ! [X35: nat,X12: nat,X21: nat > nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X12)),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_order__less__le__subst2) ).

thf(f6433,plain,
    spl124_214,
    inference(avatar_split_clause,[],[f1696,f6431]) ).

thf(f6431,plain,
    ( spl124_214
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: nat > prefix1027212443list_a,X1: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK96,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK97,X2))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_214])]) ).

thf(f1696,plain,
    ! [X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK96,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK97,X2))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1339]) ).

thf(f1339,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK96,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK97,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK96,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK97,X2)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97])],[f1163,f1338]) ).

thf(f1338,plain,
    ! [X2: nat > prefix1027212443list_a] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK96,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK97,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK96,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK97,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1163,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1162]) ).

thf(f1162,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f773]) ).

thf(f773,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f772]) ).

thf(f772,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f162]) ).

thf(f162,axiom,
    ! [X35: nat,X12: nat,X21: nat > prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X12)),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X21,X14)),vAPP(nat,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_order__less__le__subst2) ).

thf(f6429,plain,
    spl124_213,
    inference(avatar_split_clause,[],[f1687,f6427]) ).

thf(f6427,plain,
    ( spl124_213
  <=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK92,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK93,X2))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_213])]) ).

thf(f1687,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK92,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK93,X2))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1335]) ).

thf(f1335,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK92,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK93,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK92,X2)),vAPP(sTfun(nat,nat),nat,sK93,X2)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK92,sK93])],[f1150,f1334]) ).

thf(f1334,plain,
    ! [X2: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK92,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK93,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK92,X2)),vAPP(sTfun(nat,nat),nat,sK93,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1150,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1149]) ).

thf(f1149,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f759]) ).

thf(f759,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f758]) ).

thf(f758,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f157]) ).

thf(f157,axiom,
    ! [X35: nat,X12: nat,X21: nat > nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X12)),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_order__le__less__subst2) ).

thf(f6425,plain,
    spl124_212,
    inference(avatar_split_clause,[],[f1685,f6423]) ).

thf(f6423,plain,
    ( spl124_212
  <=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK90,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK91,X2))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_212])]) ).

thf(f1685,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK90,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK91,X2))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1333]) ).

thf(f1333,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK90,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK91,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK90,X2)),vAPP(sTfun(nat,nat),nat,sK91,X2)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK90,sK91])],[f1148,f1332]) ).

thf(f1332,plain,
    ! [X2: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK90,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK91,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK90,X2)),vAPP(sTfun(nat,nat),nat,sK91,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1148,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1147]) ).

thf(f1147,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f757]) ).

thf(f757,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f756]) ).

thf(f756,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f107]) ).

thf(f107,axiom,
    ! [X35: nat,X12: nat,X21: nat > nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X12)),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_order__subst2) ).

thf(f6421,plain,
    spl124_211,
    inference(avatar_split_clause,[],[f1683,f6419]) ).

thf(f6419,plain,
    ( spl124_211
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: nat > prefix1027212443list_a,X1: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK88,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK89,X2))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_211])]) ).

thf(f1683,plain,
    ! [X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK88,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK89,X2))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1331]) ).

thf(f1331,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK88,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK89,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK88,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK89,X2)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK88,sK89])],[f1146,f1330]) ).

thf(f1330,plain,
    ! [X2: nat > prefix1027212443list_a] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK88,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK89,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK88,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK89,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1146,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1145]) ).

thf(f1145,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f755]) ).

thf(f755,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f754]) ).

thf(f754,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f104]) ).

thf(f104,axiom,
    ! [X35: nat,X12: nat,X21: nat > prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X12)),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X14)),vAPP(nat,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_order__subst2) ).

thf(f6417,plain,
    spl124_210,
    inference(avatar_split_clause,[],[f1681,f6415]) ).

thf(f6415,plain,
    ( spl124_210
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: nat > prefix1027212443list_a,X1: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK86,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK87,X2))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_210])]) ).

thf(f1681,plain,
    ! [X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK86,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK87,X2))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1329]) ).

thf(f1329,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK86,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK87,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK86,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK87,X2)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK86,sK87])],[f1144,f1328]) ).

thf(f1328,plain,
    ! [X2: nat > prefix1027212443list_a] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK86,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK87,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK86,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK87,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1144,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1143]) ).

thf(f1143,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f753]) ).

thf(f753,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f752]) ).

thf(f752,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f154]) ).

thf(f154,axiom,
    ! [X35: nat,X12: nat,X21: nat > prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X21,X12)),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X14)),vAPP(nat,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_order__le__less__subst2) ).

thf(f6413,plain,
    spl124_209,
    inference(avatar_split_clause,[],[f1672,f6411]) ).

thf(f6411,plain,
    ( spl124_209
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: prefix1027212443list_a > nat,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK80,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK81,X2))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_209])]) ).

thf(f1672,plain,
    ! [X2: prefix1027212443list_a > nat,X3: nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK80,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK81,X2))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f1323,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK80,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK81,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK80,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK81,X2)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81])],[f1132,f1322]) ).

thf(f1322,plain,
    ! [X2: prefix1027212443list_a > nat] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK80,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK81,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK80,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK81,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1132,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f1131]) ).

thf(f1131,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f741]) ).

thf(f741,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f740]) ).

thf(f740,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f155]) ).

thf(f155,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a,X21: prefix1027212443list_a > nat,X42: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),X12)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X21,X12)),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X14)),vAPP(prefix1027212443list_a,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_order__le__less__subst2) ).

thf(f6409,plain,
    spl124_208,
    inference(avatar_split_clause,[],[f1670,f6407]) ).

thf(f6407,plain,
    ( spl124_208
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: prefix1027212443list_a > nat,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK78,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK79,X2))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_208])]) ).

thf(f1670,plain,
    ! [X2: prefix1027212443list_a > nat,X3: nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK78,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK79,X2))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1321]) ).

thf(f1321,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK78,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK79,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK78,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK79,X2)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK78,sK79])],[f1130,f1320]) ).

thf(f1320,plain,
    ! [X2: prefix1027212443list_a > nat] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK78,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK79,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK78,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK79,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1130,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f1129]) ).

thf(f1129,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f739]) ).

thf(f739,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f738]) ).

thf(f738,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f105]) ).

thf(f105,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a,X21: prefix1027212443list_a > nat,X42: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),X12)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X12)),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X14)),vAPP(prefix1027212443list_a,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_order__subst2) ).

thf(f6405,plain,
    spl124_207,
    inference(avatar_split_clause,[],[f1668,f6403]) ).

thf(f6403,plain,
    ( spl124_207
  <=> ! [X0: prefix1027212443list_a,X3: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK76,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK77,X2))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_207])]) ).

thf(f1668,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK76,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK77,X2))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1319]) ).

thf(f1319,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK76,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK77,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK76,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK77,X2)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK76,sK77])],[f1128,f1318]) ).

thf(f1318,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK76,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK77,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK76,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK77,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1128,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f1127]) ).

thf(f1127,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f737]) ).

thf(f737,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f736]) ).

thf(f736,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f106]) ).

thf(f106,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a,X21: prefix1027212443list_a > prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),X12)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X12)),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X14)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_order__subst2) ).

thf(f6401,plain,
    spl124_206,
    inference(avatar_split_clause,[],[f1666,f6399]) ).

thf(f6399,plain,
    ( spl124_206
  <=> ! [X0: prefix1027212443list_a,X3: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK74,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK75,X2))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_206])]) ).

thf(f1666,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK74,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK75,X2))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1317]) ).

thf(f1317,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK74,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK75,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK74,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK75,X2)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75])],[f1126,f1316]) ).

thf(f1316,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK74,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK75,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK74,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK75,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1126,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f1125]) ).

thf(f1125,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f735]) ).

thf(f735,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f734]) ).

thf(f734,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f156]) ).

thf(f156,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a,X21: prefix1027212443list_a > prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),X12)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X12)),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X14)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_order__le__less__subst2) ).

thf(f6397,plain,
    spl124_205,
    inference(avatar_split_clause,[],[f1592,f6395]) ).

thf(f6395,plain,
    ( spl124_205
  <=> ! [X4: nat,X0: nat,X2: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X2,X4) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X4) )
        | ( $true = vAPP(nat,$o,X2,X1) )
        | ( $true != vAPP(nat,$o,X2,X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_205])]) ).

thf(f1592,plain,
    ! [X2: nat > $o,X0: nat,X1: nat,X4: nat] :
      ( ( $true = vAPP(nat,$o,X2,X4) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X4) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1277]) ).

thf(f1277,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( ( ( $true = vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
        & ! [X4: nat] :
            ( ( $true = vAPP(nat,$o,X2,X4) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X4) ) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)),X1) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) ) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f1275,f1276]) ).

thf(f1276,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( ? [X3: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),X3) )
          & ! [X4: nat] :
              ( ( $true = vAPP(nat,$o,X2,X4) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X4) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X1) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
     => ( ( $true = vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
        & ! [X4: nat] :
            ( ( $true = vAPP(nat,$o,X2,X4) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X4) ) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)),X1) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1275,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( ? [X3: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),X3) )
          & ! [X4: nat] :
              ( ( $true = vAPP(nat,$o,X2,X4) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X4) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X1) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(rectify,[],[f1198]) ).

thf(f1198,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( ? [X3: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),X3) )
          & ! [X6: nat] :
              ( ( $true = vAPP(nat,$o,X2,X6) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X6) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X1) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(definition_folding,[],[f1047,f1197]) ).

thf(f1197,plain,
    ! [X3: nat,X2: nat > $o,X0: nat] :
      ( ! [X4: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
          | ? [X5: nat] :
              ( ( $true != vAPP(nat,$o,X2,X5) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X4) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X5) ) ) )
      | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1047,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( ? [X3: nat] :
          ( ! [X4: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
              | ? [X5: nat] :
                  ( ( $true != vAPP(nat,$o,X2,X5) )
                  & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X4) )
                  & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X5) ) ) )
          & ! [X6: nat] :
              ( ( $true = vAPP(nat,$o,X2,X6) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X6) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X1) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1046]) ).

thf(f1046,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( ? [X3: nat] :
          ( ! [X4: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
              | ? [X5: nat] :
                  ( ( $true != vAPP(nat,$o,X2,X5) )
                  & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X4) )
                  & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X5) ) ) )
          & ! [X6: nat] :
              ( ( $true = vAPP(nat,$o,X2,X6) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X6) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X1) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f873]) ).

thf(f873,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,X2,X0) )
       => ( ( $true != vAPP(nat,$o,X2,X1) )
         => ? [X3: nat] :
              ( ! [X4: nat] :
                  ( ! [X5: nat] :
                      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X4) )
                        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X5) ) )
                     => ( $true = vAPP(nat,$o,X2,X5) ) )
                 => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) ) )
              & ! [X6: nat] :
                  ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X3) )
                    & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X6) ) )
                 => ( $true = vAPP(nat,$o,X2,X6) ) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X1) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) ) ) ) ),
    inference(flattening,[],[f641]) ).

thf(f641,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,X2,X0) )
       => ( ( $true != vAPP(nat,$o,X2,X1) )
         => ? [X3: nat] :
              ( ! [X4: nat] :
                  ( ! [X5: nat] :
                      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X4) )
                        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X5) ) )
                     => ( $true = vAPP(nat,$o,X2,X5) ) )
                 => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) ) )
              & ! [X6: nat] :
                  ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X3) )
                    & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X6) ) )
                 => ( $true = vAPP(nat,$o,X2,X6) ) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X1) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) ) ) ) ),
    inference(fool_elimination,[],[f640]) ).

thf(f640,plain,
    ! [X0: nat,X1: nat,X2: nat > $o] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ( vAPP(nat,$o,X2,X0)
       => ( ~ vAPP(nat,$o,X2,X1)
         => ? [X3: nat] :
              ( ! [X4: nat] :
                  ( ! [X5: nat] :
                      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X4)
                        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X5) )
                     => vAPP(nat,$o,X2,X5) )
                 => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
              & ! [X6: nat] :
                  ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X3)
                    & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X6) )
                 => vAPP(nat,$o,X2,X6) )
              & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X1)
              & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) ) ) ),
    inference(rectify,[],[f51]) ).

thf(f51,axiom,
    ! [X35: nat,X12: nat,X4: nat > $o] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12)
     => ( vAPP(nat,$o,X4,X35)
       => ( ~ vAPP(nat,$o,X4,X12)
         => ? [X36: nat] :
              ( ! [X37: nat] :
                  ( ! [X14: nat] :
                      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X37)
                        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X14) )
                     => vAPP(nat,$o,X4,X14) )
                 => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X37),X36) )
              & ! [X20: nat] :
                  ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X36)
                    & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X20) )
                 => vAPP(nat,$o,X4,X20) )
              & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X36),X12)
              & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X36) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_complete__interval) ).

thf(f6349,plain,
    spl124_204,
    inference(avatar_split_clause,[],[f1406,f6347]) ).

thf(f6347,plain,
    ( spl124_204
  <=> ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_204])]) ).

thf(f1406,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ),
    inference(cnf_transformation,[],[f886]) ).

thf(f886,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ),
    inference(ennf_transformation,[],[f361]) ).

thf(f361,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    inference(fool_elimination,[],[f360]) ).

thf(f360,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ),
    inference(rectify,[],[f213]) ).

thf(f213,axiom,
    ! [X11: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212__C1_C) ).

thf(f6345,plain,
    spl124_203,
    inference(avatar_split_clause,[],[f1405,f6343]) ).

thf(f6343,plain,
    ( spl124_203
  <=> ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_203])]) ).

thf(f1405,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ),
    inference(cnf_transformation,[],[f885]) ).

thf(f885,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ),
    inference(ennf_transformation,[],[f359]) ).

thf(f359,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    inference(fool_elimination,[],[f358]) ).

thf(f358,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ),
    inference(rectify,[],[f214]) ).

thf(f214,axiom,
    ! [X11: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213__C2_C) ).

thf(f6341,plain,
    spl124_202,
    inference(avatar_split_clause,[],[f1403,f6339]) ).

thf(f1403,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) ) ),
    inference(cnf_transformation,[],[f883]) ).

thf(f883,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) ) ),
    inference(ennf_transformation,[],[f355]) ).

thf(f355,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    inference(fool_elimination,[],[f354]) ).

thf(f354,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ),
    inference(rectify,[],[f208]) ).

thf(f208,axiom,
    ! [X11: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207__C11_C) ).

thf(f6337,plain,
    spl124_201,
    inference(avatar_split_clause,[],[f1402,f6335]) ).

thf(f1402,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) ) ),
    inference(cnf_transformation,[],[f882]) ).

thf(f882,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) ) ),
    inference(ennf_transformation,[],[f353]) ).

thf(f353,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    inference(fool_elimination,[],[f352]) ).

thf(f352,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ),
    inference(rectify,[],[f207]) ).

thf(f207,axiom,
    ! [X11: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206__C21_C) ).

thf(f6325,plain,
    spl124_200,
    inference(avatar_split_clause,[],[f1588,f6323]) ).

thf(f6323,plain,
    ( spl124_200
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)),X3) )
        | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_200])]) ).

thf(f1588,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > $o] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1274]) ).

thf(f1274,plain,
    ! [X0: nat,X1: nat > $o,X2: nat] :
      ( ! [X3: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) )
          | ( ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)) )
            & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)),X3) )
            & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)) ) ) )
      | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f1272,f1273]) ).

thf(f1273,plain,
    ! [X1: nat > $o,X2: nat,X3: nat] :
      ( ? [X4: nat] :
          ( ( $true != vAPP(nat,$o,X1,X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X3) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X4) ) )
     => ( ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)),X3) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1272,plain,
    ! [X0: nat,X1: nat > $o,X2: nat] :
      ( ! [X3: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) )
          | ? [X4: nat] :
              ( ( $true != vAPP(nat,$o,X1,X4) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X3) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X4) ) ) )
      | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
    inference(rectify,[],[f1271]) ).

thf(f1271,plain,
    ! [X3: nat,X2: nat > $o,X0: nat] :
      ( ! [X4: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
          | ? [X5: nat] :
              ( ( $true != vAPP(nat,$o,X2,X5) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X5),X4) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X5) ) ) )
      | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),X3) ) ),
    inference(nnf_transformation,[],[f1197]) ).

thf(f6321,plain,
    spl124_199,
    inference(avatar_split_clause,[],[f1587,f6319]) ).

thf(f6319,plain,
    ( spl124_199
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)) )
        | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_199])]) ).

thf(f1587,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > $o] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)) )
      | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1274]) ).

thf(f6299,plain,
    spl124_198,
    inference(avatar_split_clause,[],[f1555,f6297]) ).

thf(f6297,plain,
    ( spl124_198
  <=> ! [X2: nat,X0: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK41,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_198])]) ).

thf(f1555,plain,
    ! [X2: nat,X0: nat > nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK41,X0))) ) ),
    inference(cnf_transformation,[],[f1266]) ).

thf(f1266,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK41,X0))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK40,X0)),vAPP(sTfun(nat,nat),nat,sK41,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f995,f1265]) ).

thf(f1265,plain,
    ! [X0: nat > nat] :
      ( ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK40,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK41,X0))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK40,X0)),vAPP(sTfun(nat,nat),nat,sK41,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f995,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) ) ),
    inference(ennf_transformation,[],[f583]) ).

thf(f583,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ! [X3: nat,X4: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) ) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) ) ),
    inference(fool_elimination,[],[f582]) ).

thf(f582,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ! [X3: nat,X4: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4)
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) ),
    inference(rectify,[],[f239]) ).

thf(f239,axiom,
    ! [X21: nat > nat,X0: nat,X11: nat] :
      ( ! [X64: nat,X5: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X64),X5)
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X64)),vAPP(nat,nat,X21,X5)) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X21,X0)),X11)),vAPP(nat,nat,X21,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_mono__nat__linear__lb) ).

thf(f6287,plain,
    spl124_197,
    inference(avatar_split_clause,[],[f1659,f6285]) ).

thf(f6285,plain,
    ( spl124_197
  <=> ! [X0: prefix1027212443list_a,X3: formula_a,X2: trace_1367752404list_a,X1: trace_1367752404list_a] :
        ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_197])]) ).

thf(f1659,plain,
    ! [X2: trace_1367752404list_a,X3: formula_a,X0: prefix1027212443list_a,X1: trace_1367752404list_a] :
      ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1118]) ).

thf(f1118,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: formula_a] :
      ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(flattening,[],[f1117]) ).

thf(f1117,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: formula_a] :
      ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f727]) ).

thf(f727,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: formula_a] :
      ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) )
     => ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
       => ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) ) ) ),
    inference(fool_elimination,[],[f726]) ).

thf(f726,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: formula_a] :
      ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1)
     => ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2)
       => ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) ) ) ),
    inference(rectify,[],[f33]) ).

thf(f33,axiom,
    ! [X26: prefix1027212443list_a,X16: trace_1367752404list_a,X27: trace_1367752404list_a,X17: formula_a] :
      ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X26),X16)
     => ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X26),X27)
       => ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X16),X17),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X26)) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X27),X17),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_progress__prefix__conv) ).

thf(f6283,plain,
    ( spl124_196
    | ~ spl124_18 ),
    inference(avatar_split_clause,[],[f2400,f2370,f6281]) ).

thf(f6281,plain,
    ( spl124_196
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK24,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_196])]) ).

thf(f2400,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK24,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( X0 = X1 ) )
    | ~ spl124_18 ),
    inference(equality_proxy_clausification,[],[f2399]) ).

