TSTP Solution File: ITP106^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP106^1 : 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 22:51:47 EDT 2024
% Result : Theorem 94.30s 13.80s
% Output : Refutation 94.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1493
% Syntax : Number of formulae : 6157 ( 590 unt; 130 typ; 0 def)
% Number of atoms : 94279 (11402 equ; 0 cnn)
% Maximal formula atoms : 42 ( 15 avg)
% Number of connectives : 30974 (13752 ~;14696 |; 312 &; 0 @)
% (1079 <=>;1135 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 6 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 254 ( 253 >; 1 *; 0 +; 0 <<)
% Number of symbols : 1194 (1191 usr;1091 con; 0-6 aty)
% Number of variables : 8814 ( 22 ^8527 !; 253 ?;8814 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
partia1993116613t_unit: $tType ).
thf(type_def_6,type,
set_Product_prod_a_a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
partia96731725t_unit: $tType ).
thf(type_def_9,type,
set_a: $tType ).
thf(type_def_10,type,
partia1833973666xt_a_b: $tType ).
thf(type_def_11,type,
a: $tType ).
thf(type_def_12,type,
int: $tType ).
thf(type_def_13,type,
nat: $tType ).
thf(type_def_14,type,
product_prod_a_a: $tType ).
thf(type_def_15,type,
b: $tType ).
thf(func_def_0,type,
partia1993116613t_unit: $tType ).
thf(func_def_1,type,
partia1833973666xt_a_b: $tType ).
thf(func_def_2,type,
partia96731725t_unit: $tType ).
thf(func_def_3,type,
set_Product_prod_a_a: $tType ).
thf(func_def_4,type,
product_prod_a_a: $tType ).
thf(func_def_5,type,
set_a: $tType ).
thf(func_def_6,type,
nat: $tType ).
thf(func_def_7,type,
int: $tType ).
thf(func_def_8,type,
b: $tType ).
thf(func_def_9,type,
a: $tType ).
thf(func_def_10,type,
partia206007992t_unit: partia1993116613t_unit > set_Product_prod_a_a ).
thf(func_def_11,type,
partia1955795460t_unit: partia96731725t_unit > set_a ).
thf(func_def_12,type,
partia1066395285xt_a_b: partia1833973666xt_a_b > set_a ).
thf(func_def_13,type,
units_a_Product_unit: partia96731725t_unit > set_a ).
thf(func_def_14,type,
units_a_ring_ext_a_b: partia1833973666xt_a_b > set_a ).
thf(func_def_15,type,
comm_g1684316527t_unit: partia96731725t_unit > $o ).
thf(func_def_16,type,
comm_g791708116xt_a_b: partia1833973666xt_a_b > $o ).
thf(func_def_17,type,
group_a_Product_unit: partia96731725t_unit > $o ).
thf(func_def_18,type,
group_a_ring_ext_a_b: partia1833973666xt_a_b > $o ).
thf(func_def_19,type,
mult_a_Product_unit: partia96731725t_unit > a > a > a ).
thf(func_def_20,type,
mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a ).
thf(func_def_21,type,
one_a_Product_unit: partia96731725t_unit > a ).
thf(func_def_22,type,
one_a_ring_ext_a_b: partia1833973666xt_a_b > a ).
thf(func_def_23,type,
units_873712258t_unit: partia96731725t_unit > partia96731725t_unit ).
thf(func_def_24,type,
units_1411277569xt_a_b: partia1833973666xt_a_b > partia96731725t_unit ).
thf(func_def_25,type,
minus_minus_int: int > int > int ).
thf(func_def_26,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_27,type,
plus_plus_int: int > int > int ).
thf(func_def_28,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_29,type,
uminus_uminus_int: int > int ).
thf(func_def_30,type,
suc: nat > nat ).
thf(func_def_31,type,
semiri2019852685at_int: nat > int ).
thf(func_def_32,type,
semiri1382578993at_nat: nat > nat ).
thf(func_def_33,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_34,type,
a_inv_a_b: partia1833973666xt_a_b > a > a ).
thf(func_def_35,type,
a_minus_a_b: partia1833973666xt_a_b > a > a > a ).
thf(func_def_36,type,
abelian_group_a_b: partia1833973666xt_a_b > $o ).
thf(func_def_37,type,
add_pow_a_b_int: partia1833973666xt_a_b > int > a > a ).
thf(func_def_38,type,
add_pow_a_b_nat: partia1833973666xt_a_b > nat > a > a ).
thf(func_def_39,type,
field_a_b: partia1833973666xt_a_b > $o ).
thf(func_def_40,type,
add_a_b: partia1833973666xt_a_b > a > a > a ).
thf(func_def_41,type,
more_a_b: partia1833973666xt_a_b > b ).
thf(func_def_42,type,
zero_a_b: partia1833973666xt_a_b > a ).
thf(func_def_43,type,
semiring_a_b: partia1833973666xt_a_b > $o ).
thf(func_def_44,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(func_def_45,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_46,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_47,type,
member_a: a > set_a > $o ).
thf(func_def_48,type,
r: partia1833973666xt_a_b ).
thf(func_def_49,type,
r2: a ).
thf(func_def_50,type,
r3: a ).
thf(func_def_51,type,
r4: a ).
thf(func_def_52,type,
rel: partia1993116613t_unit ).
thf(func_def_53,type,
s: a ).
thf(func_def_54,type,
s2: a ).
thf(func_def_55,type,
s3: a ).
thf(func_def_59,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_60,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_61,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_62,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_63,type,
vAND: $o > $o > $o ).
thf(func_def_64,type,
sP0: partia96731725t_unit > $o ).
thf(func_def_65,type,
sP1: partia96731725t_unit > $o ).
thf(func_def_66,type,
sP2: partia1833973666xt_a_b > $o ).
thf(func_def_67,type,
sP3: partia1833973666xt_a_b > $o ).
thf(func_def_68,type,
sP4: partia1833973666xt_a_b > $o ).
thf(func_def_69,type,
sP5: partia1833973666xt_a_b > $o ).
thf(func_def_70,type,
sP6: partia1833973666xt_a_b > $o ).
thf(func_def_71,type,
sK7: a ).
thf(func_def_72,type,
sK8: a ).
thf(func_def_73,type,
sK9: partia96731725t_unit > a ).
thf(func_def_74,type,
sK10: partia96731725t_unit > a ).
thf(func_def_75,type,
sK11: partia96731725t_unit > a ).
thf(func_def_76,type,
sK12: partia96731725t_unit > a ).
thf(func_def_77,type,
sK13: partia96731725t_unit > a ).
thf(func_def_78,type,
sK14: partia96731725t_unit > a ).
thf(func_def_79,type,
sK15: partia96731725t_unit > a ).
thf(func_def_80,type,
sK16: partia1833973666xt_a_b > a ).
thf(func_def_81,type,
sK17: partia1833973666xt_a_b > a ).
thf(func_def_82,type,
sK18: partia1833973666xt_a_b > a ).
thf(func_def_83,type,
sK19: partia1833973666xt_a_b > a ).
thf(func_def_84,type,
sK20: partia1833973666xt_a_b > a ).
thf(func_def_85,type,
sK21: partia1833973666xt_a_b > a ).
thf(func_def_86,type,
sK22: partia1833973666xt_a_b > a ).
thf(func_def_87,type,
sK23: partia1833973666xt_a_b > a ).
thf(func_def_88,type,
sK24: partia1833973666xt_a_b > a ).
thf(func_def_89,type,
sK25: partia1833973666xt_a_b > a ).
thf(func_def_90,type,
sK26: partia1833973666xt_a_b > a ).
thf(func_def_91,type,
sK27: partia1833973666xt_a_b > a ).
thf(func_def_92,type,
sK28: partia1833973666xt_a_b > a ).
thf(func_def_93,type,
sK29: partia1833973666xt_a_b > a ).
thf(func_def_94,type,
sK30: partia1833973666xt_a_b > a ).
thf(func_def_95,type,
sK31: partia1833973666xt_a_b > a ).
thf(func_def_96,type,
sK32: a > a ).
thf(func_def_97,type,
sK33: a > a ).
thf(func_def_98,type,
sK34: a > a ).
thf(func_def_99,type,
sK35: a > a ).
thf(func_def_100,type,
sK36: a > a ).
thf(func_def_101,type,
sK37: a > a ).
thf(func_def_102,type,
sK38: product_prod_a_a > a ).
thf(func_def_103,type,
sK39: product_prod_a_a > a ).
thf(func_def_104,type,
sK40: product_prod_a_a > a ).
thf(func_def_105,type,
sK41: product_prod_a_a > a ).
thf(func_def_106,type,
sK42: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a ).
thf(func_def_107,type,
sK43: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_108,type,
sK44: ( product_prod_a_a > $o ) > a ).
thf(func_def_109,type,
sK45: ( product_prod_a_a > $o ) > a ).
thf(func_def_110,type,
sK46: ( product_prod_a_a > $o ) > a ).
thf(func_def_111,type,
sK47: ( product_prod_a_a > $o ) > a ).
thf(func_def_112,type,
sK48: a > partia96731725t_unit > a ).
thf(func_def_113,type,
sK49: a > partia96731725t_unit > a ).
thf(func_def_114,type,
sK50: a > partia1833973666xt_a_b > a ).
thf(func_def_115,type,
sK51: a > partia1833973666xt_a_b > a ).
thf(func_def_116,type,
sK52: a > partia1833973666xt_a_b > a ).
thf(func_def_117,type,
sK53: ( nat > $o ) > nat ).
thf(func_def_119,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_120,type,
vOR: $o > $o > $o ).
thf(func_def_121,type,
vIMP: $o > $o > $o ).
thf(func_def_122,type,
vNOT: $o > $o ).
thf(f125238,plain,
$false,
inference(avatar_sat_refutation,[],[f1723,f1727,f1759,f1764,f1769,f1774,f1779,f1783,f1787,f1791,f1795,f1799,f1807,f1814,f1818,f1822,f1827,f1832,f1837,f1850,f1857,f1862,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1906,f1912,f1916,f1920,f1924,f1929,f1935,f1939,f1944,f1949,f1954,f1990,f1994,f1998,f2002,f2006,f2011,f2017,f2021,f2025,f2029,f2033,f2037,f2041,f2045,f2049,f2053,f2060,f2064,f2068,f2072,f2076,f2080,f2084,f2114,f2146,f2150,f2154,f2158,f2162,f2168,f2172,f2176,f2180,f2184,f2190,f2202,f2218,f2222,f2226,f2236,f2240,f2244,f2248,f2282,f2286,f2290,f2310,f2323,f2327,f2331,f2335,f2368,f2381,f2395,f2399,f2404,f2408,f2444,f2448,f2452,f2456,f2461,f2465,f2469,f2473,f2477,f2481,f2485,f2489,f2493,f2497,f2502,f3031,f3044,f3048,f3067,f3071,f3075,f3079,f3083,f3087,f3103,f3139,f3143,f3213,f3217,f3225,f3229,f3233,f3237,f3241,f3300,f3304,f3308,f3322,f3326,f3330,f3334,f3339,f3344,f3348,f3352,f3434,f3440,f3446,f3451,f3456,f3462,f3468,f3593,f3597,f3601,f3605,f3628,f3636,f3640,f3644,f3648,f3652,f3656,f3660,f3722,f3731,f3735,f3740,f3745,f3749,f3753,f3757,f3761,f3775,f3812,f3826,f3834,f3838,f3858,f3872,f3876,f3880,f3884,f3888,f3892,f3896,f3900,f3904,f3990,f4004,f4010,f4014,f4018,f4022,f4090,f4125,f4129,f4154,f4158,f4162,f4166,f4170,f4192,f4196,f4235,f4239,f4243,f4247,f4267,f4295,f4301,f4550,f4554,f4558,f4562,f4564,f4597,f4601,f4615,f4630,f4637,f4641,f4669,f4673,f4677,f4706,f4710,f4722,f4726,f4730,f4745,f4749,f4753,f4757,f4761,f4765,f4960,f4978,f4983,f4988,f5007,f5035,f5425,f5447,f5451,f5455,f5456,f5484,f5488,f5506,f5510,f5514,f5521,f5525,f5587,f5591,f5623,f5627,f5649,f5653,f5657,f5661,f5665,f5842,f5846,f5940,f5944,f5948,f5952,f5982,f5994,f5998,f6015,f6032,f6052,f6069,f6087,f6092,f6103,f6115,f6120,f6132,f6138,f6150,f6154,f6162,f6167,f6199,f6880,f7058,f7063,f7068,f7073,f7078,f7082,f7087,f7092,f7097,f7245,f7907,f9552,f9747,f9751,f9755,f9759,f9764,f9768,f9772,f9776,f9780,f9784,f9788,f9792,f9796,f9800,f9804,f9809,f9936,f9956,f9961,f9965,f9969,f9973,f9977,f9982,f9986,f9990,f9994,f10426,f10430,f10434,f10438,f10442,f10446,f10450,f10454,f10458,f10462,f10467,f10471,f10475,f10479,f10483,f10487,f10491,f10495,f10499,f10503,f10508,f10512,f13397,f14362,f14366,f14410,f14414,f14420,f14425,f14429,f14433,f14437,f14441,f14445,f14449,f14453,f14458,f14463,f14470,f14475,f14480,f15570,f15574,f15579,f16722,f16749,f16753,f16779,f16784,f16824,f16832,f16893,f16947,f16980,f16985,f16992,f16999,f17005,f17011,f17017,f17023,f17030,f17594,f17595,f17645,f17650,f17656,f17663,f17670,f17676,f17682,f17735,f17739,f17744,f17748,f17752,f17756,f17760,f17764,f17769,f17776,f17783,f17789,f17794,f17824,f17831,f17837,f17842,f17912,f18105,f18109,f18113,f18122,f18130,f18189,f18193,f18198,f18205,f18212,f18219,f18227,f18234,f18252,f18257,f18262,f18268,f18275,f18282,f18284,f18289,f18295,f18302,f18309,f18316,f18322,f18327,f18331,f18335,f18339,f18458,f18462,f18467,f18472,f18477,f18482,f18488,f18538,f18543,f18550,f18557,f18582,f18589,f18628,f18677,f18682,f18686,f18690,f18696,f18727,f18733,f18752,f18758,f18788,f18794,f18817,f18821,f18825,f18829,f18833,f18834,f18838,f18842,f18846,f18850,f18854,f18858,f18862,f18866,f18870,f18874,f18908,f18912,f18916,f18920,f18924,f18928,f18932,f18936,f18940,f18944,f18945,f19097,f19239,f19242,f19318,f19347,f19353,f19408,f19413,f19468,f19473,f19478,f19574,f19579,f19663,f19666,f19815,f19830,f19835,f19887,f19891,f19896,f19936,f20167,f20231,f20280,f20284,f20350,f20438,f20442,f20446,f20450,f20566,f20571,f20576,f20580,f20584,f20588,f20592,f20596,f20600,f20604,f20608,f20612,f20616,f20621,f20626,f20631,f20636,f21687,f27506,f27628,f27634,f27676,f27682,f27688,f27796,f27866,f27870,f27874,f27879,f27884,f27889,f27928,f27970,f27974,f27978,f27982,f28085,f28090,f28094,f28098,f28102,f28106,f28110,f28114,f28118,f28122,f28126,f28127,f28135,f28139,f28143,f28147,f28151,f28155,f28159,f28163,f28167,f28171,f28175,f30856,f30924,f30983,f31021,f31186,f31224,f31229,f31272,f31277,f31282,f31287,f31292,f35158,f35162,f35166,f35170,f35179,f35203,f35207,f35211,f35215,f35219,f35231,f35235,f35239,f35243,f35247,f35251,f35255,f35259,f35263,f35267,f35271,f35275,f35280,f35285,f35289,f35294,f35304,f35308,f35313,f35317,f35321,f35325,f35329,f35333,f35337,f35341,f38937,f38946,f38954,f38959,f38964,f38970,f38976,f38981,f38985,f38989,f38993,f38997,f39002,f39006,f39308,f39312,f39316,f39321,f39337,f39342,f39364,f39373,f39377,f39381,f39385,f39389,f39393,f39397,f39401,f39405,f39409,f39413,f39417,f39421,f39425,f39430,f40830,f40834,f40838,f40841,f41036,f41086,f41091,f41128,f41165,f41166,f41236,f41298,f41304,f41310,f41317,f41323,f41327,f41366,f41463,f41467,f41835,f41840,f41844,f41850,f41854,f41904,f41908,f41912,f41916,f41920,f41924,f41928,f41944,f41950,f41997,f42005,f42009,f42013,f42017,f42021,f42025,f42133,f42146,f42153,f42278,f42285,f42351,f42358,f42428,f42435,f42560,f42564,f42568,f42572,f42576,f42580,f42581,f42587,f42591,f42595,f42599,f42603,f42607,f42611,f42615,f42619,f42623,f42627,f42631,f42635,f42639,f42643,f42647,f42651,f42655,f42659,f42663,f42724,f42728,f42732,f42736,f42740,f42744,f42748,f42752,f42756,f42760,f42765,f42769,f42773,f42777,f42781,f42785,f42789,f42793,f42797,f42801,f42805,f42809,f42813,f42817,f42821,f42825,f42829,f42833,f42837,f42841,f42845,f42850,f42854,f42858,f50043,f63417,f76392,f86189,f86194,f86200,f86205,f86211,f86216,f86220,f86415,f86419,f86424,f86449,f86453,f86457,f86461,f86466,f86573,f86578,f86582,f86794,f86798,f86802,f91068,f91073,f91077,f91081,f91085,f91089,f91093,f91097,f91101,f91105,f91109,f91117,f91122,f91129,f91619,f91920,f91925,f91930,f91935,f91940,f91945,f92060,f92064,f92065,f92289,f92294,f92317,f92323,f92329,f92337,f92338,f92342,f92382,f92383,f92860,f93197,f93406,f93411,f93418,f93423,f93430,f93439,f93444,f93449,f93453,f93457,f93461,f93465,f94000,f94005,f94010,f94014,f94018,f94022,f94026,f94030,f94034,f94039,f94044,f94191,f94195,f94199,f94399,f94764,f95125,f95131,f95135,f95178,f95182,f95186,f95190,f95465,f95514,f95519,f95524,f95528,f95798,f95804,f95807,f96255,f96416,f96727,f96731,f96976,f97095,f97099,f97103,f97109,f97115,f97121,f97127,f97134,f97140,f97279,f97848,f98094,f98243,f98248,f98253,f98258,f98259,f99153,f99157,f99164,f99171,f99189,f99721,f99788,f99793,f99965,f99971,f100133,f100140,f100144,f100342,f100468,f100475,f100539,f100544,f100545,f101132,f101136,f101141,f101296,f101300,f101655,f101659,f102095,f102102,f102108,f102114,f102120,f102126,f102132,f102136,f102140,f102141,f102453,f102457,f102461,f102465,f103175,f103745,f103997,f104004,f104012,f104020,f104025,f104033,f104038,f105048,f105180,f105182,f105290,f105642,f105908,f105912,f105915,f106208,f106217,f106265,f114329,f114351,f114956,f115333,f115474,f115732,f115737,f115739,f116048,f116262,f116267,f116272,f116277,f116282,f116896,f116903,f117345,f117349,f117353,f117357,f117361,f117371,f117378,f117384,f117390,f117397,f117403,f117409,f117415,f117583,f117589,f118405,f118414,f118419,f118431,f118435,f118583,f118590,f118597,f118604,f118611,f118615,f118616,f118666,f118672,f118678,f118682,f118686,f118690,f118851,f118852,f118856,f119562,f119570,f119659,f119714,f119720,f119726,f119732,f119738,f119744,f119749,f119753,f119754,f119759,f119763,f119767,f119771,f119775,f119779,f119783,f120218,f121021,f121025,f121031,f121144,f121148,f121154,f121161,f121201,f121206,f121316,f121320,f121324,f121372,f121586,f121595,f121602,f121609,f121616,f121624,f121628,f121635,f121643,f121650,f121657,f121664,f121672,f121680,f121688,f121715,f121723,f121732,f121785,f121792,f121799,f121806,f121813,f121820,f121821,f121825,f121829,f121833,f121837,f121841,f121845,f121849,f122507,f122513,f122519,f122523,f122527,f122528,f122532,f123142,f123146,f123150,f123195,f123309,f123313,f123317,f123321,f123325,f123329,f123333,f123985,f123989,f123996,f124000,f124007,f124014,f124021,f124028,f124032,f124048,f124057,f124214,f124221,f124228,f124232,f124482,f124486,f124599,f124715,f124719,f124723,f124763,f124767,f124810,f124949,f124957,f124982,f124991,f125013,f125021,f125027,f125035,f125210,f125214,f125237]) ).
thf(f125237,plain,
( ~ spl54_167
| ~ spl54_236
| ~ spl54_615
| ~ spl54_1078 ),
inference(avatar_contradiction_clause,[],[f125236]) ).
thf(f125236,plain,
( $false
| ~ spl54_167
| ~ spl54_236
| ~ spl54_615
| ~ spl54_1078 ),
inference(trivial_inequality_removal,[],[f125235]) ).
thf(f125235,plain,
( ( $true = $false )
| ~ spl54_167
| ~ spl54_236
| ~ spl54_615
| ~ spl54_1078 ),
inference(forward_demodulation,[],[f125234,f38936]) ).
thf(f38936,plain,
( ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ~ spl54_615 ),
inference(avatar_component_clause,[],[f38934]) ).
thf(f38934,plain,
( spl54_615
<=> ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_615])]) ).
thf(f125234,plain,
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ~ spl54_167
| ~ spl54_236
| ~ spl54_1078 ),
inference(forward_demodulation,[],[f125230,f4982]) ).
thf(f4982,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) )
| ~ spl54_236 ),
inference(avatar_component_clause,[],[f4980]) ).
thf(f4980,plain,
( spl54_236
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_236])]) ).
thf(f125230,plain,
( ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true )
| ~ spl54_167
| ~ spl54_1078 ),
inference(trivial_inequality_removal,[],[f125222]) ).
thf(f125222,plain,
( ( $true != $true )
| ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true )
| ~ spl54_167
| ~ spl54_1078 ),
inference(superposition,[],[f125209,f3739]) ).
thf(f3739,plain,
( ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true )
| ~ spl54_167 ),
inference(avatar_component_clause,[],[f3737]) ).
thf(f3737,plain,
( spl54_167
<=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_167])]) ).
thf(f125209,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_1078 ),
inference(avatar_component_clause,[],[f125208]) ).
thf(f125208,plain,
( spl54_1078
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1078])]) ).
thf(f125214,plain,
( spl54_1079
| ~ spl54_167
| ~ spl54_270 ),
inference(avatar_split_clause,[],[f6045,f6030,f3737,f125212]) ).
thf(f125212,plain,
( spl54_1079
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1079])]) ).
thf(f6030,plain,
( spl54_270
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_270])]) ).
thf(f6045,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_167
| ~ spl54_270 ),
inference(trivial_inequality_removal,[],[f6038]) ).
thf(f6038,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_167
| ~ spl54_270 ),
inference(superposition,[],[f6031,f3739]) ).
thf(f6031,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_270 ),
inference(avatar_component_clause,[],[f6030]) ).
thf(f125210,plain,
( spl54_1078
| ~ spl54_168
| ~ spl54_270 ),
inference(avatar_split_clause,[],[f6044,f6030,f3742,f125208]) ).
thf(f3742,plain,
( spl54_168
<=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_168])]) ).
thf(f6044,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_168
| ~ spl54_270 ),
inference(trivial_inequality_removal,[],[f6039]) ).
thf(f6039,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_168
| ~ spl54_270 ),
inference(superposition,[],[f6031,f3744]) ).
thf(f3744,plain,
( ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true )
| ~ spl54_168 ),
inference(avatar_component_clause,[],[f3742]) ).
thf(f125035,plain,
( spl54_1077
| ~ spl54_49
| ~ spl54_1076 ),
inference(avatar_split_clause,[],[f125031,f125025,f2008,f125033]) ).
thf(f125033,plain,
( spl54_1077
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1077])]) ).
thf(f2008,plain,
( spl54_49
<=> ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_49])]) ).
thf(f125025,plain,
( spl54_1076
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1076])]) ).
thf(f125031,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) ) )
| ~ spl54_49
| ~ spl54_1076 ),
inference(forward_demodulation,[],[f125030,f2010]) ).
thf(f2010,plain,
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) )
| ~ spl54_49 ),
inference(avatar_component_clause,[],[f2008]) ).
thf(f125030,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1076 ),
inference(forward_demodulation,[],[f125029,f2010]) ).
thf(f125029,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1076 ),
inference(forward_demodulation,[],[f125028,f2010]) ).
thf(f125028,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1076 ),
inference(forward_demodulation,[],[f125026,f2010]) ).
thf(f125026,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1076 ),
inference(avatar_component_clause,[],[f125025]) ).
thf(f125027,plain,
( spl54_1076
| ~ spl54_2
| ~ spl54_271 ),
inference(avatar_split_clause,[],[f6060,f6050,f1725,f125025]) ).
thf(f1725,plain,
( spl54_2
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_2])]) ).
thf(f6050,plain,
( spl54_271
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_271])]) ).
thf(f6060,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_271 ),
inference(trivial_inequality_removal,[],[f6059]) ).
thf(f6059,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X2)),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X3)),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_271 ),
inference(superposition,[],[f6051,f1726]) ).
thf(f1726,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl54_2 ),
inference(avatar_component_clause,[],[f1725]) ).
thf(f6051,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2)),X3) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_271 ),
inference(avatar_component_clause,[],[f6050]) ).
thf(f125021,plain,
( spl54_1075
| ~ spl54_129
| ~ spl54_266 ),
inference(avatar_split_clause,[],[f5989,f5980,f3223,f125019]) ).
thf(f125019,plain,
( spl54_1075
<=> ! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1075])]) ).
thf(f3223,plain,
( spl54_129
<=> ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_129])]) ).
thf(f5980,plain,
( spl54_266
<=> ! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_266])]) ).
thf(f5989,plain,
( ! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_129
| ~ spl54_266 ),
inference(forward_demodulation,[],[f5983,f3224]) ).
thf(f3224,plain,
( ! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ~ spl54_129 ),
inference(avatar_component_clause,[],[f3223]) ).
thf(f5983,plain,
( ! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) ) )
| ~ spl54_129
| ~ spl54_266 ),
inference(superposition,[],[f5981,f3224]) ).
thf(f5981,plain,
( ! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) ) )
| ~ spl54_266 ),
inference(avatar_component_clause,[],[f5980]) ).
thf(f125013,plain,
( ~ spl54_22
| ~ spl54_1070
| ~ spl54_1071
| spl54_1072
| spl54_1073
| ~ spl54_1074
| ~ spl54_17
| ~ spl54_49
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_235
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f110023,f101139,f101130,f99969,f98246,f98241,f95522,f95133,f94189,f93455,f86417,f42015,f41088,f39004,f31279,f28173,f27864,f20623,f20347,f18486,f18319,f18115,f17786,f17732,f17653,f16781,f16776,f9549,f7242,f4975,f4012,f3336,f3069,f2215,f2187,f2008,f1824,f125010,f125006,f125002,f124998,f124994,f1847]) ).
thf(f1847,plain,
( spl54_22
<=> ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_22])]) ).
thf(f124994,plain,
( spl54_1070
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1070])]) ).
thf(f124998,plain,
( spl54_1071
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1071])]) ).
thf(f125002,plain,
( spl54_1072
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1072])]) ).
thf(f125006,plain,
( spl54_1073
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1073])]) ).
thf(f125010,plain,
( spl54_1074
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1074])]) ).
