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