thf(f2399,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK24,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
    | ~ spl124_18 ),
    inference(equality_proxy_clausification,[],[f2396]) ).

thf(f2396,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK24,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
    | ~ spl124_18 ),
    inference(primitive_instantiation,[],[f2371]) ).

thf(f6065,plain,
    ( spl124_195
    | ~ spl124_17 ),
    inference(avatar_split_clause,[],[f2392,f2366,f6063]) ).

thf(f6063,plain,
    ( spl124_195
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK23,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_195])]) ).

thf(f2392,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK23,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( X0 = X1 ) )
    | ~ spl124_17 ),
    inference(equality_proxy_clausification,[],[f2391]) ).

thf(f2391,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK23,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
    | ~ spl124_17 ),
    inference(equality_proxy_clausification,[],[f2388]) ).

thf(f2388,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK23,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
    | ~ spl124_17 ),
    inference(primitive_instantiation,[],[f2367]) ).

thf(f5833,plain,
    spl124_194,
    inference(avatar_split_clause,[],[f1721,f5831]) ).

thf(f5831,plain,
    ( spl124_194
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK122,X1)),vAPP(sTfun(nat,nat),nat,sK123,X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_194])]) ).

thf(f1721,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK122,X1)),vAPP(sTfun(nat,nat),nat,sK123,X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1365]) ).

thf(f5829,plain,
    spl124_193,
    inference(avatar_split_clause,[],[f1719,f5827]) ).

thf(f5827,plain,
    ( spl124_193
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK120,X1)),vAPP(sTfun(nat,nat),nat,sK121,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_193])]) ).

thf(f1719,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK120,X1)),vAPP(sTfun(nat,nat),nat,sK121,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1363]) ).

thf(f5825,plain,
    spl124_192,
    inference(avatar_split_clause,[],[f1717,f5823]) ).

thf(f5823,plain,
    ( spl124_192
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: prefix1027212443list_a,X1: prefix1027212443list_a > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK118,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK119,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_192])]) ).

thf(f1717,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: prefix1027212443list_a > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK118,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK119,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1361]) ).

thf(f5821,plain,
    spl124_191,
    inference(avatar_split_clause,[],[f1715,f5819]) ).

thf(f5819,plain,
    ( spl124_191
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK116,X1)),vAPP(sTfun(nat,nat),nat,sK117,X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_191])]) ).

thf(f1715,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK116,X1)),vAPP(sTfun(nat,nat),nat,sK117,X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1359]) ).

thf(f5817,plain,
    spl124_190,
    inference(avatar_split_clause,[],[f1713,f5815]) ).

thf(f5815,plain,
    ( spl124_190
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK114,X1)),vAPP(sTfun(nat,nat),nat,sK115,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_190])]) ).

thf(f1713,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK114,X1)),vAPP(sTfun(nat,nat),nat,sK115,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1357]) ).

thf(f5813,plain,
    spl124_189,
    inference(avatar_split_clause,[],[f1711,f5811]) ).

thf(f5811,plain,
    ( spl124_189
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: prefix1027212443list_a,X1: prefix1027212443list_a > nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK112,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK113,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_189])]) ).

thf(f1711,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: prefix1027212443list_a > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK112,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK113,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1355]) ).

thf(f5809,plain,
    spl124_188,
    inference(avatar_split_clause,[],[f1709,f5807]) ).

thf(f5807,plain,
    ( spl124_188
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: nat,X1: nat > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK110,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK111,X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_188])]) ).

thf(f1709,plain,
    ! [X2: nat,X3: nat,X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK110,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK111,X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1353]) ).

thf(f5805,plain,
    ( spl124_187
    | ~ spl124_3
    | spl124_162 ),
    inference(avatar_split_clause,[],[f5329,f5119,f2264,f5802]) ).

thf(f5802,plain,
    ( spl124_187
  <=> ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_187])]) ).

thf(f5119,plain,
    ( spl124_162
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_162])]) ).

thf(f5329,plain,
    ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) )
    | ~ spl124_3
    | spl124_162 ),
    inference(trivial_inequality_removal,[],[f5328]) ).

thf(f5328,plain,
    ( ( $true != $true )
    | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) )
    | ~ spl124_3
    | spl124_162 ),
    inference(superposition,[],[f5121,f2265]) ).

thf(f5121,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) )
    | spl124_162 ),
    inference(avatar_component_clause,[],[f5119]) ).

thf(f5800,plain,
    spl124_186,
    inference(avatar_split_clause,[],[f1707,f5798]) ).

thf(f5798,plain,
    ( spl124_186
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: nat,X1: nat > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK108,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK109,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_186])]) ).

thf(f1707,plain,
    ! [X2: nat,X3: nat,X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK108,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK109,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1351]) ).

thf(f5796,plain,
    spl124_185,
    inference(avatar_split_clause,[],[f1705,f5794]) ).

thf(f5794,plain,
    ( spl124_185
  <=> ! [X0: prefix1027212443list_a,X3: prefix1027212443list_a,X2: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK106,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK107,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_185])]) ).

thf(f1705,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK106,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK107,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1349]) ).

thf(f5792,plain,
    spl124_184,
    inference(avatar_split_clause,[],[f1703,f5790]) ).

thf(f5790,plain,
    ( spl124_184
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: nat,X1: nat > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK104,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK105,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_184])]) ).

thf(f1703,plain,
    ! [X2: nat,X3: nat,X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK104,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK105,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1347]) ).

thf(f5788,plain,
    spl124_183,
    inference(avatar_split_clause,[],[f1701,f5786]) ).

thf(f5786,plain,
    ( spl124_183
  <=> ! [X0: prefix1027212443list_a,X3: prefix1027212443list_a,X2: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK102,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK103,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_183])]) ).

thf(f1701,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK102,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK103,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)) ) ),
    inference(cnf_transformation,[],[f1345]) ).

thf(f5784,plain,
    spl124_182,
    inference(avatar_split_clause,[],[f1699,f5782]) ).

thf(f5782,plain,
    ( spl124_182
  <=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK100,X2)),vAPP(sTfun(nat,nat),nat,sK101,X2)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_182])]) ).

thf(f1699,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK100,X2)),vAPP(sTfun(nat,nat),nat,sK101,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1343]) ).

thf(f5780,plain,
    spl124_181,
    inference(avatar_split_clause,[],[f1697,f5778]) ).

thf(f5778,plain,
    ( spl124_181
  <=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK98,X2)),vAPP(sTfun(nat,nat),nat,sK99,X2)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_181])]) ).

thf(f1697,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK98,X2)),vAPP(sTfun(nat,nat),nat,sK99,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1341]) ).

thf(f5776,plain,
    spl124_180,
    inference(avatar_split_clause,[],[f1695,f5774]) ).

thf(f5774,plain,
    ( spl124_180
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: nat > prefix1027212443list_a,X1: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK96,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK97,X2)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_180])]) ).

thf(f1695,plain,
    ! [X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK96,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK97,X2)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1339]) ).

thf(f5772,plain,
    spl124_179,
    inference(avatar_split_clause,[],[f1686,f5770]) ).

thf(f5770,plain,
    ( spl124_179
  <=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK92,X2)),vAPP(sTfun(nat,nat),nat,sK93,X2)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_179])]) ).

thf(f1686,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK92,X2)),vAPP(sTfun(nat,nat),nat,sK93,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1335]) ).

thf(f5768,plain,
    spl124_178,
    inference(avatar_split_clause,[],[f1684,f5766]) ).

thf(f5766,plain,
    ( spl124_178
  <=> ! [X0: nat,X3: nat,X2: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK90,X2)),vAPP(sTfun(nat,nat),nat,sK91,X2)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_178])]) ).

thf(f1684,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK90,X2)),vAPP(sTfun(nat,nat),nat,sK91,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1333]) ).

thf(f5764,plain,
    spl124_177,
    inference(avatar_split_clause,[],[f1682,f5762]) ).

thf(f5762,plain,
    ( spl124_177
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: nat > prefix1027212443list_a,X1: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK88,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK89,X2)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_177])]) ).

thf(f1682,plain,
    ! [X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK88,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK89,X2)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1331]) ).

thf(f5716,plain,
    spl124_176,
    inference(avatar_split_clause,[],[f1680,f5714]) ).

thf(f5714,plain,
    ( spl124_176
  <=> ! [X0: nat,X3: prefix1027212443list_a,X2: nat > prefix1027212443list_a,X1: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK86,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK87,X2)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_176])]) ).

thf(f1680,plain,
    ! [X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK86,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK87,X2)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(nat,prefix1027212443list_a,X2,X1)),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1329]) ).

thf(f5712,plain,
    spl124_175,
    inference(avatar_split_clause,[],[f1671,f5710]) ).

thf(f5710,plain,
    ( spl124_175
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: prefix1027212443list_a > nat,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK80,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK81,X2)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_175])]) ).

thf(f1671,plain,
    ! [X2: prefix1027212443list_a > nat,X3: nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK80,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK81,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1323]) ).

thf(f5708,plain,
    spl124_174,
    inference(avatar_split_clause,[],[f1669,f5706]) ).

thf(f5706,plain,
    ( spl124_174
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: prefix1027212443list_a > nat,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK78,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK79,X2)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_174])]) ).

thf(f1669,plain,
    ! [X2: prefix1027212443list_a > nat,X3: nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK78,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK79,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1321]) ).

thf(f5704,plain,
    spl124_173,
    inference(avatar_split_clause,[],[f1667,f5702]) ).

thf(f5702,plain,
    ( spl124_173
  <=> ! [X0: prefix1027212443list_a,X3: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK76,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK77,X2)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_173])]) ).

thf(f1667,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK76,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK77,X2)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1319]) ).

thf(f5700,plain,
    spl124_172,
    inference(avatar_split_clause,[],[f1665,f5698]) ).

thf(f5698,plain,
    ( spl124_172
  <=> ! [X0: prefix1027212443list_a,X3: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK74,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK75,X2)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_172])]) ).

thf(f1665,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK74,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK75,X2)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1317]) ).

thf(f5696,plain,
    spl124_171,
    inference(avatar_split_clause,[],[f1593,f5694]) ).

thf(f5694,plain,
    ( spl124_171
  <=> ! [X2: nat > $o,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
        | ( $true = vAPP(nat,$o,X2,X1) )
        | ( $true != vAPP(nat,$o,X2,X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_171])]) ).

thf(f1593,plain,
    ! [X2: nat > $o,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X0),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1277]) ).

thf(f5326,plain,
    spl124_170,
    inference(avatar_split_clause,[],[f1547,f5324]) ).

thf(f5324,plain,
    ( spl124_170
  <=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_170])]) ).

thf(f1547,plain,
    ! [X2: nat,X0: nat > nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ),
    inference(cnf_transformation,[],[f1257]) ).

thf(f1257,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) ) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32])],[f1254,f1256,f1255]) ).

thf(f1255,plain,
    ! [X0: nat > nat > $o] :
      ( ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X4),X3) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1256,plain,
    ! [X0: nat > nat > $o] :
      ( ? [X5: nat,X6: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X6) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1254,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X4),X3) ) )
      | ? [X5: nat,X6: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X6) ) ) ),
    inference(rectify,[],[f990]) ).

thf(f990,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ? [X5: nat,X6: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X5) ) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ) ),
    inference(flattening,[],[f989]) ).

thf(f989,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ? [X5: nat,X6: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X5) ) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) ) ) ),
    inference(ennf_transformation,[],[f577]) ).

thf(f577,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ! [X3: nat,X4: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
     => ( ! [X5: nat,X6: nat] :
            ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X5) )
           => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) ) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ),
    inference(fool_elimination,[],[f576]) ).

thf(f576,plain,
    ! [X0: nat > nat > $o,X1: nat,X2: nat] :
      ( ! [X3: nat,X4: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X4)
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) )
     => ( ! [X5: nat,X6: nat] :
            ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),X5)
           => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ),
    inference(rectify,[],[f70]) ).

thf(f70,axiom,
    ! [X4: nat > nat > $o,X35: nat,X12: nat] :
      ( ! [X43: nat,X44: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X43),X44)
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X43),X44) )
     => ( ! [X43: nat,X44: nat] :
            ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X44),X43)
           => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X43),X44) )
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X4,X35),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_linorder__wlog) ).

thf(f5322,plain,
    spl124_169,
    inference(avatar_split_clause,[],[f1546,f5320]) ).

thf(f5320,plain,
    ( spl124_169
  <=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_169])]) ).

thf(f1546,plain,
    ! [X2: nat,X0: nat > nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ),
    inference(cnf_transformation,[],[f1257]) ).

thf(f5318,plain,
    spl124_168,
    inference(avatar_split_clause,[],[f1545,f5316]) ).

thf(f5316,plain,
    ( spl124_168
  <=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_168])]) ).

thf(f1545,plain,
    ! [X2: nat,X0: nat > nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ),
    inference(cnf_transformation,[],[f1257]) ).

thf(f5314,plain,
    spl124_167,
    inference(avatar_split_clause,[],[f1544,f5312]) ).

thf(f5312,plain,
    ( spl124_167
  <=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_167])]) ).

thf(f1544,plain,
    ! [X2: nat,X0: nat > nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK30,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK29,X0)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK31,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)) ) ),
    inference(cnf_transformation,[],[f1257]) ).

thf(f5208,plain,
    spl124_166,
    inference(avatar_split_clause,[],[f1641,f5206]) ).

thf(f5206,plain,
    ( spl124_166
  <=> ! [X0: nat,X3: formula_a,X2: trace_1367752404list_a,X1: trace_1367752404list_a] :
        ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),X0) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_166])]) ).

thf(f1641,plain,
    ! [X2: trace_1367752404list_a,X3: formula_a,X0: nat,X1: trace_1367752404list_a] :
      ( ( vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X1),X3),X0) = vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(trace_1367752404list_a,sTfun(nat,nat)),sK57,X2),X1),X0)),X0) ) ),
    inference(cnf_transformation,[],[f1291]) ).

thf(f5183,plain,
    spl124_165,
    inference(avatar_split_clause,[],[f1611,f5181]) ).

thf(f5181,plain,
    ( spl124_165
  <=> ! [X2: nat,X0: trace_1367752404list_a,X1: nat] :
        ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_165])]) ).

thf(f1611,plain,
    ! [X2: nat,X0: trace_1367752404list_a,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) ) ),
    inference(cnf_transformation,[],[f1072]) ).

thf(f1072,plain,
    ! [X0: trace_1367752404list_a,X1: nat,X2: nat] :
      ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) ) ),
    inference(flattening,[],[f1071]) ).

thf(f1071,plain,
    ! [X0: trace_1367752404list_a,X1: nat,X2: nat] :
      ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) ) ),
    inference(ennf_transformation,[],[f675]) ).

thf(f675,plain,
    ! [X0: trace_1367752404list_a,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
       => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2) ) ) ),
    inference(fool_elimination,[],[f674]) ).

thf(f674,plain,
    ! [X0: trace_1367752404list_a,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1)
       => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2) ) ) ),
    inference(rectify,[],[f241]) ).

thf(f241,axiom,
    ! [X16: trace_1367752404list_a,X9: nat,X10: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X16),X9)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X16),X10))
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X10),X9)
       => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X16),X9) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X16),X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_le___092_060tau_062__less) ).

thf(f5179,plain,
    spl124_164,
    inference(avatar_split_clause,[],[f1589,f5177]) ).

thf(f5177,plain,
    ( spl124_164
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) )
        | ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)) )
        | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X2),X1),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_164])]) ).

thf(f1589,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > $o] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X0) )
      | ( $true != vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(nat,$o),nat)),sK44,X3),X2),X1)) )
      | ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)),sP5,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1274]) ).

thf(f5175,plain,
    ( spl124_163
    | ~ spl124_26
    | ~ spl124_147 ),
    inference(avatar_split_clause,[],[f5074,f4836,f2434,f5172]) ).

thf(f5172,plain,
    ( spl124_163
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ia),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_163])]) ).

thf(f5074,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ia),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ~ spl124_26
    | ~ spl124_147 ),
    inference(trivial_inequality_removal,[],[f5043]) ).

thf(f5043,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ia),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ~ spl124_26
    | ~ spl124_147 ),
    inference(superposition,[],[f2435,f4838]) ).

thf(f5122,plain,
    ( ~ spl124_162
    | ~ spl124_30
    | ~ spl124_147 ),
    inference(avatar_split_clause,[],[f5073,f4836,f2450,f5119]) ).

thf(f5073,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) )
    | ~ spl124_30
    | ~ spl124_147 ),
    inference(trivial_inequality_removal,[],[f5044]) ).

thf(f5044,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),ia) )
    | ~ spl124_30
    | ~ spl124_147 ),
    inference(superposition,[],[f2451,f4838]) ).

thf(f5111,plain,
    spl124_161,
    inference(avatar_split_clause,[],[f1784,f5109]) ).

thf(f5109,plain,
    ( spl124_161
  <=> ! [X2: nat > nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK94,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK95,X2))) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_161])]) ).

thf(f1784,plain,
    ! [X2: nat > nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK94,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK95,X2))) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(equality_resolution,[],[f1690]) ).

thf(f1690,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK94,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK95,X2))) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1337]) ).

thf(f1337,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK94,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK95,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK94,X2)),vAPP(sTfun(nat,nat),nat,sK95,X2)) ) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f1153,f1336]) ).

thf(f1336,plain,
    ! [X2: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK94,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK95,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK94,X2)),vAPP(sTfun(nat,nat),nat,sK95,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1153,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1152]) ).

thf(f1152,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f763]) ).

thf(f763,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( ( vAPP(nat,nat,X2,X1) = X3 )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f762]) ).

thf(f762,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ( ( vAPP(nat,nat,X2,X1) = X3 )
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f113]) ).

thf(f113,axiom,
    ! [X35: nat,X12: nat,X21: nat > nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12)
     => ( ( vAPP(nat,nat,X21,X12) = X42 )
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ord__less__eq__subst) ).

thf(f5107,plain,
    spl124_160,
    inference(avatar_split_clause,[],[f1782,f5105]) ).

thf(f5105,plain,
    ( spl124_160
  <=> ! [X2: nat > nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK84,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK85,X2))) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_160])]) ).

thf(f1782,plain,
    ! [X2: nat > nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK84,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK85,X2))) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(equality_resolution,[],[f1676]) ).

thf(f1676,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK84,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK85,X2))) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1327]) ).

thf(f1327,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK84,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK85,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK84,X2)),vAPP(sTfun(nat,nat),nat,sK85,X2)) ) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK84,sK85])],[f1136,f1326]) ).

thf(f1326,plain,
    ! [X2: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK84,X2))),vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,sK85,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK84,X2)),vAPP(sTfun(nat,nat),nat,sK85,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1136,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1135]) ).

thf(f1135,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f745]) ).

thf(f745,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( vAPP(nat,nat,X2,X1) = X3 )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f744]) ).

thf(f744,plain,
    ! [X0: nat,X1: nat,X2: nat > nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( ( vAPP(nat,nat,X2,X1) = X3 )
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X4)),vAPP(nat,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f99]) ).

thf(f99,axiom,
    ! [X35: nat,X12: nat,X21: nat > nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ( ( vAPP(nat,nat,X21,X12) = X42 )
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_ord__le__eq__subst) ).

thf(f5103,plain,
    spl124_159,
    inference(avatar_split_clause,[],[f1780,f5101]) ).