thf(f1824,plain,
( spl54_17
<=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_17])]) ).
thf(f2187,plain,
( spl54_78
<=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_78])]) ).
thf(f2215,plain,
( spl54_80
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_80])]) ).
thf(f3069,plain,
( spl54_120
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_120])]) ).
thf(f3336,plain,
( spl54_141
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_141])]) ).
thf(f4012,plain,
( spl54_191
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_191])]) ).
thf(f4975,plain,
( spl54_235
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_235])]) ).
thf(f7242,plain,
( spl54_294
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_294])]) ).
thf(f9549,plain,
( spl54_295
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_295])]) ).
thf(f16776,plain,
( spl54_364
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_364])]) ).
thf(f16781,plain,
( spl54_365
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_365])]) ).
thf(f17653,plain,
( spl54_384
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_384])]) ).
thf(f17732,plain,
( spl54_389
<=> ( sK8 = vAPP(a,a,sK32,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_389])]) ).
thf(f17786,plain,
( spl54_400
<=> ( sK8 = vAPP(a,a,sK33,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_400])]) ).
thf(f18115,plain,
( spl54_410
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_410])]) ).
thf(f18319,plain,
( spl54_432
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_432])]) ).
thf(f18486,plain,
( spl54_443
<=> ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_443])]) ).
thf(f20347,plain,
( spl54_506
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_506])]) ).
thf(f20623,plain,
( spl54_525
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_525])]) ).
thf(f27864,plain,
( spl54_536
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_536])]) ).
thf(f28173,plain,
( spl54_568
<=> ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_568])]) ).
thf(f31279,plain,
( spl54_574
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_574])]) ).
thf(f39004,plain,
( spl54_629
<=> ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_629])]) ).
thf(f41088,plain,
( spl54_657
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_657])]) ).
thf(f42015,plain,
( spl54_688
<=> ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_688])]) ).
thf(f86417,plain,
( spl54_771
<=> ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_771])]) ).
thf(f93455,plain,
( spl54_823
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_823])]) ).
thf(f94189,plain,
( spl54_837
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_837])]) ).
thf(f95133,plain,
( spl54_843
<=> ! [X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_843])]) ).
thf(f95522,plain,
( spl54_851
<=> ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_851])]) ).
thf(f98241,plain,
( spl54_867
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_867])]) ).
thf(f98246,plain,
( spl54_868
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_868])]) ).
thf(f99969,plain,
( spl54_878
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_878])]) ).
thf(f101130,plain,
( spl54_887
<=> ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_887])]) ).
thf(f101139,plain,
( spl54_889
<=> ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_889])]) ).
thf(f110023,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_235
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f110022,f107413]) ).
thf(f107413,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f107412,f107244]) ).
thf(f107244,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f105868,f41090]) ).
thf(f41090,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_657 ),
inference(avatar_component_clause,[],[f41088]) ).
thf(f105868,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f93721,f105691]) ).
thf(f105691,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_688
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f105690,f16783]) ).
thf(f16783,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ~ spl54_365 ),
inference(avatar_component_clause,[],[f16781]) ).
thf(f105690,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_688
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f105689,f105541]) ).
thf(f105541,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_384
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_688
| ~ spl54_867
| ~ spl54_889 ),
inference(forward_demodulation,[],[f105540,f35102]) ).
thf(f35102,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_384
| ~ spl54_568 ),
inference(superposition,[],[f28174,f17655]) ).
thf(f17655,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_384 ),
inference(avatar_component_clause,[],[f17653]) ).
thf(f28174,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_568 ),
inference(avatar_component_clause,[],[f28173]) ).
thf(f105540,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_384
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_688
| ~ spl54_867
| ~ spl54_889 ),
inference(forward_demodulation,[],[f105539,f101280]) ).
thf(f101280,plain,
( ! [X0: int] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_889 ),
inference(forward_demodulation,[],[f101195,f3771]) ).
thf(f3771,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8) )
| ~ spl54_120
| ~ spl54_141 ),
inference(trivial_inequality_removal,[],[f3762]) ).
thf(f3762,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8) )
| ~ spl54_120
| ~ spl54_141 ),
inference(superposition,[],[f3070,f3338]) ).
thf(f3338,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_141 ),
inference(avatar_component_clause,[],[f3336]) ).
thf(f3070,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) ) )
| ~ spl54_120 ),
inference(avatar_component_clause,[],[f3069]) ).
thf(f101195,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8)) )
| ~ spl54_506
| ~ spl54_889 ),
inference(trivial_inequality_removal,[],[f101169]) ).
thf(f101169,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8)) ) )
| ~ spl54_506
| ~ spl54_889 ),
inference(superposition,[],[f101140,f20349]) ).
thf(f20349,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_506 ),
inference(avatar_component_clause,[],[f20347]) ).
thf(f101140,plain,
( ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) ) )
| ~ spl54_889 ),
inference(avatar_component_clause,[],[f101139]) ).
thf(f105539,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_384
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_688
| ~ spl54_867
| ~ spl54_889 ),
inference(forward_demodulation,[],[f105538,f35102]) ).
thf(f105538,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_688
| ~ spl54_867
| ~ spl54_889 ),
inference(forward_demodulation,[],[f99313,f101280]) ).
thf(f99313,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_443
| ~ spl54_568
| ~ spl54_688
| ~ spl54_867 ),
inference(forward_demodulation,[],[f99312,f28174]) ).
thf(f99312,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_443
| ~ spl54_688
| ~ spl54_867 ),
inference(forward_demodulation,[],[f98677,f42016]) ).
thf(f42016,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_688 ),
inference(avatar_component_clause,[],[f42015]) ).
thf(f98677,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_443
| ~ spl54_867 ),
inference(trivial_inequality_removal,[],[f98627]) ).
thf(f98627,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) )
| ~ spl54_443
| ~ spl54_867 ),
inference(superposition,[],[f98242,f18487]) ).
thf(f18487,plain,
( ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_443 ),
inference(avatar_component_clause,[],[f18486]) ).
thf(f98242,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_867 ),
inference(avatar_component_clause,[],[f98241]) ).
thf(f105689,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_141
| ~ spl54_365
| ~ spl54_432
| ~ spl54_574
| ~ spl54_629
| ~ spl54_851
| ~ spl54_868
| ~ spl54_887 ),
inference(forward_demodulation,[],[f98867,f105631]) ).
thf(f105631,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_432
| ~ spl54_574
| ~ spl54_629
| ~ spl54_851
| ~ spl54_887 ),
inference(forward_demodulation,[],[f39264,f105567]) ).
thf(f105567,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_432
| ~ spl54_574
| ~ spl54_851
| ~ spl54_887 ),
inference(forward_demodulation,[],[f105566,f16783]) ).
thf(f105566,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_432
| ~ spl54_574
| ~ spl54_851
| ~ spl54_887 ),
inference(forward_demodulation,[],[f101383,f95619]) ).
thf(f95619,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_432
| ~ spl54_574
| ~ spl54_851 ),
inference(forward_demodulation,[],[f95602,f31281]) ).
thf(f31281,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_574 ),
inference(avatar_component_clause,[],[f31279]) ).
thf(f95602,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_432
| ~ spl54_851 ),
inference(trivial_inequality_removal,[],[f95536]) ).
thf(f95536,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_432
| ~ spl54_851 ),
inference(superposition,[],[f95523,f18321]) ).
thf(f18321,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_432 ),
inference(avatar_component_clause,[],[f18319]) ).
thf(f95523,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_851 ),
inference(avatar_component_clause,[],[f95522]) ).
thf(f101383,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_887 ),
inference(forward_demodulation,[],[f101382,f16783]) ).
thf(f101382,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) )
| ~ spl54_17
| ~ spl54_887 ),
inference(trivial_inequality_removal,[],[f101302]) ).
thf(f101302,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) ) )
| ~ spl54_17
| ~ spl54_887 ),
inference(superposition,[],[f101131,f1826]) ).
thf(f1826,plain,
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $true )
| ~ spl54_17 ),
inference(avatar_component_clause,[],[f1824]) ).
thf(f101131,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) ) )
| ~ spl54_887 ),
inference(avatar_component_clause,[],[f101130]) ).
thf(f39264,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),sK8) )
| ~ spl54_141
| ~ spl54_629 ),
inference(trivial_inequality_removal,[],[f39260]) ).
thf(f39260,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),sK8) ) )
| ~ spl54_141
| ~ spl54_629 ),
inference(superposition,[],[f39005,f3338]) ).
thf(f39005,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),X1) ) )
| ~ spl54_629 ),
inference(avatar_component_clause,[],[f39004]) ).
thf(f98867,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_868 ),
inference(forward_demodulation,[],[f98866,f2217]) ).
thf(f2217,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_80 ),
inference(avatar_component_clause,[],[f2215]) ).
thf(f98866,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_17
| ~ spl54_868 ),
inference(trivial_inequality_removal,[],[f98786]) ).
thf(f98786,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_17
| ~ spl54_868 ),
inference(superposition,[],[f98247,f1826]) ).
thf(f98247,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) )
| ~ spl54_868 ),
inference(avatar_component_clause,[],[f98246]) ).
thf(f93721,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_295
| ~ spl54_400
| ~ spl54_506
| ~ spl54_568
| ~ spl54_823 ),
inference(forward_demodulation,[],[f93720,f35104]) ).
thf(f35104,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_295
| ~ spl54_568 ),
inference(superposition,[],[f28174,f9551]) ).
thf(f9551,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_295 ),
inference(avatar_component_clause,[],[f9549]) ).
thf(f93720,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_400
| ~ spl54_506
| ~ spl54_823 ),
inference(forward_demodulation,[],[f93657,f17788]) ).
thf(f17788,plain,
( ( sK8 = vAPP(a,a,sK33,sK8) )
| ~ spl54_400 ),
inference(avatar_component_clause,[],[f17786]) ).
thf(f93657,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK8))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_506
| ~ spl54_823 ),
inference(trivial_inequality_removal,[],[f93631]) ).
thf(f93631,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK8))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_506
| ~ spl54_823 ),
inference(superposition,[],[f93456,f20349]) ).
thf(f93456,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_823 ),
inference(avatar_component_clause,[],[f93455]) ).
thf(f107412,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_78
| ~ spl54_120
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_389
| ~ spl54_432
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_771
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_878
| ~ spl54_889 ),
inference(forward_demodulation,[],[f107411,f95619]) ).
thf(f107411,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_78
| ~ spl54_120
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_389
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_771
| ~ spl54_837
| ~ spl54_843
| ~ spl54_878
| ~ spl54_889 ),
inference(forward_demodulation,[],[f105341,f105962]) ).
thf(f105962,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_389
| ~ spl54_536
| ~ spl54_568
| ~ spl54_837
| ~ spl54_878 ),
inference(forward_demodulation,[],[f105961,f91622]) ).
thf(f91622,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536 ),
inference(trivial_inequality_removal,[],[f27908]) ).
thf(f27908,plain,
( ( $true = $false )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536 ),
inference(forward_demodulation,[],[f27892,f3338]) ).
thf(f27892,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_389
| ~ spl54_536 ),
inference(superposition,[],[f27865,f17734]) ).
thf(f17734,plain,
( ( sK8 = vAPP(a,a,sK32,sK8) )
| ~ spl54_389 ),
inference(avatar_component_clause,[],[f17732]) ).
thf(f27865,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_536 ),
inference(avatar_component_clause,[],[f27864]) ).
thf(f105961,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_389
| ~ spl54_536
| ~ spl54_568
| ~ spl54_837
| ~ spl54_878 ),
inference(forward_demodulation,[],[f105809,f100057]) ).
thf(f100057,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_568
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100056,f35104]) ).
thf(f100056,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_294
| ~ spl54_364
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100051,f16778]) ).
thf(f16778,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ~ spl54_364 ),
inference(avatar_component_clause,[],[f16776]) ).
thf(f100051,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8)) )
| ~ spl54_294
| ~ spl54_878 ),
inference(trivial_inequality_removal,[],[f99973]) ).
thf(f99973,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8)) )
| ~ spl54_294
| ~ spl54_878 ),
inference(superposition,[],[f99970,f7244]) ).
thf(f7244,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_294 ),
inference(avatar_component_clause,[],[f7242]) ).
thf(f99970,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0) ) )
| ~ spl54_878 ),
inference(avatar_component_clause,[],[f99969]) ).
thf(f105809,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_837 ),
inference(forward_demodulation,[],[f94807,f91622]) ).
thf(f94807,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8)) )
| ~ spl54_141
| ~ spl54_837 ),
inference(trivial_inequality_removal,[],[f94803]) ).
thf(f94803,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8)) )
| ~ spl54_141
| ~ spl54_837 ),
inference(superposition,[],[f94190,f3338]) ).
thf(f94190,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) ) )
| ~ spl54_837 ),
inference(avatar_component_clause,[],[f94189]) ).
thf(f105341,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_78
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_525
| ~ spl54_771
| ~ spl54_843
| ~ spl54_889 ),
inference(trivial_inequality_removal,[],[f105340]) ).
thf(f105340,plain,
( ! [X0: nat] :
( ( $true = $false )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_78
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_525
| ~ spl54_771
| ~ spl54_843
| ~ spl54_889 ),
inference(forward_demodulation,[],[f105339,f2189]) ).
thf(f2189,plain,
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $true )
| ~ spl54_78 ),
inference(avatar_component_clause,[],[f2187]) ).
thf(f105339,plain,
( ! [X0: nat] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $false ) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_525
| ~ spl54_771
| ~ spl54_843
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104930,f20625]) ).
thf(f20625,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_525 ),
inference(avatar_component_clause,[],[f20623]) ).
thf(f104930,plain,
( ! [X0: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $false ) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_771
| ~ spl54_843
| ~ spl54_889 ),
inference(forward_demodulation,[],[f95137,f101280]) ).
thf(f95137,plain,
( ! [X0: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $false ) )
| ~ spl54_771
| ~ spl54_843 ),
inference(superposition,[],[f95134,f86418]) ).
thf(f86418,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_771 ),
inference(avatar_component_clause,[],[f86417]) ).
thf(f95134,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_843 ),
inference(avatar_component_clause,[],[f95133]) ).
thf(f110022,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_235
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f110021,f107413]) ).
thf(f110021,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_235
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f19191,f107413]) ).
thf(f19191,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_49
| ~ spl54_191
| ~ spl54_235
| ~ spl54_410 ),
inference(forward_demodulation,[],[f19190,f18117]) ).
thf(f18117,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_410 ),
inference(avatar_component_clause,[],[f18115]) ).
thf(f19190,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_49
| ~ spl54_191
| ~ spl54_235
| ~ spl54_410 ),
inference(forward_demodulation,[],[f19189,f2010]) ).
thf(f19189,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_49
| ~ spl54_191
| ~ spl54_235
| ~ spl54_410 ),
inference(forward_demodulation,[],[f19188,f2010]) ).
thf(f19188,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_191
| ~ spl54_235
| ~ spl54_410 ),
inference(forward_demodulation,[],[f19187,f18117]) ).
thf(f19187,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_191
| ~ spl54_235
| ~ spl54_410 ),
inference(forward_demodulation,[],[f4992,f18117]) ).
thf(f4992,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_191
| ~ spl54_235 ),
inference(superposition,[],[f4013,f4977]) ).
thf(f4977,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) )
| ~ spl54_235 ),
inference(avatar_component_clause,[],[f4975]) ).
thf(f4013,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X2 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) )
| ~ spl54_191 ),
inference(avatar_component_clause,[],[f4012]) ).
thf(f124991,plain,
( spl54_1069
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_389
| ~ spl54_536
| ~ spl54_568
| ~ spl54_837
| ~ spl54_878 ),
inference(avatar_split_clause,[],[f105962,f99969,f94189,f28173,f27864,f17732,f16776,f9549,f7242,f3336,f124988]) ).
thf(f124988,plain,
( spl54_1069
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1069])]) ).
thf(f124982,plain,
( ~ spl54_22
| spl54_1064
| ~ spl54_1065
| ~ spl54_1066
| ~ spl54_1067
| spl54_1068
| ~ spl54_17
| ~ spl54_49
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_236
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f110020,f101139,f101130,f99969,f98246,f98241,f95522,f95133,f94189,f93455,f86417,f42015,f41088,f39004,f31279,f28173,f27864,f20623,f20347,f18486,f18319,f18115,f17786,f17732,f17653,f16781,f16776,f9549,f7242,f4980,f4012,f3336,f3069,f2215,f2187,f2008,f1824,f124979,f124975,f124971,f124967,f124963,f1847]) ).
thf(f124963,plain,
( spl54_1064
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1064])]) ).
thf(f124967,plain,
( spl54_1065
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1065])]) ).
thf(f124971,plain,
( spl54_1066
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1066])]) ).
thf(f124975,plain,
( spl54_1067
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1067])]) ).
thf(f124979,plain,
( spl54_1068
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1068])]) ).
thf(f110020,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) != sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = sK8 )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_236
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f110019,f107244]) ).
thf(f110019,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) != sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_236
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f110018,f2010]) ).
thf(f110018,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) != sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_236
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f110017,f2010]) ).
thf(f110017,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) != sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_236
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f110016,f107413]) ).
thf(f110016,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = sK8 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_191
| ~ spl54_236
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_410
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f19194,f107413]) ).
thf(f19194,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_191
| ~ spl54_236
| ~ spl54_410 ),
inference(forward_demodulation,[],[f19193,f18117]) ).
thf(f19193,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_191
| ~ spl54_236
| ~ spl54_410 ),
inference(forward_demodulation,[],[f4999,f18117]) ).
thf(f4999,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_191
| ~ spl54_236 ),
inference(superposition,[],[f4013,f4982]) ).
thf(f124957,plain,
( spl54_1063
| ~ spl54_18
| ~ spl54_271 ),
inference(avatar_split_clause,[],[f6065,f6050,f1829,f124955]) ).
thf(f124955,plain,
( spl54_1063
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1063])]) ).
thf(f1829,plain,
( spl54_18
<=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_18])]) ).
thf(f6065,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_271 ),
inference(trivial_inequality_removal,[],[f6054]) ).
thf(f6054,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_271 ),
inference(superposition,[],[f6051,f1831]) ).
thf(f1831,plain,
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
| ~ spl54_18 ),
inference(avatar_component_clause,[],[f1829]) ).
thf(f124949,plain,
( spl54_1062
| ~ spl54_19
| ~ spl54_271 ),
inference(avatar_split_clause,[],[f6064,f6050,f1834,f124947]) ).
thf(f124947,plain,
( spl54_1062
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1062])]) ).
thf(f1834,plain,
( spl54_19
<=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_19])]) ).
thf(f6064,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_271 ),
inference(trivial_inequality_removal,[],[f6055]) ).
thf(f6055,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_271 ),
inference(superposition,[],[f6051,f1836]) ).
thf(f1836,plain,
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
| ~ spl54_19 ),
inference(avatar_component_clause,[],[f1834]) ).
thf(f124810,plain,
( spl54_1061
| ~ spl54_32
| ~ spl54_49
| ~ spl54_271 ),
inference(avatar_split_clause,[],[f15623,f6050,f2008,f1899,f124808]) ).
thf(f124808,plain,
( spl54_1061
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),sK8) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1061])]) ).
thf(f1899,plain,
( spl54_32
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_32])]) ).
thf(f15623,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),sK8) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_271 ),
inference(forward_demodulation,[],[f15622,f2010]) ).
thf(f15622,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_271 ),
inference(forward_demodulation,[],[f15621,f2010]) ).
thf(f15621,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_271 ),
inference(forward_demodulation,[],[f7846,f2010]) ).
thf(f7846,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_271 ),
inference(trivial_inequality_removal,[],[f7767]) ).
thf(f7767,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_271 ),
inference(superposition,[],[f6051,f1901]) ).
thf(f1901,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_32 ),
inference(avatar_component_clause,[],[f1899]) ).
thf(f124767,plain,
( spl54_1060
| ~ spl54_16
| ~ spl54_270 ),
inference(avatar_split_clause,[],[f6034,f6030,f1820,f124765]) ).
thf(f124765,plain,
( spl54_1060
<=> ! [X2: a,X0: product_prod_a_a,X1: a] :
( ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(product_prod_a_a,a,sK41,X0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(product_prod_a_a,a,sK40,X0)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(product_prod_a_a,a,sK41,X0)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1060])]) ).
thf(f1820,plain,
( spl54_16
<=> ! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK40,X0)),vAPP(product_prod_a_a,a,sK41,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_16])]) ).
thf(f6034,plain,
( ! [X2: a,X0: product_prod_a_a,X1: a] :
( ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(product_prod_a_a,a,sK41,X0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(product_prod_a_a,a,sK40,X0)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(product_prod_a_a,a,sK41,X0)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_16
| ~ spl54_270 ),
inference(superposition,[],[f6031,f1821]) ).
thf(f1821,plain,
( ! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK40,X0)),vAPP(product_prod_a_a,a,sK41,X0)) = X0 )
| ~ spl54_16 ),
inference(avatar_component_clause,[],[f1820]) ).
thf(f124763,plain,
( spl54_1059
| ~ spl54_15
| ~ spl54_270 ),
inference(avatar_split_clause,[],[f6033,f6030,f1816,f124761]) ).
thf(f124761,plain,
( spl54_1059
<=> ! [X2: a,X0: product_prod_a_a,X1: a] :
( ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(product_prod_a_a,a,sK39,X0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(product_prod_a_a,a,sK38,X0)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(product_prod_a_a,a,sK39,X0)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1059])]) ).
thf(f1816,plain,
( spl54_15
<=> ! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK38,X0)),vAPP(product_prod_a_a,a,sK39,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_15])]) ).
thf(f6033,plain,
( ! [X2: a,X0: product_prod_a_a,X1: a] :
( ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(product_prod_a_a,a,sK39,X0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(product_prod_a_a,a,sK38,X0)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(product_prod_a_a,a,sK39,X0)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_15
| ~ spl54_270 ),
inference(superposition,[],[f6031,f1817]) ).
thf(f1817,plain,
( ! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK38,X0)),vAPP(product_prod_a_a,a,sK39,X0)) = X0 )
| ~ spl54_15 ),
inference(avatar_component_clause,[],[f1816]) ).
thf(f124723,plain,
( spl54_1058
| ~ spl54_2
| ~ spl54_270 ),
inference(avatar_split_clause,[],[f6042,f6030,f1725,f124721]) ).
thf(f124721,plain,
( spl54_1058
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X1))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1058])]) ).
thf(f6042,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X1))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_2
| ~ spl54_270 ),
inference(trivial_inequality_removal,[],[f6041]) ).
thf(f6041,plain,
( ! [X2: a,X3: a,X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X1))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_2
| ~ spl54_270 ),
inference(superposition,[],[f6031,f1726]) ).
thf(f124719,plain,
( spl54_1057
| ~ spl54_9
| ~ spl54_35
| ~ spl54_244 ),
inference(avatar_split_clause,[],[f5498,f5482,f1914,f1785,f124717]) ).
thf(f124717,plain,
( spl54_1057
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1057])]) ).
thf(f1785,plain,
( spl54_9
<=> ! [X0: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_9])]) ).
thf(f1914,plain,
( spl54_35
<=> ! [X0: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_35])]) ).
thf(f5482,plain,
( spl54_244
<=> ! [X2: a,X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),vAPP(partia96731725t_unit,a,sK14,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(partia96731725t_unit,a,sK15,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_244])]) ).
thf(f5498,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_244 ),
inference(forward_demodulation,[],[f5497,f1786]) ).
thf(f1786,plain,
( ! [X0: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ~ spl54_9 ),
inference(avatar_component_clause,[],[f1785]) ).
thf(f5497,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_244 ),
inference(forward_demodulation,[],[f5496,f1786]) ).
thf(f5496,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_244 ),
inference(forward_demodulation,[],[f5490,f1786]) ).
thf(f5490,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_35
| ~ spl54_244 ),
inference(superposition,[],[f5483,f1915]) ).
thf(f1915,plain,
( ! [X0: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ~ spl54_35 ),
inference(avatar_component_clause,[],[f1914]) ).
thf(f5483,plain,
( ! [X2: a,X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,sK15,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,X0)) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),vAPP(partia96731725t_unit,a,sK14,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_244 ),
inference(avatar_component_clause,[],[f5482]) ).
thf(f124715,plain,
( spl54_1056
| ~ spl54_8
| ~ spl54_34
| ~ spl54_244 ),
inference(avatar_split_clause,[],[f5495,f5482,f1910,f1781,f124713]) ).
thf(f124713,plain,
( spl54_1056
<=> ! [X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1056])]) ).
thf(f1781,plain,
( spl54_8
<=> ! [X0: partia96731725t_unit] : ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_8])]) ).
thf(f1910,plain,
( spl54_34
<=> ! [X0: partia96731725t_unit] : ( vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_34])]) ).
thf(f5495,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_244 ),
inference(forward_demodulation,[],[f5494,f1782]) ).
thf(f1782,plain,
( ! [X0: partia96731725t_unit] : ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ~ spl54_8 ),
inference(avatar_component_clause,[],[f1781]) ).
thf(f5494,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_244 ),
inference(forward_demodulation,[],[f5493,f1782]) ).
thf(f5493,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_244 ),
inference(forward_demodulation,[],[f5489,f1782]) ).
thf(f5489,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_34
| ~ spl54_244 ),
inference(superposition,[],[f5483,f1911]) ).
thf(f1911,plain,
( ! [X0: partia96731725t_unit] : ( vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ~ spl54_34 ),
inference(avatar_component_clause,[],[f1910]) ).
thf(f124599,plain,
( spl54_691
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_568
| ~ spl54_657
| ~ spl54_834
| ~ spl54_878 ),
inference(avatar_split_clause,[],[f105932,f99969,f94032,f41088,f28173,f16776,f9549,f7242,f3336,f42130]) ).
thf(f42130,plain,
( spl54_691
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_691])]) ).
thf(f94032,plain,
( spl54_834
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_834])]) ).
thf(f105932,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_568
| ~ spl54_657
| ~ spl54_834
| ~ spl54_878 ),
inference(forward_demodulation,[],[f105854,f100057]) ).
thf(f105854,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_141
| ~ spl54_657
| ~ spl54_834 ),
inference(forward_demodulation,[],[f96593,f41090]) ).
thf(f96593,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8)) )
| ~ spl54_141
| ~ spl54_834 ),
inference(trivial_inequality_removal,[],[f96589]) ).
thf(f96589,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8)) )
| ~ spl54_141
| ~ spl54_834 ),
inference(superposition,[],[f94033,f3338]) ).
thf(f94033,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) ) )
| ~ spl54_834 ),
inference(avatar_component_clause,[],[f94032]) ).
thf(f124486,plain,
( spl54_1055
| ~ spl54_2
| ~ spl54_268 ),
inference(avatar_split_clause,[],[f6023,f5996,f1725,f124484]) ).
thf(f124484,plain,
( spl54_1055
<=> ! [X0: a,X3: a,X2: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1055])]) ).
thf(f5996,plain,
( spl54_268
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_268])]) ).
thf(f6023,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_268 ),
inference(trivial_inequality_removal,[],[f6022]) ).
thf(f6022,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_268 ),
inference(superposition,[],[f5997,f1726]) ).
thf(f5997,plain,
( ! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_268 ),
inference(avatar_component_clause,[],[f5996]) ).
thf(f124482,plain,
( spl54_1054
| ~ spl54_2
| ~ spl54_267 ),
inference(avatar_split_clause,[],[f6006,f5992,f1725,f124480]) ).
thf(f124480,plain,
( spl54_1054
<=> ! [X0: a,X3: a,X2: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1054])]) ).
thf(f5992,plain,
( spl54_267
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_267])]) ).