thf(f5101,plain,
    ( spl124_159
  <=> ! [X2: nat > prefix1027212443list_a,X0: nat,X1: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),vAPP(nat,prefix1027212443list_a,X2,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2))) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_159])]) ).

thf(f1780,plain,
    ! [X2: nat > prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),vAPP(nat,prefix1027212443list_a,X2,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2))) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(equality_resolution,[],[f1674]) ).

thf(f1674,plain,
    ! [X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2))) )
      | ( vAPP(nat,prefix1027212443list_a,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1325]) ).

thf(f1325,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2)) ) )
      | ( vAPP(nat,prefix1027212443list_a,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK82,sK83])],[f1134,f1324]) ).

thf(f1324,plain,
    ! [X2: nat > prefix1027212443list_a] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2))),vAPP(nat,prefix1027212443list_a,X2,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1134,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( vAPP(nat,prefix1027212443list_a,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1133]) ).

thf(f1133,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( vAPP(nat,prefix1027212443list_a,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f743]) ).

thf(f743,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( vAPP(nat,prefix1027212443list_a,X2,X1) = X3 )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f742]) ).

thf(f742,plain,
    ! [X0: nat,X1: nat,X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( ( vAPP(nat,prefix1027212443list_a,X2,X1) = X3 )
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X4)),vAPP(nat,prefix1027212443list_a,X2,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f96]) ).

thf(f96,axiom,
    ! [X35: nat,X12: nat,X21: nat > prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ( ( vAPP(nat,prefix1027212443list_a,X21,X12) = X42 )
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X14)),vAPP(nat,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_ord__le__eq__subst) ).

thf(f5099,plain,
    spl124_158,
    inference(avatar_split_clause,[],[f1778,f5097]) ).

thf(f5097,plain,
    ( spl124_158
  <=> ! [X2: prefix1027212443list_a > nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),vAPP(prefix1027212443list_a,nat,X2,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_158])]) ).

thf(f1778,plain,
    ! [X2: prefix1027212443list_a > nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),vAPP(prefix1027212443list_a,nat,X2,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(equality_resolution,[],[f1664]) ).

thf(f1664,plain,
    ! [X2: prefix1027212443list_a > nat,X3: nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2))) )
      | ( vAPP(prefix1027212443list_a,nat,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1315]) ).

thf(f1315,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2)) ) )
      | ( vAPP(prefix1027212443list_a,nat,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73])],[f1124,f1314]) ).

thf(f1314,plain,
    ! [X2: prefix1027212443list_a > nat] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2))),vAPP(prefix1027212443list_a,nat,X2,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1124,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( vAPP(prefix1027212443list_a,nat,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f1123]) ).

thf(f1123,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( vAPP(prefix1027212443list_a,nat,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f733]) ).

thf(f733,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( vAPP(prefix1027212443list_a,nat,X2,X1) = X3 )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f732]) ).

thf(f732,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > nat,X3: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( ( vAPP(prefix1027212443list_a,nat,X2,X1) = X3 )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X4)),vAPP(prefix1027212443list_a,nat,X2,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f97]) ).

thf(f97,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a,X21: prefix1027212443list_a > nat,X42: nat] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),X12)
     => ( ( vAPP(prefix1027212443list_a,nat,X21,X12) = X42 )
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X14)),vAPP(prefix1027212443list_a,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_ord__le__eq__subst) ).

thf(f5095,plain,
    spl124_157,
    inference(avatar_split_clause,[],[f1776,f5093]) ).

thf(f5093,plain,
    ( spl124_157
  <=> ! [X2: prefix1027212443list_a > prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_157])]) ).

thf(f1776,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(equality_resolution,[],[f1662]) ).

thf(f1662,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2))) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1313]) ).

thf(f1313,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2)) ) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f1122,f1312]) ).

thf(f1312,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1122,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f1121]) ).

thf(f1121,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f731]) ).

thf(f731,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1) = X3 )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) ) ) ) ),
    inference(fool_elimination,[],[f730]) ).

thf(f730,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1) = X3 )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) ) ) ),
    inference(rectify,[],[f98]) ).

thf(f98,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a,X21: prefix1027212443list_a > prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),X12)
     => ( ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X12) = X42 )
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X14)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X35)),X42) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_ord__le__eq__subst) ).

thf(f5091,plain,
    spl124_156,
    inference(avatar_split_clause,[],[f1766,f5089]) ).

thf(f5089,plain,
    ( spl124_156
  <=> ! [X2: nat,X1: nat > nat,X3: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK55,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK56,X1))) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_156])]) ).

thf(f1766,plain,
    ! [X2: nat,X3: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK55,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK56,X1))) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ),
    inference(equality_resolution,[],[f1629]) ).

thf(f1629,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK55,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK56,X1))) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1289]) ).

thf(f1289,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK55,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK56,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK55,X1)),vAPP(sTfun(nat,nat),nat,sK56,X1)) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56])],[f1087,f1288]) ).

thf(f1288,plain,
    ! [X1: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK55,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK56,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK55,X1)),vAPP(sTfun(nat,nat),nat,sK56,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1087,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(flattening,[],[f1086]) ).

thf(f1086,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f699]) ).

thf(f699,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,nat,X1,X2) = X0 )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f698]) ).

thf(f698,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,nat,X1,X2) = X0 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f112]) ).

thf(f112,axiom,
    ! [X35: nat,X21: nat > nat,X12: nat,X42: nat] :
      ( ( vAPP(nat,nat,X21,X12) = X35 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),vAPP(nat,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_ord__eq__less__subst) ).

thf(f5087,plain,
    spl124_155,
    inference(avatar_split_clause,[],[f1764,f5085]) ).

thf(f5085,plain,
    ( spl124_155
  <=> ! [X2: nat,X1: nat > nat,X3: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK53,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK54,X1))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_155])]) ).

thf(f1764,plain,
    ! [X2: nat,X3: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK53,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK54,X1))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ),
    inference(equality_resolution,[],[f1627]) ).

thf(f1627,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK53,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK54,X1))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1287]) ).

thf(f1287,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK53,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK54,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK53,X1)),vAPP(sTfun(nat,nat),nat,sK54,X1)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54])],[f1085,f1286]) ).

thf(f1286,plain,
    ! [X1: nat > nat] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK53,X1))),vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,sK54,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK53,X1)),vAPP(sTfun(nat,nat),nat,sK54,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1085,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(flattening,[],[f1084]) ).

thf(f1084,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f697]) ).

thf(f697,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,nat,X1,X2) = X0 )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f696]) ).

thf(f696,plain,
    ! [X0: nat,X1: nat > nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,nat,X1,X2) = X0 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X4)),vAPP(nat,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f103]) ).

thf(f103,axiom,
    ! [X35: nat,X21: nat > nat,X12: nat,X42: nat] :
      ( ( vAPP(nat,nat,X21,X12) = X35 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X14)),vAPP(nat,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),vAPP(nat,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ord__eq__le__subst) ).

thf(f5083,plain,
    spl124_154,
    inference(avatar_split_clause,[],[f1762,f5081]) ).

thf(f5081,plain,
    ( spl124_154
  <=> ! [X2: nat,X1: nat > prefix1027212443list_a,X3: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X2)),vAPP(nat,prefix1027212443list_a,X1,X3)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1))) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_154])]) ).

thf(f1762,plain,
    ! [X2: nat,X3: nat,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X2)),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ),
    inference(equality_resolution,[],[f1625]) ).

thf(f1625,plain,
    ! [X2: nat,X3: nat,X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1285]) ).

thf(f1285,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1)) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52])],[f1083,f1284]) ).

thf(f1284,plain,
    ! [X1: nat > prefix1027212443list_a] :
      ( ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1))),vAPP(nat,prefix1027212443list_a,X1,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1083,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(flattening,[],[f1082]) ).

thf(f1082,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ? [X4: nat,X5: nat] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f695]) ).

thf(f695,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( vAPP(nat,prefix1027212443list_a,X1,X2) = X0 )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
       => ( ! [X4: nat,X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f694]) ).

thf(f694,plain,
    ! [X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a,X2: nat,X3: nat] :
      ( ( vAPP(nat,prefix1027212443list_a,X1,X2) = X0 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
       => ( ! [X4: nat,X5: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X4)),vAPP(nat,prefix1027212443list_a,X1,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) ) ) ),
    inference(rectify,[],[f100]) ).

thf(f100,axiom,
    ! [X35: prefix1027212443list_a,X21: nat > prefix1027212443list_a,X12: nat,X42: nat] :
      ( ( vAPP(nat,prefix1027212443list_a,X21,X12) = X35 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X42)
       => ( ! [X14: nat,X13: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X21,X14)),vAPP(nat,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),vAPP(nat,prefix1027212443list_a,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_ord__eq__le__subst) ).

thf(f5079,plain,
    spl124_153,
    inference(avatar_split_clause,[],[f1760,f5077]) ).

thf(f5077,plain,
    ( spl124_153
  <=> ! [X2: prefix1027212443list_a,X1: prefix1027212443list_a > nat,X3: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X2)),vAPP(prefix1027212443list_a,nat,X1,X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_153])]) ).

thf(f1760,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X1: prefix1027212443list_a > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X2)),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ),
    inference(equality_resolution,[],[f1623]) ).

thf(f1623,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: prefix1027212443list_a > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,nat,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f1283,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,nat,X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50])],[f1081,f1282]) ).

thf(f1282,plain,
    ! [X1: prefix1027212443list_a > nat] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1))),vAPP(prefix1027212443list_a,nat,X1,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1081,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,nat,X1,X2) != X0 ) ),
    inference(flattening,[],[f1080]) ).

thf(f1080,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,nat,X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f693]) ).

thf(f693,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,nat,X1,X2) = X0 )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) ) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f692]) ).

thf(f692,plain,
    ! [X0: nat,X1: prefix1027212443list_a > nat,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,nat,X1,X2) = X0 )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X4)),vAPP(prefix1027212443list_a,nat,X1,X5)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) ) ) ),
    inference(rectify,[],[f101]) ).

thf(f101,axiom,
    ! [X35: nat,X21: prefix1027212443list_a > nat,X12: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,nat,X21,X12) = X35 )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X21,X14)),vAPP(prefix1027212443list_a,nat,X21,X13)) )
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),vAPP(prefix1027212443list_a,nat,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_ord__eq__le__subst) ).

thf(f5041,plain,
    spl124_152,
    inference(avatar_split_clause,[],[f1758,f5039]) ).

thf(f5039,plain,
    ( spl124_152
  <=> ! [X2: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1))) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_152])]) ).

thf(f1758,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ),
    inference(equality_resolution,[],[f1621]) ).

thf(f1621,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1))) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1281]) ).

thf(f1281,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1)) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48])],[f1079,f1280]) ).

thf(f1280,plain,
    ! [X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
     => ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1))),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1))) )
        & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1079,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(flattening,[],[f1078]) ).

thf(f1078,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ? [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
          ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
          & ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) ) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f691]) ).

thf(f691,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2) = X0 )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5) )
             => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) ) )
         => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) ) ) ) ),
    inference(fool_elimination,[],[f690]) ).

thf(f690,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X2: prefix1027212443list_a,X3: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2) = X0 )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3)
       => ( ! [X4: prefix1027212443list_a,X5: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X4),X5)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X4)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X5)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) ) ) ),
    inference(rectify,[],[f102]) ).

thf(f102,axiom,
    ! [X35: prefix1027212443list_a,X21: prefix1027212443list_a > prefix1027212443list_a,X12: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X12) = X35 )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X42)
       => ( ! [X14: prefix1027212443list_a,X13: prefix1027212443list_a] :
              ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X14),X13)
             => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X14)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X13)) )
         => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),vAPP(prefix1027212443list_a,prefix1027212443list_a,X21,X42)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_ord__eq__le__subst) ).

thf(f5037,plain,
    spl124_151,
    inference(avatar_split_clause,[],[f1553,f5035]) ).

thf(f5035,plain,
    ( spl124_151
  <=> ! [X2: nat,X0: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK38,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK39,X0))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_151])]) ).

thf(f1553,plain,
    ! [X2: nat,X0: nat > nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK38,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK39,X0))) ) ),
    inference(cnf_transformation,[],[f1264]) ).

thf(f1264,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK38,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK39,X0))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK38,X0)),vAPP(sTfun(nat,nat),nat,sK39,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f994,f1263]) ).

thf(f1263,plain,
    ! [X0: nat > nat] :
      ( ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK38,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK39,X0))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK38,X0)),vAPP(sTfun(nat,nat),nat,sK39,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f994,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) ) ),
    inference(flattening,[],[f993]) ).

thf(f993,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ? [X3: nat,X4: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) ) ) ),
    inference(ennf_transformation,[],[f581]) ).

thf(f581,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ! [X3: nat,X4: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4) )
         => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) ) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ) ),
    inference(fool_elimination,[],[f580]) ).

thf(f580,plain,
    ! [X0: nat > nat,X1: nat,X2: nat] :
      ( ! [X3: nat,X4: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X4)
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)) )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) ) ),
    inference(rectify,[],[f27]) ).

thf(f27,axiom,
    ! [X21: nat > nat,X9: nat,X10: nat] :
      ( ! [X22: nat,X23: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X22),X23)
         => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X21,X22)),vAPP(nat,nat,X21,X23)) )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X10)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X21,X9)),vAPP(nat,nat,X21,X10)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_less__mono__imp__le__mono) ).

thf(f4949,plain,
    spl124_150,
    inference(avatar_split_clause,[],[f1660,f4947]) ).

thf(f4947,plain,
    ( spl124_150
  <=> ! [X0: prefix1027212443list_a,X3: nat,X2: trace_1367752404list_a,X1: trace_1367752404list_a] :
        ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X3) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
        | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_150])]) ).

thf(f1660,plain,
    ! [X2: trace_1367752404list_a,X3: nat,X0: prefix1027212443list_a,X1: trace_1367752404list_a] :
      ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1120]) ).

thf(f1120,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: nat] :
      ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(flattening,[],[f1119]) ).

thf(f1119,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: nat] :
      ( ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f729]) ).

thf(f729,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: nat] :
      ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) )
     => ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
       => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)) )
         => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X3) ) ) ) ),
    inference(fool_elimination,[],[f728]) ).

thf(f728,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: trace_1367752404list_a,X3: nat] :
      ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1)
     => ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2)
       => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0))
         => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X1),X3) ) ) ) ),
    inference(rectify,[],[f242]) ).

thf(f242,axiom,
    ! [X55: prefix1027212443list_a,X2: trace_1367752404list_a,X65: trace_1367752404list_a,X9: nat] :
      ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X55),X2)
     => ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X55),X65)
       => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X55))
         => ( vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X9) = vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X65),X9) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241__092_060tau_062__prefix__conv) ).

thf(f4945,plain,
    spl124_149,
    inference(avatar_split_clause,[],[f1554,f4943]) ).

thf(f4943,plain,
    ( spl124_149
  <=> ! [X2: nat,X0: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK40,X0)),vAPP(sTfun(nat,nat),nat,sK41,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_149])]) ).

thf(f1554,plain,
    ! [X2: nat,X0: nat > nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK40,X0)),vAPP(sTfun(nat,nat),nat,sK41,X0)) ) ),
    inference(cnf_transformation,[],[f1266]) ).

thf(f4893,plain,
    spl124_148,
    inference(avatar_split_clause,[],[f1688,f4891]) ).

thf(f4891,plain,
    ( spl124_148
  <=> ! [X0: nat,X3: formula_a,X2: trace_1367752404list_a,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0)),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_148])]) ).

thf(f1688,plain,
    ! [X2: trace_1367752404list_a,X3: formula_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0)),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1151]) ).

thf(f1151,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a,X3: formula_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0)),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f761]) ).

thf(f761,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a,X3: formula_a] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0)),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X1)) ) ),
    inference(fool_elimination,[],[f760]) ).

thf(f760,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a,X3: formula_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X0)),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X2),X3),X1)) ),
    inference(rectify,[],[f22]) ).

thf(f22,axiom,
    ! [X10: nat,X18: nat,X16: trace_1367752404list_a,X17: formula_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X10),X18)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X16),X17),X10)),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X16),X17),X18)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_progress__mono) ).

thf(f4839,plain,
    ( spl124_147
    | ~ spl124_23
    | ~ spl124_143 ),
    inference(avatar_split_clause,[],[f4826,f4802,f2415,f4836]) ).

thf(f4802,plain,
    ( spl124_143
  <=> ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_143])]) ).

thf(f4826,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ~ spl124_23
    | ~ spl124_143 ),
    inference(trivial_inequality_removal,[],[f4817]) ).

thf(f4817,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
    | ~ spl124_23
    | ~ spl124_143 ),
    inference(superposition,[],[f4803,f2416]) ).

thf(f4803,plain,
    ( ! [X0: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) ) )
    | ~ spl124_143 ),
    inference(avatar_component_clause,[],[f4802]) ).

thf(f4816,plain,
    spl124_146,
    inference(avatar_split_clause,[],[f1591,f4814]) ).

thf(f4814,plain,
    ( spl124_146
  <=> ! [X2: nat > $o,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)),X1) )
        | ( $true = vAPP(nat,$o,X2,X1) )
        | ( $true != vAPP(nat,$o,X2,X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_146])]) ).

thf(f1591,plain,
    ! [X2: nat > $o,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)),X1) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1277]) ).

thf(f4812,plain,
    spl124_145,
    inference(avatar_split_clause,[],[f1590,f4810]) ).

thf(f4810,plain,
    ( spl124_145
  <=> ! [X2: nat > $o,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
        | ( $true = vAPP(nat,$o,X2,X1) )
        | ( $true != vAPP(nat,$o,X2,X0) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_145])]) ).

thf(f1590,plain,
    ! [X2: nat > $o,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK45,X2),X1),X0)) )
      | ( $true = vAPP(nat,$o,X2,X1) )
      | ( $true != vAPP(nat,$o,X2,X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1277]) ).

thf(f4808,plain,
    spl124_144,
    inference(avatar_split_clause,[],[f1559,f4806]) ).

thf(f4806,plain,
    ( spl124_144
  <=> ! [X4: nat,X0: nat > $o,X2: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK42,X0)) )
        | ( $true != vAPP(nat,$o,X0,X4) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)),X2) )
        | ( $true != vAPP(nat,$o,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_144])]) ).

thf(f1559,plain,
    ! [X2: nat,X0: nat > $o,X1: nat,X4: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK42,X0)) )
      | ( $true != vAPP(nat,$o,X0,X4) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)),X2) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(cnf_transformation,[],[f1270]) ).

thf(f1270,plain,
    ! [X0: nat > $o,X1: nat,X2: nat] :
      ( ( ! [X4: nat] :
            ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK42,X0)) )
            | ( $true != vAPP(nat,$o,X0,X4) ) )
        & ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) ) )
      | ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)),X2) )
        & ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) ) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f1267,f1269,f1268]) ).

thf(f1268,plain,
    ! [X0: nat > $o] :
      ( ? [X3: nat] :
          ( ! [X4: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
              | ( $true != vAPP(nat,$o,X0,X4) ) )
          & ( $true = vAPP(nat,$o,X0,X3) ) )
     => ( ! [X4: nat] :
            ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK42,X0)) )
            | ( $true != vAPP(nat,$o,X0,X4) ) )
        & ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1269,plain,
    ! [X0: nat > $o,X2: nat] :
      ( ? [X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X2) )
          & ( $true = vAPP(nat,$o,X0,X5) ) )
     => ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)),X2) )
        & ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1267,plain,
    ! [X0: nat > $o,X1: nat,X2: nat] :
      ( ? [X3: nat] :
          ( ! [X4: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X3) )
              | ( $true != vAPP(nat,$o,X0,X4) ) )
          & ( $true = vAPP(nat,$o,X0,X3) ) )
      | ? [X5: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X2) )
          & ( $true = vAPP(nat,$o,X0,X5) ) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(rectify,[],[f997]) ).

thf(f997,plain,
    ! [X0: nat > $o,X1: nat,X2: nat] :
      ( ? [X4: nat] :
          ( ! [X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X4) )
              | ( $true != vAPP(nat,$o,X0,X5) ) )
          & ( $true = vAPP(nat,$o,X0,X4) ) )
      | ? [X3: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
          & ( $true = vAPP(nat,$o,X0,X3) ) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(flattening,[],[f996]) ).

thf(f996,plain,
    ! [X0: nat > $o,X1: nat,X2: nat] :
      ( ? [X4: nat] :
          ( ! [X5: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X4) )
              | ( $true != vAPP(nat,$o,X0,X5) ) )
          & ( $true = vAPP(nat,$o,X0,X4) ) )
      | ? [X3: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
          & ( $true = vAPP(nat,$o,X0,X3) ) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(ennf_transformation,[],[f585]) ).

thf(f585,plain,
    ! [X0: nat > $o,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
     => ( ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
           => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) ) )
       => ? [X4: nat] :
            ( ! [X5: nat] :
                ( ( $true = vAPP(nat,$o,X0,X5) )
               => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X4) ) )
            & ( $true = vAPP(nat,$o,X0,X4) ) ) ) ),
    inference(fool_elimination,[],[f584]) ).

thf(f584,plain,
    ! [X0: nat > $o,X1: nat,X2: nat] :
      ( vAPP(nat,$o,X0,X1)
     => ( ! [X3: nat] :
            ( vAPP(nat,$o,X0,X3)
           => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X2) )
       => ? [X4: nat] :
            ( ! [X5: nat] :
                ( vAPP(nat,$o,X0,X5)
               => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X5),X4) )
            & vAPP(nat,$o,X0,X4) ) ) ),
    inference(rectify,[],[f20]) ).

thf(f20,axiom,
    ! [X4: nat > $o,X11: nat,X12: nat] :
      ( vAPP(nat,$o,X4,X11)
     => ( ! [X13: nat] :
            ( vAPP(nat,$o,X4,X13)
           => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X13),X12) )
       => ? [X14: nat] :
            ( ! [X15: nat] :
                ( vAPP(nat,$o,X4,X15)
               => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X15),X14) )
            & vAPP(nat,$o,X4,X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_Nat_Oex__has__greatest__nat) ).

thf(f4804,plain,
    spl124_143,
    inference(avatar_split_clause,[],[f1404,f4802]) ).

thf(f1404,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ),
    inference(cnf_transformation,[],[f884]) ).

thf(f884,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) ) ),
    inference(ennf_transformation,[],[f357]) ).

thf(f357,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) ) ),
    inference(fool_elimination,[],[f356]) ).

thf(f356,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) ),
    inference(rectify,[],[f212]) ).

thf(f212,axiom,
    ! [X11: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211__C3_C) ).

thf(f4677,plain,
    ( spl124_142
    | ~ spl124_16 ),
    inference(avatar_split_clause,[],[f2380,f2362,f4675]) ).

thf(f4675,plain,
    ( spl124_142
  <=> ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK22,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_142])]) ).

thf(f2380,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK22,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( X0 = X1 ) )
    | ~ spl124_16 ),
    inference(equality_proxy_clausification,[],[f2379]) ).

thf(f2379,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( vAPP(sTfun(nat,$o),nat,sK22,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
    | ~ spl124_16 ),
    inference(equality_proxy_clausification,[],[f2376]) ).

thf(f2376,plain,
    ( ! [X0: nat,X1: nat] :
        ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK22,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
    | ~ spl124_16 ),
    inference(primitive_instantiation,[],[f2363]) ).

thf(f4286,plain,
    spl124_141,
    inference(avatar_split_clause,[],[f1785,f4284]) ).

thf(f4284,plain,
    ( spl124_141
  <=> ! [X2: nat > nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK94,X2)),vAPP(sTfun(nat,nat),nat,sK95,X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_141])]) ).

thf(f1785,plain,
    ! [X2: nat > nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK94,X2)),vAPP(sTfun(nat,nat),nat,sK95,X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(equality_resolution,[],[f1689]) ).

thf(f1689,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK94,X2)),vAPP(sTfun(nat,nat),nat,sK95,X2)) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1337]) ).

thf(f4282,plain,
    spl124_140,
    inference(avatar_split_clause,[],[f1783,f4280]) ).

thf(f4280,plain,
    ( spl124_140
  <=> ! [X2: nat > nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK84,X2)),vAPP(sTfun(nat,nat),nat,sK85,X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_140])]) ).

thf(f1783,plain,
    ! [X2: nat > nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK84,X2)),vAPP(sTfun(nat,nat),nat,sK85,X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(equality_resolution,[],[f1675]) ).

thf(f1675,plain,
    ! [X2: nat > nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK84,X2)),vAPP(sTfun(nat,nat),nat,sK85,X2)) )
      | ( vAPP(nat,nat,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1327]) ).

thf(f4278,plain,
    spl124_139,
    inference(avatar_split_clause,[],[f1781,f4276]) ).

thf(f4276,plain,
    ( spl124_139
  <=> ! [X2: nat > prefix1027212443list_a,X0: nat,X1: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),vAPP(nat,prefix1027212443list_a,X2,X1)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_139])]) ).

thf(f1781,plain,
    ! [X2: nat > prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),vAPP(nat,prefix1027212443list_a,X2,X1)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(equality_resolution,[],[f1673]) ).

thf(f1673,plain,
    ! [X2: nat > prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK82,X2)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK83,X2)) )
      | ( vAPP(nat,prefix1027212443list_a,X2,X1) != X3 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1325]) ).

thf(f4274,plain,
    spl124_138,
    inference(avatar_split_clause,[],[f1779,f4272]) ).

thf(f4272,plain,
    ( spl124_138
  <=> ! [X2: prefix1027212443list_a > nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),vAPP(prefix1027212443list_a,nat,X2,X1)) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_138])]) ).

thf(f1779,plain,
    ! [X2: prefix1027212443list_a > nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),vAPP(prefix1027212443list_a,nat,X2,X1)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(equality_resolution,[],[f1663]) ).

thf(f1663,plain,
    ! [X2: prefix1027212443list_a > nat,X3: nat,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X2,X0)),X3) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK72,X2)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK73,X2)) )
      | ( vAPP(prefix1027212443list_a,nat,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1315]) ).

thf(f4270,plain,
    spl124_137,
    inference(avatar_split_clause,[],[f1777,f4268]) ).

thf(f4268,plain,
    ( spl124_137
  <=> ! [X2: prefix1027212443list_a > prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_137])]) ).

thf(f1777,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(equality_resolution,[],[f1661]) ).

thf(f1661,plain,
    ! [X2: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X0)),X3) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK70,X2)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK71,X2)) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X2,X1) != X3 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1313]) ).

thf(f4266,plain,
    spl124_136,
    inference(avatar_split_clause,[],[f1767,f4264]) ).

thf(f4264,plain,
    ( spl124_136
  <=> ! [X2: nat,X1: nat > nat,X3: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK55,X1)),vAPP(sTfun(nat,nat),nat,sK56,X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_136])]) ).

thf(f1767,plain,
    ! [X2: nat,X3: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK55,X1)),vAPP(sTfun(nat,nat),nat,sK56,X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) ),
    inference(equality_resolution,[],[f1628]) ).

thf(f1628,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK55,X1)),vAPP(sTfun(nat,nat),nat,sK56,X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1289]) ).

thf(f4262,plain,
    spl124_135,
    inference(avatar_split_clause,[],[f1765,f4260]) ).

thf(f4260,plain,
    ( spl124_135
  <=> ! [X2: nat,X1: nat > nat,X3: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK53,X1)),vAPP(sTfun(nat,nat),nat,sK54,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_135])]) ).

thf(f1765,plain,
    ! [X2: nat,X3: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X1,X2)),vAPP(nat,nat,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK53,X1)),vAPP(sTfun(nat,nat),nat,sK54,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ),
    inference(equality_resolution,[],[f1626]) ).

thf(f1626,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,nat),nat,sK53,X1)),vAPP(sTfun(nat,nat),nat,sK54,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,nat,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1287]) ).

thf(f4258,plain,
    spl124_134,
    inference(avatar_split_clause,[],[f1763,f4256]) ).

thf(f4256,plain,
    ( spl124_134
  <=> ! [X2: nat,X1: nat > prefix1027212443list_a,X3: nat] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X2)),vAPP(nat,prefix1027212443list_a,X1,X3)) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_134])]) ).

thf(f1763,plain,
    ! [X2: nat,X3: nat,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(nat,prefix1027212443list_a,X1,X2)),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) ) ),
    inference(equality_resolution,[],[f1624]) ).

thf(f1624,plain,
    ! [X2: nat,X3: nat,X0: prefix1027212443list_a,X1: nat > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(nat,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,prefix1027212443list_a),nat,sK51,X1)),vAPP(sTfun(nat,prefix1027212443list_a),nat,sK52,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1285]) ).

thf(f4254,plain,
    spl124_133,
    inference(avatar_split_clause,[],[f1761,f4252]) ).

thf(f4252,plain,
    ( spl124_133
  <=> ! [X2: prefix1027212443list_a,X1: prefix1027212443list_a > nat,X3: prefix1027212443list_a] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X2)),vAPP(prefix1027212443list_a,nat,X1,X3)) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_133])]) ).

thf(f1761,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X1: prefix1027212443list_a > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,X1,X2)),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ),
    inference(equality_resolution,[],[f1622]) ).

thf(f1622,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: nat,X1: prefix1027212443list_a > nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(prefix1027212443list_a,nat,X1,X3)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK49,X1)),vAPP(sTfun(prefix1027212443list_a,nat),prefix1027212443list_a,sK50,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,nat,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1283]) ).

thf(f4250,plain,
    ( spl124_132
    | ~ spl124_3
    | ~ spl124_93 ),
    inference(avatar_split_clause,[],[f4081,f3161,f2264,f4248]) ).

thf(f4248,plain,
    ( spl124_132
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_132])]) ).

thf(f3161,plain,
    ( spl124_93
  <=> ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_93])]) ).

thf(f4081,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X0) )
    | ~ spl124_3
    | ~ spl124_93 ),
    inference(trivial_inequality_removal,[],[f4080]) ).

thf(f4080,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X0) ) )
    | ~ spl124_3
    | ~ spl124_93 ),
    inference(superposition,[],[f3162,f2265]) ).

thf(f3162,plain,
    ( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X0) )
    | ~ spl124_93 ),
    inference(avatar_component_clause,[],[f3161]) ).

thf(f4246,plain,
    spl124_131,
    inference(avatar_split_clause,[],[f1759,f4244]) ).

thf(f4244,plain,
    ( spl124_131
  <=> ! [X2: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a,X3: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
        | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1)) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_131])]) ).

thf(f1759,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2)),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) ) ),
    inference(equality_resolution,[],[f1620]) ).

thf(f1620,plain,
    ! [X2: prefix1027212443list_a,X3: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a > prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X3)) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK47,X1)),vAPP(sTfun(prefix1027212443list_a,prefix1027212443list_a),prefix1027212443list_a,sK48,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X3) )
      | ( vAPP(prefix1027212443list_a,prefix1027212443list_a,X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1281]) ).

thf(f4242,plain,
    spl124_130,
    inference(avatar_split_clause,[],[f1640,f4240]) ).

thf(f4240,plain,
    ( spl124_130
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_130])]) ).

thf(f1640,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1107]) ).

thf(f1107,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1106]) ).

thf(f1106,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f715]) ).

thf(f715,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ) ),
    inference(fool_elimination,[],[f714]) ).

thf(f714,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ),
    inference(rectify,[],[f271]) ).

thf(f271,axiom,
    ! [X9: nat,X10: nat,X11: nat,X62: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),X62)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X10) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X9),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X10),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_add__mono__thms__linordered__field_I5_J) ).

thf(f4238,plain,
    spl124_129,
    inference(avatar_split_clause,[],[f1639,f4236]) ).

thf(f4236,plain,
    ( spl124_129
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_129])]) ).

thf(f1639,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1105]) ).

thf(f1105,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1104]) ).

thf(f1104,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f713]) ).

thf(f713,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ) ),
    inference(fool_elimination,[],[f712]) ).

thf(f712,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ),
    inference(rectify,[],[f281]) ).

thf(f281,axiom,
    ! [X9: nat,X10: nat,X11: nat,X62: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X11),X62)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X10) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X9),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X10),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_add__mono__thms__linordered__field_I3_J) ).

thf(f4234,plain,
    spl124_128,
    inference(avatar_split_clause,[],[f1637,f4232]) ).

thf(f4232,plain,
    ( spl124_128
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_128])]) ).

thf(f1637,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1101]) ).

thf(f1101,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1100]) ).

thf(f1100,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f709]) ).

thf(f709,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ) ),
    inference(fool_elimination,[],[f708]) ).

thf(f708,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ),
    inference(rectify,[],[f282]) ).

thf(f282,axiom,
    ! [X9: nat,X10: nat,X11: nat,X62: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),X62)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X10) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X9),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X10),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_add__mono__thms__linordered__field_I4_J) ).

thf(f4230,plain,
    spl124_127,
    inference(avatar_split_clause,[],[f1636,f4228]) ).

thf(f4228,plain,
    ( spl124_127
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_127])]) ).

thf(f1636,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1099]) ).

thf(f1099,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1098]) ).

thf(f1098,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f707]) ).

thf(f707,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ) ),
    inference(fool_elimination,[],[f706]) ).

thf(f706,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X3)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3)) ),
    inference(rectify,[],[f263]) ).

thf(f263,axiom,
    ! [X9: nat,X10: nat,X11: nat,X62: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X11),X62)
        & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X10) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X9),X11)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X10),X62)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_add__mono__thms__linordered__semiring_I1_J) ).

thf(f4226,plain,
    spl124_126,
    inference(avatar_split_clause,[],[f1552,f4224]) ).

thf(f4224,plain,
    ( spl124_126
  <=> ! [X2: nat,X0: nat > nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK38,X0)),vAPP(sTfun(nat,nat),nat,sK39,X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_126])]) ).

thf(f1552,plain,
    ! [X2: nat,X0: nat > nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,nat),nat,sK38,X0)),vAPP(sTfun(nat,nat),nat,sK39,X0)) ) ),
    inference(cnf_transformation,[],[f1264]) ).

thf(f4148,plain,
    spl124_125,
    inference(avatar_split_clause,[],[f1558,f4146]) ).

thf(f4146,plain,
    ( spl124_125
  <=> ! [X4: nat,X0: nat > $o,X2: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK42,X0)) )
        | ( $true != vAPP(nat,$o,X0,X4) )
        | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) )
        | ( $true != vAPP(nat,$o,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_125])]) ).

thf(f1558,plain,
    ! [X2: nat,X0: nat > $o,X1: nat,X4: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),vAPP(sTfun(nat,$o),nat,sK42,X0)) )
      | ( $true != vAPP(nat,$o,X0,X4) )
      | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(cnf_transformation,[],[f1270]) ).

thf(f3976,plain,
    ( spl124_124
    | ~ spl124_96
    | ~ spl124_97
    | ~ spl124_118 ),
    inference(avatar_split_clause,[],[f3918,f3913,f3267,f3263,f3973]) ).

thf(f3913,plain,
    ( spl124_118
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_118])]) ).

thf(f3918,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) )
    | ~ spl124_96
    | ~ spl124_97
    | ~ spl124_118 ),
    inference(forward_demodulation,[],[f3917,f3264]) ).

thf(f3917,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) )
    | ~ spl124_97
    | ~ spl124_118 ),
    inference(forward_demodulation,[],[f3915,f3268]) ).

thf(f3915,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) )
    | ~ spl124_118 ),
    inference(avatar_component_clause,[],[f3913]) ).

thf(f3971,plain,
    ( spl124_123
    | ~ spl124_96
    | ~ spl124_97
    | ~ spl124_117 ),
    inference(avatar_split_clause,[],[f3911,f3906,f3267,f3263,f3968]) ).

thf(f3906,plain,
    ( spl124_117
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_117])]) ).

thf(f3911,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) )
    | ~ spl124_96
    | ~ spl124_97
    | ~ spl124_117 ),
    inference(forward_demodulation,[],[f3910,f3264]) ).

thf(f3910,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) )
    | ~ spl124_97
    | ~ spl124_117 ),
    inference(forward_demodulation,[],[f3908,f3268]) ).

thf(f3908,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) )
    | ~ spl124_117 ),
    inference(avatar_component_clause,[],[f3906]) ).

thf(f3966,plain,
    spl124_122,
    inference(avatar_split_clause,[],[f2252,f3963]) ).

thf(f2252,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)),
    inference(forward_demodulation,[],[f2251,f1517]) ).

thf(f1517,plain,
    ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
    inference(cnf_transformation,[],[f867]) ).

thf(f867,plain,
    ! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
    inference(rectify,[],[f258]) ).

thf(f258,axiom,
    ! [X12: nat,X35: nat,X42: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),X42)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add_Oleft__commute) ).

thf(f2251,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)),
    inference(forward_demodulation,[],[f1736,f1518]) ).

thf(f1736,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) = $true,
    inference(cnf_transformation,[],[f827]) ).

thf(f827,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)) = $true,
    inference(fool_elimination,[],[f826]) ).

thf(f826,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)),
    inference(rectify,[],[f215]) ).

thf(f215,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),j)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062) ).

thf(f3961,plain,
    spl124_121,
    inference(avatar_split_clause,[],[f2250,f3958]) ).

thf(f2250,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)),
    inference(forward_demodulation,[],[f2249,f1517]) ).

thf(f2249,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,b),one_one_nat))),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)),
    inference(forward_demodulation,[],[f1735,f1518]) ).

thf(f1735,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) = $true,
    inference(cnf_transformation,[],[f825]) ).

thf(f825,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)) = $true,
    inference(fool_elimination,[],[f824]) ).

thf(f824,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)),
    inference(rectify,[],[f216]) ).

thf(f216,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ja)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062) ).

thf(f3956,plain,
    spl124_120,
    inference(avatar_split_clause,[],[f1734,f3953]) ).

thf(f3953,plain,
    ( spl124_120
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_120])]) ).

thf(f1734,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(cnf_transformation,[],[f823]) ).

thf(f823,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(fool_elimination,[],[f822]) ).

thf(f822,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(rectify,[],[f196]) ).

thf(f196,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Until_Oprems) ).

thf(f3951,plain,
    spl124_119,
    inference(avatar_split_clause,[],[f1733,f3948]) ).

thf(f3948,plain,
    ( spl124_119
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_119])]) ).

thf(f1733,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(cnf_transformation,[],[f821]) ).

thf(f821,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(fool_elimination,[],[f820]) ).

thf(f820,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(rectify,[],[f199]) ).

thf(f199,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,ia),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),vAPP(formula_a,formula_a,vAPP(i,sTfun(formula_a,formula_a),vAPP(formula_a,sTfun(i,sTfun(formula_a,formula_a)),until_a,phi_1),i2),phi_2)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(f3916,plain,
    spl124_118,
    inference(avatar_split_clause,[],[f1398,f3913]) ).