thf(f6006,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_267 ),
inference(trivial_inequality_removal,[],[f6005]) ).
thf(f6005,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_267 ),
inference(superposition,[],[f5993,f1726]) ).
thf(f5993,plain,
( ! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_267 ),
inference(avatar_component_clause,[],[f5992]) ).
thf(f124232,plain,
( spl54_1053
| ~ spl54_49
| ~ spl54_1051 ),
inference(avatar_split_clause,[],[f124224,f124219,f2008,f124230]) ).
thf(f124230,plain,
( spl54_1053
<=> ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1053])]) ).
thf(f124219,plain,
( spl54_1051
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1051])]) ).
thf(f124224,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) ) )
| ~ spl54_49
| ~ spl54_1051 ),
inference(forward_demodulation,[],[f124223,f2010]) ).
thf(f124223,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1051 ),
inference(forward_demodulation,[],[f124222,f2010]) ).
thf(f124222,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1051 ),
inference(forward_demodulation,[],[f124220,f2010]) ).
thf(f124220,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1051 ),
inference(avatar_component_clause,[],[f124219]) ).
thf(f124228,plain,
( spl54_1052
| ~ spl54_49
| ~ spl54_1050 ),
inference(avatar_split_clause,[],[f124217,f124212,f2008,f124226]) ).
thf(f124226,plain,
( spl54_1052
<=> ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1052])]) ).
thf(f124212,plain,
( spl54_1050
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1050])]) ).
thf(f124217,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) ) )
| ~ spl54_49
| ~ spl54_1050 ),
inference(forward_demodulation,[],[f124216,f2010]) ).
thf(f124216,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1050 ),
inference(forward_demodulation,[],[f124215,f2010]) ).
thf(f124215,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1050 ),
inference(forward_demodulation,[],[f124213,f2010]) ).
thf(f124213,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1050 ),
inference(avatar_component_clause,[],[f124212]) ).
thf(f124221,plain,
( spl54_1051
| ~ spl54_2
| ~ spl54_265 ),
inference(avatar_split_clause,[],[f5973,f5950,f1725,f124219]) ).
thf(f5950,plain,
( spl54_265
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_265])]) ).
thf(f5973,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_265 ),
inference(trivial_inequality_removal,[],[f5972]) ).
thf(f5972,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_265 ),
inference(superposition,[],[f5951,f1726]) ).
thf(f5951,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_265 ),
inference(avatar_component_clause,[],[f5950]) ).
thf(f124214,plain,
( spl54_1050
| ~ spl54_2
| ~ spl54_264 ),
inference(avatar_split_clause,[],[f5960,f5946,f1725,f124212]) ).
thf(f5946,plain,
( spl54_264
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_264])]) ).
thf(f5960,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_264 ),
inference(trivial_inequality_removal,[],[f5959]) ).
thf(f5959,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_264 ),
inference(superposition,[],[f5947,f1726]) ).
thf(f5947,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_264 ),
inference(avatar_component_clause,[],[f5946]) ).
thf(f124057,plain,
( spl54_1049
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1048 ),
inference(avatar_split_clause,[],[f124053,f124046,f16940,f2008,f124055]) ).
thf(f124055,plain,
( spl54_1049
<=> ! [X2: a,X0: nat,X1: a] :
( ( sK8 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1049])]) ).
thf(f16940,plain,
( spl54_370
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_370])]) ).
thf(f124046,plain,
( spl54_1048
<=> ! [X2: a,X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1048])]) ).
thf(f124053,plain,
( ! [X2: a,X0: nat,X1: a] :
( ( sK8 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( X1 = X2 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1048 ),
inference(forward_demodulation,[],[f124052,f16942]) ).
thf(f16942,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_370 ),
inference(avatar_component_clause,[],[f16940]) ).
thf(f124052,plain,
( ! [X2: a,X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1048 ),
inference(forward_demodulation,[],[f124051,f2010]) ).
thf(f124051,plain,
( ! [X2: a,X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1048 ),
inference(forward_demodulation,[],[f124050,f2010]) ).
thf(f124050,plain,
( ! [X2: a,X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1048 ),
inference(forward_demodulation,[],[f124049,f2010]) ).
thf(f124049,plain,
( ! [X2: a,X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_370
| ~ spl54_1048 ),
inference(forward_demodulation,[],[f124047,f16942]) ).
thf(f124047,plain,
( ! [X2: a,X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_1048 ),
inference(avatar_component_clause,[],[f124046]) ).
thf(f124048,plain,
( spl54_1048
| ~ spl54_164
| ~ spl54_223 ),
inference(avatar_split_clause,[],[f4712,f4704,f3720,f124046]) ).
thf(f3720,plain,
( spl54_164
<=> ! [X0: nat,X1: a] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_164])]) ).
thf(f4704,plain,
( spl54_223
<=> ! [X2: a,X0: a,X1: a] :
( ( X0 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_223])]) ).
thf(f4712,plain,
( ! [X2: a,X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_164
| ~ spl54_223 ),
inference(superposition,[],[f4705,f3721]) ).
thf(f3721,plain,
( ! [X0: nat,X1: a] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),X1) )
| ~ spl54_164 ),
inference(avatar_component_clause,[],[f3720]) ).
thf(f4705,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( X0 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) )
| ~ spl54_223 ),
inference(avatar_component_clause,[],[f4704]) ).
thf(f124032,plain,
( spl54_1047
| ~ spl54_9
| ~ spl54_35
| ~ spl54_228 ),
inference(avatar_split_clause,[],[f4771,f4743,f1914,f1785,f124030]) ).
thf(f124030,plain,
( spl54_1047
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1047])]) ).
thf(f4743,plain,
( spl54_228
<=> ! [X2: a,X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),vAPP(partia96731725t_unit,a,sK14,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_228])]) ).
thf(f4771,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_228 ),
inference(forward_demodulation,[],[f4770,f1786]) ).
thf(f4770,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_228 ),
inference(forward_demodulation,[],[f4767,f1786]) ).
thf(f4767,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_35
| ~ spl54_228 ),
inference(superposition,[],[f4744,f1915]) ).
thf(f4744,plain,
( ! [X2: a,X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),vAPP(partia96731725t_unit,a,sK14,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_228 ),
inference(avatar_component_clause,[],[f4743]) ).
thf(f124028,plain,
( spl54_1046
| ~ spl54_8
| ~ spl54_34
| ~ spl54_228 ),
inference(avatar_split_clause,[],[f4769,f4743,f1910,f1781,f124026]) ).
thf(f124026,plain,
( spl54_1046
<=> ! [X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1046])]) ).
thf(f4769,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_228 ),
inference(forward_demodulation,[],[f4768,f1782]) ).
thf(f4768,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_228 ),
inference(forward_demodulation,[],[f4766,f1782]) ).
thf(f4766,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_34
| ~ spl54_228 ),
inference(superposition,[],[f4744,f1911]) ).
thf(f124021,plain,
( spl54_1045
| ~ spl54_18
| ~ spl54_265 ),
inference(avatar_split_clause,[],[f5978,f5950,f1829,f124019]) ).
thf(f124019,plain,
( spl54_1045
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1045])]) ).
thf(f5978,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_265 ),
inference(trivial_inequality_removal,[],[f5967]) ).
thf(f5967,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_265 ),
inference(superposition,[],[f5951,f1831]) ).
thf(f124014,plain,
( spl54_1044
| ~ spl54_19
| ~ spl54_265 ),
inference(avatar_split_clause,[],[f5977,f5950,f1834,f124012]) ).
thf(f124012,plain,
( spl54_1044
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1044])]) ).
thf(f5977,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_265 ),
inference(trivial_inequality_removal,[],[f5968]) ).
thf(f5968,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_265 ),
inference(superposition,[],[f5951,f1836]) ).
thf(f124007,plain,
( spl54_1043
| ~ spl54_18
| ~ spl54_264 ),
inference(avatar_split_clause,[],[f5965,f5946,f1829,f124005]) ).
thf(f124005,plain,
( spl54_1043
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1043])]) ).
thf(f5965,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_264 ),
inference(trivial_inequality_removal,[],[f5954]) ).
thf(f5954,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_264 ),
inference(superposition,[],[f5947,f1831]) ).
thf(f124000,plain,
( spl54_1042
| ~ spl54_19
| ~ spl54_264 ),
inference(avatar_split_clause,[],[f5964,f5946,f1834,f123998]) ).
thf(f123998,plain,
( spl54_1042
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1042])]) ).
thf(f5964,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_264 ),
inference(trivial_inequality_removal,[],[f5955]) ).
thf(f5955,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_264 ),
inference(superposition,[],[f5947,f1836]) ).
thf(f123996,plain,
( spl54_1041
| ~ spl54_2
| spl54_490 ),
inference(avatar_split_clause,[],[f121718,f19405,f1725,f123993]) ).
thf(f123993,plain,
( spl54_1041
<=> ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1041])]) ).
thf(f19405,plain,
( spl54_490
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_490])]) ).
thf(f121718,plain,
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_2
| spl54_490 ),
inference(trivial_inequality_removal,[],[f121717]) ).
thf(f121717,plain,
( ( $true != $true )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_2
| spl54_490 ),
inference(superposition,[],[f19406,f1726]) ).
thf(f19406,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| spl54_490 ),
inference(avatar_component_clause,[],[f19405]) ).
thf(f123989,plain,
( spl54_1040
| ~ spl54_35
| ~ spl54_225 ),
inference(avatar_split_clause,[],[f4732,f4720,f1914,f123987]) ).
thf(f123987,plain,
( spl54_1040
<=> ! [X0: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,sK11,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,a,sK12,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)))),vAPP(partia96731725t_unit,a,sK13,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,sK11,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,sK12,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,a,sK13,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1040])]) ).
thf(f4720,plain,
( spl54_225
<=> ! [X0: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,a,sK12,X0))),vAPP(partia96731725t_unit,a,sK13,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,a,sK13,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_225])]) ).
thf(f4732,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,sK11,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,a,sK12,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)))),vAPP(partia96731725t_unit,a,sK13,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,sK11,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,sK12,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,a,sK13,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_35
| ~ spl54_225 ),
inference(superposition,[],[f4721,f1915]) ).
thf(f4721,plain,
( ! [X0: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,a,sK12,X0))),vAPP(partia96731725t_unit,a,sK13,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,a,sK13,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) )
| ~ spl54_225 ),
inference(avatar_component_clause,[],[f4720]) ).
thf(f123985,plain,
( spl54_1039
| ~ spl54_34
| ~ spl54_225 ),
inference(avatar_split_clause,[],[f4731,f4720,f1910,f123983]) ).
thf(f123983,plain,
( spl54_1039
<=> ! [X0: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,a,sK12,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)))),vAPP(partia96731725t_unit,a,sK13,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,a,sK13,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1039])]) ).
thf(f4731,plain,
( ! [X0: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,a,sK12,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)))),vAPP(partia96731725t_unit,a,sK13,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,a,sK13,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_34
| ~ spl54_225 ),
inference(superposition,[],[f4721,f1911]) ).
thf(f123333,plain,
( spl54_1038
| ~ spl54_2
| ~ spl54_261 ),
inference(avatar_split_clause,[],[f5929,f5844,f1725,f123331]) ).
thf(f123331,plain,
( spl54_1038
<=> ! [X0: a,X3: a,X2: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1038])]) ).
thf(f5844,plain,
( spl54_261
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_261])]) ).
thf(f5929,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_261 ),
inference(trivial_inequality_removal,[],[f5928]) ).
thf(f5928,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_261 ),
inference(superposition,[],[f5845,f1726]) ).
thf(f5845,plain,
( ! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_261 ),
inference(avatar_component_clause,[],[f5844]) ).
thf(f123329,plain,
( spl54_1037
| ~ spl54_2
| ~ spl54_260 ),
inference(avatar_split_clause,[],[f5916,f5840,f1725,f123327]) ).
thf(f123327,plain,
( spl54_1037
<=> ! [X0: a,X3: a,X2: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X0),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1037])]) ).
thf(f5840,plain,
( spl54_260
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_260])]) ).
thf(f5916,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X0),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_260 ),
inference(trivial_inequality_removal,[],[f5915]) ).
thf(f5915,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X0),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_260 ),
inference(superposition,[],[f5841,f1726]) ).
thf(f5841,plain,
( ! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_260 ),
inference(avatar_component_clause,[],[f5840]) ).
thf(f123325,plain,
( spl54_1036
| ~ spl54_2
| ~ spl54_259 ),
inference(avatar_split_clause,[],[f5903,f5663,f1725,f123323]) ).
thf(f123323,plain,
( spl54_1036
<=> ! [X0: a,X3: a,X2: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1036])]) ).
thf(f5663,plain,
( spl54_259
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_259])]) ).
thf(f5903,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_259 ),
inference(trivial_inequality_removal,[],[f5902]) ).
thf(f5902,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_259 ),
inference(superposition,[],[f5664,f1726]) ).
thf(f5664,plain,
( ! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_259 ),
inference(avatar_component_clause,[],[f5663]) ).
thf(f123321,plain,
( spl54_1035
| ~ spl54_2
| ~ spl54_258 ),
inference(avatar_split_clause,[],[f5889,f5659,f1725,f123319]) ).
thf(f123319,plain,
( spl54_1035
<=> ! [X0: a,X3: a,X2: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1035])]) ).
thf(f5659,plain,
( spl54_258
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_258])]) ).
thf(f5889,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_258 ),
inference(trivial_inequality_removal,[],[f5888]) ).
thf(f5888,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_258 ),
inference(superposition,[],[f5660,f1726]) ).
thf(f5660,plain,
( ! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_258 ),
inference(avatar_component_clause,[],[f5659]) ).
thf(f123317,plain,
( spl54_1034
| ~ spl54_2
| ~ spl54_257 ),
inference(avatar_split_clause,[],[f5874,f5655,f1725,f123315]) ).
thf(f123315,plain,
( spl54_1034
<=> ! [X0: a,X3: a,X2: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1034])]) ).
thf(f5655,plain,
( spl54_257
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_257])]) ).
thf(f5874,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_257 ),
inference(trivial_inequality_removal,[],[f5873]) ).
thf(f5873,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_257 ),
inference(superposition,[],[f5656,f1726]) ).
thf(f5656,plain,
( ! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_257 ),
inference(avatar_component_clause,[],[f5655]) ).
thf(f123313,plain,
( spl54_1033
| ~ spl54_2
| ~ spl54_256 ),
inference(avatar_split_clause,[],[f5861,f5651,f1725,f123311]) ).
thf(f123311,plain,
( spl54_1033
<=> ! [X0: a,X3: a,X2: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1033])]) ).
thf(f5651,plain,
( spl54_256
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_256])]) ).
thf(f5861,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_256 ),
inference(trivial_inequality_removal,[],[f5860]) ).
thf(f5860,plain,
( ! [X2: a,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_256 ),
inference(superposition,[],[f5652,f1726]) ).
thf(f5652,plain,
( ! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) )
| ~ spl54_256 ),
inference(avatar_component_clause,[],[f5651]) ).
thf(f123309,plain,
( spl54_1032
| ~ spl54_2
| ~ spl54_255 ),
inference(avatar_split_clause,[],[f5850,f5647,f1725,f123307]) ).
thf(f123307,plain,
( spl54_1032
<=> ! [X0: a,X3: a,X2: a,X1: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1032])]) ).
thf(f5647,plain,
( spl54_255
<=> ! [X0: partia96731725t_unit,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_255])]) ).
thf(f5850,plain,
( ! [X2: a,X3: a,X0: a,X1: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_255 ),
inference(trivial_inequality_removal,[],[f5849]) ).
thf(f5849,plain,
( ! [X2: a,X3: a,X0: a,X1: partia96731725t_unit] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X3)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X3),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_255 ),
inference(superposition,[],[f5648,f1726]) ).
thf(f5648,plain,
( ! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) )
| ~ spl54_255 ),
inference(avatar_component_clause,[],[f5647]) ).
thf(f123195,plain,
( spl54_1031
| ~ spl54_49
| ~ spl54_1030 ),
inference(avatar_split_clause,[],[f123151,f123148,f2008,f123193]) ).
thf(f123193,plain,
( spl54_1031
<=> ! [X2: nat,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1031])]) ).
thf(f123148,plain,
( spl54_1030
<=> ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1030])]) ).
thf(f123151,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_1030 ),
inference(forward_demodulation,[],[f123149,f2010]) ).
thf(f123149,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1030 ),
inference(avatar_component_clause,[],[f123148]) ).
thf(f123150,plain,
( spl54_1030
| ~ spl54_2
| ~ spl54_254 ),
inference(avatar_split_clause,[],[f5634,f5625,f1725,f123148]) ).
thf(f5625,plain,
( spl54_254
<=> ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_254])]) ).
thf(f5634,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_254 ),
inference(trivial_inequality_removal,[],[f5633]) ).
thf(f5633,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_254 ),
inference(superposition,[],[f5626,f1726]) ).
thf(f5626,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) )
| ~ spl54_254 ),
inference(avatar_component_clause,[],[f5625]) ).
thf(f123146,plain,
( spl54_1029
| ~ spl54_9
| ~ spl54_35
| ~ spl54_214 ),
inference(avatar_split_clause,[],[f4609,f4595,f1914,f1785,f123144]) ).
thf(f123144,plain,
( spl54_1029
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1029])]) ).
thf(f4595,plain,
( spl54_214
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(partia96731725t_unit,a,sK15,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_214])]) ).
thf(f4609,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_214 ),
inference(forward_demodulation,[],[f4608,f1786]) ).
thf(f4608,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_214 ),
inference(forward_demodulation,[],[f4603,f1786]) ).
thf(f4603,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_35
| ~ spl54_214 ),
inference(superposition,[],[f4596,f1915]) ).
thf(f4596,plain,
( ! [X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,sK15,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_214 ),
inference(avatar_component_clause,[],[f4595]) ).
thf(f123142,plain,
( spl54_1028
| ~ spl54_8
| ~ spl54_34
| ~ spl54_214 ),
inference(avatar_split_clause,[],[f4607,f4595,f1910,f1781,f123140]) ).
thf(f123140,plain,
( spl54_1028
<=> ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1028])]) ).
thf(f4607,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_214 ),
inference(forward_demodulation,[],[f4606,f1782]) ).
thf(f4606,plain,
( ! [X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_214 ),
inference(forward_demodulation,[],[f4602,f1782]) ).
thf(f4602,plain,
( ! [X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_34
| ~ spl54_214 ),
inference(superposition,[],[f4596,f1911]) ).
thf(f122532,plain,
( spl54_1027
| ~ spl54_49
| ~ spl54_1023 ),
inference(avatar_split_clause,[],[f122515,f122511,f2008,f122530]) ).
thf(f122530,plain,
( spl54_1027
<=> ! [X2: a,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1027])]) ).
thf(f122511,plain,
( spl54_1023
<=> ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1023])]) ).
thf(f122515,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_1023 ),
inference(forward_demodulation,[],[f122514,f2010]) ).
thf(f122514,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1023 ),
inference(forward_demodulation,[],[f122512,f2010]) ).
thf(f122512,plain,
( ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1023 ),
inference(avatar_component_clause,[],[f122511]) ).
thf(f122528,plain,
( spl54_667
| ~ spl54_17
| ~ spl54_365
| ~ spl54_432
| ~ spl54_574
| ~ spl54_851
| ~ spl54_887 ),
inference(avatar_split_clause,[],[f105567,f101130,f95522,f31279,f18319,f16781,f1824,f41364]) ).
thf(f41364,plain,
( spl54_667
<=> ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_667])]) ).
thf(f122527,plain,
( spl54_1026
| ~ spl54_49
| ~ spl54_1022 ),
inference(avatar_split_clause,[],[f122509,f122505,f2008,f122525]) ).
thf(f122525,plain,
( spl54_1026
<=> ! [X2: a,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1026])]) ).
thf(f122505,plain,
( spl54_1022
<=> ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1022])]) ).
thf(f122509,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_1022 ),
inference(forward_demodulation,[],[f122508,f2010]) ).
thf(f122508,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1022 ),
inference(forward_demodulation,[],[f122506,f2010]) ).
thf(f122506,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1022 ),
inference(avatar_component_clause,[],[f122505]) ).
thf(f122523,plain,
( spl54_1025
| ~ spl54_32
| ~ spl54_49
| ~ spl54_265 ),
inference(avatar_split_clause,[],[f15620,f5950,f2008,f1899,f122521]) ).
thf(f122521,plain,
( spl54_1025
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1025])]) ).
thf(f15620,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_265 ),
inference(forward_demodulation,[],[f15619,f2010]) ).
thf(f15619,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_265 ),
inference(forward_demodulation,[],[f7847,f2010]) ).
thf(f7847,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_265 ),
inference(trivial_inequality_removal,[],[f7766]) ).
thf(f7766,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_265 ),
inference(superposition,[],[f5951,f1901]) ).
thf(f122519,plain,
( spl54_1024
| ~ spl54_32
| ~ spl54_49
| ~ spl54_264 ),
inference(avatar_split_clause,[],[f15618,f5946,f2008,f1899,f122517]) ).
thf(f122517,plain,
( spl54_1024
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1024])]) ).
thf(f15618,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X1)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_264 ),
inference(forward_demodulation,[],[f15617,f2010]) ).
thf(f15617,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_264 ),
inference(forward_demodulation,[],[f7848,f2010]) ).
thf(f7848,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_264 ),
inference(trivial_inequality_removal,[],[f7765]) ).
thf(f7765,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_264 ),
inference(superposition,[],[f5947,f1901]) ).
thf(f122513,plain,
( spl54_1023
| ~ spl54_2
| ~ spl54_252 ),
inference(avatar_split_clause,[],[f5613,f5589,f1725,f122511]) ).
thf(f5589,plain,
( spl54_252
<=> ! [X2: int,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_252])]) ).
thf(f5613,plain,
( ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_252 ),
inference(trivial_inequality_removal,[],[f5612]) ).
thf(f5612,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_252 ),
inference(superposition,[],[f5590,f1726]) ).
thf(f5590,plain,
( ! [X2: int,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_252 ),
inference(avatar_component_clause,[],[f5589]) ).
thf(f122507,plain,
( spl54_1022
| ~ spl54_2
| ~ spl54_251 ),
inference(avatar_split_clause,[],[f5598,f5585,f1725,f122505]) ).
thf(f5585,plain,
( spl54_251
<=> ! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_251])]) ).
thf(f5598,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_251 ),
inference(trivial_inequality_removal,[],[f5597]) ).
thf(f5597,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_251 ),
inference(superposition,[],[f5586,f1726]) ).
thf(f5586,plain,
( ! [X2: nat,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_251 ),
inference(avatar_component_clause,[],[f5585]) ).
thf(f121849,plain,
( spl54_1021
| ~ spl54_49
| ~ spl54_1013 ),
inference(avatar_split_clause,[],[f121816,f121811,f2008,f121847]) ).
thf(f121847,plain,
( spl54_1021
<=> ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1021])]) ).
thf(f121811,plain,
( spl54_1013
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1013])]) ).
thf(f121816,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),X0) ) )
| ~ spl54_49
| ~ spl54_1013 ),
inference(forward_demodulation,[],[f121815,f2010]) ).
thf(f121815,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1013 ),
inference(forward_demodulation,[],[f121814,f2010]) ).
thf(f121814,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1013 ),
inference(forward_demodulation,[],[f121812,f2010]) ).
thf(f121812,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1013 ),
inference(avatar_component_clause,[],[f121811]) ).
thf(f121845,plain,
( spl54_1020
| ~ spl54_49
| ~ spl54_1012 ),
inference(avatar_split_clause,[],[f121809,f121804,f2008,f121843]) ).
thf(f121843,plain,
( spl54_1020
<=> ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1020])]) ).
thf(f121804,plain,
( spl54_1012
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1012])]) ).
thf(f121809,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) ) )
| ~ spl54_49
| ~ spl54_1012 ),
inference(forward_demodulation,[],[f121808,f2010]) ).
thf(f121808,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1012 ),
inference(forward_demodulation,[],[f121807,f2010]) ).
thf(f121807,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1012 ),
inference(forward_demodulation,[],[f121805,f2010]) ).
thf(f121805,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1012 ),
inference(avatar_component_clause,[],[f121804]) ).
thf(f121841,plain,
( spl54_1019
| ~ spl54_49
| ~ spl54_1011 ),
inference(avatar_split_clause,[],[f121802,f121797,f2008,f121839]) ).
thf(f121839,plain,
( spl54_1019
<=> ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1019])]) ).
thf(f121797,plain,
( spl54_1011
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1011])]) ).
thf(f121802,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) ) )
| ~ spl54_49
| ~ spl54_1011 ),
inference(forward_demodulation,[],[f121801,f2010]) ).
thf(f121801,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1011 ),
inference(forward_demodulation,[],[f121800,f2010]) ).
thf(f121800,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1011 ),
inference(forward_demodulation,[],[f121798,f2010]) ).
thf(f121798,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1011 ),
inference(avatar_component_clause,[],[f121797]) ).
thf(f121837,plain,
( spl54_1018
| ~ spl54_49
| ~ spl54_1010 ),
inference(avatar_split_clause,[],[f121795,f121790,f2008,f121835]) ).
thf(f121835,plain,
( spl54_1018
<=> ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1018])]) ).
thf(f121790,plain,
( spl54_1010
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1010])]) ).
thf(f121795,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_1010 ),
inference(forward_demodulation,[],[f121794,f2010]) ).
thf(f121794,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1010 ),
inference(forward_demodulation,[],[f121793,f2010]) ).
thf(f121793,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1010 ),
inference(forward_demodulation,[],[f121791,f2010]) ).
thf(f121791,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1010 ),
inference(avatar_component_clause,[],[f121790]) ).
thf(f121833,plain,
( spl54_1017
| ~ spl54_49
| ~ spl54_1009 ),
inference(avatar_split_clause,[],[f121788,f121783,f2008,f121831]) ).
thf(f121831,plain,
( spl54_1017
<=> ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1017])]) ).
thf(f121783,plain,
( spl54_1009
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1009])]) ).
thf(f121788,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_1009 ),
inference(forward_demodulation,[],[f121787,f2010]) ).
thf(f121787,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1009 ),
inference(forward_demodulation,[],[f121786,f2010]) ).
thf(f121786,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_1009 ),
inference(forward_demodulation,[],[f121784,f2010]) ).
thf(f121784,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_1009 ),
inference(avatar_component_clause,[],[f121783]) ).
thf(f121829,plain,
( spl54_1016
| ~ spl54_41
| ~ spl54_270 ),
inference(avatar_split_clause,[],[f6048,f6030,f1941,f121827]) ).
thf(f121827,plain,
( spl54_1016
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1016])]) ).
thf(f1941,plain,
( spl54_41
<=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r2),s)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_41])]) ).
thf(f6048,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_41
| ~ spl54_270 ),
inference(trivial_inequality_removal,[],[f6035]) ).
thf(f6035,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_41
| ~ spl54_270 ),
inference(superposition,[],[f6031,f1943]) ).
thf(f1943,plain,
( ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r2),s)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true )
| ~ spl54_41 ),
inference(avatar_component_clause,[],[f1941]) ).
thf(f121825,plain,
( spl54_1015
| ~ spl54_42
| ~ spl54_270 ),
inference(avatar_split_clause,[],[f6047,f6030,f1946,f121823]) ).
thf(f121823,plain,
( spl54_1015
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s2))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1015])]) ).
thf(f1946,plain,
( spl54_42
<=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r3),s2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_42])]) ).
thf(f6047,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s2))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_42
| ~ spl54_270 ),
inference(trivial_inequality_removal,[],[f6036]) ).