thf(f1398,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)),
    inference(cnf_transformation,[],[f1202]) ).

thf(f1202,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f881,f1201]) ).

thf(f1201,plain,
    ( ? [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)) ) )
   => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),sK7)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f881,plain,
    ? [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)) ) ),
    inference(flattening,[],[f880]) ).

thf(f880,plain,
    ? [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)) ) ),
    inference(ennf_transformation,[],[f830]) ).

thf(f830,plain,
    ~ ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)) )
       => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ) ),
    inference(flattening,[],[f349]) ).

thf(f349,plain,
    ~ ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0)) )
       => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ) ),
    inference(fool_elimination,[],[f348]) ).

thf(f348,plain,
    ~ ! [X0: nat] :
        ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X0))
       => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)))
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    inference(rectify,[],[f244]) ).

thf(f244,axiom,
    ~ ! [X23: nat] :
        ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma),X23))
       => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)))
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(f3909,plain,
    spl124_117,
    inference(avatar_split_clause,[],[f1395,f3906]) ).

thf(f1395,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)),
    inference(cnf_transformation,[],[f1200]) ).

thf(f1200,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
    & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f879,f1199]) ).

thf(f1199,plain,
    ( ? [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)) ) )
   => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),sK6)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f879,plain,
    ? [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)) ) ),
    inference(flattening,[],[f878]) ).

thf(f878,plain,
    ? [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)) ) ),
    inference(ennf_transformation,[],[f829]) ).

thf(f829,plain,
    ~ ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)) )
       => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ) ),
    inference(flattening,[],[f347]) ).

thf(f347,plain,
    ~ ! [X0: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0)) )
       => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ) ),
    inference(fool_elimination,[],[f346]) ).

thf(f346,plain,
    ~ ! [X0: nat] :
        ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X0))
       => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)))
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    inference(rectify,[],[f243]) ).

thf(f243,axiom,
    ~ ! [X23: nat] :
        ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),one_one_nat)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),X23))
       => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)))
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X23),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(f3896,plain,
    spl124_116,
    inference(avatar_split_clause,[],[f1560,f3894]) ).

thf(f1560,plain,
    ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: trace_1367752404list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X2),X1) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f999]) ).

thf(f999,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X2),X1) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(flattening,[],[f998]) ).

thf(f998,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X2),X1) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f587]) ).

thf(f587,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) )
     => ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X2),X1) )
       => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
          | ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) ) ) ) ),
    inference(fool_elimination,[],[f586]) ).

thf(f586,plain,
    ! [X0: prefix1027212443list_a,X1: trace_1367752404list_a,X2: prefix1027212443list_a] :
      ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1)
     => ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X2),X1)
       => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0)
          | vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X2) ) ) ),
    inference(rectify,[],[f205]) ).

thf(f205,axiom,
    ! [X26: prefix1027212443list_a,X16: trace_1367752404list_a,X52: prefix1027212443list_a] :
      ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X26),X16)
     => ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X52),X16)
       => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X52),X26)
          | vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X26),X52) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_prefix__of__imp__linear) ).

thf(f3881,plain,
    spl124_115,
    inference(avatar_split_clause,[],[f1540,f3879]) ).

thf(f1540,plain,
    ! [X3: nat,X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X3) )
      | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) ),
    inference(cnf_transformation,[],[f1251]) ).

thf(f1251,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)) )
        & ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X3) ) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X1) ) )
      | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f1249,f1250]) ).

thf(f1250,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ? [X2: nat] :
          ( ( $true != vAPP(nat,$o,X0,X2) )
          & ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,X0,X3) )
              | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
     => ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)) )
        & ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X3) ) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X1) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1249,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ? [X2: nat] :
          ( ( $true != vAPP(nat,$o,X0,X2) )
          & ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,X0,X3) )
              | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) != $true ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
      | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) ),
    inference(rectify,[],[f1248]) ).

thf(f1248,plain,
    ! [X1: nat > $o,X0: nat] :
      ( ? [X4: nat] :
          ( ( $true != vAPP(nat,$o,X1,X4) )
          & ! [X5: nat] :
              ( ( $true = vAPP(nat,$o,X1,X5) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X0) ) )
      | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) ) ),
    inference(nnf_transformation,[],[f1195]) ).

thf(f1195,plain,
    ! [X1: nat > $o,X0: nat] :
      ( ? [X4: nat] :
          ( ( $true != vAPP(nat,$o,X1,X4) )
          & ! [X5: nat] :
              ( ( $true = vAPP(nat,$o,X1,X5) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X0) ) )
      | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f3684,plain,
    spl124_114,
    inference(avatar_split_clause,[],[f1691,f3682]) ).

thf(f3682,plain,
    ( spl124_114
  <=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
        ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
        | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_114])]) ).

thf(f1691,plain,
    ! [X2: nat,X3: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
      | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1155]) ).

thf(f1155,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
      | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1154]) ).

thf(f1154,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true )
      | ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f765]) ).

thf(f765,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
       => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) = $true ) ) ),
    inference(fool_elimination,[],[f764]) ).

thf(f764,plain,
    ! [X0: nat,X1: nat,X2: nat,X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3) )
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X3) ) ),
    inference(rectify,[],[f220]) ).

thf(f220,axiom,
    ! [X11: nat,X62: nat,X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X11),X62)
     => ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X11),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X62) )
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_less__add__eq__less) ).

thf(f3680,plain,
    spl124_113,
    inference(avatar_split_clause,[],[f1542,f3678]) ).

thf(f3678,plain,
    ( spl124_113
  <=> ! [X2: nat,X0: nat,X1: nat > $o] :
        ( ( $true = vAPP(nat,$o,X1,X2) )
        | ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_113])]) ).

thf(f1542,plain,
    ! [X2: nat,X0: nat,X1: nat > $o] :
      ( ( $true = vAPP(nat,$o,X1,X2) )
      | ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) ) ),
    inference(cnf_transformation,[],[f1253]) ).

thf(f1253,plain,
    ! [X0: nat,X1: nat > $o,X2: nat] :
      ( ( $true = vAPP(nat,$o,X1,X2) )
      | ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) )
      | ( ( $true != vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f1196,f1252]) ).

thf(f1252,plain,
    ! [X0: nat,X1: nat > $o] :
      ( ? [X3: nat] :
          ( ( $true != vAPP(nat,$o,X1,X3) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X3) ) )
     => ( ( $true != vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1196,plain,
    ! [X0: nat,X1: nat > $o,X2: nat] :
      ( ( $true = vAPP(nat,$o,X1,X2) )
      | ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) )
      | ? [X3: nat] :
          ( ( $true != vAPP(nat,$o,X1,X3) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X3) ) ) ),
    inference(definition_folding,[],[f988,f1195]) ).

thf(f988,plain,
    ! [X0: nat,X1: nat > $o,X2: nat] :
      ( ( $true = vAPP(nat,$o,X1,X2) )
      | ? [X4: nat] :
          ( ( $true != vAPP(nat,$o,X1,X4) )
          & ! [X5: nat] :
              ( ( $true = vAPP(nat,$o,X1,X5) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X0) ) )
      | ? [X3: nat] :
          ( ( $true != vAPP(nat,$o,X1,X3) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X3) ) ) ),
    inference(flattening,[],[f987]) ).

thf(f987,plain,
    ! [X0: nat,X1: nat > $o,X2: nat] :
      ( ( $true = vAPP(nat,$o,X1,X2) )
      | ? [X4: nat] :
          ( ( $true != vAPP(nat,$o,X1,X4) )
          & ! [X5: nat] :
              ( ( $true = vAPP(nat,$o,X1,X5) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) ) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X0) ) )
      | ? [X3: nat] :
          ( ( $true != vAPP(nat,$o,X1,X3) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X3) ) ) ),
    inference(ennf_transformation,[],[f575]) ).

thf(f575,plain,
    ! [X0: nat,X1: nat > $o,X2: nat] :
      ( ! [X3: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X3) )
         => ( $true = vAPP(nat,$o,X1,X3) ) )
     => ( ! [X4: nat] :
            ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X0) )
           => ( ! [X5: nat] :
                  ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5) )
                 => ( $true = vAPP(nat,$o,X1,X5) ) )
             => ( $true = vAPP(nat,$o,X1,X4) ) ) )
       => ( $true = vAPP(nat,$o,X1,X2) ) ) ),
    inference(fool_elimination,[],[f574]) ).

thf(f574,plain,
    ! [X0: nat,X1: nat > $o,X2: nat] :
      ( ! [X3: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X3)
         => vAPP(nat,$o,X1,X3) )
     => ( ! [X4: nat] :
            ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X4),X0)
           => ( ! [X5: nat] :
                  ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X4),X5)
                 => vAPP(nat,$o,X1,X5) )
             => vAPP(nat,$o,X1,X4) ) )
       => vAPP(nat,$o,X1,X2) ) ),
    inference(rectify,[],[f50]) ).

thf(f50,axiom,
    ! [X1: nat,X4: nat > $o,X0: nat] :
      ( ! [X33: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X33)
         => vAPP(nat,$o,X4,X33) )
     => ( ! [X33: nat] :
            ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X33),X1)
           => ( ! [X34: nat] :
                  ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X33),X34)
                 => vAPP(nat,$o,X4,X34) )
             => vAPP(nat,$o,X4,X33) ) )
       => vAPP(nat,$o,X4,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__descend__induct) ).

thf(f3649,plain,
    spl124_112,
    inference(avatar_split_clause,[],[f1557,f3647]) ).

thf(f3647,plain,
    ( spl124_112
  <=> ! [X2: nat,X0: nat > $o,X1: nat] :
        ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)),X2) )
        | ( $true != vAPP(nat,$o,X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_112])]) ).

thf(f1557,plain,
    ! [X2: nat,X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)),X2) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(cnf_transformation,[],[f1270]) ).

thf(f3434,plain,
    spl124_111,
    inference(avatar_split_clause,[],[f1616,f3432]) ).

thf(f3432,plain,
    ( spl124_111
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_111])]) ).

thf(f1616,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
    inference(cnf_transformation,[],[f1077]) ).

thf(f1077,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
    inference(ennf_transformation,[],[f685]) ).

thf(f685,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
    inference(fool_elimination,[],[f684]) ).

thf(f684,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ),
    inference(rectify,[],[f278]) ).

thf(f278,axiom,
    ! [X35: nat,X42: nat,X12: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X42)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),X42))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_add__less__imp__less__right) ).

thf(f3430,plain,
    spl124_110,
    inference(avatar_split_clause,[],[f1615,f3428]) ).

thf(f3428,plain,
    ( spl124_110
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_110])]) ).

thf(f1615,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
    inference(cnf_transformation,[],[f1076]) ).

thf(f1076,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
    inference(ennf_transformation,[],[f683]) ).

thf(f683,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
    inference(fool_elimination,[],[f682]) ).

thf(f682,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ),
    inference(rectify,[],[f277]) ).

thf(f277,axiom,
    ! [X42: nat,X35: nat,X12: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X35)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X12))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_add__less__imp__less__left) ).

thf(f3426,plain,
    spl124_109,
    inference(avatar_split_clause,[],[f1614,f3424]) ).

thf(f3424,plain,
    ( spl124_109
  <=> ! [X2: nat,X0: trace_1367752404list_a,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_109])]) ).

thf(f1614,plain,
    ! [X2: nat,X0: trace_1367752404list_a,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) ) ),
    inference(cnf_transformation,[],[f1075]) ).

thf(f1075,plain,
    ! [X0: trace_1367752404list_a,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) ) ),
    inference(ennf_transformation,[],[f681]) ).

thf(f681,plain,
    ! [X0: trace_1367752404list_a,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
    inference(fool_elimination,[],[f680]) ).

thf(f680,plain,
    ! [X0: trace_1367752404list_a,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X1)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X0),X2))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ),
    inference(rectify,[],[f217]) ).

thf(f217,axiom,
    ! [X16: trace_1367752404list_a,X9: nat,X10: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X16),X9)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X16),X10))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_less___092_060tau_062D) ).

thf(f3422,plain,
    spl124_108,
    inference(avatar_split_clause,[],[f1613,f3420]) ).

thf(f3420,plain,
    ( spl124_108
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_108])]) ).

thf(f1613,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
    inference(cnf_transformation,[],[f1074]) ).

thf(f1074,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) ) ),
    inference(ennf_transformation,[],[f679]) ).

thf(f679,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
    inference(fool_elimination,[],[f678]) ).

thf(f678,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ),
    inference(rectify,[],[f269]) ).

thf(f269,axiom,
    ! [X42: nat,X35: nat,X12: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X35)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X12))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_add__le__imp__le__left) ).

thf(f3418,plain,
    spl124_107,
    inference(avatar_split_clause,[],[f1612,f3416]) ).

thf(f3416,plain,
    ( spl124_107
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_107])]) ).

thf(f1612,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
    inference(cnf_transformation,[],[f1073]) ).

thf(f1073,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
    inference(ennf_transformation,[],[f677]) ).

thf(f677,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
    inference(fool_elimination,[],[f676]) ).

thf(f676,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ),
    inference(rectify,[],[f270]) ).

thf(f270,axiom,
    ! [X35: nat,X42: nat,X12: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X42)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),X42))
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_add__le__imp__le__right) ).

thf(f3414,plain,
    spl124_106,
    inference(avatar_split_clause,[],[f1604,f3412]) ).

thf(f1604,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1065]) ).

thf(f1065,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f663]) ).

thf(f663,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
    inference(fool_elimination,[],[f662]) ).

thf(f662,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
    inference(rectify,[],[f276]) ).

thf(f276,axiom,
    ! [X35: nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X42)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_add__strict__right__mono) ).

thf(f3410,plain,
    spl124_105,
    inference(avatar_split_clause,[],[f1603,f3408]) ).

thf(f1603,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1064]) ).

thf(f1064,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f661]) ).

thf(f661,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
    inference(fool_elimination,[],[f660]) ).

thf(f660,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
    inference(rectify,[],[f275]) ).

thf(f275,axiom,
    ! [X35: nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X35)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_add__strict__left__mono) ).

thf(f3406,plain,
    spl124_104,
    inference(avatar_split_clause,[],[f1585,f3404]) ).

thf(f3404,plain,
    ( spl124_104
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_104])]) ).

thf(f1585,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1043]) ).

thf(f1043,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f637]) ).

thf(f637,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
    inference(fool_elimination,[],[f636]) ).

thf(f636,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
    inference(rectify,[],[f265]) ).

thf(f265,axiom,
    ! [X35: nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X35)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X42),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_add__left__mono) ).

thf(f3386,plain,
    spl124_103,
    inference(avatar_split_clause,[],[f1583,f3384]) ).

thf(f3384,plain,
    ( spl124_103
  <=> ! [X2: nat,X0: nat,X1: nat] :
        ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_103])]) ).

thf(f1583,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1041]) ).

thf(f1041,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f633]) ).

thf(f633,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
    inference(fool_elimination,[],[f632]) ).

thf(f632,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
    inference(rectify,[],[f267]) ).

thf(f267,axiom,
    ! [X35: nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X42)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X12),X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_add__right__mono) ).

thf(f3382,plain,
    spl124_102,
    inference(avatar_split_clause,[],[f1582,f3380]) ).

thf(f1582,plain,
    ! [X2: trace_1367752404list_a,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1040]) ).

thf(f1040,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f631]) ).

thf(f631,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X1)) ) ),
    inference(fool_elimination,[],[f630]) ).

thf(f630,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X0)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X1)) ),
    inference(rectify,[],[f219]) ).

thf(f219,axiom,
    ! [X9: nat,X10: nat,X2: trace_1367752404list_a] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X10)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X9)),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218__092_060tau_062__mono) ).

thf(f3376,plain,
    spl124_101,
    inference(avatar_split_clause,[],[f2248,f3373]) ).

thf(f3373,plain,
    ( spl124_101
  <=> ( ord_less_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_101])]) ).

thf(f2248,plain,
    ord_less_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),vAPP(nat,sTfun(nat,nat),plus_plus_nat,one_one_nat)),
    inference(forward_demodulation,[],[f1389,f1382]) ).

thf(f1382,plain,
    plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat),
    inference(cnf_transformation,[],[f321]) ).

thf(f321,plain,
    plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat),
    inference(fool_elimination,[],[f320]) ).

thf(f320,plain,
    ( plus_plus_nat
    = ( ^ [X0: nat,X1: nat] : vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) ) ),
    inference(rectify,[],[f257]) ).

thf(f257,axiom,
    ( plus_plus_nat
    = ( ^ [X39: nat,X38: nat] : vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X38),X39) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add_Ocommute) ).

thf(f1389,plain,
    ord_less_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat),one_one_nat)),
    inference(cnf_transformation,[],[f335]) ).

thf(f335,plain,
    ord_less_nat = vAPP(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,ord_less_eq_nat),vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat),one_one_nat)),
    inference(fool_elimination,[],[f334]) ).

thf(f334,plain,
    ( ord_less_nat
    = ( ^ [X0: nat] : vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),one_one_nat)) ) ),
    inference(rectify,[],[f283]) ).

thf(f283,axiom,
    ( ord_less_nat
    = ( ^ [X39: nat] : vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X39),one_one_nat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_discrete) ).

thf(f3371,plain,
    spl124_100,
    inference(avatar_split_clause,[],[f1539,f3369]) ).

thf(f1539,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)),X1) )
      | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) ),
    inference(cnf_transformation,[],[f1251]) ).

thf(f3278,plain,
    spl124_99,
    inference(avatar_split_clause,[],[f1732,f3275]) ).

thf(f1732,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) = $true,
    inference(cnf_transformation,[],[f819]) ).

thf(f819,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)) = $true,
    inference(fool_elimination,[],[f818]) ).

thf(f818,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),
    inference(rectify,[],[f209]) ).

thf(f209,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),k)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,sigma2),ia)),b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_that) ).

thf(f3273,plain,
    spl124_98,
    inference(avatar_split_clause,[],[f1543,f3271]) ).

thf(f1543,plain,
    ! [X2: nat,X0: nat,X1: nat > $o] :
      ( ( $true = vAPP(nat,$o,X1,X2) )
      | ( $true = vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X0),X1) )
      | ( $true != vAPP(nat,$o,X1,vAPP(nat,nat,vAPP(sTfun(nat,$o),sTfun(nat,nat),sK28,X1),X0)) ) ),
    inference(cnf_transformation,[],[f1253]) ).

thf(f3269,plain,
    spl124_97,
    inference(avatar_split_clause,[],[f1518,f3267]) ).

thf(f3265,plain,
    spl124_96,
    inference(avatar_split_clause,[],[f1517,f3263]) ).

thf(f3191,plain,
    spl124_95,
    inference(avatar_split_clause,[],[f1618,f3189]) ).

thf(f1618,plain,
    ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0))) ),
    inference(cnf_transformation,[],[f1279]) ).

thf(f1279,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0))) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f687,f1278]) ).

thf(f1278,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a] :
      ( ? [X3: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3)) )
          & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0))) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f687,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a] :
    ? [X3: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3)) )
      & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ) ),
    inference(fool_elimination,[],[f686]) ).

thf(f686,plain,
    ! [X0: nat,X1: nat,X2: trace_1367752404list_a] :
    ? [X3: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X3))
      & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X3) ),
    inference(rectify,[],[f218]) ).