thf(f6036,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s2))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_42
| ~ spl54_270 ),
inference(superposition,[],[f6031,f1948]) ).
thf(f1948,plain,
( ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r3),s2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true )
| ~ spl54_42 ),
inference(avatar_component_clause,[],[f1946]) ).
thf(f121821,plain,
( spl54_673
| ~ spl54_120
| ~ spl54_141
| ~ spl54_293
| ~ spl54_443
| ~ spl54_506
| ~ spl54_666
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f104295,f101139,f41325,f20347,f18486,f7094,f3336,f3069,f41848]) ).
thf(f41848,plain,
( spl54_673
<=> ! [X0: int] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_673])]) ).
thf(f7094,plain,
( spl54_293
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_293])]) ).
thf(f41325,plain,
( spl54_666
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_666])]) ).
thf(f104295,plain,
( ! [X1: int] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_293
| ~ spl54_443
| ~ spl54_506
| ~ spl54_666
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104294,f7096]) ).
thf(f7096,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_293 ),
inference(avatar_component_clause,[],[f7094]) ).
thf(f104294,plain,
( ! [X1: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_443
| ~ spl54_506
| ~ spl54_666
| ~ spl54_889 ),
inference(forward_demodulation,[],[f101257,f101280]) ).
thf(f101257,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_443
| ~ spl54_666
| ~ spl54_889 ),
inference(forward_demodulation,[],[f101207,f41619]) ).
thf(f41619,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_443
| ~ spl54_666 ),
inference(trivial_inequality_removal,[],[f41572]) ).
thf(f41572,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_443
| ~ spl54_666 ),
inference(superposition,[],[f41326,f18487]) ).
thf(f41326,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) ) )
| ~ spl54_666 ),
inference(avatar_component_clause,[],[f41325]) ).
thf(f101207,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) )
| ~ spl54_443
| ~ spl54_889 ),
inference(trivial_inequality_removal,[],[f101157]) ).
thf(f101157,plain,
( ! [X0: int,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) ) )
| ~ spl54_443
| ~ spl54_889 ),
inference(superposition,[],[f101140,f18487]) ).
thf(f121820,plain,
( spl54_1014
| ~ spl54_43
| ~ spl54_270 ),
inference(avatar_split_clause,[],[f6046,f6030,f1951,f121818]) ).
thf(f121818,plain,
( spl54_1014
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1014])]) ).
thf(f1951,plain,
( spl54_43
<=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r4),s3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_43])]) ).
thf(f6046,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_43
| ~ spl54_270 ),
inference(trivial_inequality_removal,[],[f6037]) ).
thf(f6037,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) )
| ~ spl54_43
| ~ spl54_270 ),
inference(superposition,[],[f6031,f1953]) ).
thf(f1953,plain,
( ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r4),s3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true )
| ~ spl54_43 ),
inference(avatar_component_clause,[],[f1951]) ).
thf(f121813,plain,
( spl54_1013
| ~ spl54_2
| ~ spl54_250 ),
inference(avatar_split_clause,[],[f5579,f5523,f1725,f121811]) ).
thf(f5523,plain,
( spl54_250
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_250])]) ).
thf(f5579,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_250 ),
inference(trivial_inequality_removal,[],[f5578]) ).
thf(f5578,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_250 ),
inference(superposition,[],[f5524,f1726]) ).
thf(f5524,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_250 ),
inference(avatar_component_clause,[],[f5523]) ).
thf(f121806,plain,
( spl54_1012
| ~ spl54_2
| ~ spl54_249 ),
inference(avatar_split_clause,[],[f5567,f5519,f1725,f121804]) ).
thf(f5519,plain,
( spl54_249
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_249])]) ).
thf(f5567,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_249 ),
inference(trivial_inequality_removal,[],[f5566]) ).
thf(f5566,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_249 ),
inference(superposition,[],[f5520,f1726]) ).
thf(f5520,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_249 ),
inference(avatar_component_clause,[],[f5519]) ).
thf(f121799,plain,
( spl54_1011
| ~ spl54_2
| ~ spl54_248 ),
inference(avatar_split_clause,[],[f5556,f5512,f1725,f121797]) ).
thf(f5512,plain,
( spl54_248
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_248])]) ).
thf(f5556,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_248 ),
inference(trivial_inequality_removal,[],[f5555]) ).
thf(f5555,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_248 ),
inference(superposition,[],[f5513,f1726]) ).
thf(f5513,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_248 ),
inference(avatar_component_clause,[],[f5512]) ).
thf(f121792,plain,
( spl54_1010
| ~ spl54_2
| ~ spl54_247 ),
inference(avatar_split_clause,[],[f5545,f5508,f1725,f121790]) ).
thf(f5508,plain,
( spl54_247
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_247])]) ).
thf(f5545,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_247 ),
inference(trivial_inequality_removal,[],[f5544]) ).
thf(f5544,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_247 ),
inference(superposition,[],[f5509,f1726]) ).
thf(f5509,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_247 ),
inference(avatar_component_clause,[],[f5508]) ).
thf(f121785,plain,
( spl54_1009
| ~ spl54_2
| ~ spl54_246 ),
inference(avatar_split_clause,[],[f5532,f5504,f1725,f121783]) ).
thf(f5504,plain,
( spl54_246
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_246])]) ).
thf(f5532,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_246 ),
inference(trivial_inequality_removal,[],[f5531]) ).
thf(f5531,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_246 ),
inference(superposition,[],[f5505,f1726]) ).
thf(f5505,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_246 ),
inference(avatar_component_clause,[],[f5504]) ).
thf(f121732,plain,
( spl54_1008
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1007 ),
inference(avatar_split_clause,[],[f121728,f121721,f16940,f2008,f121730]) ).
thf(f121730,plain,
( spl54_1008
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1008])]) ).
thf(f121721,plain,
( spl54_1007
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1007])]) ).
thf(f121728,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1007 ),
inference(forward_demodulation,[],[f121727,f16942]) ).
thf(f121727,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1007 ),
inference(forward_demodulation,[],[f121726,f2010]) ).
thf(f121726,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1007 ),
inference(forward_demodulation,[],[f121725,f2010]) ).
thf(f121725,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1007 ),
inference(forward_demodulation,[],[f121724,f2010]) ).
thf(f121724,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) ) )
| ~ spl54_370
| ~ spl54_1007 ),
inference(forward_demodulation,[],[f121722,f16942]) ).
thf(f121722,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) ) )
| ~ spl54_1007 ),
inference(avatar_component_clause,[],[f121721]) ).
thf(f121723,plain,
( spl54_1007
| ~ spl54_129
| ~ spl54_223 ),
inference(avatar_split_clause,[],[f4711,f4704,f3223,f121721]) ).
thf(f4711,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) ) )
| ~ spl54_129
| ~ spl54_223 ),
inference(superposition,[],[f4705,f3224]) ).
thf(f121715,plain,
( ~ spl54_490
| ~ spl54_488
| ~ spl54_496 ),
inference(avatar_split_clause,[],[f19606,f19576,f19345,f19405]) ).
thf(f19345,plain,
( spl54_488
<=> ! [X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_488])]) ).
thf(f19576,plain,
( spl54_496
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),vAPP(a,a,sK32,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_496])]) ).
thf(f19606,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_488
| ~ spl54_496 ),
inference(trivial_inequality_removal,[],[f19598]) ).
thf(f19598,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_488
| ~ spl54_496 ),
inference(superposition,[],[f19346,f19578]) ).
thf(f19578,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),vAPP(a,a,sK32,sK7)) )
| ~ spl54_496 ),
inference(avatar_component_clause,[],[f19576]) ).
thf(f19346,plain,
( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_488 ),
inference(avatar_component_clause,[],[f19345]) ).
thf(f121688,plain,
( spl54_1006
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1005 ),
inference(avatar_split_clause,[],[f121684,f121678,f16940,f2008,f121686]) ).
thf(f121686,plain,
( spl54_1006
<=> ! [X0: nat,X1: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1006])]) ).
thf(f121678,plain,
( spl54_1005
<=> ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1005])]) ).
thf(f121684,plain,
( ! [X0: nat,X1: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1005 ),
inference(forward_demodulation,[],[f121683,f16942]) ).
thf(f121683,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1005 ),
inference(forward_demodulation,[],[f121682,f2010]) ).
thf(f121682,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_1005 ),
inference(forward_demodulation,[],[f121681,f2010]) ).
thf(f121681,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_370
| ~ spl54_1005 ),
inference(forward_demodulation,[],[f121679,f16942]) ).
thf(f121679,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_1005 ),
inference(avatar_component_clause,[],[f121678]) ).
thf(f121680,plain,
( spl54_1005
| ~ spl54_164
| ~ spl54_200 ),
inference(avatar_split_clause,[],[f4184,f4164,f3720,f121678]) ).
thf(f4164,plain,
( spl54_200
<=> ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_200])]) ).
thf(f4184,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)) ) )
| ~ spl54_164
| ~ spl54_200 ),
inference(superposition,[],[f4165,f3721]) ).
thf(f4165,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_200 ),
inference(avatar_component_clause,[],[f4164]) ).
thf(f121672,plain,
( spl54_1004
| ~ spl54_18
| ~ spl54_252 ),
inference(avatar_split_clause,[],[f5617,f5589,f1829,f121670]) ).
thf(f121670,plain,
( spl54_1004
<=> ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1004])]) ).
thf(f5617,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_252 ),
inference(trivial_inequality_removal,[],[f5608]) ).
thf(f5608,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_252 ),
inference(superposition,[],[f5590,f1831]) ).
thf(f121664,plain,
( spl54_1003
| ~ spl54_18
| ~ spl54_251 ),
inference(avatar_split_clause,[],[f5602,f5585,f1829,f121662]) ).
thf(f121662,plain,
( spl54_1003
<=> ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1003])]) ).
thf(f5602,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_251 ),
inference(trivial_inequality_removal,[],[f5593]) ).
thf(f5593,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_251 ),
inference(superposition,[],[f5586,f1831]) ).
thf(f121657,plain,
( spl54_1002
| ~ spl54_18
| ~ spl54_250 ),
inference(avatar_split_clause,[],[f5583,f5523,f1829,f121655]) ).
thf(f121655,plain,
( spl54_1002
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1002])]) ).
thf(f5583,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_250 ),
inference(trivial_inequality_removal,[],[f5574]) ).
thf(f5574,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_250 ),
inference(superposition,[],[f5524,f1831]) ).
thf(f121650,plain,
( spl54_1001
| ~ spl54_19
| ~ spl54_250 ),
inference(avatar_split_clause,[],[f5582,f5523,f1834,f121648]) ).
thf(f121648,plain,
( spl54_1001
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1001])]) ).
thf(f5582,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_250 ),
inference(trivial_inequality_removal,[],[f5575]) ).
thf(f5575,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_250 ),
inference(superposition,[],[f5524,f1836]) ).
thf(f121643,plain,
( spl54_1000
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_249 ),
inference(avatar_split_clause,[],[f5572,f5519,f3223,f1834,f1811,f121641]) ).
thf(f121641,plain,
( spl54_1000
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1000])]) ).
thf(f1811,plain,
( spl54_14
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_14])]) ).
thf(f5572,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_249 ),
inference(forward_demodulation,[],[f5570,f3242]) ).
thf(f3242,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_14
| ~ spl54_129 ),
inference(superposition,[],[f3224,f1813]) ).
thf(f1813,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_14 ),
inference(avatar_component_clause,[],[f1811]) ).
thf(f5570,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_249 ),
inference(trivial_inequality_removal,[],[f5563]) ).
thf(f5563,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_249 ),
inference(superposition,[],[f5520,f1836]) ).
thf(f121635,plain,
( spl54_999
| ~ spl54_18
| ~ spl54_249 ),
inference(avatar_split_clause,[],[f5571,f5519,f1829,f121633]) ).
thf(f121633,plain,
( spl54_999
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_999])]) ).
thf(f5571,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_249 ),
inference(trivial_inequality_removal,[],[f5562]) ).
thf(f5562,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_249 ),
inference(superposition,[],[f5520,f1831]) ).
thf(f121628,plain,
( spl54_998
| ~ spl54_18
| ~ spl54_248 ),
inference(avatar_split_clause,[],[f5560,f5512,f1829,f121626]) ).
thf(f121626,plain,
( spl54_998
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_998])]) ).
thf(f5560,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_248 ),
inference(trivial_inequality_removal,[],[f5551]) ).
thf(f5551,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_248 ),
inference(superposition,[],[f5513,f1831]) ).
thf(f121624,plain,
( spl54_997
| ~ spl54_285
| ~ spl54_368 ),
inference(avatar_split_clause,[],[f16899,f16886,f7055,f121621]) ).
thf(f121621,plain,
( spl54_997
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_997])]) ).
thf(f7055,plain,
( spl54_285
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_285])]) ).
thf(f16886,plain,
( spl54_368
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_368])]) ).
thf(f16899,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))) )
| ~ spl54_285
| ~ spl54_368 ),
inference(superposition,[],[f7057,f16888]) ).
thf(f16888,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_368 ),
inference(avatar_component_clause,[],[f16886]) ).
thf(f7057,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))) )
| ~ spl54_285 ),
inference(avatar_component_clause,[],[f7055]) ).
thf(f121616,plain,
( spl54_996
| ~ spl54_19
| ~ spl54_248 ),
inference(avatar_split_clause,[],[f5559,f5512,f1834,f121614]) ).
thf(f121614,plain,
( spl54_996
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_996])]) ).
thf(f5559,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_248 ),
inference(trivial_inequality_removal,[],[f5552]) ).
thf(f5552,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_248 ),
inference(superposition,[],[f5513,f1836]) ).
thf(f121609,plain,
( spl54_995
| ~ spl54_18
| ~ spl54_247 ),
inference(avatar_split_clause,[],[f5549,f5508,f1829,f121607]) ).
thf(f121607,plain,
( spl54_995
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_995])]) ).
thf(f5549,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_247 ),
inference(trivial_inequality_removal,[],[f5540]) ).
thf(f5540,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_247 ),
inference(superposition,[],[f5509,f1831]) ).
thf(f121602,plain,
( spl54_994
| ~ spl54_19
| ~ spl54_247 ),
inference(avatar_split_clause,[],[f5548,f5508,f1834,f121600]) ).
thf(f121600,plain,
( spl54_994
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_994])]) ).
thf(f5548,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_247 ),
inference(trivial_inequality_removal,[],[f5541]) ).
thf(f5541,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_247 ),
inference(superposition,[],[f5509,f1836]) ).
thf(f121595,plain,
( spl54_993
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_246 ),
inference(avatar_split_clause,[],[f5538,f5504,f3223,f1834,f1811,f121593]) ).
thf(f121593,plain,
( spl54_993
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_993])]) ).
thf(f5538,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_246 ),
inference(forward_demodulation,[],[f5537,f3242]) ).
thf(f5537,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_246 ),
inference(forward_demodulation,[],[f5535,f3242]) ).
thf(f5535,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_246 ),
inference(trivial_inequality_removal,[],[f5528]) ).
thf(f5528,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_246 ),
inference(superposition,[],[f5505,f1836]) ).
thf(f121586,plain,
( spl54_992
| ~ spl54_18
| ~ spl54_246 ),
inference(avatar_split_clause,[],[f5536,f5504,f1829,f121584]) ).
thf(f121584,plain,
( spl54_992
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_992])]) ).
thf(f5536,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_246 ),
inference(trivial_inequality_removal,[],[f5527]) ).
thf(f5527,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_246 ),
inference(superposition,[],[f5505,f1831]) ).
thf(f121372,plain,
( spl54_991
| ~ spl54_2
| ~ spl54_243 ),
inference(avatar_split_clause,[],[f5476,f5453,f1725,f121370]) ).
thf(f121370,plain,
( spl54_991
<=> ! [X0: a,X3: a,X2: nat,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_991])]) ).
thf(f5453,plain,
( spl54_243
<=> ! [X0: partia1833973666xt_a_b,X3: nat,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_243])]) ).
thf(f5476,plain,
( ! [X2: nat,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_243 ),
inference(trivial_inequality_removal,[],[f5475]) ).
thf(f5475,plain,
( ! [X2: nat,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),X3)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_243 ),
inference(superposition,[],[f5454,f1726]) ).
thf(f5454,plain,
( ! [X2: a,X3: nat,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_243 ),
inference(avatar_component_clause,[],[f5453]) ).
thf(f121324,plain,
( spl54_990
| ~ spl54_2
| ~ spl54_242 ),
inference(avatar_split_clause,[],[f5464,f5449,f1725,f121322]) ).
thf(f121322,plain,
( spl54_990
<=> ! [X0: a,X3: a,X2: nat,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_990])]) ).
thf(f5449,plain,
( spl54_242
<=> ! [X0: partia1833973666xt_a_b,X3: nat,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_242])]) ).
thf(f5464,plain,
( ! [X2: nat,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_242 ),
inference(trivial_inequality_removal,[],[f5463]) ).
thf(f5463,plain,
( ! [X2: nat,X3: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X3),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X1),X2),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_242 ),
inference(superposition,[],[f5450,f1726]) ).
thf(f5450,plain,
( ! [X2: a,X3: nat,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_242 ),
inference(avatar_component_clause,[],[f5449]) ).
thf(f121320,plain,
( spl54_989
| ~ spl54_9
| ~ spl54_198 ),
inference(avatar_split_clause,[],[f4172,f4156,f1785,f121318]) ).
thf(f121318,plain,
( spl54_989
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_989])]) ).
thf(f4156,plain,
( spl54_198
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_198])]) ).
thf(f4172,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_198 ),
inference(superposition,[],[f4157,f1786]) ).
thf(f4157,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_198 ),
inference(avatar_component_clause,[],[f4156]) ).
thf(f121316,plain,
( spl54_988
| ~ spl54_8
| ~ spl54_198 ),
inference(avatar_split_clause,[],[f4171,f4156,f1781,f121314]) ).
thf(f121314,plain,
( spl54_988
<=> ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_988])]) ).
thf(f4171,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_198 ),
inference(superposition,[],[f4157,f1782]) ).
thf(f121206,plain,
( spl54_987
| ~ spl54_49
| ~ spl54_986 ),
inference(avatar_split_clause,[],[f121202,f121199,f2008,f121204]) ).
thf(f121204,plain,
( spl54_987
<=> ! [X2: int,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_987])]) ).
thf(f121199,plain,
( spl54_986
<=> ! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_986])]) ).
thf(f121202,plain,
( ! [X2: int,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) ) )
| ~ spl54_49
| ~ spl54_986 ),
inference(forward_demodulation,[],[f121200,f2010]) ).
thf(f121200,plain,
( ! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_986 ),
inference(avatar_component_clause,[],[f121199]) ).
thf(f121201,plain,
( spl54_986
| ~ spl54_2
| ~ spl54_240 ),
inference(avatar_split_clause,[],[f5432,f5423,f1725,f121199]) ).
thf(f5423,plain,
( spl54_240
<=> ! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_240])]) ).
thf(f5432,plain,
( ! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_240 ),
inference(trivial_inequality_removal,[],[f5431]) ).
thf(f5431,plain,
( ! [X2: int,X0: a,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_240 ),
inference(superposition,[],[f5424,f1726]) ).
thf(f5424,plain,
( ! [X2: int,X0: a,X1: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) ) )
| ~ spl54_240 ),
inference(avatar_component_clause,[],[f5423]) ).
thf(f121161,plain,
( spl54_985
| ~ spl54_49
| ~ spl54_370
| ~ spl54_984 ),
inference(avatar_split_clause,[],[f121157,f121152,f16940,f2008,f121159]) ).
thf(f121159,plain,
( spl54_985
<=> ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_985])]) ).
thf(f121152,plain,
( spl54_984
<=> ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_984])]) ).
thf(f121157,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_984 ),
inference(forward_demodulation,[],[f121156,f2010]) ).
thf(f121156,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_984 ),
inference(forward_demodulation,[],[f121155,f2010]) ).
thf(f121155,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1) ) )
| ~ spl54_370
| ~ spl54_984 ),
inference(forward_demodulation,[],[f121153,f16942]) ).
thf(f121153,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1) ) )
| ~ spl54_984 ),
inference(avatar_component_clause,[],[f121152]) ).
thf(f121154,plain,
( spl54_984
| ~ spl54_164
| ~ spl54_175 ),
inference(avatar_split_clause,[],[f3828,f3824,f3720,f121152]) ).
thf(f3824,plain,
( spl54_175
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_175])]) ).
thf(f3828,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1) ) )
| ~ spl54_164
| ~ spl54_175 ),
inference(superposition,[],[f3825,f3721]) ).
thf(f3825,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X0 ) )
| ~ spl54_175 ),
inference(avatar_component_clause,[],[f3824]) ).
thf(f121148,plain,
( spl54_983
| ~ spl54_32
| ~ spl54_254 ),
inference(avatar_split_clause,[],[f7849,f5625,f1899,f121146]) ).
thf(f121146,plain,
( spl54_983
<=> ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_983])]) ).
thf(f7849,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_32
| ~ spl54_254 ),
inference(trivial_inequality_removal,[],[f7764]) ).
thf(f7764,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_254 ),
inference(superposition,[],[f5626,f1901]) ).
thf(f121144,plain,
( ~ spl54_22
| ~ spl54_368
| ~ spl54_11
| ~ spl54_370 ),
inference(avatar_split_clause,[],[f41076,f16940,f1793,f16886,f1847]) ).
thf(f1793,plain,
( spl54_11
<=> ! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_11])]) ).
thf(f41076,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_11
| ~ spl54_370 ),
inference(superposition,[],[f1794,f16942]) ).
thf(f1794,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) )
| ~ spl54_11 ),
inference(avatar_component_clause,[],[f1793]) ).
thf(f121031,plain,
( spl54_982
| ~ spl54_32
| ~ spl54_49
| ~ spl54_251 ),
inference(avatar_split_clause,[],[f15877,f5585,f2008,f1899,f121029]) ).
thf(f121029,plain,
( spl54_982
<=> ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_982])]) ).
thf(f15877,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_251 ),
inference(forward_demodulation,[],[f14914,f2010]) ).
thf(f14914,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_251 ),
inference(trivial_inequality_removal,[],[f7762]) ).
thf(f7762,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_251 ),
inference(superposition,[],[f5586,f1901]) ).
thf(f121025,plain,
( spl54_981
| ~ spl54_32
| ~ spl54_49
| ~ spl54_252 ),
inference(avatar_split_clause,[],[f15876,f5589,f2008,f1899,f121023]) ).
thf(f121023,plain,
( spl54_981
<=> ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_981])]) ).
thf(f15876,plain,
( ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_252 ),
inference(forward_demodulation,[],[f14915,f2010]) ).
thf(f14915,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_252 ),
inference(trivial_inequality_removal,[],[f7763]) ).
thf(f7763,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_252 ),
inference(superposition,[],[f5590,f1901]) ).
thf(f121021,plain,
( spl54_980
| ~ spl54_2
| ~ spl54_234 ),
inference(avatar_split_clause,[],[f4967,f4958,f1725,f121019]) ).
thf(f121019,plain,
( spl54_980
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_980])]) ).
thf(f4958,plain,
( spl54_234
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_234])]) ).
thf(f4967,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_234 ),
inference(trivial_inequality_removal,[],[f4966]) ).
thf(f4966,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_234 ),
inference(superposition,[],[f4959,f1726]) ).
thf(f4959,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_234 ),
inference(avatar_component_clause,[],[f4958]) ).
thf(f120218,plain,
( ~ spl54_452
| ~ spl54_368
| spl54_576 ),
inference(avatar_split_clause,[],[f116085,f31289,f16886,f18679]) ).
thf(f18679,plain,
( spl54_452
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_452])]) ).
thf(f31289,plain,
( spl54_576
<=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_576])]) ).
thf(f116085,plain,
( ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_368
| spl54_576 ),
inference(superposition,[],[f31291,f16888]) ).
thf(f31291,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) != sK8 )
| spl54_576 ),
inference(avatar_component_clause,[],[f31289]) ).
thf(f119783,plain,
( spl54_979
| ~ spl54_17
| ~ spl54_129
| ~ spl54_365
| ~ spl54_886
| ~ spl54_906
| ~ spl54_970 ),
inference(avatar_split_clause,[],[f119745,f119742,f103743,f100542,f16781,f3223,f1824,f119781]) ).
thf(f119781,plain,
( spl54_979
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_979])]) ).
thf(f100542,plain,
( spl54_886
<=> ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_886])]) ).
thf(f103743,plain,
( spl54_906
<=> ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_906])]) ).
thf(f119742,plain,
( spl54_970
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_970])]) ).
thf(f119745,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_129
| ~ spl54_365
| ~ spl54_886
| ~ spl54_906
| ~ spl54_970 ),
inference(forward_demodulation,[],[f119743,f105152]) ).
thf(f105152,plain,
( ! [X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8) )
| ~ spl54_17
| ~ spl54_129
| ~ spl54_365
| ~ spl54_886
| ~ spl54_906 ),
inference(forward_demodulation,[],[f105141,f101059]) ).
thf(f101059,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_886 ),
inference(forward_demodulation,[],[f101058,f16783]) ).
thf(f101058,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) )
| ~ spl54_17
| ~ spl54_886 ),
inference(trivial_inequality_removal,[],[f100978]) ).
thf(f100978,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) ) )
| ~ spl54_17
| ~ spl54_886 ),
inference(superposition,[],[f100543,f1826]) ).
thf(f100543,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) ) )
| ~ spl54_886 ),
inference(avatar_component_clause,[],[f100542]) ).
thf(f105141,plain,
( ! [X0: nat,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_129
| ~ spl54_906 ),
inference(superposition,[],[f3224,f103744]) ).
thf(f103744,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_906 ),
inference(avatar_component_clause,[],[f103743]) ).
thf(f119743,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) ) )
| ~ spl54_970 ),
inference(avatar_component_clause,[],[f119742]) ).
thf(f119779,plain,
( spl54_978
| ~ spl54_17
| ~ spl54_129
| ~ spl54_365
| ~ spl54_886
| ~ spl54_906
| ~ spl54_969 ),
inference(avatar_split_clause,[],[f119740,f119736,f103743,f100542,f16781,f3223,f1824,f119777]) ).
thf(f119777,plain,
( spl54_978
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_978])]) ).
thf(f119736,plain,
( spl54_969
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_969])]) ).
thf(f119740,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_129
| ~ spl54_365
| ~ spl54_886
| ~ spl54_906
| ~ spl54_969 ),
inference(forward_demodulation,[],[f119739,f105152]) ).
thf(f119739,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_129
| ~ spl54_365
| ~ spl54_886
| ~ spl54_906
| ~ spl54_969 ),
inference(forward_demodulation,[],[f119737,f105152]) ).
thf(f119737,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) )
| ~ spl54_969 ),
inference(avatar_component_clause,[],[f119736]) ).
thf(f119775,plain,
( spl54_977
| ~ spl54_49
| ~ spl54_968 ),
inference(avatar_split_clause,[],[f119734,f119730,f2008,f119773]) ).
thf(f119773,plain,
( spl54_977
<=> ! [X2: a,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_977])]) ).
thf(f119730,plain,
( spl54_968
<=> ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_968])]) ).
thf(f119734,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),X0) ) )
| ~ spl54_49
| ~ spl54_968 ),
inference(forward_demodulation,[],[f119733,f2010]) ).
thf(f119733,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_968 ),
inference(forward_demodulation,[],[f119731,f2010]) ).
thf(f119731,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_968 ),
inference(avatar_component_clause,[],[f119730]) ).
thf(f119771,plain,
( spl54_976
| ~ spl54_49
| ~ spl54_967 ),
inference(avatar_split_clause,[],[f119728,f119724,f2008,f119769]) ).