thf(f218,axiom,
    ! [X9: nat,X7: nat,X2: trace_1367752404list_a] :
    ? [X23: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),vAPP(nat,nat,vAPP(trace_1367752404list_a,sTfun(nat,nat),tau_Pr257024512list_a,X2),X23))
      & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X23) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_ex__le___092_060tau_062) ).

thf(f3187,plain,
    spl124_94,
    inference(avatar_split_clause,[],[f1556,f3185]) ).

thf(f1556,plain,
    ! [X2: nat,X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)) )
      | ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK43,X2),X0)) )
      | ( $true != vAPP(nat,$o,X0,X1) ) ),
    inference(cnf_transformation,[],[f1270]) ).

thf(f3163,plain,
    ( spl124_93
    | ~ spl124_11
    | ~ spl124_30 ),
    inference(avatar_split_clause,[],[f2496,f2450,f2331,f3161]) ).

thf(f2496,plain,
    ( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X0) )
    | ~ spl124_11
    | ~ spl124_30 ),
    inference(trivial_inequality_removal,[],[f2492]) ).

thf(f2492,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK21,X0)),X0) ) )
    | ~ spl124_11
    | ~ spl124_30 ),
    inference(superposition,[],[f2451,f2332]) ).

thf(f3106,plain,
    spl124_92,
    inference(avatar_split_clause,[],[f1598,f3104]) ).

thf(f1598,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1057]) ).

thf(f1057,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1056]) ).

thf(f1056,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f651]) ).

thf(f651,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ) ),
    inference(fool_elimination,[],[f650]) ).

thf(f650,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ),
    inference(rectify,[],[f141]) ).

thf(f141,axiom,
    ! [X12: nat,X35: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X12),X35)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X42),X12)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X42),X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_dual__order_Ostrict__trans) ).

thf(f3102,plain,
    spl124_91,
    inference(avatar_split_clause,[],[f1578,f3100]) ).

thf(f1578,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1035]) ).

thf(f1035,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1034]) ).

thf(f1034,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f623]) ).

thf(f623,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ) ),
    inference(fool_elimination,[],[f622]) ).

thf(f622,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ),
    inference(rectify,[],[f193]) ).

thf(f193,axiom,
    ! [X12: nat,X35: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X35)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X42),X12)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X42),X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_dual__order_Ostrict__trans1) ).

thf(f3098,plain,
    spl124_90,
    inference(avatar_split_clause,[],[f1577,f3096]) ).

thf(f1577,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1033]) ).

thf(f1033,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1032]) ).

thf(f1032,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f621]) ).

thf(f621,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ) ),
    inference(fool_elimination,[],[f620]) ).

thf(f620,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
    inference(rectify,[],[f185]) ).

thf(f185,axiom,
    ! [X35: nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X12),X42)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_order_Ostrict__trans1) ).

thf(f3094,plain,
    spl124_89,
    inference(avatar_split_clause,[],[f1573,f3092]) ).

thf(f1573,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1025]) ).

thf(f1025,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(flattening,[],[f1024]) ).

thf(f1024,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f613]) ).

thf(f613,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ) ),
    inference(fool_elimination,[],[f612]) ).

thf(f612,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
    inference(rectify,[],[f87]) ).

thf(f87,axiom,
    ! [X35: nat,X12: nat,X42: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X42)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_order_Otrans) ).

thf(f3090,plain,
    ( spl124_88
    | ~ spl124_11
    | ~ spl124_26 ),
    inference(avatar_split_clause,[],[f2468,f2434,f2331,f3088]) ).

thf(f2468,plain,
    ( ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,X0)) )
    | ~ spl124_11
    | ~ spl124_26 ),
    inference(trivial_inequality_removal,[],[f2464]) ).

thf(f2464,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,sK21,X0)) ) )
    | ~ spl124_11
    | ~ spl124_26 ),
    inference(superposition,[],[f2435,f2332]) ).

thf(f3086,plain,
    spl124_87,
    inference(avatar_split_clause,[],[f1569,f3084]) ).

thf(f1569,plain,
    ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1017]) ).

thf(f1017,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f1016]) ).

thf(f1016,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f605]) ).

thf(f605,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
       => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X1) ) ) ),
    inference(fool_elimination,[],[f604]) ).

thf(f604,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0)
       => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X1) ) ),
    inference(rectify,[],[f68]) ).

thf(f68,axiom,
    ! [X12: prefix1027212443list_a,X35: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X35)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X42),X12)
       => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X42),X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_dual__order_Otrans) ).

thf(f3082,plain,
    spl124_86,
    inference(avatar_split_clause,[],[f1565,f3080]) ).

thf(f1565,plain,
    ! [X2: trace_1367752404list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1009]) ).

thf(f1009,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: trace_1367752404list_a] :
      ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f1008]) ).

thf(f1008,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: trace_1367752404list_a] :
      ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) )
      | ( $true != vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f597]) ).

thf(f597,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: trace_1367752404list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2) )
       => ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) ) ) ),
    inference(fool_elimination,[],[f596]) ).

thf(f596,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: trace_1367752404list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X1),X2)
       => vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X2) ) ),
    inference(rectify,[],[f204]) ).

thf(f204,axiom,
    ! [X26: prefix1027212443list_a,X52: prefix1027212443list_a,X2: trace_1367752404list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X26),X52)
     => ( vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X52),X2)
       => vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X26),X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_prefix__of__antimono) ).

thf(f3078,plain,
    spl124_85,
    inference(avatar_split_clause,[],[f1562,f3076]) ).

thf(f1562,plain,
    ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1003]) ).

thf(f1003,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(flattening,[],[f1002]) ).

thf(f1002,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f591]) ).

thf(f591,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2) )
       => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) ) ) ),
    inference(fool_elimination,[],[f590]) ).

thf(f590,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X2)
       => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X2) ) ),
    inference(rectify,[],[f186]) ).

thf(f186,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X35),X12)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X42)
       => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X35),X42) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_order_Ostrict__trans2) ).

thf(f3074,plain,
    spl124_84,
    inference(avatar_split_clause,[],[f1561,f3072]) ).

thf(f1561,plain,
    ! [X2: prefix1027212443list_a,X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f1001]) ).

thf(f1001,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(flattening,[],[f1000]) ).

thf(f1000,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f589]) ).

thf(f589,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0) )
       => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) ) ) ),
    inference(fool_elimination,[],[f588]) ).

thf(f588,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a,X2: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X2),X0)
       => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X2),X1) ) ),
    inference(rectify,[],[f194]) ).

thf(f194,axiom,
    ! [X12: prefix1027212443list_a,X35: prefix1027212443list_a,X42: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X12),X35)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X42),X12)
       => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X42),X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_dual__order_Ostrict__trans2) ).

thf(f3062,plain,
    spl124_83,
    inference(avatar_split_clause,[],[f1541,f3060]) ).

thf(f1541,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK27,X1),X0)) )
      | ( $true != vAPP(sTfun(nat,$o),$o,vAPP(nat,sTfun(sTfun(nat,$o),$o),sP4,X1),X0) ) ),
    inference(cnf_transformation,[],[f1251]) ).

thf(f3013,plain,
    ( spl124_82
    | ~ spl124_3
    | ~ spl124_15 ),
    inference(avatar_split_clause,[],[f2360,f2347,f2264,f3011]) ).

thf(f2347,plain,
    ( spl124_15
  <=> ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_15])]) ).

thf(f2360,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X0)),X0) )
    | ~ spl124_3
    | ~ spl124_15 ),
    inference(trivial_inequality_removal,[],[f2359]) ).

thf(f2359,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X0)),X0) ) )
    | ~ spl124_3
    | ~ spl124_15 ),
    inference(superposition,[],[f2348,f2265]) ).

thf(f2348,plain,
    ( ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X2)),X2) )
    | ~ spl124_15 ),
    inference(avatar_component_clause,[],[f2347]) ).

thf(f2869,plain,
    spl124_81,
    inference(avatar_split_clause,[],[f1610,f2867]) ).

thf(f1610,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
    inference(cnf_transformation,[],[f1070]) ).

thf(f1070,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
    inference(ennf_transformation,[],[f673]) ).

thf(f673,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
    inference(fool_elimination,[],[f672]) ).

thf(f672,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ),
    inference(rectify,[],[f227]) ).

thf(f227,axiom,
    ! [X9: nat,X10: nat,X11: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X9),X10)),X11)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add__lessD1) ).

thf(f2865,plain,
    spl124_80,
    inference(avatar_split_clause,[],[f1607,f2863]) ).

thf(f1607,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
    inference(cnf_transformation,[],[f1067]) ).

thf(f1067,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
    inference(ennf_transformation,[],[f874]) ).

thf(f874,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
     => ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ) ),
    inference(flattening,[],[f667]) ).

thf(f667,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) )
     => ~ ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
         => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ) ),
    inference(fool_elimination,[],[f666]) ).

thf(f666,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2)
     => ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2)
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) ) ),
    inference(rectify,[],[f228]) ).

thf(f228,axiom,
    ! [X0: nat,X11: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X11)),X1)
     => ~ ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
         => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X11),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add__leE) ).

thf(f2861,plain,
    spl124_79,
    inference(avatar_split_clause,[],[f1606,f2859]) ).

thf(f1606,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X2) ) ),
    inference(cnf_transformation,[],[f1067]) ).

thf(f2857,plain,
    spl124_78,
    inference(avatar_split_clause,[],[f1602,f2855]) ).

thf(f1602,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1063]) ).

thf(f1063,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f659]) ).

thf(f659,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
    inference(fool_elimination,[],[f658]) ).

thf(f658,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
    inference(rectify,[],[f221]) ).

thf(f221,axiom,
    ! [X9: nat,X10: nat,X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X10)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_trans__less__add2) ).

thf(f2853,plain,
    spl124_77,
    inference(avatar_split_clause,[],[f1601,f2851]) ).

thf(f1601,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1062]) ).

thf(f1062,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f657]) ).

thf(f657,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
    inference(fool_elimination,[],[f656]) ).

thf(f656,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
    inference(rectify,[],[f222]) ).

thf(f222,axiom,
    ! [X9: nat,X10: nat,X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),X10)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X9),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X10),X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_trans__less__add1) ).

thf(f2849,plain,
    ( spl124_76
    | ~ spl124_3
    | ~ spl124_14 ),
    inference(avatar_split_clause,[],[f2358,f2343,f2264,f2847]) ).

thf(f2847,plain,
    ( spl124_76
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK10,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_76])]) ).

thf(f2343,plain,
    ( spl124_14
  <=> ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK10,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_14])]) ).

thf(f2358,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK10,X0)) )
    | ~ spl124_3
    | ~ spl124_14 ),
    inference(trivial_inequality_removal,[],[f2357]) ).

thf(f2357,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK10,X0)) ) )
    | ~ spl124_3
    | ~ spl124_14 ),
    inference(superposition,[],[f2344,f2265]) ).

thf(f2344,plain,
    ( ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK10,X2)) )
    | ~ spl124_14 ),
    inference(avatar_component_clause,[],[f2343]) ).

thf(f2845,plain,
    spl124_75,
    inference(avatar_split_clause,[],[f1581,f2843]) ).

thf(f1581,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1039]) ).

thf(f1039,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f629]) ).

thf(f629,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
    inference(fool_elimination,[],[f628]) ).

thf(f628,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ),
    inference(rectify,[],[f237]) ).

thf(f237,axiom,
    ! [X9: nat,X10: nat,X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X10)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_trans__le__add2) ).

thf(f2841,plain,
    spl124_74,
    inference(avatar_split_clause,[],[f1580,f2839]) ).

thf(f1580,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1038]) ).

thf(f1038,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f627]) ).

thf(f627,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
    inference(fool_elimination,[],[f626]) ).

thf(f626,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
    inference(rectify,[],[f236]) ).

thf(f236,axiom,
    ! [X9: nat,X10: nat,X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),X10)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X9),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X10),X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_trans__le__add1) ).

thf(f2837,plain,
    spl124_73,
    inference(avatar_split_clause,[],[f1487,f2835]) ).

thf(f1487,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1240]) ).

thf(f1240,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f957,f1239]) ).

thf(f1239,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
     => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK26,X1),X0)) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f957,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f515]) ).

thf(f515,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 ) ),
    inference(fool_elimination,[],[f514]) ).

thf(f514,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 ) ),
    inference(rectify,[],[f233]) ).

thf(f233,axiom,
    ! [X11: nat,X62: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X11),X62)
     => ? [X5: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X11),X5) = X62 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_le__Suc__ex) ).

thf(f2833,plain,
    spl124_72,
    inference(avatar_split_clause,[],[f1485,f2831]) ).

thf(f1485,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f1238]) ).

thf(f1238,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f955,f1237]) ).

thf(f1237,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
     => ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK25,X1),X0)) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f955,plain,
    ! [X0: nat,X1: nat] :
      ( ? [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) = X1 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f511]) ).

thf(f511,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ~ ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != X1 ) ),
    inference(fool_elimination,[],[f510]) ).

thf(f510,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ~ ! [X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2) != X1 ) ),
    inference(rectify,[],[f266]) ).

thf(f266,axiom,
    ! [X35: nat,X12: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
     => ~ ! [X36: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X36) != X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_less__eqE) ).

thf(f2797,plain,
    ( spl124_71
    | ~ spl124_3
    | ~ spl124_13 ),
    inference(avatar_split_clause,[],[f2356,f2339,f2264,f2795]) ).

thf(f2795,plain,
    ( spl124_71
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK9,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_71])]) ).

thf(f2339,plain,
    ( spl124_13
  <=> ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK9,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_13])]) ).

thf(f2356,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK9,X0)) )
    | ~ spl124_3
    | ~ spl124_13 ),
    inference(trivial_inequality_removal,[],[f2355]) ).

thf(f2355,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK9,X0)) ) )
    | ~ spl124_3
    | ~ spl124_13 ),
    inference(superposition,[],[f2340,f2265]) ).

thf(f2340,plain,
    ( ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK9,X2)) )
    | ~ spl124_13 ),
    inference(avatar_component_clause,[],[f2339]) ).

thf(f2769,plain,
    spl124_70,
    inference(avatar_split_clause,[],[f1731,f2766]) ).

thf(f1731,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(cnf_transformation,[],[f817]) ).

thf(f817,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(fool_elimination,[],[f816]) ).

thf(f816,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(f2764,plain,
    spl124_69,
    inference(avatar_split_clause,[],[f1730,f2761]) ).

thf(f1730,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(cnf_transformation,[],[f815]) ).

thf(f815,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(fool_elimination,[],[f814]) ).

thf(f814,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,i3),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).

thf(f2759,plain,
    spl124_68,
    inference(avatar_split_clause,[],[f1729,f2756]) ).

thf(f1729,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(cnf_transformation,[],[f813]) ).

thf(f813,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(fool_elimination,[],[f812]) ).

thf(f812,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(rectify,[],[f12]) ).

thf(f12,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(f2754,plain,
    spl124_67,
    inference(avatar_split_clause,[],[f1728,f2751]) ).

thf(f1728,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(cnf_transformation,[],[f811]) ).

thf(f811,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(fool_elimination,[],[f810]) ).

thf(f810,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(rectify,[],[f14]) ).

thf(f14,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,j),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(f2749,plain,
    spl124_66,
    inference(avatar_split_clause,[],[f1727,f2746]) ).

thf(f1727,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(cnf_transformation,[],[f809]) ).

thf(f809,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(fool_elimination,[],[f808]) ).

thf(f808,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(rectify,[],[f46]) ).

thf(f46,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(f2744,plain,
    spl124_65,
    inference(avatar_split_clause,[],[f1726,f2741]) ).

thf(f1726,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(cnf_transformation,[],[f807]) ).

thf(f807,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))) = $true,
    inference(fool_elimination,[],[f806]) ).

thf(f806,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(rectify,[],[f62]) ).

thf(f62,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,ja),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062) ).

thf(f2739,plain,
    ( spl124_64
    | ~ spl124_3
    | ~ spl124_12 ),
    inference(avatar_split_clause,[],[f2354,f2335,f2264,f2737]) ).

thf(f2335,plain,
    ( spl124_12
  <=> ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_12])]) ).

thf(f2354,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X0)),X0) )
    | ~ spl124_3
    | ~ spl124_12 ),
    inference(trivial_inequality_removal,[],[f2353]) ).

thf(f2353,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X0)),X0) ) )
    | ~ spl124_3
    | ~ spl124_12 ),
    inference(superposition,[],[f2336,f2265]) ).

thf(f2336,plain,
    ( ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X2)),X2) )
    | ~ spl124_12 ),
    inference(avatar_component_clause,[],[f2335]) ).

thf(f2735,plain,
    spl124_63,
    inference(avatar_split_clause,[],[f1400,f2732]) ).

thf(f1400,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(cnf_transformation,[],[f1202]) ).

thf(f2730,plain,
    spl124_62,
    inference(avatar_split_clause,[],[f1399,f2727]) ).

thf(f1399,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK7),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(cnf_transformation,[],[f1202]) ).

thf(f2725,plain,
    spl124_61,
    inference(avatar_split_clause,[],[f1397,f2722]) ).

thf(f1397,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_2),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(cnf_transformation,[],[f1200]) ).

thf(f2720,plain,
    spl124_60,
    inference(avatar_split_clause,[],[f1396,f2717]) ).

thf(f1396,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,sK6),vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,sigma2),phi_1),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi))),
    inference(cnf_transformation,[],[f1200]) ).

thf(f2694,plain,
    spl124_59,
    inference(avatar_split_clause,[],[f1534,f2692]) ).

thf(f1534,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1247]) ).

thf(f1247,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X2),X1),X0) ) ),
    inference(rectify,[],[f1246]) ).

thf(f1246,plain,
    ! [X2: nat,X1: nat,X0: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X2) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X0),X1),X2) ) ),
    inference(nnf_transformation,[],[f1190]) ).

thf(f2690,plain,
    spl124_58,
    inference(avatar_split_clause,[],[f1533,f2688]) ).

thf(f1533,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP0,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1247]) ).

thf(f2686,plain,
    spl124_57,
    inference(avatar_split_clause,[],[f1532,f2684]) ).

thf(f1532,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1245]) ).

thf(f1245,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X2),X1),X0) ) ),
    inference(rectify,[],[f1244]) ).

thf(f1244,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X1),X0),X2) ) ),
    inference(nnf_transformation,[],[f1191]) ).

thf(f2682,plain,
    spl124_56,
    inference(avatar_split_clause,[],[f1531,f2680]) ).

thf(f1531,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP1,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1245]) ).

thf(f2678,plain,
    spl124_55,
    inference(avatar_split_clause,[],[f1530,f2676]) ).

thf(f1530,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1243]) ).

thf(f1243,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ),
    inference(rectify,[],[f1242]) ).

thf(f1242,plain,
    ! [X1: nat,X2: nat,X0: nat] :
      ( ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X0),X2),X1) ) ),
    inference(nnf_transformation,[],[f1192]) ).

thf(f2674,plain,
    spl124_54,
    inference(avatar_split_clause,[],[f1529,f2672]) ).

thf(f1529,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP2,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1243]) ).

thf(f2670,plain,
    spl124_53,
    inference(avatar_split_clause,[],[f1528,f2668]) ).

thf(f1528,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1241]) ).

thf(f1241,plain,
    ! [X0: nat,X1: nat,X2: nat] :
      ( ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
        & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
    inference(nnf_transformation,[],[f1193]) ).

thf(f2662,plain,
    spl124_52,
    inference(avatar_split_clause,[],[f1527,f2660]) ).

thf(f1527,plain,
    ! [X2: nat,X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),sP3,X2),X1),X0) ) ),
    inference(cnf_transformation,[],[f1241]) ).

thf(f2658,plain,
    spl124_51,
    inference(avatar_split_clause,[],[f1475,f2656]) ).

thf(f1475,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f938]) ).

thf(f938,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f491]) ).

thf(f491,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) ) ),
    inference(fool_elimination,[],[f490]) ).

thf(f490,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X0)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X1)) ),
    inference(rectify,[],[f197]) ).

thf(f197,axiom,
    ! [X26: prefix1027212443list_a,X52: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X26),X52)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X26)),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,X52)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_plen__mono) ).

thf(f2645,plain,
    spl124_50,
    inference(avatar_split_clause,[],[f1462,f2643]) ).

thf(f1462,plain,
    ! [X3: nat,X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( $true = vAPP(nat,$o,X0,X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK24,X0)) ) ),
    inference(cnf_transformation,[],[f1236]) ).

thf(f1236,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) )
        & ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK24,X0)) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f921,f1235]) ).

thf(f1235,plain,
    ! [X0: nat > $o] :
      ( ? [X2: nat] :
          ( ( $true != vAPP(nat,$o,X0,X2) )
          & ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,X0,X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) ) )
     => ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) )
        & ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK24,X0)) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f921,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ? [X2: nat] :
          ( ( $true != vAPP(nat,$o,X0,X2) )
          & ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,X0,X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) ) ) ),
    inference(ennf_transformation,[],[f467]) ).

thf(f467,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ! [X2: nat] :
          ( ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
             => ( $true = vAPP(nat,$o,X0,X3) ) )
         => ( $true = vAPP(nat,$o,X0,X2) ) )
     => ( $true = vAPP(nat,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f466]) ).

thf(f466,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ! [X2: nat] :
          ( ! [X3: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2)
             => vAPP(nat,$o,X0,X3) )
         => vAPP(nat,$o,X0,X2) )
     => vAPP(nat,$o,X0,X1) ),
    inference(rectify,[],[f9]) ).

thf(f9,axiom,
    ! [X4: nat > $o,X1: nat] :
      ( ! [X5: nat] :
          ( ! [X6: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X5)
             => vAPP(nat,$o,X4,X6) )
         => vAPP(nat,$o,X4,X5) )
     => vAPP(nat,$o,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_nat__less__induct) ).

thf(f2641,plain,
    spl124_49,
    inference(avatar_split_clause,[],[f1460,f2639]) ).

thf(f1460,plain,
    ! [X3: nat,X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( $true = vAPP(nat,$o,X0,X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK23,X0)) ) ),
    inference(cnf_transformation,[],[f1234]) ).

thf(f1234,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK23,X0)) )
        & ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK23,X0)) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f920,f1233]) ).

thf(f1233,plain,
    ! [X0: nat > $o] :
      ( ? [X2: nat] :
          ( ( $true != vAPP(nat,$o,X0,X2) )
          & ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,X0,X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) ) )
     => ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK23,X0)) )
        & ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK23,X0)) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f920,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ? [X2: nat] :
          ( ( $true != vAPP(nat,$o,X0,X2) )
          & ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,X0,X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) ) ) ),
    inference(ennf_transformation,[],[f465]) ).

thf(f465,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ! [X2: nat] :
          ( ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) )
             => ( $true = vAPP(nat,$o,X0,X3) ) )
         => ( $true = vAPP(nat,$o,X0,X2) ) )
     => ( $true = vAPP(nat,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f464]) ).

thf(f464,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ! [X2: nat] :
          ( ! [X3: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2)
             => vAPP(nat,$o,X0,X3) )
         => vAPP(nat,$o,X0,X2) )
     => vAPP(nat,$o,X0,X1) ),
    inference(rectify,[],[f131]) ).

thf(f131,axiom,
    ! [X4: nat > $o,X35: nat] :
      ( ! [X14: nat] :
          ( ! [X15: nat] :
              ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X15),X14)
             => vAPP(nat,$o,X4,X15) )
         => vAPP(nat,$o,X4,X14) )
     => vAPP(nat,$o,X4,X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__induct) ).

thf(f2637,plain,
    spl124_48,
    inference(avatar_split_clause,[],[f1459,f2635]) ).

thf(f1459,plain,
    ! [X3: nat,X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( $true = vAPP(nat,$o,X0,X3) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK22,X0)) ) ),
    inference(cnf_transformation,[],[f1232]) ).

thf(f1232,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK22,X0)) ) )
        & ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK22,X0)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f919,f1231]) ).

thf(f1231,plain,
    ! [X0: nat > $o] :
      ( ? [X2: nat] :
          ( ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,X0,X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) )
          & ( $true != vAPP(nat,$o,X0,X2) ) )
     => ( ! [X3: nat] :
            ( ( $true = vAPP(nat,$o,X0,X3) )
            | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),vAPP(sTfun(nat,$o),nat,sK22,X0)) ) )
        & ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK22,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f919,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ? [X2: nat] :
          ( ! [X3: nat] :
              ( ( $true = vAPP(nat,$o,X0,X3) )
              | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) )
          & ( $true != vAPP(nat,$o,X0,X2) ) ) ),
    inference(ennf_transformation,[],[f850]) ).

thf(f850,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,X0,X2) )
         => ? [X3: nat] :
              ( ( $true != vAPP(nat,$o,X0,X3) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) ) )
     => ( $true = vAPP(nat,$o,X0,X1) ) ),
    inference(flattening,[],[f463]) ).

thf(f463,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,X0,X2) )
         => ? [X3: nat] :
              ( ( $true != vAPP(nat,$o,X0,X3) )
              & ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) ) )
     => ( $true = vAPP(nat,$o,X0,X1) ) ),
    inference(fool_elimination,[],[f462]) ).

thf(f462,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ! [X2: nat] :
          ( ~ vAPP(nat,$o,X0,X2)
         => ? [X3: nat] :
              ( ~ vAPP(nat,$o,X0,X3)
              & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X2) ) )
     => vAPP(nat,$o,X0,X1) ),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    ! [X4: nat > $o,X1: nat] :
      ( ! [X5: nat] :
          ( ~ vAPP(nat,$o,X4,X5)
         => ? [X6: nat] :
              ( ~ vAPP(nat,$o,X4,X6)
              & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X6),X5) ) )
     => vAPP(nat,$o,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_infinite__descent) ).

thf(f2621,plain,
    ( spl124_47
    | ~ spl124_3
    | ~ spl124_36 ),
    inference(avatar_split_clause,[],[f2577,f2527,f2264,f2619]) ).

thf(f2619,plain,
    ( spl124_47
  <=> ! [X0: prefix1027212443list_a] : ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_47])]) ).

thf(f2527,plain,
    ( spl124_36
  <=> ! [X0: prefix1027212443list_a] : ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_36])]) ).

thf(f2577,plain,
    ( ! [X0: prefix1027212443list_a] : ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X0) )
    | ~ spl124_3
    | ~ spl124_36 ),
    inference(trivial_inequality_removal,[],[f2576]) ).

thf(f2576,plain,
    ( ! [X0: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $false = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X0) ) )
    | ~ spl124_3
    | ~ spl124_36 ),
    inference(superposition,[],[f2528,f2265]) ).

thf(f2528,plain,
    ( ! [X0: prefix1027212443list_a] : ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X0) )
    | ~ spl124_36 ),
    inference(avatar_component_clause,[],[f2527]) ).

thf(f2617,plain,
    spl124_46,
    inference(avatar_split_clause,[],[f1619,f2615]) ).

thf(f1619,plain,
    ! [X2: nat,X0: trace_1367752404list_a,X1: formula_a] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),X2) ),
    inference(cnf_transformation,[],[f689]) ).

thf(f689,plain,
    ! [X0: trace_1367752404list_a,X1: formula_a,X2: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),X2) ),
    inference(fool_elimination,[],[f688]) ).

thf(f688,plain,
    ! [X0: trace_1367752404list_a,X1: formula_a,X2: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X0),X1),X2)),X2),
    inference(rectify,[],[f21]) ).

thf(f21,axiom,
    ! [X16: trace_1367752404list_a,X17: formula_a,X10: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,vAPP(nat,nat,vAPP(formula_a,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(formula_a,sTfun(nat,nat)),monito1457594016ress_a,X16),X17),X10)),X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_progress__le) ).

thf(f2613,plain,
    spl124_45,
    inference(avatar_split_clause,[],[f1617,f2611]) ).

thf(f1617,plain,
    ! [X2: trace_1367752404list_a,X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(trace_1367752404list_a,sTfun(nat,sTfun(nat,nat)),sK46,X2),X1),X0)) ),
    inference(cnf_transformation,[],[f1279]) ).

thf(f2575,plain,
    spl124_44,
    inference(avatar_split_clause,[],[f1423,f2573]) ).

thf(f1423,plain,
    ! [X2: nat,X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK19,X0)),X2) ) ),
    inference(cnf_transformation,[],[f1226]) ).

thf(f1226,plain,
    ! [X0: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK19,X0)),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f898,f1225]) ).

thf(f1225,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) )
     => ! [X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK19,X0)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f898,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
    inference(ennf_transformation,[],[f395]) ).

thf(f395,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
    inference(fool_elimination,[],[f394]) ).

thf(f394,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ),
    inference(rectify,[],[f39]) ).

thf(f39,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_pinf_I7_J) ).

thf(f2571,plain,
    spl124_43,
    inference(avatar_split_clause,[],[f1422,f2569]) ).

thf(f1422,plain,
    ! [X2: nat,X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK18,X0)) ) ),
    inference(cnf_transformation,[],[f1224]) ).

thf(f1224,plain,
    ! [X0: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK18,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f897,f1223]) ).

thf(f1223,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
     => ! [X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK18,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f897,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ),
    inference(ennf_transformation,[],[f393]) ).

thf(f393,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) ),
    inference(fool_elimination,[],[f392]) ).

thf(f392,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ),
    inference(rectify,[],[f44]) ).

thf(f44,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X19)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_minf_I5_J) ).

thf(f2567,plain,
    spl124_42,
    inference(avatar_split_clause,[],[f1421,f2565]) ).

thf(f1421,plain,
    ! [X2: nat,X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK17,X0)),X2) ) ),
    inference(cnf_transformation,[],[f1222]) ).

thf(f1222,plain,
    ! [X0: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK17,X0)),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f896,f1221]) ).

thf(f1221,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) )
     => ! [X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK17,X0)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f896,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
    inference(ennf_transformation,[],[f391]) ).

thf(f391,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
    inference(fool_elimination,[],[f390]) ).

thf(f390,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ),
    inference(rectify,[],[f24]) ).

thf(f24,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_pinf_I8_J) ).

thf(f2563,plain,
    spl124_41,
    inference(avatar_split_clause,[],[f1420,f2561]) ).

thf(f1420,plain,
    ! [X2: nat,X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK16,X0)) ) ),
    inference(cnf_transformation,[],[f1220]) ).

thf(f1220,plain,
    ! [X0: nat,X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK16,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f895,f1219]) ).

thf(f1219,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
     => ! [X2: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK16,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f895,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ),
    inference(ennf_transformation,[],[f389]) ).

thf(f389,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) ),
    inference(fool_elimination,[],[f388]) ).

thf(f388,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ),
    inference(rectify,[],[f25]) ).

thf(f25,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X19)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X20),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_minf_I6_J) ).

thf(f2559,plain,
    spl124_40,
    inference(avatar_split_clause,[],[f1419,f2557]) ).

thf(f1419,plain,
    ! [X2: nat,X0: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK15,X0)),X2) ) ),
    inference(cnf_transformation,[],[f1218]) ).

thf(f1218,plain,
    ! [X0: nat,X2: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK15,X0)),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f894,f1217]) ).

thf(f1217,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) )
     => ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK15,X0)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f894,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
    inference(ennf_transformation,[],[f839]) ).

thf(f839,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) ),
    inference(flattening,[],[f387]) ).

thf(f387,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ) ),
    inference(fool_elimination,[],[f386]) ).

thf(f386,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X0) ),
    inference(rectify,[],[f38]) ).

thf(f38,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_pinf_I5_J) ).

thf(f2555,plain,
    spl124_39,
    inference(avatar_split_clause,[],[f1418,f2553]) ).

thf(f1418,plain,
    ! [X2: nat,X0: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK14,X0)) ) ),
    inference(cnf_transformation,[],[f1216]) ).

thf(f1216,plain,
    ! [X0: nat,X2: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK14,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f893,f1215]) ).

thf(f1215,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
     => ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK14,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f893,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ),
    inference(ennf_transformation,[],[f838]) ).

thf(f838,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
    inference(flattening,[],[f385]) ).

thf(f385,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ) ),
    inference(fool_elimination,[],[f384]) ).

thf(f384,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X2) ),
    inference(rectify,[],[f45]) ).

thf(f45,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X19)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X3),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_minf_I7_J) ).

thf(f2551,plain,
    spl124_38,
    inference(avatar_split_clause,[],[f1417,f2549]) ).

thf(f1417,plain,
    ! [X2: nat,X0: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X2) ) ),
    inference(cnf_transformation,[],[f1214]) ).

thf(f1214,plain,
    ! [X0: nat,X2: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f892,f1213]) ).

thf(f1213,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) )
     => ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK13,X0)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f892,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
    inference(ennf_transformation,[],[f837]) ).

thf(f837,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) ),
    inference(flattening,[],[f383]) ).

thf(f383,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ) ),
    inference(fool_elimination,[],[f382]) ).

thf(f382,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X2),X0) ),
    inference(rectify,[],[f23]) ).

thf(f23,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X20),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_pinf_I6_J) ).

thf(f2547,plain,
    spl124_37,
    inference(avatar_split_clause,[],[f1416,f2545]) ).

thf(f1416,plain,
    ! [X2: nat,X0: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK12,X0)) ) ),
    inference(cnf_transformation,[],[f1212]) ).

thf(f1212,plain,
    ! [X0: nat,X2: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK12,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f891,f1211]) ).

thf(f1211,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
     => ! [X2: nat] :
          ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK12,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f891,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ),
    inference(ennf_transformation,[],[f836]) ).

thf(f836,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
    inference(flattening,[],[f381]) ).

thf(f381,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
     => ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ) ),
    inference(fool_elimination,[],[f380]) ).

thf(f380,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X2) ),
    inference(rectify,[],[f26]) ).

thf(f26,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X19)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X3),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_minf_I8_J) ).

thf(f2529,plain,
    ( spl124_36
    | ~ spl124_5
    | ~ spl124_28 ),
    inference(avatar_split_clause,[],[f2478,f2442,f2302,f2527]) ).

thf(f2302,plain,
    ( spl124_5
  <=> ! [X0: prefix1027212443list_a] : ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_5])]) ).

thf(f2478,plain,
    ( ! [X0: prefix1027212443list_a] : ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X0) )
    | ~ spl124_5
    | ~ spl124_28 ),
    inference(trivial_inequality_removal,[],[f2475]) ).

thf(f2475,plain,
    ( ! [X0: prefix1027212443list_a] :
        ( ( $true != $true )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X0) ) )
    | ~ spl124_5
    | ~ spl124_28 ),
    inference(superposition,[],[f2443,f2303]) ).

thf(f2303,plain,
    ( ! [X0: prefix1027212443list_a] : ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X0) )
    | ~ spl124_5 ),
    inference(avatar_component_clause,[],[f2302]) ).

thf(f2513,plain,
    spl124_35,
    inference(avatar_split_clause,[],[f1471,f2511]) ).

thf(f2511,plain,
    ( spl124_35
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( X0 = X1 )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_35])]) ).

thf(f1471,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 = X1 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f932]) ).

thf(f932,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 = X1 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(flattening,[],[f931]) ).

thf(f931,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 = X1 )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f483]) ).

thf(f483,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0) )
       => ( X0 = X1 ) ) ),
    inference(fool_elimination,[],[f482]) ).

thf(f482,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X1),X0)
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f75]) ).

thf(f75,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),X12)
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X35)
       => ( X12 = X35 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_order__class_Oorder_Oantisym) ).

thf(f2509,plain,
    spl124_34,
    inference(avatar_split_clause,[],[f1445,f2507]) ).

thf(f1445,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f906]) ).

thf(f906,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f905]) ).

thf(f905,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f439]) ).

thf(f439,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
       => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) ) ),
    inference(fool_elimination,[],[f438]) ).

thf(f438,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) ) ),
    inference(rectify,[],[f53]) ).

thf(f53,axiom,
    ! [X35: nat,X12: nat] :
      ( ( X12 != X35 )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_order_Onot__eq__order__implies__strict) ).

thf(f2505,plain,
    spl124_33,
    inference(avatar_split_clause,[],[f1444,f2503]) ).

thf(f2503,plain,
    ( spl124_33
  <=> ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
        ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
        | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_33])]) ).

thf(f1444,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f904]) ).

thf(f904,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f903]) ).

thf(f903,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f437]) ).

thf(f437,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 != X1 )
     => ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
       => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ) ),
    inference(fool_elimination,[],[f436]) ).

thf(f436,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( X0 != X1 )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
       => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(rectify,[],[f52]) ).

thf(f52,axiom,
    ! [X35: prefix1027212443list_a,X12: prefix1027212443list_a] :
      ( ( X12 != X35 )
     => ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X35),X12)
       => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X35),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_order_Onot__eq__order__implies__strict) ).

thf(f2501,plain,
    spl124_32,
    inference(avatar_split_clause,[],[f1437,f2499]) ).

thf(f1437,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f840]) ).

thf(f840,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f423]) ).

thf(f423,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true )
      | ( X0 = X1 ) ),
    inference(fool_elimination,[],[f422]) ).

thf(f422,plain,
    ! [X0: nat,X1: nat] :
      ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
      | ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
      | ( X0 = X1 ) ),
    inference(rectify,[],[f201]) ).

thf(f201,axiom,
    ! [X35: nat,X12: nat] :
      ( ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X12),X35)
      | ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X35),X12)
      | ( X12 = X35 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_verit__la__disequality) ).

thf(f2472,plain,
    spl124_31,
    inference(avatar_split_clause,[],[f2246,f2470]) ).

thf(f2470,plain,
    ( spl124_31
  <=> ! [X0: nat,X1: nat] :
        ( ( X0 != X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_31])]) ).

thf(f2246,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) = $false ) ),
    inference(binary_proxy_clausification,[],[f2245]) ).

thf(f2245,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 != X1 )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
    inference(equality_proxy_clausification,[],[f2244]) ).

thf(f2244,plain,
    ! [X0: nat,X1: nat] :
      ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
    inference(not_proxy_clausification,[],[f2239]) ).

thf(f2239,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) )
      | ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0)) ) ),
    inference(binary_proxy_clausification,[],[f1431]) ).

thf(f2452,plain,
    spl124_30,
    inference(avatar_split_clause,[],[f1495,f2450]) ).

thf(f1495,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f965]) ).

thf(f965,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f853]) ).

thf(f853,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true ) ),
    inference(flattening,[],[f531]) ).

thf(f531,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true ) ),
    inference(fool_elimination,[],[f530]) ).

thf(f530,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ),
    inference(rectify,[],[f119]) ).

thf(f119,axiom,
    ! [X35: nat,X12: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X35),X12)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X12),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_order_Oasym) ).

thf(f2448,plain,
    spl124_29,
    inference(avatar_split_clause,[],[f1486,f2446]) ).