thf(f119769,plain,
( spl54_976
<=> ! [X2: a,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_976])]) ).
thf(f119724,plain,
( spl54_967
<=> ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_967])]) ).
thf(f119728,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_967 ),
inference(forward_demodulation,[],[f119727,f2010]) ).
thf(f119727,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_967 ),
inference(forward_demodulation,[],[f119725,f2010]) ).
thf(f119725,plain,
( ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_967 ),
inference(avatar_component_clause,[],[f119724]) ).
thf(f119767,plain,
( spl54_975
| ~ spl54_49
| ~ spl54_966 ),
inference(avatar_split_clause,[],[f119722,f119718,f2008,f119765]) ).
thf(f119765,plain,
( spl54_975
<=> ! [X2: a,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_975])]) ).
thf(f119718,plain,
( spl54_966
<=> ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_966])]) ).
thf(f119722,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),X0) ) )
| ~ spl54_49
| ~ spl54_966 ),
inference(forward_demodulation,[],[f119721,f2010]) ).
thf(f119721,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_966 ),
inference(forward_demodulation,[],[f119719,f2010]) ).
thf(f119719,plain,
( ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_966 ),
inference(avatar_component_clause,[],[f119718]) ).
thf(f119763,plain,
( spl54_974
| ~ spl54_49
| ~ spl54_965 ),
inference(avatar_split_clause,[],[f119716,f119712,f2008,f119761]) ).
thf(f119761,plain,
( spl54_974
<=> ! [X2: a,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_974])]) ).
thf(f119712,plain,
( spl54_965
<=> ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_965])]) ).
thf(f119716,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_965 ),
inference(forward_demodulation,[],[f119715,f2010]) ).
thf(f119715,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_965 ),
inference(forward_demodulation,[],[f119713,f2010]) ).
thf(f119713,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_965 ),
inference(avatar_component_clause,[],[f119712]) ).
thf(f119759,plain,
( spl54_973
| ~ spl54_32
| ~ spl54_49
| ~ spl54_247 ),
inference(avatar_split_clause,[],[f15885,f5508,f2008,f1899,f119757]) ).
thf(f119757,plain,
( spl54_973
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_973])]) ).
thf(f15885,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_247 ),
inference(forward_demodulation,[],[f15884,f2010]) ).
thf(f15884,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_247 ),
inference(forward_demodulation,[],[f14910,f2010]) ).
thf(f14910,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_247 ),
inference(trivial_inequality_removal,[],[f7758]) ).
thf(f7758,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_247 ),
inference(superposition,[],[f5509,f1901]) ).
thf(f119754,plain,
( ~ spl54_452
| ~ spl54_400
| spl54_757 ),
inference(avatar_split_clause,[],[f93730,f42847,f17786,f18679]) ).
thf(f42847,plain,
( spl54_757
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_757])]) ).
thf(f93730,plain,
( ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_400
| spl54_757 ),
inference(superposition,[],[f42849,f17788]) ).
thf(f42849,plain,
( ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK8)) )
| spl54_757 ),
inference(avatar_component_clause,[],[f42847]) ).
thf(f119753,plain,
( spl54_972
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_260 ),
inference(avatar_split_clause,[],[f15709,f5840,f2008,f1899,f1766,f119751]) ).
thf(f119751,plain,
( spl54_972
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_972])]) ).
thf(f1766,plain,
( spl54_5
<=> ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_5])]) ).
thf(f15709,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_260 ),
inference(trivial_inequality_removal,[],[f15708]) ).
thf(f15708,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_260 ),
inference(forward_demodulation,[],[f15707,f1768]) ).
thf(f1768,plain,
( ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) = $true )
| ~ spl54_5 ),
inference(avatar_component_clause,[],[f1766]) ).
thf(f15707,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_260 ),
inference(forward_demodulation,[],[f15706,f2010]) ).
thf(f15706,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_260 ),
inference(forward_demodulation,[],[f7811,f2010]) ).
thf(f7811,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_260 ),
inference(trivial_inequality_removal,[],[f7802]) ).
thf(f7802,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_260 ),
inference(superposition,[],[f5841,f1901]) ).
thf(f119749,plain,
( spl54_971
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_259 ),
inference(avatar_split_clause,[],[f15696,f5663,f2008,f1899,f1761,f119747]) ).
thf(f119747,plain,
( spl54_971
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),sK8) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_971])]) ).
thf(f1761,plain,
( spl54_4
<=> ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_4])]) ).
thf(f15696,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),sK8) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_259 ),
inference(trivial_inequality_removal,[],[f15695]) ).
thf(f15695,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),sK8) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_259 ),
inference(forward_demodulation,[],[f15694,f1763]) ).
thf(f1763,plain,
( ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) = $true )
| ~ spl54_4 ),
inference(avatar_component_clause,[],[f1761]) ).
thf(f15694,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_259 ),
inference(forward_demodulation,[],[f15693,f2010]) ).
thf(f15693,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_259 ),
inference(forward_demodulation,[],[f7812,f2010]) ).
thf(f7812,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_259 ),
inference(trivial_inequality_removal,[],[f7801]) ).
thf(f7801,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_259 ),
inference(superposition,[],[f5664,f1901]) ).
thf(f119744,plain,
( spl54_970
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_258 ),
inference(avatar_split_clause,[],[f15678,f5659,f2008,f1899,f1761,f119742]) ).
thf(f15678,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_258 ),
inference(trivial_inequality_removal,[],[f15677]) ).
thf(f15677,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_258 ),
inference(forward_demodulation,[],[f15676,f1763]) ).
thf(f15676,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_258 ),
inference(forward_demodulation,[],[f15675,f2010]) ).
thf(f15675,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_258 ),
inference(forward_demodulation,[],[f7813,f2010]) ).
thf(f7813,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_258 ),
inference(trivial_inequality_removal,[],[f7800]) ).
thf(f7800,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_258 ),
inference(superposition,[],[f5660,f1901]) ).
thf(f119738,plain,
( spl54_969
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_257 ),
inference(avatar_split_clause,[],[f15671,f5655,f2008,f1899,f1761,f119736]) ).
thf(f15671,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_257 ),
inference(trivial_inequality_removal,[],[f15670]) ).
thf(f15670,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_257 ),
inference(forward_demodulation,[],[f15669,f1763]) ).
thf(f15669,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_257 ),
inference(forward_demodulation,[],[f15668,f2010]) ).
thf(f15668,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_257 ),
inference(forward_demodulation,[],[f7814,f2010]) ).
thf(f7814,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_257 ),
inference(trivial_inequality_removal,[],[f7799]) ).
thf(f7799,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_257 ),
inference(superposition,[],[f5656,f1901]) ).
thf(f119732,plain,
( spl54_968
| ~ spl54_2
| ~ spl54_233 ),
inference(avatar_split_clause,[],[f4952,f4763,f1725,f119730]) ).
thf(f4763,plain,
( spl54_233
<=> ! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_233])]) ).
thf(f4952,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_233 ),
inference(trivial_inequality_removal,[],[f4951]) ).
thf(f4951,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_233 ),
inference(superposition,[],[f4764,f1726]) ).
thf(f4764,plain,
( ! [X2: nat,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_233 ),
inference(avatar_component_clause,[],[f4763]) ).
thf(f119726,plain,
( spl54_967
| ~ spl54_2
| ~ spl54_232 ),
inference(avatar_split_clause,[],[f4940,f4759,f1725,f119724]) ).
thf(f4759,plain,
( spl54_232
<=> ! [X2: int,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_232])]) ).
thf(f4940,plain,
( ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_232 ),
inference(trivial_inequality_removal,[],[f4939]) ).
thf(f4939,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_232 ),
inference(superposition,[],[f4760,f1726]) ).
thf(f4760,plain,
( ! [X2: int,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_232 ),
inference(avatar_component_clause,[],[f4759]) ).
thf(f119720,plain,
( spl54_966
| ~ spl54_2
| ~ spl54_231 ),
inference(avatar_split_clause,[],[f4929,f4755,f1725,f119718]) ).
thf(f4755,plain,
( spl54_231
<=> ! [X2: int,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_231])]) ).
thf(f4929,plain,
( ! [X2: a,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_231 ),
inference(trivial_inequality_removal,[],[f4928]) ).
thf(f4928,plain,
( ! [X2: a,X0: a,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_231 ),
inference(superposition,[],[f4756,f1726]) ).
thf(f4756,plain,
( ! [X2: int,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_231 ),
inference(avatar_component_clause,[],[f4755]) ).
thf(f119714,plain,
( spl54_965
| ~ spl54_2
| ~ spl54_230 ),
inference(avatar_split_clause,[],[f4777,f4751,f1725,f119712]) ).
thf(f4751,plain,
( spl54_230
<=> ! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_230])]) ).
thf(f4777,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_230 ),
inference(trivial_inequality_removal,[],[f4776]) ).
thf(f4776,plain,
( ! [X2: a,X0: a,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_230 ),
inference(superposition,[],[f4752,f1726]) ).
thf(f4752,plain,
( ! [X2: nat,X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_230 ),
inference(avatar_component_clause,[],[f4751]) ).
thf(f119659,plain,
( spl54_964
| ~ spl54_90 ),
inference(avatar_split_clause,[],[f2311,f2308,f119657]) ).
thf(f119657,plain,
( spl54_964
<=> ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1))),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(sTfun(nat,$o),nat,sK53,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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_964])]) ).
thf(f2308,plain,
( spl54_90
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK53,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_90])]) ).
thf(f2311,plain,
( ! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1))),X0) )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(sTfun(nat,$o),nat,sK53,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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)))) ) )
| ~ spl54_90 ),
inference(leibniz_equality_elimination,[],[f2309]) ).
thf(f2309,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK53,X0)) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,X1) ) )
| ~ spl54_90 ),
inference(avatar_component_clause,[],[f2308]) ).
thf(f119570,plain,
( spl54_963
| ~ spl54_49
| ~ spl54_370
| ~ spl54_962 ),
inference(avatar_split_clause,[],[f119566,f119560,f16940,f2008,f119568]) ).
thf(f119568,plain,
( spl54_963
<=> ! [X0: a,X1: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_963])]) ).
thf(f119560,plain,
( spl54_962
<=> ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_962])]) ).
thf(f119566,plain,
( ! [X0: a,X1: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_962 ),
inference(forward_demodulation,[],[f119565,f16942]) ).
thf(f119565,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_962 ),
inference(forward_demodulation,[],[f119564,f2010]) ).
thf(f119564,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_962 ),
inference(forward_demodulation,[],[f119563,f2010]) ).
thf(f119563,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) ) )
| ~ spl54_370
| ~ spl54_962 ),
inference(forward_demodulation,[],[f119561,f16942]) ).
thf(f119561,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) ) )
| ~ spl54_962 ),
inference(avatar_component_clause,[],[f119560]) ).
thf(f119562,plain,
( spl54_962
| ~ spl54_129
| ~ spl54_200 ),
inference(avatar_split_clause,[],[f4183,f4164,f3223,f119560]) ).
thf(f4183,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) ) )
| ~ spl54_129
| ~ spl54_200 ),
inference(superposition,[],[f4165,f3224]) ).
thf(f118856,plain,
( spl54_961
| ~ spl54_49
| ~ spl54_955 ),
inference(avatar_split_clause,[],[f118674,f118670,f2008,f118854]) ).
thf(f118854,plain,
( spl54_961
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_961])]) ).
thf(f118670,plain,
( spl54_955
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_955])]) ).
thf(f118674,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_955 ),
inference(forward_demodulation,[],[f118673,f2010]) ).
thf(f118673,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_955 ),
inference(forward_demodulation,[],[f118671,f2010]) ).
thf(f118671,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_955 ),
inference(avatar_component_clause,[],[f118670]) ).
thf(f118852,plain,
( spl54_452
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_568
| ~ spl54_878 ),
inference(avatar_split_clause,[],[f100057,f99969,f28173,f16776,f9549,f7242,f18679]) ).
thf(f118851,plain,
( spl54_960
| ~ spl54_49
| ~ spl54_954 ),
inference(avatar_split_clause,[],[f118668,f118664,f2008,f118849]) ).
thf(f118849,plain,
( spl54_960
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_960])]) ).
thf(f118664,plain,
( spl54_954
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_954])]) ).
thf(f118668,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_954 ),
inference(forward_demodulation,[],[f118667,f2010]) ).
thf(f118667,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_954 ),
inference(forward_demodulation,[],[f118665,f2010]) ).
thf(f118665,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_954 ),
inference(avatar_component_clause,[],[f118664]) ).
thf(f118690,plain,
( spl54_959
| ~ spl54_49
| ~ spl54_951 ),
inference(avatar_split_clause,[],[f118607,f118602,f2008,f118688]) ).
thf(f118688,plain,
( spl54_959
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_959])]) ).
thf(f118602,plain,
( spl54_951
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_951])]) ).
thf(f118607,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) != X1 ) )
| ~ spl54_49
| ~ spl54_951 ),
inference(forward_demodulation,[],[f118606,f2010]) ).
thf(f118606,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) != X1 ) )
| ~ spl54_49
| ~ spl54_951 ),
inference(forward_demodulation,[],[f118605,f2010]) ).
thf(f118605,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) != X1 ) )
| ~ spl54_49
| ~ spl54_951 ),
inference(forward_demodulation,[],[f118603,f2010]) ).
thf(f118603,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) != X1 ) )
| ~ spl54_951 ),
inference(avatar_component_clause,[],[f118602]) ).
thf(f118686,plain,
( spl54_958
| ~ spl54_49
| ~ spl54_950 ),
inference(avatar_split_clause,[],[f118600,f118595,f2008,f118684]) ).
thf(f118684,plain,
( spl54_958
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) != X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_958])]) ).
thf(f118595,plain,
( spl54_950
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_950])]) ).
thf(f118600,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) != X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) )
| ~ spl54_49
| ~ spl54_950 ),
inference(forward_demodulation,[],[f118599,f2010]) ).
thf(f118599,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) )
| ~ spl54_49
| ~ spl54_950 ),
inference(forward_demodulation,[],[f118598,f2010]) ).
thf(f118598,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) )
| ~ spl54_49
| ~ spl54_950 ),
inference(forward_demodulation,[],[f118596,f2010]) ).
thf(f118596,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) )
| ~ spl54_950 ),
inference(avatar_component_clause,[],[f118595]) ).
thf(f118682,plain,
( spl54_957
| ~ spl54_49
| ~ spl54_949 ),
inference(avatar_split_clause,[],[f118593,f118588,f2008,f118680]) ).
thf(f118680,plain,
( spl54_957
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_957])]) ).
thf(f118588,plain,
( spl54_949
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_949])]) ).
thf(f118593,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X2 ) )
| ~ spl54_49
| ~ spl54_949 ),
inference(forward_demodulation,[],[f118592,f2010]) ).
thf(f118592,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X2 ) )
| ~ spl54_49
| ~ spl54_949 ),
inference(forward_demodulation,[],[f118591,f2010]) ).
thf(f118591,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X2 ) )
| ~ spl54_49
| ~ spl54_949 ),
inference(forward_demodulation,[],[f118589,f2010]) ).
thf(f118589,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X2 ) )
| ~ spl54_949 ),
inference(avatar_component_clause,[],[f118588]) ).
thf(f118678,plain,
( spl54_956
| ~ spl54_49
| ~ spl54_948 ),
inference(avatar_split_clause,[],[f118586,f118581,f2008,f118676]) ).
thf(f118676,plain,
( spl54_956
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) != X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_956])]) ).
thf(f118581,plain,
( spl54_948
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_948])]) ).
thf(f118586,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) != X0 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) )
| ~ spl54_49
| ~ spl54_948 ),
inference(forward_demodulation,[],[f118585,f2010]) ).
thf(f118585,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) )
| ~ spl54_49
| ~ spl54_948 ),
inference(forward_demodulation,[],[f118584,f2010]) ).
thf(f118584,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) )
| ~ spl54_49
| ~ spl54_948 ),
inference(forward_demodulation,[],[f118582,f2010]) ).
thf(f118582,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) )
| ~ spl54_948 ),
inference(avatar_component_clause,[],[f118581]) ).
thf(f118672,plain,
( spl54_955
| ~ spl54_2
| ~ spl54_222 ),
inference(avatar_split_clause,[],[f4696,f4675,f1725,f118670]) ).
thf(f4675,plain,
( spl54_222
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_222])]) ).
thf(f4696,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_222 ),
inference(trivial_inequality_removal,[],[f4695]) ).
thf(f4695,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_222 ),
inference(superposition,[],[f4676,f1726]) ).
thf(f4676,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_222 ),
inference(avatar_component_clause,[],[f4675]) ).
thf(f118666,plain,
( spl54_954
| ~ spl54_2
| ~ spl54_221 ),
inference(avatar_split_clause,[],[f4683,f4671,f1725,f118664]) ).
thf(f4671,plain,
( spl54_221
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_221])]) ).
thf(f4683,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_221 ),
inference(trivial_inequality_removal,[],[f4682]) ).
thf(f4682,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_221 ),
inference(superposition,[],[f4672,f1726]) ).
thf(f4672,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_221 ),
inference(avatar_component_clause,[],[f4671]) ).
thf(f118616,plain,
( spl54_370
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f107244,f101139,f101130,f98246,f98241,f95522,f93455,f42015,f41088,f39004,f31279,f28173,f20347,f18486,f18319,f17786,f17653,f16781,f9549,f3336,f3069,f2215,f1824,f16940]) ).
thf(f118615,plain,
( spl54_953
| ~ spl54_9
| ~ spl54_35
| ~ spl54_205 ),
inference(avatar_split_clause,[],[f4258,f4237,f1914,f1785,f118613]) ).
thf(f118613,plain,
( spl54_953
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_953])]) ).
thf(f4237,plain,
( spl54_205
<=> ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_205])]) ).
thf(f4258,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_205 ),
inference(forward_demodulation,[],[f4257,f1786]) ).
thf(f4257,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_9
| ~ spl54_35
| ~ spl54_205 ),
inference(forward_demodulation,[],[f4254,f1786]) ).
thf(f4254,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_35
| ~ spl54_205 ),
inference(superposition,[],[f4238,f1915]) ).
thf(f4238,plain,
( ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) )
| ~ spl54_205 ),
inference(avatar_component_clause,[],[f4237]) ).
thf(f118611,plain,
( spl54_952
| ~ spl54_8
| ~ spl54_34
| ~ spl54_205 ),
inference(avatar_split_clause,[],[f4256,f4237,f1910,f1781,f118609]) ).
thf(f118609,plain,
( spl54_952
<=> ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_952])]) ).
thf(f4256,plain,
( ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_205 ),
inference(forward_demodulation,[],[f4255,f1782]) ).
thf(f4255,plain,
( ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_8
| ~ spl54_34
| ~ spl54_205 ),
inference(forward_demodulation,[],[f4253,f1782]) ).
thf(f4253,plain,
( ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_34
| ~ spl54_205 ),
inference(superposition,[],[f4238,f1911]) ).
thf(f118604,plain,
spl54_951,
inference(avatar_split_clause,[],[f1529,f118602]) ).
thf(f1529,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) != X1 ) ),
inference(equality_proxy_clausification,[],[f1528]) ).
thf(f1528,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1) ) ),
inference(equality_proxy_clausification,[],[f1524]) ).
thf(f1524,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2))),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1) ) ),
inference(binary_proxy_clausification,[],[f1393]) ).
thf(f1393,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2))),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f958]) ).
thf(f958,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2))),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f957]) ).
thf(f957,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2))),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f586]) ).
thf(f586,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2))),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1) ) ) ) ),
inference(fool_elimination,[],[f585]) ).
thf(f585,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
= ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) ) ) ) ),
inference(rectify,[],[f220]) ).
thf(f220,axiom,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) = X0 )
= ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_add_Oinv__solve__right) ).
thf(f118597,plain,
spl54_950,
inference(avatar_split_clause,[],[f1527,f118595]) ).
thf(f1527,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2) = X1 ) ),
inference(equality_proxy_clausification,[],[f1526]) ).
thf(f1526,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2)) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1) ) ),
inference(equality_proxy_clausification,[],[f1525]) ).
thf(f1525,plain,
! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X2))),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)),X1) ) ),
inference(binary_proxy_clausification,[],[f1393]) ).
thf(f118590,plain,
spl54_949,
inference(avatar_split_clause,[],[f1517,f118588]) ).
thf(f1517,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X2 ) ),
inference(equality_proxy_clausification,[],[f1516]) ).
thf(f1516,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X2) ) ),
inference(equality_proxy_clausification,[],[f1512]) ).
thf(f1512,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X2) ) ),
inference(binary_proxy_clausification,[],[f1395]) ).
thf(f1395,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f962]) ).
thf(f962,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f961]) ).
thf(f961,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f590]) ).
thf(f590,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X2) ) ) ) ),
inference(fool_elimination,[],[f589]) ).
thf(f589,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
= ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) ) ) ) ),
inference(rectify,[],[f222]) ).
thf(f222,axiom,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) = X0 )
= ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_add_Oinv__solve__left) ).
thf(f118583,plain,
spl54_948,
inference(avatar_split_clause,[],[f1515,f118581]) ).
thf(f1515,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X2 ) ),
inference(equality_proxy_clausification,[],[f1514]) ).
thf(f1514,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X2) ) ),
inference(equality_proxy_clausification,[],[f1513]) ).
thf(f1513,plain,
! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X2) ) ),
inference(binary_proxy_clausification,[],[f1395]) ).
thf(f118435,plain,
( spl54_947
| ~ spl54_49
| ~ spl54_945 ),
inference(avatar_split_clause,[],[f118420,f118417,f2008,f118433]) ).
thf(f118433,plain,
( spl54_947
<=> ! [X2: nat,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_947])]) ).
thf(f118417,plain,
( spl54_945
<=> ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_945])]) ).
thf(f118420,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) ) )
| ~ spl54_49
| ~ spl54_945 ),
inference(forward_demodulation,[],[f118418,f2010]) ).
thf(f118418,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_945 ),
inference(avatar_component_clause,[],[f118417]) ).
thf(f118431,plain,
( spl54_946
| ~ spl54_49
| ~ spl54_944 ),
inference(avatar_split_clause,[],[f118415,f118412,f2008,f118429]) ).
thf(f118429,plain,
( spl54_946
<=> ! [X2: int,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_946])]) ).
thf(f118412,plain,
( spl54_944
<=> ! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_944])]) ).
thf(f118415,plain,
( ! [X2: int,X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) ) )
| ~ spl54_49
| ~ spl54_944 ),
inference(forward_demodulation,[],[f118413,f2010]) ).
thf(f118413,plain,
( ! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_944 ),
inference(avatar_component_clause,[],[f118412]) ).
thf(f118419,plain,
( spl54_945
| ~ spl54_2
| ~ spl54_219 ),
inference(avatar_split_clause,[],[f4659,f4639,f1725,f118417]) ).
thf(f4639,plain,
( spl54_219
<=> ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_219])]) ).
thf(f4659,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_219 ),
inference(trivial_inequality_removal,[],[f4658]) ).
thf(f4658,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_219 ),
inference(superposition,[],[f4640,f1726]) ).
thf(f4640,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) ) )
| ~ spl54_219 ),
inference(avatar_component_clause,[],[f4639]) ).
thf(f118414,plain,
( spl54_944
| ~ spl54_2
| ~ spl54_218 ),
inference(avatar_split_clause,[],[f4647,f4635,f1725,f118412]) ).
thf(f4635,plain,
( spl54_218
<=> ! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_218])]) ).
thf(f4647,plain,
( ! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_218 ),
inference(trivial_inequality_removal,[],[f4646]) ).
thf(f4646,plain,
( ! [X2: int,X0: a,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_218 ),
inference(superposition,[],[f4636,f1726]) ).
thf(f4636,plain,
( ! [X2: int,X0: a,X1: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) ) )
| ~ spl54_218 ),
inference(avatar_component_clause,[],[f4635]) ).
thf(f118405,plain,
( spl54_943
| ~ spl54_18
| ~ spl54_174
| ~ spl54_240 ),
inference(avatar_split_clause,[],[f5437,f5423,f3810,f1829,f118403]) ).
thf(f118403,plain,
( spl54_943
<=> ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_943])]) ).
thf(f3810,plain,
( spl54_174
<=> ! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_174])]) ).
thf(f5437,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_174
| ~ spl54_240 ),
inference(forward_demodulation,[],[f5436,f3820]) ).
thf(f3820,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_174 ),
inference(trivial_inequality_removal,[],[f3813]) ).
thf(f3813,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) )
| ~ spl54_18
| ~ spl54_174 ),
inference(superposition,[],[f3811,f1831]) ).
thf(f3811,plain,
( ! [X0: a,X1: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) ) )
| ~ spl54_174 ),
inference(avatar_component_clause,[],[f3810]) ).
thf(f5436,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_18
| ~ spl54_240 ),
inference(trivial_inequality_removal,[],[f5427]) ).
thf(f5427,plain,
( ! [X0: int,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) ) )
| ~ spl54_18
| ~ spl54_240 ),
inference(superposition,[],[f5424,f1831]) ).
thf(f117589,plain,
( spl54_942
| ~ spl54_17
| ~ spl54_49
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889
| ~ spl54_941 ),
inference(avatar_split_clause,[],[f117585,f117581,f101139,f101130,f98246,f98241,f95522,f93455,f42015,f41088,f39004,f31279,f28173,f20347,f18486,f18319,f17786,f17653,f16781,f9549,f3336,f3069,f2215,f2008,f1824,f117587]) ).
thf(f117587,plain,
( spl54_942
<=> ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_942])]) ).
thf(f117581,plain,
( spl54_941
<=> ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_941])]) ).
thf(f117585,plain,
( ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) ) )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889
| ~ spl54_941 ),
inference(forward_demodulation,[],[f117584,f2010]) ).
thf(f117584,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889
| ~ spl54_941 ),
inference(forward_demodulation,[],[f117582,f107244]) ).
thf(f117582,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_941 ),
inference(avatar_component_clause,[],[f117581]) ).
thf(f117583,plain,
( spl54_941
| ~ spl54_14
| ~ spl54_19
| ~ spl54_70
| ~ spl54_129
| ~ spl54_252 ),
inference(avatar_split_clause,[],[f5619,f5589,f3223,f2152,f1834,f1811,f117581]) ).
thf(f2152,plain,
( spl54_70
<=> ! [X0: int] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_70])]) ).
thf(f5619,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_70
| ~ spl54_129
| ~ spl54_252 ),
inference(forward_demodulation,[],[f5618,f3242]) ).
thf(f5618,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_70
| ~ spl54_252 ),
inference(forward_demodulation,[],[f5616,f2153]) ).
thf(f2153,plain,
( ! [X0: int] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_70 ),
inference(avatar_component_clause,[],[f2152]) ).
thf(f5616,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_252 ),
inference(trivial_inequality_removal,[],[f5609]) ).
thf(f5609,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_252 ),
inference(superposition,[],[f5590,f1836]) ).
thf(f117415,plain,
( spl54_940
| ~ spl54_17
| ~ spl54_49
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889
| ~ spl54_939 ),
inference(avatar_split_clause,[],[f117411,f117407,f101139,f101130,f98246,f98241,f95522,f93455,f42015,f41088,f39004,f31279,f28173,f20347,f18486,f18319,f17786,f17653,f16781,f9549,f3336,f3069,f2215,f2008,f1824,f117413]) ).
thf(f117413,plain,
( spl54_940
<=> ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_940])]) ).
thf(f117407,plain,
( spl54_939
<=> ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_939])]) ).