thf(f1486,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f956]) ).

thf(f956,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) != $true ) ),
    inference(ennf_transformation,[],[f852]) ).

thf(f852,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true ) ),
    inference(flattening,[],[f513]) ).

thf(f513,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) != $true ) ),
    inference(fool_elimination,[],[f512]) ).

thf(f512,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X0) ),
    inference(rectify,[],[f146]) ).

thf(f146,axiom,
    ! [X8: nat,X7: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X8),X7)
     => ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X7),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_leD) ).

thf(f2444,plain,
    spl124_28,
    inference(avatar_split_clause,[],[f1474,f2442]) ).

thf(f1474,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f937]) ).

thf(f937,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f851]) ).

thf(f851,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) ) ),
    inference(flattening,[],[f489]) ).

thf(f489,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
     => ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) ) ),
    inference(fool_elimination,[],[f488]) ).

thf(f488,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1)
     => ~ vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X1),X0) ),
    inference(rectify,[],[f145]) ).

thf(f145,axiom,
    ! [X8: prefix1027212443list_a,X7: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X8),X7)
     => ~ vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X7),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_leD) ).

thf(f2440,plain,
    spl124_27,
    inference(avatar_split_clause,[],[f1464,f2438]) ).

thf(f1464,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(cnf_transformation,[],[f922]) ).

thf(f922,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) )
      | ( $true != vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) ) ),
    inference(ennf_transformation,[],[f469]) ).

thf(f469,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1) )
     => ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ) ),
    inference(fool_elimination,[],[f468]) ).

thf(f468,plain,
    ! [X0: prefix1027212443list_a,X1: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X0),X1)
     => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X1) ),
    inference(rectify,[],[f54]) ).

thf(f54,axiom,
    ! [X12: prefix1027212443list_a,X35: prefix1027212443list_a] :
      ( vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le887097159list_a,X12),X35)
     => vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X12),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_dual__order_Ostrict__implies__order) ).

thf(f2436,plain,
    spl124_26,
    inference(avatar_split_clause,[],[f1449,f2434]) ).

thf(f1449,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ),
    inference(cnf_transformation,[],[f910]) ).

thf(f910,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true )
      | ( ( X0 != X1 )
        & ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) != $true ) ) ),
    inference(ennf_transformation,[],[f447]) ).

thf(f447,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 = X1 )
        | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ) )
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ),
    inference(fool_elimination,[],[f446]) ).

thf(f446,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 = X1 )
        | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
    inference(rectify,[],[f29]) ).

thf(f29,axiom,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 = X1 )
        | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_less__or__eq__imp__le) ).

thf(f2432,plain,
    spl124_25,
    inference(avatar_split_clause,[],[f1438,f2430]) ).

thf(f1438,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ),
    inference(cnf_transformation,[],[f425]) ).

thf(f425,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0) = $true )
      | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) = $true ) ),
    inference(fool_elimination,[],[f424]) ).

thf(f424,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),X0)
      | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X1) ),
    inference(rectify,[],[f91]) ).

thf(f91,axiom,
    ! [X7: nat,X8: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X8),X7)
      | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_linear) ).

thf(f2421,plain,
    spl124_24,
    inference(avatar_split_clause,[],[f1510,f2419]) ).

thf(f1510,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ),
    inference(cnf_transformation,[],[f561]) ).

thf(f561,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)) ),
    inference(fool_elimination,[],[f560]) ).

thf(f560,plain,
    ! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),
    inference(rectify,[],[f230]) ).

thf(f230,axiom,
    ! [X1: nat,X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_le__add2) ).

thf(f2417,plain,
    spl124_23,
    inference(avatar_split_clause,[],[f1509,f2415]) ).

thf(f1509,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ),
    inference(cnf_transformation,[],[f559]) ).

thf(f559,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) ),
    inference(fool_elimination,[],[f558]) ).

thf(f558,plain,
    ! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),
    inference(rectify,[],[f229]) ).

thf(f229,axiom,
    ! [X1: nat,X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_le__add1) ).

thf(f2413,plain,
    spl124_22,
    inference(avatar_split_clause,[],[f1508,f2411]) ).

thf(f1508,plain,
    ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
    inference(cnf_transformation,[],[f860]) ).

thf(f860,plain,
    ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
    inference(flattening,[],[f557]) ).

thf(f557,plain,
    ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) ),
    inference(fool_elimination,[],[f556]) ).

thf(f556,plain,
    ! [X0: nat,X1: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0),
    inference(rectify,[],[f225]) ).

thf(f225,axiom,
    ! [X9: nat,X10: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X9),X10)),X9),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__add__less1) ).

thf(f2409,plain,
    spl124_21,
    inference(avatar_split_clause,[],[f1507,f2407]) ).

thf(f1507,plain,
    ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ),
    inference(cnf_transformation,[],[f859]) ).

thf(f859,plain,
    ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ),
    inference(flattening,[],[f555]) ).

thf(f555,plain,
    ! [X0: nat,X1: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) ),
    inference(fool_elimination,[],[f554]) ).

thf(f554,plain,
    ! [X0: nat,X1: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1),
    inference(rectify,[],[f224]) ).

thf(f224,axiom,
    ! [X10: nat,X9: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X10),X9)),X9),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_not__add__less2) ).

thf(f2405,plain,
    spl124_20,
    inference(avatar_split_clause,[],[f1382,f2402]) ).

thf(f2402,plain,
    ( spl124_20
  <=> ( plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_20])]) ).

thf(f2384,plain,
    ( spl124_19
    | ~ spl124_3
    | ~ spl124_4 ),
    inference(avatar_split_clause,[],[f2320,f2298,f2264,f2382]) ).

thf(f2382,plain,
    ( spl124_19
  <=> ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_19])]) ).

thf(f2298,plain,
    ( spl124_4
  <=> ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_4])]) ).

thf(f2320,plain,
    ( ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) )
    | ~ spl124_3
    | ~ spl124_4 ),
    inference(trivial_inequality_removal,[],[f2319]) ).

thf(f2319,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ) )
    | ~ spl124_3
    | ~ spl124_4 ),
    inference(superposition,[],[f2299,f2265]) ).

thf(f2299,plain,
    ( ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) )
    | ~ spl124_4 ),
    inference(avatar_component_clause,[],[f2298]) ).

thf(f2372,plain,
    spl124_18,
    inference(avatar_split_clause,[],[f1463,f2370]) ).

thf(f1463,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) ) ),
    inference(cnf_transformation,[],[f1236]) ).

thf(f2368,plain,
    spl124_17,
    inference(avatar_split_clause,[],[f1461,f2366]) ).

thf(f1461,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK23,X0)) ) ),
    inference(cnf_transformation,[],[f1234]) ).

thf(f2364,plain,
    spl124_16,
    inference(avatar_split_clause,[],[f1458,f2362]) ).

thf(f1458,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( $true = vAPP(nat,$o,X0,X1) )
      | ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK22,X0)) ) ),
    inference(cnf_transformation,[],[f1232]) ).

thf(f2349,plain,
    spl124_15,
    inference(avatar_split_clause,[],[f1740,f2347]) ).

thf(f1740,plain,
    ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X2)),X2) ),
    inference(equality_resolution,[],[f1415]) ).

thf(f1415,plain,
    ! [X2: nat,X0: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X0)),X2) ) ),
    inference(cnf_transformation,[],[f1210]) ).

thf(f1210,plain,
    ! [X0: nat,X2: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X0)),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f890,f1209]) ).

thf(f1209,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( X0 != X2 )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) )
     => ! [X2: nat] :
          ( ( X0 != X2 )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK11,X0)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f890,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
    inference(ennf_transformation,[],[f379]) ).

thf(f379,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
     => ( X0 != X2 ) ),
    inference(fool_elimination,[],[f378]) ).

thf(f378,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
     => ( X0 != X2 ) ),
    inference(rectify,[],[f36]) ).

thf(f36,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
     => ( X3 != X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_pinf_I3_J) ).

thf(f2345,plain,
    spl124_14,
    inference(avatar_split_clause,[],[f1739,f2343]) ).

thf(f1739,plain,
    ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK10,X2)) ),
    inference(equality_resolution,[],[f1414]) ).

thf(f1414,plain,
    ! [X2: nat,X0: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK10,X0)) ) ),
    inference(cnf_transformation,[],[f1208]) ).

thf(f1208,plain,
    ! [X0: nat,X2: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK10,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f889,f1207]) ).

thf(f1207,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( X0 != X2 )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
     => ! [X2: nat] :
          ( ( X0 != X2 )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK10,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f889,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ),
    inference(ennf_transformation,[],[f377]) ).

thf(f377,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
     => ( X0 != X2 ) ),
    inference(fool_elimination,[],[f376]) ).

thf(f376,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1)
     => ( X0 != X2 ) ),
    inference(rectify,[],[f43]) ).

thf(f43,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X19)
     => ( X3 != X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_minf_I4_J) ).

thf(f2341,plain,
    spl124_13,
    inference(avatar_split_clause,[],[f1738,f2339]) ).

thf(f1738,plain,
    ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK9,X2)) ),
    inference(equality_resolution,[],[f1413]) ).

thf(f1413,plain,
    ! [X2: nat,X0: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK9,X0)) ) ),
    inference(cnf_transformation,[],[f1206]) ).

thf(f1206,plain,
    ! [X0: nat,X2: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK9,X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f888,f1205]) ).

thf(f1205,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( X0 != X2 )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) )
     => ! [X2: nat] :
          ( ( X0 != X2 )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),vAPP(nat,nat,sK9,X0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f888,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) ) ),
    inference(ennf_transformation,[],[f375]) ).

thf(f375,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1) )
     => ( X0 != X2 ) ),
    inference(fool_elimination,[],[f374]) ).

thf(f374,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X2),X1)
     => ( X0 != X2 ) ),
    inference(rectify,[],[f42]) ).

thf(f42,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X20),X19)
     => ( X3 != X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_minf_I3_J) ).

thf(f2337,plain,
    spl124_12,
    inference(avatar_split_clause,[],[f1737,f2335]) ).

thf(f1737,plain,
    ! [X2: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X2)),X2) ),
    inference(equality_resolution,[],[f1412]) ).

thf(f1412,plain,
    ! [X2: nat,X0: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X0)),X2) ) ),
    inference(cnf_transformation,[],[f1204]) ).

thf(f1204,plain,
    ! [X0: nat,X2: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X0)),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f887,f1203]) ).

thf(f1203,plain,
    ! [X0: nat] :
      ( ? [X1: nat] :
        ! [X2: nat] :
          ( ( X0 != X2 )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) )
     => ! [X2: nat] :
          ( ( X0 != X2 )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,vAPP(nat,nat,sK8,X0)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f887,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( X0 != X2 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) ) ),
    inference(ennf_transformation,[],[f373]) ).

thf(f373,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2) )
     => ( X0 != X2 ) ),
    inference(fool_elimination,[],[f372]) ).

thf(f372,plain,
    ! [X0: nat] :
    ? [X1: nat] :
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X2)
     => ( X0 != X2 ) ),
    inference(rectify,[],[f37]) ).

thf(f37,axiom,
    ! [X3: nat] :
    ? [X19: nat] :
    ! [X20: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X19),X20)
     => ( X3 != X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_pinf_I4_J) ).

thf(f2333,plain,
    spl124_11,
    inference(avatar_split_clause,[],[f1425,f2331]) ).

thf(f1425,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,X0)) ),
    inference(cnf_transformation,[],[f1230]) ).

thf(f1230,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f399,f1229]) ).

thf(f1229,plain,
    ! [X0: nat] :
      ( ? [X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),vAPP(nat,nat,sK21,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f399,plain,
    ! [X0: nat] :
    ? [X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1) = $true ),
    inference(fool_elimination,[],[f398]) ).

thf(f398,plain,
    ! [X0: nat] :
    ? [X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X1),
    inference(rectify,[],[f116]) ).

thf(f116,axiom,
    ! [X7: nat] :
    ? [X48: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X7),X48),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_gt__ex) ).

thf(f2329,plain,
    spl124_10,
    inference(avatar_split_clause,[],[f1424,f2327]) ).

thf(f1424,plain,
    ! [X0: prefix1027212443list_a] : ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),vAPP(prefix1027212443list_a,trace_1367752404list_a,sK20,X0)) ),
    inference(cnf_transformation,[],[f1228]) ).

thf(f1228,plain,
    ! [X0: prefix1027212443list_a] : ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),vAPP(prefix1027212443list_a,trace_1367752404list_a,sK20,X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f397,f1227]) ).

thf(f1227,plain,
    ! [X0: prefix1027212443list_a] :
      ( ? [X1: trace_1367752404list_a] : ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) )
     => ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),vAPP(prefix1027212443list_a,trace_1367752404list_a,sK20,X0)) ) ),
    introduced(choice_axiom,[]) ).

thf(f397,plain,
    ! [X0: prefix1027212443list_a] :
    ? [X1: trace_1367752404list_a] : ( $true = vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1) ),
    inference(fool_elimination,[],[f396]) ).

thf(f396,plain,
    ! [X0: prefix1027212443list_a] :
    ? [X1: trace_1367752404list_a] : vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X0),X1),
    inference(rectify,[],[f203]) ).

thf(f203,axiom,
    ! [X55: prefix1027212443list_a] :
    ? [X48: trace_1367752404list_a] : vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,X55),X48),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ex__prefix__of) ).

thf(f2325,plain,
    ( spl124_9
    | spl124_2
    | ~ spl124_3 ),
    inference(avatar_split_clause,[],[f2278,f2264,f2259,f2322]) ).

thf(f2259,plain,
    ( spl124_2
  <=> ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_2])]) ).

thf(f2278,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) = $false )
    | spl124_2
    | ~ spl124_3 ),
    inference(trivial_inequality_removal,[],[f2276]) ).

thf(f2276,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) = $false )
    | spl124_2
    | ~ spl124_3 ),
    inference(superposition,[],[f2261,f2265]) ).

thf(f2261,plain,
    ( ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) != $true )
    | spl124_2 ),
    inference(avatar_component_clause,[],[f2259]) ).

thf(f2318,plain,
    spl124_8,
    inference(avatar_split_clause,[],[f1725,f2315]) ).

thf(f1725,plain,
    vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma) = $true,
    inference(cnf_transformation,[],[f805]) ).

thf(f805,plain,
    vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma) = $true,
    inference(fool_elimination,[],[f804]) ).

thf(f804,plain,
    vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I1_J) ).

thf(f2313,plain,
    spl124_7,
    inference(avatar_split_clause,[],[f1724,f2310]) ).

thf(f1724,plain,
    vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma2) = $true,
    inference(cnf_transformation,[],[f803]) ).

thf(f803,plain,
    vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma2) = $true,
    inference(fool_elimination,[],[f802]) ).

thf(f802,plain,
    vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma2),
    inference(rectify,[],[f13]) ).

thf(f13,axiom,
    vAPP(trace_1367752404list_a,$o,vAPP(prefix1027212443list_a,sTfun(trace_1367752404list_a,$o),prefix1041802747list_a,pi),sigma2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_assms_I2_J) ).

thf(f2308,plain,
    spl124_6,
    inference(avatar_split_clause,[],[f1428,f2306]) ).

thf(f1428,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
    inference(cnf_transformation,[],[f405]) ).

thf(f405,plain,
    ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0) ),
    inference(fool_elimination,[],[f404]) ).

thf(f404,plain,
    ! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X0),X0),
    inference(rectify,[],[f48]) ).

thf(f48,axiom,
    ! [X7: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq_nat,X7),X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_order__refl) ).

thf(f2304,plain,
    spl124_5,
    inference(avatar_split_clause,[],[f1426,f2302]) ).

thf(f1426,plain,
    ! [X0: prefix1027212443list_a] : ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X0) ),
    inference(cnf_transformation,[],[f401]) ).

thf(f401,plain,
    ! [X0: prefix1027212443list_a] : ( $true = vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X0) ),
    inference(fool_elimination,[],[f400]) ).

thf(f400,plain,
    ! [X0: prefix1027212443list_a] : vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X0),X0),
    inference(rectify,[],[f47]) ).

thf(f47,axiom,
    ! [X7: prefix1027212443list_a] : vAPP(prefix1027212443list_a,$o,vAPP(prefix1027212443list_a,sTfun(prefix1027212443list_a,$o),ord_le699472955list_a,X7),X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_order__refl) ).

thf(f2300,plain,
    spl124_4,
    inference(avatar_split_clause,[],[f1407,f2298]) ).

thf(f1407,plain,
    ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
    inference(cnf_transformation,[],[f831]) ).

thf(f831,plain,
    ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
    inference(flattening,[],[f363]) ).

thf(f363,plain,
    ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0) ),
    inference(fool_elimination,[],[f362]) ).

thf(f362,plain,
    ! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X0),X0),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ! [X1: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_less__not__refl) ).

thf(f2266,plain,
    spl124_3,
    inference(avatar_split_clause,[],[f287,f2264]) ).

thf(f287,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f2262,plain,
    ~ spl124_2,
    inference(avatar_split_clause,[],[f1366,f2259]) ).

thf(f1366,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) != $true,
    inference(cnf_transformation,[],[f828]) ).

thf(f828,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) != $true,
    inference(flattening,[],[f289]) ).

thf(f289,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)) != $true,
    inference(fool_elimination,[],[f288]) ).

thf(f288,plain,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),
    inference(rectify,[],[f285]) ).

thf(f285,negated_conjecture,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),
    inference(negated_conjecture,[],[f284]) ).

thf(f284,conjecture,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_nat,k),vAPP(prefix1027212443list_a,nat,plen_P694648887list_a,pi)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(f2257,plain,
    ~ spl124_1,
    inference(avatar_split_clause,[],[f286,f2254]) ).

thf(f2254,plain,
    ( spl124_1
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl124_1])]) ).

thf(f286,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : ITP125^1 : TPTP v8.2.0. Released v7.5.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.33  % Computer : n005.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Sat May 18 18:38:38 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.34  % (418)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (423)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)
% 0.14/0.37  % (421)WARNING: value z3 for option sas not known
% 0.14/0.37  % (422)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (419)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (420)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (421)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)
% 0.14/0.37  % (424)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)
% 0.14/0.37  % (425)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)
% 0.14/0.40  % (425)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.40  % Exception at run slice level
% 0.14/0.40  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.41  % Exception at run slice level
% 0.19/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.41  % Exception at run slice level
% 0.19/0.41  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.42  % (426)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.43  % (427)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)
% 0.19/0.43  % (428)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)
% 0.19/0.45  % (426)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.46  % (427)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.46  % Exception at run slice level
% 0.19/0.46  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.47  % (429)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)
% 5.28/1.16  % (423)First to succeed.
% 6.25/1.24  % (423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-418"
% 6.25/1.25  % (423)Refutation found. Thanks to Tanya!
% 6.25/1.25  % SZS status Theorem for theBenchmark
% 6.25/1.25  % SZS output start Proof for theBenchmark
% See solution above
% 6.25/1.27  % (423)------------------------------
% 6.25/1.27  % (423)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.25/1.27  % (423)Termination reason: Refutation
% 6.25/1.27  
% 6.25/1.27  % (423)Memory used [KB]: 9615
% 6.25/1.27  % (423)Time elapsed: 0.878 s
% 6.25/1.27  % (423)Instructions burned: 3052 (million)
% 6.25/1.27  % (418)Success in time 0.929 s
%------------------------------------------------------------------------------