thf(f117411,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) ) )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889
| ~ spl54_939 ),
inference(forward_demodulation,[],[f117410,f2010]) ).
thf(f117410,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_384
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_823
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889
| ~ spl54_939 ),
inference(forward_demodulation,[],[f117408,f107244]) ).
thf(f117408,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_939 ),
inference(avatar_component_clause,[],[f117407]) ).
thf(f117409,plain,
( spl54_939
| ~ spl54_14
| ~ spl54_19
| ~ spl54_68
| ~ spl54_129
| ~ spl54_251 ),
inference(avatar_split_clause,[],[f5604,f5585,f3223,f2144,f1834,f1811,f117407]) ).
thf(f2144,plain,
( spl54_68
<=> ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_68])]) ).
thf(f5604,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_68
| ~ spl54_129
| ~ spl54_251 ),
inference(forward_demodulation,[],[f5603,f3242]) ).
thf(f5603,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_68
| ~ spl54_251 ),
inference(forward_demodulation,[],[f5601,f2145]) ).
thf(f2145,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_68 ),
inference(avatar_component_clause,[],[f2144]) ).
thf(f5601,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_251 ),
inference(trivial_inequality_removal,[],[f5594]) ).
thf(f5594,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_251 ),
inference(superposition,[],[f5586,f1836]) ).
thf(f117403,plain,
( spl54_938
| ~ spl54_18
| ~ spl54_233 ),
inference(avatar_split_clause,[],[f4956,f4763,f1829,f117401]) ).
thf(f117401,plain,
( spl54_938
<=> ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_938])]) ).
thf(f4956,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_233 ),
inference(trivial_inequality_removal,[],[f4947]) ).
thf(f4947,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_233 ),
inference(superposition,[],[f4764,f1831]) ).
thf(f117397,plain,
( spl54_937
| ~ spl54_19
| ~ spl54_233 ),
inference(avatar_split_clause,[],[f4955,f4763,f1834,f117395]) ).
thf(f117395,plain,
( spl54_937
<=> ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_937])]) ).
thf(f4955,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_233 ),
inference(trivial_inequality_removal,[],[f4948]) ).
thf(f4948,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_233 ),
inference(superposition,[],[f4764,f1836]) ).
thf(f117390,plain,
( spl54_936
| ~ spl54_18
| ~ spl54_232 ),
inference(avatar_split_clause,[],[f4944,f4759,f1829,f117388]) ).
thf(f117388,plain,
( spl54_936
<=> ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_936])]) ).
thf(f4944,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_232 ),
inference(trivial_inequality_removal,[],[f4935]) ).
thf(f4935,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_232 ),
inference(superposition,[],[f4760,f1831]) ).
thf(f117384,plain,
( spl54_935
| ~ spl54_18
| ~ spl54_231 ),
inference(avatar_split_clause,[],[f4933,f4755,f1829,f117382]) ).
thf(f117382,plain,
( spl54_935
<=> ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_935])]) ).
thf(f4933,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_231 ),
inference(trivial_inequality_removal,[],[f4924]) ).
thf(f4924,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_231 ),
inference(superposition,[],[f4756,f1831]) ).
thf(f117378,plain,
( spl54_934
| ~ spl54_19
| ~ spl54_231 ),
inference(avatar_split_clause,[],[f4932,f4755,f1834,f117376]) ).
thf(f117376,plain,
( spl54_934
<=> ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_934])]) ).
thf(f4932,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_231 ),
inference(trivial_inequality_removal,[],[f4925]) ).
thf(f4925,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_231 ),
inference(superposition,[],[f4756,f1836]) ).
thf(f117371,plain,
( spl54_933
| ~ spl54_18
| ~ spl54_230 ),
inference(avatar_split_clause,[],[f4780,f4751,f1829,f117369]) ).
thf(f117369,plain,
( spl54_933
<=> ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_933])]) ).
thf(f4780,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_230 ),
inference(trivial_inequality_removal,[],[f4773]) ).
thf(f4773,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_230 ),
inference(superposition,[],[f4752,f1831]) ).
thf(f117361,plain,
( spl54_932
| ~ spl54_2
| ~ spl54_216 ),
inference(avatar_split_clause,[],[f4621,f4613,f1725,f117359]) ).
thf(f117359,plain,
( spl54_932
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_932])]) ).
thf(f4613,plain,
( spl54_216
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_216])]) ).
thf(f4621,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_216 ),
inference(trivial_inequality_removal,[],[f4620]) ).
thf(f4620,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_216 ),
inference(superposition,[],[f4614,f1726]) ).
thf(f4614,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_216 ),
inference(avatar_component_clause,[],[f4613]) ).
thf(f117357,plain,
spl54_931,
inference(avatar_split_clause,[],[f1471,f117355]) ).
thf(f117355,plain,
( spl54_931
<=> ! [X0: partia96731725t_unit,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( X2 != X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_931])]) ).
thf(f1471,plain,
! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[],[f1470]) ).
thf(f1470,plain,
! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) ) ),
inference(equality_proxy_clausification,[],[f1466]) ).
thf(f1466,plain,
! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) ) ),
inference(binary_proxy_clausification,[],[f1412]) ).
thf(f1412,plain,
! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f982]) ).
thf(f982,plain,
! [X0: partia96731725t_unit,X1: a,X2: a,X3: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(flattening,[],[f981]) ).
thf(f981,plain,
! [X0: partia96731725t_unit,X1: a,X2: a,X3: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(ennf_transformation,[],[f604]) ).
thf(f604,plain,
! [X0: partia96731725t_unit,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) ) ) ) ) ),
inference(fool_elimination,[],[f603]) ).
thf(f603,plain,
! [X0: partia96731725t_unit,X1: a,X2: a,X3: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1) )
= ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[],[f200]) ).
thf(f200,axiom,
! [X36: partia96731725t_unit,X7: a,X8: a,X9: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X8),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X9),X7) )
= ( X8 = X9 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_Group_Ogroup_Oright__cancel) ).
thf(f117353,plain,
spl54_930,
inference(avatar_split_clause,[],[f1469,f117351]) ).
thf(f117351,plain,
( spl54_930
<=> ! [X0: partia96731725t_unit,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_930])]) ).
thf(f1469,plain,
! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( X2 = X3 ) ),
inference(equality_proxy_clausification,[],[f1468]) ).
thf(f1468,plain,
! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) ) ),
inference(equality_proxy_clausification,[],[f1467]) ).
thf(f1467,plain,
! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) ) ),
inference(binary_proxy_clausification,[],[f1412]) ).
thf(f117349,plain,
spl54_929,
inference(avatar_split_clause,[],[f1465,f117347]) ).
thf(f117347,plain,
( spl54_929
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( X2 = X3 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_929])]) ).
thf(f1465,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( X2 = X3 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1) ) ),
inference(equality_proxy_clausification,[],[f1464]) ).
thf(f1464,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( X2 = X3 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)) ) ),
inference(equality_proxy_clausification,[],[f1460]) ).
thf(f1460,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)) ) ),
inference(binary_proxy_clausification,[],[f1414]) ).
thf(f1414,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f986]) ).
thf(f986,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(flattening,[],[f985]) ).
thf(f985,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(ennf_transformation,[],[f608]) ).
thf(f608,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)) ) ) ) ) ),
inference(fool_elimination,[],[f607]) ).
thf(f607,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1) )
= ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[],[f201]) ).
thf(f201,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a,X9: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X8),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X9),X7) )
= ( X8 = X9 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Group_Ogroup_Oright__cancel) ).
thf(f117345,plain,
spl54_928,
inference(avatar_split_clause,[],[f1463,f117343]) ).
thf(f117343,plain,
( spl54_928
<=> ! [X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( X2 != X3 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_928])]) ).
thf(f1463,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( X2 != X3 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1) ) ),
inference(equality_proxy_clausification,[],[f1462]) ).
thf(f1462,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( X2 != X3 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)) ) ),
inference(equality_proxy_clausification,[],[f1461]) ).
thf(f1461,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X2),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)) ) ),
inference(binary_proxy_clausification,[],[f1414]) ).
thf(f116903,plain,
( spl54_927
| ~ spl54_49
| ~ spl54_907 ),
inference(avatar_split_clause,[],[f104040,f103995,f2008,f116901]) ).
thf(f116901,plain,
( spl54_927
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_927])]) ).
thf(f103995,plain,
( spl54_907
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_907])]) ).
thf(f104040,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_907 ),
inference(forward_demodulation,[],[f103996,f2010]) ).
thf(f103996,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_907 ),
inference(avatar_component_clause,[],[f103995]) ).
thf(f116896,plain,
( spl54_926
| ~ spl54_49
| ~ spl54_908 ),
inference(avatar_split_clause,[],[f104039,f104002,f2008,f116894]) ).
thf(f116894,plain,
( spl54_926
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_926])]) ).
thf(f104002,plain,
( spl54_908
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_908])]) ).
thf(f104039,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_49
| ~ spl54_908 ),
inference(forward_demodulation,[],[f104003,f2010]) ).
thf(f104003,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_908 ),
inference(avatar_component_clause,[],[f104002]) ).
thf(f116282,plain,
( spl54_925
| ~ spl54_635
| ~ spl54_909 ),
inference(avatar_split_clause,[],[f104013,f104010,f39340,f116280]) ).
thf(f116280,plain,
( spl54_925
<=> ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_925])]) ).
thf(f39340,plain,
( spl54_635
<=> ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_635])]) ).
thf(f104010,plain,
( spl54_909
<=> ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_909])]) ).
thf(f104013,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) )
| ~ spl54_635
| ~ spl54_909 ),
inference(forward_demodulation,[],[f104011,f39341]) ).
thf(f39341,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) )
| ~ spl54_635 ),
inference(avatar_component_clause,[],[f39340]) ).
thf(f104011,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8))) )
| ~ spl54_909 ),
inference(avatar_component_clause,[],[f104010]) ).
thf(f116277,plain,
( spl54_924
| ~ spl54_49
| ~ spl54_863 ),
inference(avatar_split_clause,[],[f105359,f97125,f2008,f116275]) ).
thf(f116275,plain,
( spl54_924
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_924])]) ).
thf(f97125,plain,
( spl54_863
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_863])]) ).
thf(f105359,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_863 ),
inference(forward_demodulation,[],[f97126,f2010]) ).
thf(f97126,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_863 ),
inference(avatar_component_clause,[],[f97125]) ).
thf(f116272,plain,
( spl54_923
| ~ spl54_49
| ~ spl54_859 ),
inference(avatar_split_clause,[],[f104765,f97101,f2008,f116270]) ).
thf(f116270,plain,
( spl54_923
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_923])]) ).
thf(f97101,plain,
( spl54_859
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_859])]) ).
thf(f104765,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_859 ),
inference(forward_demodulation,[],[f97102,f2010]) ).
thf(f97102,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_859 ),
inference(avatar_component_clause,[],[f97101]) ).
thf(f116267,plain,
( spl54_922
| ~ spl54_49
| ~ spl54_862 ),
inference(avatar_split_clause,[],[f104764,f97119,f2008,f116265]) ).
thf(f116265,plain,
( spl54_922
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_922])]) ).
thf(f97119,plain,
( spl54_862
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_862])]) ).
thf(f104764,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_862 ),
inference(forward_demodulation,[],[f97120,f2010]) ).
thf(f97120,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_862 ),
inference(avatar_component_clause,[],[f97119]) ).
thf(f116262,plain,
( spl54_876
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_688
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_875
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f105864,f101139,f101130,f99786,f98246,f98241,f95522,f42015,f39004,f31279,f28173,f20347,f18486,f18319,f17653,f16781,f3336,f3069,f2215,f1824,f99791]) ).
thf(f99791,plain,
( spl54_876
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_876])]) ).
thf(f99786,plain,
( spl54_875
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_875])]) ).
thf(f105864,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_688
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_875
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f99787,f105691]) ).
thf(f99787,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_875 ),
inference(avatar_component_clause,[],[f99786]) ).
thf(f116048,plain,
( spl54_368
| ~ spl54_17
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f107413,f101139,f101130,f99969,f98246,f98241,f95522,f95133,f94189,f93455,f86417,f42015,f41088,f39004,f31279,f28173,f27864,f20623,f20347,f18486,f18319,f17786,f17732,f17653,f16781,f16776,f9549,f7242,f3336,f3069,f2215,f2187,f1824,f16886]) ).
thf(f115739,plain,
( spl54_886
| ~ spl54_17
| ~ spl54_365
| ~ spl54_432
| ~ spl54_574
| ~ spl54_851
| ~ spl54_885
| ~ spl54_887 ),
inference(avatar_split_clause,[],[f105641,f101130,f100537,f95522,f31279,f18319,f16781,f1824,f100542]) ).
thf(f100537,plain,
( spl54_885
<=> ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_885])]) ).
thf(f105641,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_432
| ~ spl54_574
| ~ spl54_851
| ~ spl54_885
| ~ spl54_887 ),
inference(forward_demodulation,[],[f100538,f105567]) ).
thf(f100538,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_885 ),
inference(avatar_component_clause,[],[f100537]) ).
thf(f115737,plain,
( spl54_921
| ~ spl54_49
| ~ spl54_817 ),
inference(avatar_split_clause,[],[f104705,f93421,f2008,f115735]) ).
thf(f115735,plain,
( spl54_921
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_921])]) ).
thf(f93421,plain,
( spl54_817
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_817])]) ).
thf(f104705,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_817 ),
inference(forward_demodulation,[],[f93422,f2010]) ).
thf(f93422,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_817 ),
inference(avatar_component_clause,[],[f93421]) ).
thf(f115732,plain,
( spl54_920
| ~ spl54_49
| ~ spl54_815 ),
inference(avatar_split_clause,[],[f104704,f93409,f2008,f115730]) ).
thf(f115730,plain,
( spl54_920
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_920])]) ).
thf(f93409,plain,
( spl54_815
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_815])]) ).
thf(f104704,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_815 ),
inference(forward_demodulation,[],[f93410,f2010]) ).
thf(f93410,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_815 ),
inference(avatar_component_clause,[],[f93409]) ).
thf(f115474,plain,
( spl54_919
| ~ spl54_17
| ~ spl54_49
| ~ spl54_129
| ~ spl54_141
| ~ spl54_365
| ~ spl54_368
| ~ spl54_389
| ~ spl54_432
| ~ spl54_442
| ~ spl54_536
| ~ spl54_574
| ~ spl54_666
| ~ spl54_836
| ~ spl54_851
| ~ spl54_886
| ~ spl54_906
| ~ spl54_908 ),
inference(avatar_split_clause,[],[f111499,f104002,f103743,f100542,f95522,f94042,f41325,f31279,f27864,f18480,f18319,f17732,f16886,f16781,f3336,f3223,f2008,f1824,f115472]) ).
thf(f115472,plain,
( spl54_919
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_919])]) ).
thf(f18480,plain,
( spl54_442
<=> ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_442])]) ).
thf(f94042,plain,
( spl54_836
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_836])]) ).
thf(f111499,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) ) )
| ~ spl54_17
| ~ spl54_49
| ~ spl54_129
| ~ spl54_141
| ~ spl54_365
| ~ spl54_368
| ~ spl54_389
| ~ spl54_432
| ~ spl54_442
| ~ spl54_536
| ~ spl54_574
| ~ spl54_666
| ~ spl54_836
| ~ spl54_851
| ~ spl54_886
| ~ spl54_906
| ~ spl54_908 ),
inference(forward_demodulation,[],[f111498,f2010]) ).
thf(f111498,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_17
| ~ spl54_129
| ~ spl54_141
| ~ spl54_365
| ~ spl54_368
| ~ spl54_389
| ~ spl54_432
| ~ spl54_442
| ~ spl54_536
| ~ spl54_574
| ~ spl54_666
| ~ spl54_836
| ~ spl54_851
| ~ spl54_886
| ~ spl54_906
| ~ spl54_908 ),
inference(forward_demodulation,[],[f104007,f105152]) ).
thf(f104007,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_129
| ~ spl54_141
| ~ spl54_368
| ~ spl54_389
| ~ spl54_432
| ~ spl54_442
| ~ spl54_536
| ~ spl54_574
| ~ spl54_666
| ~ spl54_836
| ~ spl54_851
| ~ spl54_908 ),
inference(forward_demodulation,[],[f104006,f3224]) ).
thf(f104006,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_141
| ~ spl54_368
| ~ spl54_389
| ~ spl54_432
| ~ spl54_442
| ~ spl54_536
| ~ spl54_574
| ~ spl54_666
| ~ spl54_836
| ~ spl54_851
| ~ spl54_908 ),
inference(forward_demodulation,[],[f104005,f103332]) ).
thf(f103332,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_141
| ~ spl54_368
| ~ spl54_389
| ~ spl54_432
| ~ spl54_442
| ~ spl54_536
| ~ spl54_574
| ~ spl54_666
| ~ spl54_836
| ~ spl54_851 ),
inference(forward_demodulation,[],[f103331,f98389]) ).
thf(f98389,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_368
| ~ spl54_389
| ~ spl54_536 ),
inference(forward_demodulation,[],[f27909,f16888]) ).
thf(f27909,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536 ),
inference(trivial_inequality_removal,[],[f27908]) ).
thf(f103331,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8)) )
| ~ spl54_368
| ~ spl54_432
| ~ spl54_442
| ~ spl54_574
| ~ spl54_666
| ~ spl54_836
| ~ spl54_851 ),
inference(forward_demodulation,[],[f97484,f95620]) ).
thf(f95620,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8) )
| ~ spl54_368
| ~ spl54_432
| ~ spl54_574
| ~ spl54_851 ),
inference(forward_demodulation,[],[f95619,f16888]) ).
thf(f97484,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8))) )
| ~ spl54_368
| ~ spl54_442
| ~ spl54_666
| ~ spl54_836 ),
inference(forward_demodulation,[],[f94158,f16888]) ).
thf(f94158,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_442
| ~ spl54_666
| ~ spl54_836 ),
inference(forward_demodulation,[],[f94107,f41616]) ).
thf(f41616,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_442
| ~ spl54_666 ),
inference(trivial_inequality_removal,[],[f41575]) ).
thf(f41575,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_442
| ~ spl54_666 ),
inference(superposition,[],[f41326,f18481]) ).
thf(f18481,plain,
( ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_442 ),
inference(avatar_component_clause,[],[f18480]) ).
thf(f94107,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) )
| ~ spl54_442
| ~ spl54_836 ),
inference(trivial_inequality_removal,[],[f94063]) ).
thf(f94063,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) ) )
| ~ spl54_442
| ~ spl54_836 ),
inference(superposition,[],[f94043,f18481]) ).
thf(f94043,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) ) )
| ~ spl54_836 ),
inference(avatar_component_clause,[],[f94042]) ).
thf(f104005,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_368
| ~ spl54_908 ),
inference(forward_demodulation,[],[f104003,f16888]) ).
thf(f115333,plain,
( spl54_836
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_688
| ~ spl54_835
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f105865,f101139,f101130,f98246,f98241,f95522,f94037,f42015,f39004,f31279,f28173,f20347,f18486,f18319,f17653,f16781,f3336,f3069,f2215,f1824,f94042]) ).
thf(f94037,plain,
( spl54_835
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_835])]) ).
thf(f105865,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_688
| ~ spl54_835
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f94038,f105691]) ).
thf(f94038,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_835 ),
inference(avatar_component_clause,[],[f94037]) ).
thf(f114956,plain,
( spl54_918
| ~ spl54_17
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_496
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f109425,f101139,f101130,f99969,f98246,f98241,f95522,f95133,f94189,f93455,f86417,f42015,f41088,f39004,f31279,f28173,f27864,f20623,f20347,f19576,f18486,f18319,f17786,f17732,f17653,f16781,f16776,f9549,f7242,f3336,f3069,f2215,f2187,f1824,f114953]) ).
thf(f114953,plain,
( spl54_918
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),vAPP(a,a,sK32,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_918])]) ).
thf(f109425,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),vAPP(a,a,sK32,sK7)) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_496
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f19578,f107413]) ).
thf(f114351,plain,
( spl54_866
| ~ spl54_17
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_659
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f109097,f101139,f101130,f99969,f98246,f98241,f95522,f95133,f94189,f93455,f86417,f42015,f41162,f41088,f39004,f31279,f28173,f27864,f20623,f20347,f18486,f18319,f17786,f17732,f17653,f16781,f16776,f9549,f7242,f3336,f3069,f2215,f2187,f1824,f98091]) ).
thf(f98091,plain,
( spl54_866
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,sK8)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_866])]) ).
thf(f41162,plain,
( spl54_659
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_659])]) ).
thf(f109097,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,sK8)),sK8) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_294
| ~ spl54_295
| ~ spl54_364
| ~ spl54_365
| ~ spl54_384
| ~ spl54_389
| ~ spl54_400
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_525
| ~ spl54_536
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_657
| ~ spl54_659
| ~ spl54_688
| ~ spl54_771
| ~ spl54_823
| ~ spl54_837
| ~ spl54_843
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_878
| ~ spl54_887
| ~ spl54_889 ),
inference(forward_demodulation,[],[f41164,f107413]) ).
thf(f41164,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_659 ),
inference(avatar_component_clause,[],[f41162]) ).
thf(f114329,plain,
( spl54_410
| spl54_22
| ~ spl54_49
| ~ spl54_503 ),
inference(avatar_split_clause,[],[f106997,f20228,f2008,f1847,f18115]) ).
thf(f20228,plain,
( spl54_503
<=> ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_503])]) ).
thf(f106997,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_49
| ~ spl54_503 ),
inference(trivial_inequality_removal,[],[f106996]) ).
thf(f106996,plain,
( ( $true = $false )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_49
| ~ spl54_503 ),
inference(forward_demodulation,[],[f17634,f20230]) ).
thf(f20230,plain,
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_503 ),
inference(avatar_component_clause,[],[f20228]) ).
thf(f17634,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_49 ),
inference(forward_demodulation,[],[f1128,f2010]) ).
thf(f1128,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) ),
inference(cnf_transformation,[],[f1024]) ).
thf(f1024,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != sK7 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f719,f1023]) ).
thf(f1023,plain,
( ? [X0: a] :
( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
=> ( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != sK7 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f719,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ? [X0: a] :
( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) ),
inference(flattening,[],[f718]) ).
thf(f718,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ? [X0: a] :
( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) ),
inference(ennf_transformation,[],[f300]) ).
thf(f300,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
=> ( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 )
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ) ) )
=> ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true ) ) ),
inference(fool_elimination,[],[f299]) ).
thf(f299,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
=> ( ! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 )
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) )
=> vAPP(partia1833973666xt_a_b,$o,field_a_b,r) ) ),
inference(rectify,[],[f89]) ).
thf(f89,axiom,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
=> ( ! [X25: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X25),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X25 )
=> ? [X32: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X25),X32) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X32),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) )
=> vAPP(partia1833973666xt_a_b,$o,field_a_b,r) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_cring__fieldI2) ).
thf(f106265,plain,
( spl54_370
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_432
| ~ spl54_574
| ~ spl54_629
| ~ spl54_851
| ~ spl54_887 ),
inference(avatar_split_clause,[],[f105631,f101130,f95522,f39004,f31279,f18319,f16781,f3336,f1824,f16940]) ).
thf(f106217,plain,
( spl54_917
| ~ spl54_674
| ~ spl54_906 ),
inference(avatar_split_clause,[],[f104179,f103743,f41852,f106215]) ).
thf(f106215,plain,
( spl54_917
<=> ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_917])]) ).
thf(f41852,plain,
( spl54_674
<=> ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_674])]) ).
thf(f104179,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) )
| ~ spl54_674
| ~ spl54_906 ),
inference(forward_demodulation,[],[f41853,f103744]) ).
thf(f41853,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_674 ),
inference(avatar_component_clause,[],[f41852]) ).
thf(f106208,plain,
( spl54_916
| ~ spl54_633
| ~ spl54_672
| ~ spl54_682
| ~ spl54_906 ),
inference(avatar_split_clause,[],[f104063,f103743,f41942,f41842,f39319,f106206]) ).
thf(f106206,plain,
( spl54_916
<=> ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(nat,int,semiri2019852685at_int,X0)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_916])]) ).
thf(f39319,plain,
( spl54_633
<=> ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_633])]) ).
thf(f41842,plain,
( spl54_672
<=> ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_672])]) ).
thf(f41942,plain,
( spl54_682
<=> ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_682])]) ).
thf(f104063,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(nat,int,semiri2019852685at_int,X0)),sK8) )
| ~ spl54_633
| ~ spl54_672
| ~ spl54_682
| ~ spl54_906 ),
inference(forward_demodulation,[],[f104062,f103744]) ).
thf(f104062,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(nat,int,semiri2019852685at_int,X0)),sK8) )
| ~ spl54_633
| ~ spl54_672
| ~ spl54_682 ),
inference(forward_demodulation,[],[f41943,f104061]) ).
thf(f104061,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(nat,int,semiri2019852685at_int,X0)),sK8) )
| ~ spl54_633
| ~ spl54_672 ),
inference(forward_demodulation,[],[f41843,f39320]) ).
thf(f39320,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) )
| ~ spl54_633 ),
inference(avatar_component_clause,[],[f39319]) ).
thf(f41843,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_672 ),
inference(avatar_component_clause,[],[f41842]) ).
thf(f41943,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_682 ),
inference(avatar_component_clause,[],[f41942]) ).
thf(f105915,plain,
( spl54_836
| ~ spl54_17
| ~ spl54_80
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_432
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_574
| ~ spl54_629
| ~ spl54_688
| ~ spl54_835
| ~ spl54_851
| ~ spl54_867
| ~ spl54_868
| ~ spl54_887
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f105865,f101139,f101130,f98246,f98241,f95522,f94037,f42015,f39004,f31279,f28173,f20347,f18486,f18319,f17653,f16781,f3336,f3069,f2215,f1824,f94042]) ).
thf(f105912,plain,
( spl54_915
| ~ spl54_633
| ~ spl54_672 ),
inference(avatar_split_clause,[],[f104061,f41842,f39319,f105910]) ).
thf(f105910,plain,
( spl54_915
<=> ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(nat,int,semiri2019852685at_int,X0)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_915])]) ).
thf(f105908,plain,
( spl54_914
| ~ spl54_632
| ~ spl54_633 ),
inference(avatar_split_clause,[],[f104060,f39319,f39314,f105906]) ).
thf(f105906,plain,
( spl54_914
<=> ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_914])]) ).
thf(f39314,plain,
( spl54_632
<=> ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_632])]) ).
thf(f104060,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_632
| ~ spl54_633 ),
inference(forward_demodulation,[],[f39315,f39320]) ).
thf(f39315,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_632 ),
inference(avatar_component_clause,[],[f39314]) ).
thf(f105642,plain,
( spl54_370
| ~ spl54_17
| ~ spl54_120
| ~ spl54_141
| ~ spl54_293
| ~ spl54_295
| ~ spl54_365
| ~ spl54_366
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_666
| ~ spl54_823
| ~ spl54_836
| ~ spl54_869
| ~ spl54_879
| ~ spl54_889 ),
inference(avatar_split_clause,[],[f104348,f101139,f100131,f98251,f94042,f93455,f41325,f28173,f20347,f18486,f16821,f16781,f9549,f7094,f3336,f3069,f1824,f16940]) ).
thf(f16821,plain,
( spl54_366
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_366])]) ).
thf(f98251,plain,
( spl54_869
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_869])]) ).
thf(f100131,plain,
( spl54_879
<=> ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_879])]) ).
thf(f104348,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_120
| ~ spl54_141
| ~ spl54_293
| ~ spl54_295
| ~ spl54_365
| ~ spl54_366
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_666
| ~ spl54_823
| ~ spl54_836
| ~ spl54_869
| ~ spl54_879
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104347,f104295]) ).
thf(f104347,plain,
( ! [X0: int,X1: int] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) )
| ~ spl54_17
| ~ spl54_120
| ~ spl54_141
| ~ spl54_293
| ~ spl54_295
| ~ spl54_365
| ~ spl54_366
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_666
| ~ spl54_823
| ~ spl54_836
| ~ spl54_869
| ~ spl54_879
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104346,f104072]) ).
thf(f104072,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_366
| ~ spl54_568
| ~ spl54_823
| ~ spl54_836
| ~ spl54_869 ),
inference(forward_demodulation,[],[f104071,f94126]) ).
thf(f94126,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_836 ),
inference(forward_demodulation,[],[f94125,f16783]) ).
thf(f94125,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) )
| ~ spl54_17
| ~ spl54_836 ),
inference(trivial_inequality_removal,[],[f94045]) ).
thf(f94045,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) )
| ~ spl54_17
| ~ spl54_836 ),
inference(superposition,[],[f94043,f1826]) ).
thf(f104071,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_295
| ~ spl54_365
| ~ spl54_366
| ~ spl54_568
| ~ spl54_823
| ~ spl54_836
| ~ spl54_869 ),
inference(forward_demodulation,[],[f99599,f94126]) ).
thf(f99599,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_141
| ~ spl54_295
| ~ spl54_366
| ~ spl54_568
| ~ spl54_823
| ~ spl54_869 ),
inference(forward_demodulation,[],[f93672,f99147]) ).
thf(f99147,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_141
| ~ spl54_295
| ~ spl54_568
| ~ spl54_869 ),
inference(forward_demodulation,[],[f99024,f35104]) ).
thf(f99024,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_141
| ~ spl54_869 ),
inference(trivial_inequality_removal,[],[f99020]) ).
thf(f99020,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_141
| ~ spl54_869 ),
inference(superposition,[],[f98252,f3338]) ).
thf(f98252,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_869 ),
inference(avatar_component_clause,[],[f98251]) ).
thf(f93672,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_366
| ~ spl54_823 ),
inference(trivial_inequality_removal,[],[f93616]) ).
thf(f93616,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_366
| ~ spl54_823 ),
inference(superposition,[],[f93456,f16823]) ).
thf(f16823,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_366 ),
inference(avatar_component_clause,[],[f16821]) ).
thf(f104346,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_293
| ~ spl54_443
| ~ spl54_506
| ~ spl54_666
| ~ spl54_879
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104345,f104295]) ).
thf(f104345,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),sK8) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_293
| ~ spl54_443
| ~ spl54_506
| ~ spl54_666
| ~ spl54_879
| ~ spl54_889 ),
inference(forward_demodulation,[],[f100132,f104295]) ).
thf(f100132,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),sK8)) )
| ~ spl54_879 ),
inference(avatar_component_clause,[],[f100131]) ).
thf(f105290,plain,
( spl54_370
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_629
| ~ spl54_886 ),
inference(avatar_split_clause,[],[f104172,f100542,f39004,f16781,f3336,f1824,f16940]) ).
thf(f104172,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_629
| ~ spl54_886 ),
inference(forward_demodulation,[],[f39264,f101059]) ).
thf(f105182,plain,
( spl54_368
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_300
| ~ spl54_311
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_497
| ~ spl54_498
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_776
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889
| ~ spl54_913 ),
inference(avatar_split_clause,[],[f105181,f105177,f101139,f100542,f99969,f99791,f98251,f98241,f93463,f86459,f42015,f41321,f39004,f28173,f20347,f19832,f19827,f18486,f17673,f17653,f16781,f14472,f9806,f9761,f3336,f3223,f3069,f2187,f1824,f16886]) ).
thf(f9761,plain,
( spl54_300
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_300])]) ).
thf(f9806,plain,
( spl54_311
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_311])]) ).
thf(f14472,plain,
( spl54_362
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_362])]) ).
thf(f17673,plain,
( spl54_387
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_387])]) ).
thf(f19827,plain,
( spl54_497
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_497])]) ).
thf(f19832,plain,
( spl54_498
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_498])]) ).
thf(f41321,plain,
( spl54_665
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_665])]) ).
thf(f86459,plain,
( spl54_776
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_776])]) ).
thf(f93463,plain,
( spl54_825
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_825])]) ).
thf(f105177,plain,
( spl54_913
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_913])]) ).
thf(f105181,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_300
| ~ spl54_311
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_497
| ~ spl54_498
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_776
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889
| ~ spl54_913 ),
inference(forward_demodulation,[],[f105179,f104807]) ).
thf(f104807,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_300
| ~ spl54_311
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_497
| ~ spl54_498
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_776
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104806,f104528]) ).
thf(f104528,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_300
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_497
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104527,f104517]) ).
thf(f104517,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_688
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104516,f104512]) ).
thf(f104512,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_362
| ~ spl54_365
| ~ spl54_387
| ~ spl54_629
| ~ spl54_825
| ~ spl54_869
| ~ spl54_886 ),
inference(forward_demodulation,[],[f104511,f14474]) ).
thf(f14474,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_362 ),
inference(avatar_component_clause,[],[f14472]) ).
thf(f104511,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_362
| ~ spl54_365
| ~ spl54_387
| ~ spl54_629
| ~ spl54_825
| ~ spl54_869
| ~ spl54_886 ),
inference(forward_demodulation,[],[f104510,f104172]) ).
thf(f104510,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_362
| ~ spl54_387
| ~ spl54_825
| ~ spl54_869 ),
inference(forward_demodulation,[],[f99051,f104150]) ).
thf(f104150,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_362
| ~ spl54_387
| ~ spl54_825 ),
inference(forward_demodulation,[],[f93957,f17675]) ).
thf(f17675,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_387 ),
inference(avatar_component_clause,[],[f17673]) ).
thf(f93957,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_362
| ~ spl54_825 ),
inference(forward_demodulation,[],[f93936,f17585]) ).
thf(f17585,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_129
| ~ spl54_362 ),
inference(superposition,[],[f3224,f14474]) ).
thf(f93936,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_78
| ~ spl54_825 ),
inference(trivial_inequality_removal,[],[f93878]) ).
thf(f93878,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_78
| ~ spl54_825 ),
inference(superposition,[],[f93464,f2189]) ).
thf(f93464,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) )
| ~ spl54_825 ),
inference(avatar_component_clause,[],[f93463]) ).
thf(f99051,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_78
| ~ spl54_869 ),
inference(trivial_inequality_removal,[],[f98993]) ).
thf(f98993,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_78
| ~ spl54_869 ),
inference(superposition,[],[f98252,f2189]) ).
thf(f104516,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ~ spl54_17
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_688
| ~ spl54_867
| ~ spl54_869
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104515,f104499]) ).
thf(f104499,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_384
| ~ spl54_568
| ~ spl54_629
| ~ spl54_869
| ~ spl54_886 ),
inference(forward_demodulation,[],[f99063,f104172]) ).
thf(f99063,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_17
| ~ spl54_384
| ~ spl54_568
| ~ spl54_869 ),
inference(forward_demodulation,[],[f99062,f35102]) ).
thf(f99062,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_17
| ~ spl54_869 ),
inference(trivial_inequality_removal,[],[f98982]) ).
thf(f98982,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_17
| ~ spl54_869 ),
inference(superposition,[],[f98252,f1826]) ).
thf(f104515,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) )
| ~ spl54_17
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_688
| ~ spl54_867
| ~ spl54_869
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104514,f104443]) ).
thf(f104443,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) )
| ~ spl54_17
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_688
| ~ spl54_867
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104442,f101280]) ).
thf(f104442,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) )
| ~ spl54_17
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_443
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_688
| ~ spl54_867
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104441,f101280]) ).
thf(f104441,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_443
| ~ spl54_568
| ~ spl54_629
| ~ spl54_688
| ~ spl54_867
| ~ spl54_886 ),
inference(forward_demodulation,[],[f99313,f104172]) ).
thf(f104514,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8)) )
| ~ spl54_17
| ~ spl54_120
| ~ spl54_141
| ~ spl54_365
| ~ spl54_443
| ~ spl54_506
| ~ spl54_629
| ~ spl54_869
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104513,f101280]) ).
thf(f104513,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_443
| ~ spl54_629
| ~ spl54_869
| ~ spl54_886 ),
inference(forward_demodulation,[],[f99047,f104172]) ).
thf(f99047,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_443
| ~ spl54_869 ),
inference(trivial_inequality_removal,[],[f98997]) ).
thf(f98997,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_443
| ~ spl54_869 ),
inference(superposition,[],[f98252,f18487]) ).
thf(f104527,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_300
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_497
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104526,f104499]) ).
thf(f104526,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_300
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_497
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104525,f9763]) ).
thf(f9763,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_300 ),
inference(avatar_component_clause,[],[f9761]) ).
thf(f104525,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_497
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104524,f104517]) ).
thf(f104524,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_497
| ~ spl54_629
| ~ spl54_665
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886 ),
inference(forward_demodulation,[],[f104523,f104448]) ).
thf(f104448,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_497
| ~ spl54_629
| ~ spl54_665
| ~ spl54_867
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886 ),
inference(forward_demodulation,[],[f104447,f104360]) ).
thf(f104360,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_497
| ~ spl54_665
| ~ spl54_876
| ~ spl54_878 ),
inference(forward_demodulation,[],[f99924,f104351]) ).
thf(f104351,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_497
| ~ spl54_665
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100031,f41523]) ).
thf(f41523,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_497
| ~ spl54_665 ),
inference(trivial_inequality_removal,[],[f41490]) ).
thf(f41490,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_497
| ~ spl54_665 ),
inference(superposition,[],[f41322,f19829]) ).
thf(f19829,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_497 ),
inference(avatar_component_clause,[],[f19827]) ).
thf(f41322,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) ) )
| ~ spl54_665 ),
inference(avatar_component_clause,[],[f41321]) ).
thf(f100031,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_497
| ~ spl54_878 ),
inference(trivial_inequality_removal,[],[f99993]) ).
thf(f99993,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_497
| ~ spl54_878 ),
inference(superposition,[],[f99970,f19829]) ).
thf(f99924,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))) )
| ~ spl54_497
| ~ spl54_665
| ~ spl54_876 ),
inference(forward_demodulation,[],[f99853,f41523]) ).
thf(f99853,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) )
| ~ spl54_497
| ~ spl54_876 ),
inference(trivial_inequality_removal,[],[f99815]) ).
thf(f99815,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) )
| ~ spl54_497
| ~ spl54_876 ),
inference(superposition,[],[f99792,f19829]) ).
thf(f99792,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) )
| ~ spl54_876 ),
inference(avatar_component_clause,[],[f99791]) ).
thf(f104447,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_497
| ~ spl54_629
| ~ spl54_867
| ~ spl54_886 ),
inference(forward_demodulation,[],[f98671,f104172]) ).
thf(f98671,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_497
| ~ spl54_867 ),
inference(trivial_inequality_removal,[],[f98633]) ).
thf(f98633,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_497
| ~ spl54_867 ),
inference(superposition,[],[f98242,f19829]) ).
thf(f104523,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_365
| ~ spl54_497
| ~ spl54_629
| ~ spl54_869
| ~ spl54_886 ),
inference(forward_demodulation,[],[f99041,f104172]) ).
thf(f99041,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_497
| ~ spl54_869 ),
inference(trivial_inequality_removal,[],[f99003]) ).
thf(f99003,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_497
| ~ spl54_869 ),
inference(superposition,[],[f98252,f19829]) ).
thf(f104806,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_311
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_498
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_776
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104805,f9808]) ).
thf(f9808,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_311 ),
inference(avatar_component_clause,[],[f9806]) ).
thf(f104805,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_120
| ~ spl54_129
| ~ spl54_141
| ~ spl54_362
| ~ spl54_365
| ~ spl54_384
| ~ spl54_387
| ~ spl54_443
| ~ spl54_498
| ~ spl54_506
| ~ spl54_568
| ~ spl54_629
| ~ spl54_665
| ~ spl54_688
| ~ spl54_776
| ~ spl54_825
| ~ spl54_867
| ~ spl54_869
| ~ spl54_876
| ~ spl54_878
| ~ spl54_886
| ~ spl54_889 ),
inference(forward_demodulation,[],[f104804,f104517]) ).
thf(f104804,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))) )
| ~ spl54_498
| ~ spl54_665
| ~ spl54_776
| ~ spl54_876
| ~ spl54_878 ),
inference(forward_demodulation,[],[f96472,f104359]) ).
thf(f104359,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_498
| ~ spl54_665
| ~ spl54_876
| ~ spl54_878 ),
inference(forward_demodulation,[],[f99935,f104350]) ).
thf(f104350,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_498
| ~ spl54_665
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100027,f41521]) ).
thf(f41521,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_498
| ~ spl54_665 ),
inference(trivial_inequality_removal,[],[f41492]) ).
thf(f41492,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_498
| ~ spl54_665 ),
inference(superposition,[],[f41322,f19834]) ).
thf(f19834,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_498 ),
inference(avatar_component_clause,[],[f19832]) ).
thf(f100027,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_498
| ~ spl54_878 ),
inference(trivial_inequality_removal,[],[f99997]) ).
thf(f99997,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_498
| ~ spl54_878 ),
inference(superposition,[],[f99970,f19834]) ).
thf(f99935,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))) )
| ~ spl54_498
| ~ spl54_665
| ~ spl54_876 ),
inference(forward_demodulation,[],[f99849,f41521]) ).
thf(f99849,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) )
| ~ spl54_498
| ~ spl54_876 ),
inference(trivial_inequality_removal,[],[f99819]) ).
thf(f99819,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8)) )
| ~ spl54_498
| ~ spl54_876 ),
inference(superposition,[],[f99792,f19834]) ).
thf(f96472,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8)) )
| ~ spl54_498
| ~ spl54_776 ),
inference(trivial_inequality_removal,[],[f96442]) ).
thf(f96442,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))))),sK8)) )
| ~ spl54_498
| ~ spl54_776 ),
inference(superposition,[],[f86460,f19834]) ).
thf(f86460,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) ) )
| ~ spl54_776 ),
inference(avatar_component_clause,[],[f86459]) ).
thf(f105179,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_913 ),
inference(avatar_component_clause,[],[f105177]) ).
thf(f105180,plain,
( spl54_913
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_810
| ~ spl54_886 ),
inference(avatar_split_clause,[],[f104609,f100542,f92327,f20347,f3336,f3069,f105177]) ).
thf(f92327,plain,
( spl54_810
<=> ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_810])]) ).
thf(f104609,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_810
| ~ spl54_886 ),
inference(forward_demodulation,[],[f104608,f101116]) ).
thf(f101116,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_886 ),
inference(forward_demodulation,[],[f101031,f3771]) ).
thf(f101031,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8)) )
| ~ spl54_506
| ~ spl54_886 ),
inference(trivial_inequality_removal,[],[f101005]) ).
thf(f101005,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK8)),sK8)) ) )
| ~ spl54_506
| ~ spl54_886 ),
inference(superposition,[],[f100543,f20349]) ).
thf(f104608,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_120
| ~ spl54_141
| ~ spl54_506
| ~ spl54_810
| ~ spl54_886 ),
inference(forward_demodulation,[],[f92328,f101116]) ).
thf(f92328,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_810 ),
inference(avatar_component_clause,[],[f92327]) ).
thf(f105048,plain,
( spl54_657
| ~ spl54_17
| ~ spl54_365
| ~ spl54_874
| ~ spl54_886 ),
inference(avatar_split_clause,[],[f104165,f100542,f99169,f16781,f1824,f41088]) ).
thf(f99169,plain,
( spl54_874
<=> ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_874])]) ).
thf(f104165,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_874
| ~ spl54_886 ),
inference(forward_demodulation,[],[f104164,f101059]) ).
thf(f104164,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),sK8) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_874
| ~ spl54_886 ),
inference(forward_demodulation,[],[f104163,f101059]) ).
thf(f104163,plain,
( ! [X0: nat,X1: nat] : ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) )
| ~ spl54_17
| ~ spl54_365
| ~ spl54_874
| ~ spl54_886 ),
inference(forward_demodulation,[],[f99170,f101059]) ).
thf(f99170,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),sK8) )
| ~ spl54_874 ),
inference(avatar_component_clause,[],[f99169]) ).
thf(f104038,plain,
( spl54_370
| ~ spl54_141
| ~ spl54_368
| ~ spl54_432
| ~ spl54_574
| ~ spl54_629
| ~ spl54_851 ),
inference(avatar_split_clause,[],[f103321,f95522,f39004,f31279,f18319,f16886,f3336,f16940]) ).
thf(f103321,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_141
| ~ spl54_368
| ~ spl54_432
| ~ spl54_574
| ~ spl54_629
| ~ spl54_851 ),
inference(forward_demodulation,[],[f39264,f95620]) ).
thf(f104033,plain,
( spl54_912
| ~ spl54_18
| ~ spl54_219
| ~ spl54_254 ),
inference(avatar_split_clause,[],[f5639,f5625,f4639,f1829,f104031]) ).
thf(f104031,plain,
( spl54_912
<=> ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_912])]) ).
thf(f5639,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_219
| ~ spl54_254 ),
inference(forward_demodulation,[],[f5638,f4662]) ).
thf(f4662,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_219 ),
inference(trivial_inequality_removal,[],[f4655]) ).
thf(f4655,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) )
| ~ spl54_18
| ~ spl54_219 ),
inference(superposition,[],[f4640,f1831]) ).
thf(f5638,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_254 ),
inference(trivial_inequality_removal,[],[f5629]) ).
thf(f5629,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_18
| ~ spl54_254 ),
inference(superposition,[],[f5626,f1831]) ).
thf(f104025,plain,
( spl54_911
| ~ spl54_18
| ~ spl54_219 ),
inference(avatar_split_clause,[],[f4662,f4639,f1829,f104023]) ).
thf(f104023,plain,
( spl54_911
<=> ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_911])]) ).
thf(f104020,plain,
( spl54_910
| ~ spl54_18
| ~ spl54_218 ),
inference(avatar_split_clause,[],[f4650,f4635,f1829,f104018]) ).
thf(f104018,plain,
( spl54_910
<=> ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_910])]) ).
thf(f4650,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_218 ),
inference(trivial_inequality_removal,[],[f4643]) ).
thf(f4643,plain,
( ! [X0: int,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_18
| ~ spl54_218 ),
inference(superposition,[],[f4636,f1831]) ).
thf(f104012,plain,
( spl54_909
| ~ spl54_32
| ~ spl54_240 ),
inference(avatar_split_clause,[],[f7439,f5423,f1899,f104010]) ).
thf(f7439,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8))) )
| ~ spl54_32
| ~ spl54_240 ),
inference(trivial_inequality_removal,[],[f5430]) ).
thf(f5430,plain,
( ! [X0: int,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8))) ) )
| ~ spl54_32
| ~ spl54_240 ),
inference(superposition,[],[f5424,f1901]) ).
thf(f104004,plain,
( spl54_908
| ~ spl54_18
| ~ spl54_222 ),
inference(avatar_split_clause,[],[f4699,f4675,f1829,f104002]) ).
thf(f4699,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_222 ),
inference(trivial_inequality_removal,[],[f4692]) ).
thf(f4692,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_222 ),
inference(superposition,[],[f4676,f1831]) ).
thf(f103997,plain,
( spl54_907
| ~ spl54_18
| ~ spl54_221 ),
inference(avatar_split_clause,[],[f4686,f4671,f1829,f103995]) ).
thf(f4686,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_221 ),
inference(trivial_inequality_removal,[],[f4679]) ).
thf(f4679,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_221 ),
inference(superposition,[],[f4672,f1831]) ).
thf(f103745,plain,
( spl54_906
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_572
| ~ spl54_674
| ~ spl54_852 ),
inference(avatar_split_clause,[],[f103305,f95526,f41852,f31269,f18286,f16886,f7242,f4168,f103743]) ).
thf(f4168,plain,
( spl54_201
<=> ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_201])]) ).
thf(f18286,plain,
( spl54_427
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_427])]) ).
thf(f31269,plain,
( spl54_572
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_572])]) ).
thf(f95526,plain,
( spl54_852
<=> ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_852])]) ).
thf(f103305,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_572
| ~ spl54_674
| ~ spl54_852 ),
inference(forward_demodulation,[],[f41853,f95756]) ).
thf(f95756,plain,
( ! [X0: int] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_572
| ~ spl54_852 ),
inference(forward_demodulation,[],[f95755,f16888]) ).
thf(f95755,plain,
( ! [X0: int] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_427
| ~ spl54_572
| ~ spl54_852 ),
inference(forward_demodulation,[],[f95733,f31309]) ).
thf(f31309,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_427
| ~ spl54_572 ),
inference(trivial_inequality_removal,[],[f31308]) ).
thf(f31308,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_427
| ~ spl54_572 ),
inference(forward_demodulation,[],[f31307,f7244]) ).
thf(f31307,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_201
| ~ spl54_427
| ~ spl54_572 ),
inference(trivial_inequality_removal,[],[f31306]) ).
thf(f31306,plain,
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_201
| ~ spl54_427
| ~ spl54_572 ),
inference(forward_demodulation,[],[f31300,f18288]) ).
thf(f18288,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_427 ),
inference(avatar_component_clause,[],[f18286]) ).
thf(f31300,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_201
| ~ spl54_572 ),
inference(trivial_inequality_removal,[],[f31296]) ).
thf(f31296,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_201
| ~ spl54_572 ),
inference(superposition,[],[f4169,f31271]) ).
thf(f31271,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)) )
| ~ spl54_572 ),
inference(avatar_component_clause,[],[f31269]) ).
thf(f4169,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) ) )
| ~ spl54_201 ),
inference(avatar_component_clause,[],[f4168]) ).
thf(f95733,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_427
| ~ spl54_852 ),
inference(trivial_inequality_removal,[],[f95671]) ).
thf(f95671,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_427
| ~ spl54_852 ),
inference(superposition,[],[f95527,f18288]) ).
thf(f95527,plain,
( ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_852 ),
inference(avatar_component_clause,[],[f95526]) ).
thf(f103175,plain,
( spl54_370
| ~ spl54_17
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_449
| ~ spl54_525
| ~ spl54_572
| ~ spl54_633
| ~ spl54_852
| ~ spl54_873 ),
inference(avatar_split_clause,[],[f102201,f99162,f95526,f39319,f31269,f20623,f18587,f18286,f16886,f7242,f4168,f1824,f16940]) ).
thf(f18587,plain,
( spl54_449
<=> ! [X0: a] :
( ( sK8 != X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) = sK8 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_449])]) ).
thf(f99162,plain,
( spl54_873
<=> ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_873])]) ).
thf(f102201,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_449
| ~ spl54_525
| ~ spl54_572
| ~ spl54_633
| ~ spl54_852
| ~ spl54_873 ),
inference(forward_demodulation,[],[f101935,f99737]) ).
thf(f99737,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_572
| ~ spl54_633
| ~ spl54_852
| ~ spl54_873 ),
inference(forward_demodulation,[],[f99736,f95756]) ).
thf(f99736,plain,
( ! [X0: int] : ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),sK8) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_572
| ~ spl54_633
| ~ spl54_852
| ~ spl54_873 ),
inference(forward_demodulation,[],[f99735,f95756]) ).
thf(f99735,plain,
( ! [X0: int,X1: int] : ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8)) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_572
| ~ spl54_633
| ~ spl54_852
| ~ spl54_873 ),
inference(forward_demodulation,[],[f99723,f95756]) ).
thf(f99723,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X1)),sK8) )
| ~ spl54_633
| ~ spl54_873 ),
inference(superposition,[],[f99163,f39320]) ).
thf(f99163,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8)) )
| ~ spl54_873 ),
inference(avatar_component_clause,[],[f99162]) ).
thf(f101935,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_17
| ~ spl54_368
| ~ spl54_449
| ~ spl54_525 ),
inference(forward_demodulation,[],[f94432,f101684]) ).
thf(f101684,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_17
| ~ spl54_368
| ~ spl54_449 ),
inference(trivial_inequality_removal,[],[f101683]) ).
thf(f101683,plain,
( ( sK8 != sK8 )
| ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_17
| ~ spl54_368
| ~ spl54_449 ),
inference(forward_demodulation,[],[f19039,f16888]) ).
thf(f19039,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_17
| ~ spl54_449 ),
inference(inner_rewriting,[],[f18609]) ).
thf(f18609,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = sK8 )
| ~ spl54_17
| ~ spl54_449 ),
inference(trivial_inequality_removal,[],[f18590]) ).
thf(f18590,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = sK8 )
| ~ spl54_17
| ~ spl54_449 ),
inference(superposition,[],[f18588,f1826]) ).
thf(f18588,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 != X0 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) = sK8 ) )
| ~ spl54_449 ),
inference(avatar_component_clause,[],[f18587]) ).
thf(f94432,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_368
| ~ spl54_525 ),
inference(superposition,[],[f20625,f16888]) ).
thf(f102465,plain,
( spl54_905
| ~ spl54_49
| ~ spl54_898 ),
inference(avatar_split_clause,[],[f102128,f102124,f2008,f102463]) ).
thf(f102463,plain,
( spl54_905
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_905])]) ).
thf(f102124,plain,
( spl54_898
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_898])]) ).
thf(f102128,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_49
| ~ spl54_898 ),
inference(forward_demodulation,[],[f102127,f2010]) ).
thf(f102127,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_898 ),
inference(forward_demodulation,[],[f102125,f2010]) ).
thf(f102125,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_898 ),
inference(avatar_component_clause,[],[f102124]) ).
thf(f102461,plain,
( spl54_904
| ~ spl54_49
| ~ spl54_897 ),
inference(avatar_split_clause,[],[f102122,f102118,f2008,f102459]) ).
thf(f102459,plain,
( spl54_904
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_904])]) ).
thf(f102118,plain,
( spl54_897
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_897])]) ).
thf(f102122,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) ) )
| ~ spl54_49
| ~ spl54_897 ),
inference(forward_demodulation,[],[f102121,f2010]) ).
thf(f102121,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_897 ),
inference(forward_demodulation,[],[f102119,f2010]) ).
thf(f102119,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_897 ),
inference(avatar_component_clause,[],[f102118]) ).
thf(f102457,plain,
( spl54_903
| ~ spl54_49
| ~ spl54_896 ),
inference(avatar_split_clause,[],[f102116,f102112,f2008,f102455]) ).
thf(f102455,plain,
( spl54_903
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_903])]) ).
thf(f102112,plain,
( spl54_896
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_896])]) ).
thf(f102116,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_896 ),
inference(forward_demodulation,[],[f102115,f2010]) ).
thf(f102115,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_896 ),
inference(forward_demodulation,[],[f102113,f2010]) ).
thf(f102113,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_896 ),
inference(avatar_component_clause,[],[f102112]) ).
thf(f102453,plain,
( spl54_902
| ~ spl54_49
| ~ spl54_895 ),
inference(avatar_split_clause,[],[f102110,f102106,f2008,f102451]) ).
thf(f102451,plain,
( spl54_902
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_902])]) ).
thf(f102106,plain,
( spl54_895
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_895])]) ).
thf(f102110,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 ) )
| ~ spl54_49
| ~ spl54_895 ),
inference(forward_demodulation,[],[f102109,f2010]) ).
thf(f102109,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 ) )
| ~ spl54_49
| ~ spl54_895 ),
inference(forward_demodulation,[],[f102107,f2010]) ).
thf(f102107,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 ) )
| ~ spl54_895 ),
inference(avatar_component_clause,[],[f102106]) ).
thf(f102141,plain,
( spl54_370
| ~ spl54_17
| ~ spl54_366
| ~ spl54_368
| ~ spl54_449
| ~ spl54_629
| ~ spl54_667 ),
inference(avatar_split_clause,[],[f101688,f41364,f39004,f18587,f16886,f16821,f1824,f16940]) ).
thf(f101688,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_366
| ~ spl54_368
| ~ spl54_449
| ~ spl54_629
| ~ spl54_667 ),
inference(forward_demodulation,[],[f101687,f41365]) ).
thf(f41365,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8) )
| ~ spl54_667 ),
inference(avatar_component_clause,[],[f41364]) ).
thf(f101687,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),sK8) )
| ~ spl54_17
| ~ spl54_366
| ~ spl54_368
| ~ spl54_449
| ~ spl54_629 ),
inference(forward_demodulation,[],[f39289,f101684]) ).
thf(f39289,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_366
| ~ spl54_629 ),
inference(trivial_inequality_removal,[],[f39235]) ).
thf(f39235,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_366
| ~ spl54_629 ),
inference(superposition,[],[f39005,f16823]) ).
thf(f102140,plain,
( spl54_901
| ~ spl54_49
| ~ spl54_894 ),
inference(avatar_split_clause,[],[f102104,f102100,f2008,f102138]) ).
thf(f102138,plain,
( spl54_901
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_901])]) ).
thf(f102100,plain,
( spl54_894
<=> ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_894])]) ).
thf(f102104,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 ) )
| ~ spl54_49
| ~ spl54_894 ),
inference(forward_demodulation,[],[f102103,f2010]) ).
thf(f102103,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 ) )
| ~ spl54_49
| ~ spl54_894 ),
inference(forward_demodulation,[],[f102101,f2010]) ).
thf(f102101,plain,
( ! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 ) )
| ~ spl54_894 ),
inference(avatar_component_clause,[],[f102100]) ).
thf(f102136,plain,
( spl54_900
| ~ spl54_49
| ~ spl54_893 ),
inference(avatar_split_clause,[],[f102098,f102093,f2008,f102134]) ).
thf(f102134,plain,
( spl54_900
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_900])]) ).
thf(f102093,plain,
( spl54_893
<=> ! [X2: a,X0: a,X1: a] :
( ( X1 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_893])]) ).
thf(f102098,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_49
| ~ spl54_893 ),
inference(forward_demodulation,[],[f102097,f2010]) ).
thf(f102097,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_49
| ~ spl54_893 ),
inference(forward_demodulation,[],[f102096,f2010]) ).
thf(f102096,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_49
| ~ spl54_893 ),
inference(forward_demodulation,[],[f102094,f2010]) ).
thf(f102094,plain,
( ! [X2: a,X0: a,X1: a] :
( ( X1 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_893 ),
inference(avatar_component_clause,[],[f102093]) ).
thf(f102132,plain,
( spl54_899
| ~ spl54_49
| ~ spl54_892 ),
inference(avatar_split_clause,[],[f101658,f101653,f2008,f102130]) ).
thf(f102130,plain,
( spl54_899
<=> ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_899])]) ).
thf(f101653,plain,
( spl54_892
<=> ! [X2: a,X0: a,X1: a] :
( ( X1 != X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_892])]) ).
thf(f101658,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_49
| ~ spl54_892 ),
inference(forward_demodulation,[],[f101657,f2010]) ).
thf(f101657,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_49
| ~ spl54_892 ),
inference(forward_demodulation,[],[f101656,f2010]) ).
thf(f101656,plain,
( ! [X2: a,X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_49
| ~ spl54_892 ),
inference(forward_demodulation,[],[f101654,f2010]) ).
thf(f101654,plain,
( ! [X2: a,X0: a,X1: a] :
( ( X1 != X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_892 ),
inference(avatar_component_clause,[],[f101653]) ).
thf(f102126,plain,
( spl54_898
| ~ spl54_2
| ~ spl54_213 ),
inference(avatar_split_clause,[],[f4589,f4560,f1725,f102124]) ).
thf(f4560,plain,
( spl54_213
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_213])]) ).
thf(f4589,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_213 ),
inference(trivial_inequality_removal,[],[f4588]) ).
thf(f4588,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_213 ),
inference(superposition,[],[f4561,f1726]) ).
thf(f4561,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_213 ),
inference(avatar_component_clause,[],[f4560]) ).
thf(f102120,plain,
( spl54_897
| ~ spl54_2
| ~ spl54_212 ),
inference(avatar_split_clause,[],[f4580,f4556,f1725,f102118]) ).
thf(f4556,plain,
( spl54_212
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_212])]) ).
thf(f4580,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_212 ),
inference(trivial_inequality_removal,[],[f4579]) ).
thf(f4579,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_212 ),
inference(superposition,[],[f4557,f1726]) ).
thf(f4557,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_212 ),
inference(avatar_component_clause,[],[f4556]) ).
thf(f102114,plain,
( spl54_896
| ~ spl54_2
| ~ spl54_211 ),
inference(avatar_split_clause,[],[f4570,f4552,f1725,f102112]) ).
thf(f4552,plain,
( spl54_211
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_211])]) ).
thf(f4570,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_211 ),
inference(trivial_inequality_removal,[],[f4569]) ).
thf(f4569,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_211 ),
inference(superposition,[],[f4553,f1726]) ).
thf(f4553,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_211 ),
inference(avatar_component_clause,[],[f4552]) ).
thf(f102108,plain,
spl54_895,
inference(avatar_split_clause,[],[f1535,f102106]) ).
thf(f1535,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1534]) ).
thf(f1534,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1530]) ).
thf(f1530,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1374]) ).
thf(f1374,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(cnf_transformation,[],[f924]) ).
thf(f924,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(flattening,[],[f923]) ).
thf(f923,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(ennf_transformation,[],[f548]) ).
thf(f548,plain,
! [X0: a,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ) ) ),
inference(fool_elimination,[],[f547]) ).
thf(f547,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
= ( X1 = X2 ) ) ) ) ),
inference(rectify,[],[f193]) ).
thf(f193,axiom,
! [X7: a,X8: a,X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X8) )
= ( X8 = X9 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Units__l__cancel) ).
thf(f102102,plain,
spl54_894,
inference(avatar_split_clause,[],[f1533,f102100]) ).
thf(f1533,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f1532]) ).
thf(f1532,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1531]) ).
thf(f1531,plain,
! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1374]) ).
thf(f102095,plain,
spl54_893,
inference(avatar_split_clause,[],[f1505,f102093]) ).
thf(f1505,plain,
! [X2: a,X0: a,X1: a] :
( ( X1 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ),
inference(equality_proxy_clausification,[],[f1504]) ).
thf(f1504,plain,
! [X2: a,X0: a,X1: a] :
( ( X1 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ),
inference(equality_proxy_clausification,[],[f1500]) ).
thf(f1500,plain,
! [X2: a,X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1397]) ).
thf(f1397,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f966]) ).
thf(f966,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f965]) ).
thf(f965,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f594]) ).
thf(f594,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ) ) ),
inference(fool_elimination,[],[f593]) ).
thf(f593,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
= ( X1 = X2 ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f38,axiom,
! [X7: a,X8: a,X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X9),X7) )
= ( X8 = X9 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_local_Oadd_Oright__cancel) ).
thf(f101659,plain,
( spl54_370
| ~ spl54_129
| ~ spl54_141
| ~ spl54_201
| ~ spl54_283
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_443
| ~ spl54_525
| ~ spl54_572
| ~ spl54_635
| ~ spl54_658
| ~ spl54_665
| ~ spl54_852
| ~ spl54_878 ),
inference(avatar_split_clause,[],[f100635,f99969,f95526,f41321,f41125,f39340,f31269,f20623,f18486,f18286,f16886,f7242,f6164,f4168,f3336,f3223,f16940]) ).
thf(f6164,plain,
( spl54_283
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_283])]) ).
thf(f41125,plain,
( spl54_658
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_658])]) ).
thf(f100635,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_129
| ~ spl54_141
| ~ spl54_201
| ~ spl54_283
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_443
| ~ spl54_525
| ~ spl54_572
| ~ spl54_635
| ~ spl54_658
| ~ spl54_665
| ~ spl54_852
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100634,f94437]) ).
thf(f94437,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_368
| ~ spl54_658 ),
inference(superposition,[],[f41127,f16888]) ).
thf(f41127,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ~ spl54_658 ),
inference(avatar_component_clause,[],[f41125]) ).
thf(f100634,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_129
| ~ spl54_141
| ~ spl54_201
| ~ spl54_283
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_443
| ~ spl54_525
| ~ spl54_572
| ~ spl54_635
| ~ spl54_658
| ~ spl54_665
| ~ spl54_852
| ~ spl54_878 ),
inference(forward_demodulation,[],[f94432,f100579]) ).
thf(f100579,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_129
| ~ spl54_141
| ~ spl54_201
| ~ spl54_283
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_443
| ~ spl54_572
| ~ spl54_635
| ~ spl54_658
| ~ spl54_665
| ~ spl54_852
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100578,f6166]) ).
thf(f6166,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_283 ),
inference(avatar_component_clause,[],[f6164]) ).
thf(f100578,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_129
| ~ spl54_141
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_443
| ~ spl54_572
| ~ spl54_635
| ~ spl54_658
| ~ spl54_665
| ~ spl54_852
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100089,f100128]) ).
thf(f100128,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_368
| ~ spl54_658
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100014,f94437]) ).
thf(f100014,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8)) )
| ~ spl54_141
| ~ spl54_878 ),
inference(trivial_inequality_removal,[],[f100010]) ).
thf(f100010,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8)) )
| ~ spl54_141
| ~ spl54_878 ),
inference(superposition,[],[f99970,f3338]) ).
thf(f100089,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8)) )
| ~ spl54_129
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_443
| ~ spl54_572
| ~ spl54_635
| ~ spl54_665
| ~ spl54_852
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100088,f95756]) ).
thf(f100088,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8))) )
| ~ spl54_129
| ~ spl54_368
| ~ spl54_443
| ~ spl54_635
| ~ spl54_665
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100087,f39348]) ).
thf(f39348,plain,
( ! [X0: int,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) )
| ~ spl54_129
| ~ spl54_635 ),
inference(superposition,[],[f3224,f39341]) ).
thf(f100087,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8))) )
| ~ spl54_368
| ~ spl54_443
| ~ spl54_665
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100086,f16888]) ).
thf(f100086,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_443
| ~ spl54_665
| ~ spl54_878 ),
inference(forward_demodulation,[],[f100037,f41530]) ).
thf(f41530,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_443
| ~ spl54_665 ),
inference(trivial_inequality_removal,[],[f41483]) ).
thf(f41483,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_443
| ~ spl54_665 ),
inference(superposition,[],[f41322,f18487]) ).
thf(f100037,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) )
| ~ spl54_443
| ~ spl54_878 ),
inference(trivial_inequality_removal,[],[f99987]) ).
thf(f99987,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) ) )
| ~ spl54_443
| ~ spl54_878 ),
inference(superposition,[],[f99970,f18487]) ).
thf(f101655,plain,
spl54_892,
inference(avatar_split_clause,[],[f1503,f101653]) ).
thf(f1503,plain,
! [X2: a,X0: a,X1: a] :
( ( X1 != X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ),
inference(equality_proxy_clausification,[],[f1502]) ).
thf(f1502,plain,
! [X2: a,X0: a,X1: a] :
( ( X1 != X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ),
inference(equality_proxy_clausification,[],[f1501]) ).
thf(f1501,plain,
! [X2: a,X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1397]) ).
thf(f101300,plain,
( spl54_891
| ~ spl54_49
| ~ spl54_883 ),
inference(avatar_split_clause,[],[f100549,f100466,f2008,f101298]) ).
thf(f101298,plain,
( spl54_891
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_891])]) ).
thf(f100466,plain,
( spl54_883
<=> ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_883])]) ).
thf(f100549,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) )
| ~ spl54_49
| ~ spl54_883 ),
inference(forward_demodulation,[],[f100548,f2010]) ).
thf(f100548,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) )
| ~ spl54_49
| ~ spl54_883 ),
inference(forward_demodulation,[],[f100467,f2010]) ).
thf(f100467,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) )
| ~ spl54_883 ),
inference(avatar_component_clause,[],[f100466]) ).
thf(f101296,plain,
( spl54_890
| ~ spl54_32
| ~ spl54_49
| ~ spl54_231 ),
inference(avatar_split_clause,[],[f15892,f4755,f2008,f1899,f101294]) ).
thf(f101294,plain,
( spl54_890
<=> ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),sK8) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_890])]) ).
thf(f15892,plain,
( ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),sK8) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_231 ),
inference(forward_demodulation,[],[f14905,f2010]) ).
thf(f14905,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_231 ),
inference(trivial_inequality_removal,[],[f7753]) ).
thf(f7753,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_231 ),
inference(superposition,[],[f4756,f1901]) ).
thf(f101141,plain,
( spl54_889
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_572
| ~ spl54_852
| ~ spl54_888 ),
inference(avatar_split_clause,[],[f101137,f101134,f95526,f31269,f18286,f16886,f7242,f4168,f101139]) ).
thf(f101134,plain,
( spl54_888
<=> ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_888])]) ).
thf(f101137,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_201
| ~ spl54_294
| ~ spl54_368
| ~ spl54_427
| ~ spl54_572
| ~ spl54_852
| ~ spl54_888 ),
inference(forward_demodulation,[],[f101135,f95756]) ).
thf(f101135,plain,
( ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) ) )
| ~ spl54_888 ),
inference(avatar_component_clause,[],[f101134]) ).
thf(f101136,plain,
( spl54_888
| ~ spl54_32
| ~ spl54_49
| ~ spl54_232 ),
inference(avatar_split_clause,[],[f15891,f4759,f2008,f1899,f101134]) ).
thf(f15891,plain,
( ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_232 ),
inference(forward_demodulation,[],[f14906,f2010]) ).
thf(f14906,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_232 ),
inference(trivial_inequality_removal,[],[f7754]) ).
thf(f7754,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_232 ),
inference(superposition,[],[f4760,f1901]) ).
thf(f101132,plain,
( spl54_887
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_243 ),
inference(avatar_split_clause,[],[f15665,f5453,f2008,f1899,f1761,f101130]) ).
thf(f15665,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_243 ),
inference(trivial_inequality_removal,[],[f15664]) ).
thf(f15664,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_243 ),
inference(forward_demodulation,[],[f15663,f1763]) ).
thf(f15663,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_243 ),
inference(forward_demodulation,[],[f7816,f2010]) ).
thf(f7816,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_243 ),
inference(trivial_inequality_removal,[],[f7797]) ).
thf(f7797,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_243 ),
inference(superposition,[],[f5454,f1901]) ).
thf(f100545,plain,
( spl54_370
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_151
| ~ spl54_283
| ~ spl54_368
| ~ spl54_658
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834 ),
inference(avatar_split_clause,[],[f99366,f94032,f42130,f41321,f41125,f16886,f6164,f3466,f3336,f3223,f2187,f16940]) ).
thf(f3466,plain,
( spl54_151
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_151])]) ).
thf(f99366,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_151
| ~ spl54_283
| ~ spl54_368
| ~ spl54_658
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834 ),
inference(forward_demodulation,[],[f99365,f94437]) ).
thf(f99365,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_151
| ~ spl54_283
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834 ),
inference(forward_demodulation,[],[f18890,f96663]) ).
thf(f96663,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_283
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834 ),
inference(forward_demodulation,[],[f96662,f42132]) ).
thf(f42132,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) )
| ~ spl54_691 ),
inference(avatar_component_clause,[],[f42130]) ).
thf(f96662,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_283
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834 ),
inference(forward_demodulation,[],[f96661,f6166]) ).
thf(f96661,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8))),sK8) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834 ),
inference(forward_demodulation,[],[f96660,f42132]) ).
thf(f96660,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8)) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_368
| ~ spl54_665
| ~ spl54_834 ),
inference(forward_demodulation,[],[f96659,f16888]) ).
thf(f96659,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_665
| ~ spl54_834 ),
inference(forward_demodulation,[],[f96620,f41553]) ).
thf(f41553,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_665 ),
inference(forward_demodulation,[],[f41534,f3224]) ).
thf(f41534,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_78
| ~ spl54_665 ),
inference(trivial_inequality_removal,[],[f41479]) ).
thf(f41479,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_78
| ~ spl54_665 ),
inference(superposition,[],[f41322,f2189]) ).
thf(f96620,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) )
| ~ spl54_78
| ~ spl54_834 ),
inference(trivial_inequality_removal,[],[f96562]) ).
thf(f96562,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) )
| ~ spl54_78
| ~ spl54_834 ),
inference(superposition,[],[f94033,f2189]) ).
thf(f18890,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_141
| ~ spl54_151 ),
inference(trivial_inequality_removal,[],[f18880]) ).
thf(f18880,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_141
| ~ spl54_151 ),
inference(superposition,[],[f3467,f3338]) ).
thf(f3467,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_151 ),
inference(avatar_component_clause,[],[f3466]) ).
thf(f100544,plain,
( spl54_886
| ~ spl54_667
| ~ spl54_885 ),
inference(avatar_split_clause,[],[f100540,f100537,f41364,f100542]) ).
thf(f100540,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_667
| ~ spl54_885 ),
inference(forward_demodulation,[],[f100538,f41365]) ).
thf(f100539,plain,
( spl54_885
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_242 ),
inference(avatar_split_clause,[],[f15662,f5449,f2008,f1899,f1761,f100537]) ).
thf(f15662,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_242 ),
inference(trivial_inequality_removal,[],[f15661]) ).
thf(f15661,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_242 ),
inference(forward_demodulation,[],[f15660,f1763]) ).
thf(f15660,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_242 ),
inference(forward_demodulation,[],[f7817,f2010]) ).
thf(f7817,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_242 ),
inference(trivial_inequality_removal,[],[f7796]) ).
thf(f7796,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_242 ),
inference(superposition,[],[f5450,f1901]) ).
thf(f100475,plain,
( spl54_884
| ~ spl54_49
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_151
| ~ spl54_283
| ~ spl54_368
| ~ spl54_658
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_883 ),
inference(avatar_split_clause,[],[f100471,f100466,f94032,f42130,f41321,f41125,f16886,f6164,f3466,f3336,f3223,f2187,f2008,f100473]) ).
thf(f100473,plain,
( spl54_884
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_884])]) ).
thf(f100471,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) )
| ~ spl54_49
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_151
| ~ spl54_283
| ~ spl54_368
| ~ spl54_658
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_883 ),
inference(forward_demodulation,[],[f100470,f2010]) ).
thf(f100470,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) )
| ~ spl54_49
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_151
| ~ spl54_283
| ~ spl54_368
| ~ spl54_658
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_883 ),
inference(forward_demodulation,[],[f100469,f2010]) ).
thf(f100469,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_141
| ~ spl54_151
| ~ spl54_283
| ~ spl54_368
| ~ spl54_658
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_883 ),
inference(forward_demodulation,[],[f100467,f99366]) ).
thf(f100468,plain,
( spl54_883
| ~ spl54_129
| ~ spl54_175 ),
inference(avatar_split_clause,[],[f3827,f3824,f3223,f100466]) ).
thf(f3827,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) = X0 ) )
| ~ spl54_129
| ~ spl54_175 ),
inference(superposition,[],[f3825,f3224]) ).
thf(f100342,plain,
( spl54_882
| ~ spl54_2
| ~ spl54_204 ),
inference(avatar_split_clause,[],[f4251,f4233,f1725,f100340]) ).
thf(f100340,plain,
( spl54_882
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_882])]) ).
thf(f4233,plain,
( spl54_204
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_204])]) ).
thf(f4251,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_2
| ~ spl54_204 ),
inference(trivial_inequality_removal,[],[f4250]) ).
thf(f4250,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_2
| ~ spl54_204 ),
inference(superposition,[],[f4234,f1726]) ).
thf(f4234,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) )
| ~ spl54_204 ),
inference(avatar_component_clause,[],[f4233]) ).
thf(f100144,plain,
( spl54_881
| ~ spl54_2
| ~ spl54_203 ),
inference(avatar_split_clause,[],[f4227,f4194,f1725,f100142]) ).
thf(f100142,plain,
( spl54_881
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_881])]) ).
thf(f4194,plain,
( spl54_203
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_203])]) ).
thf(f4227,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_203 ),
inference(trivial_inequality_removal,[],[f4226]) ).
thf(f4226,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)) = X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_203 ),
inference(superposition,[],[f4195,f1726]) ).
thf(f4195,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_203 ),
inference(avatar_component_clause,[],[f4194]) ).
thf(f100140,plain,
( spl54_880
| ~ spl54_2
| ~ spl54_202 ),
inference(avatar_split_clause,[],[f4217,f4190,f1725,f100138]) ).
thf(f100138,plain,
( spl54_880
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),X0)) = X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_880])]) ).
thf(f4190,plain,
( spl54_202
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_202])]) ).
thf(f4217,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),X0)) = X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_202 ),
inference(trivial_inequality_removal,[],[f4216]) ).
thf(f4216,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X2)),X0)) = X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_202 ),
inference(superposition,[],[f4191,f1726]) ).
thf(f4191,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_202 ),
inference(avatar_component_clause,[],[f4190]) ).
thf(f100133,plain,
( spl54_879
| ~ spl54_32
| ~ spl54_174
| ~ spl54_240 ),
inference(avatar_split_clause,[],[f7645,f5423,f3810,f1899,f100131]) ).
thf(f7645,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),sK8)) )
| ~ spl54_32
| ~ spl54_174
| ~ spl54_240 ),
inference(forward_demodulation,[],[f6704,f7618]) ).
thf(f7618,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) )
| ~ spl54_32
| ~ spl54_174 ),
inference(trivial_inequality_removal,[],[f6583]) ).
thf(f6583,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) ) )
| ~ spl54_32
| ~ spl54_174 ),
inference(superposition,[],[f3811,f1901]) ).
thf(f6704,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8))) )
| ~ spl54_32
| ~ spl54_240 ),
inference(trivial_inequality_removal,[],[f6603]) ).
thf(f6603,plain,
( ! [X0: int,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8))) ) )
| ~ spl54_32
| ~ spl54_240 ),
inference(superposition,[],[f5424,f1901]) ).
thf(f99971,plain,
( spl54_878
| ~ spl54_78
| ~ spl54_129
| ~ spl54_283
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_877 ),
inference(avatar_split_clause,[],[f99967,f99963,f94032,f42130,f41321,f16886,f6164,f3223,f2187,f99969]) ).
thf(f99963,plain,
( spl54_877
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_877])]) ).
thf(f99967,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_283
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_877 ),
inference(forward_demodulation,[],[f99966,f3224]) ).
thf(f99966,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_283
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_877 ),
inference(forward_demodulation,[],[f99964,f96663]) ).
thf(f99964,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_877 ),
inference(avatar_component_clause,[],[f99963]) ).
thf(f99965,plain,
( spl54_877
| ~ spl54_32
| ~ spl54_49
| ~ spl54_222 ),
inference(avatar_split_clause,[],[f15894,f4675,f2008,f1899,f99963]) ).
thf(f15894,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_222 ),
inference(forward_demodulation,[],[f14903,f2010]) ).
thf(f14903,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_222 ),
inference(trivial_inequality_removal,[],[f7751]) ).
thf(f7751,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_222 ),
inference(superposition,[],[f4676,f1901]) ).
thf(f99793,plain,
( spl54_876
| ~ spl54_78
| ~ spl54_129
| ~ spl54_283
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_875 ),
inference(avatar_split_clause,[],[f99789,f99786,f94032,f42130,f41321,f16886,f6164,f3223,f2187,f99791]) ).
thf(f99789,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_78
| ~ spl54_129
| ~ spl54_283
| ~ spl54_368
| ~ spl54_665
| ~ spl54_691
| ~ spl54_834
| ~ spl54_875 ),
inference(forward_demodulation,[],[f99787,f96663]) ).
thf(f99788,plain,
( spl54_875
| ~ spl54_32
| ~ spl54_49
| ~ spl54_221 ),
inference(avatar_split_clause,[],[f15624,f4671,f2008,f1899,f99786]) ).
thf(f15624,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_221 ),
inference(forward_demodulation,[],[f7529,f2010]) ).
thf(f7529,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_221 ),
inference(trivial_inequality_removal,[],[f5299]) ).
thf(f5299,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_221 ),
inference(superposition,[],[f4672,f1901]) ).
thf(f99721,plain,
( spl54_835
| ~ spl54_49
| ~ spl54_368
| ~ spl54_863 ),
inference(avatar_split_clause,[],[f99339,f97125,f16886,f2008,f94037]) ).
thf(f99339,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_49
| ~ spl54_368
| ~ spl54_863 ),
inference(forward_demodulation,[],[f97128,f2010]) ).
thf(f97128,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_368
| ~ spl54_863 ),
inference(forward_demodulation,[],[f97126,f16888]) ).
thf(f99189,plain,
( spl54_370
| ~ spl54_78
| ~ spl54_368
| ~ spl54_525
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_843
| ~ spl54_848 ),
inference(avatar_split_clause,[],[f95858,f95463,f95133,f86417,f42130,f41848,f20623,f16886,f2187,f16940]) ).
thf(f95463,plain,
( spl54_848
<=> ! [X0: nat,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1))),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_848])]) ).
thf(f95858,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_78
| ~ spl54_368
| ~ spl54_525
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_843
| ~ spl54_848 ),
inference(forward_demodulation,[],[f94432,f95819]) ).
thf(f95819,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_78
| ~ spl54_368
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_843
| ~ spl54_848 ),
inference(trivial_inequality_removal,[],[f95818]) ).
thf(f95818,plain,
( ( $true = $false )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_78
| ~ spl54_368
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_843
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95817,f2189]) ).
thf(f95817,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $false )
| ~ spl54_368
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_843
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95154,f95808]) ).
thf(f95808,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_368
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95504,f42132]) ).
thf(f95504,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_368
| ~ spl54_673
| ~ spl54_771
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95503,f41849]) ).
thf(f41849,plain,
( ! [X0: int] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) )
| ~ spl54_673 ),
inference(avatar_component_clause,[],[f41848]) ).
thf(f95503,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8)),sK8) )
| ~ spl54_368
| ~ spl54_771
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95476,f16888]) ).
thf(f95476,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_771
| ~ spl54_848 ),
inference(superposition,[],[f95464,f86418]) ).
thf(f95464,plain,
( ! [X0: nat,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1))),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ~ spl54_848 ),
inference(avatar_component_clause,[],[f95463]) ).
thf(f95154,plain,
( ! [X0: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $false ) )
| ~ spl54_368
| ~ spl54_673
| ~ spl54_771
| ~ spl54_843 ),
inference(forward_demodulation,[],[f95153,f41849]) ).
thf(f95153,plain,
( ! [X0: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $false ) )
| ~ spl54_368
| ~ spl54_771
| ~ spl54_843 ),
inference(forward_demodulation,[],[f95137,f16888]) ).
thf(f99171,plain,
( spl54_874
| ~ spl54_32
| ~ spl54_219 ),
inference(avatar_split_clause,[],[f14901,f4639,f1899,f99169]) ).
thf(f14901,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),sK8) )
| ~ spl54_32
| ~ spl54_219 ),
inference(trivial_inequality_removal,[],[f7749]) ).
thf(f7749,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),sK8) ) )
| ~ spl54_32
| ~ spl54_219 ),
inference(superposition,[],[f4640,f1901]) ).
thf(f99164,plain,
( spl54_873
| ~ spl54_32
| ~ spl54_218 ),
inference(avatar_split_clause,[],[f14900,f4635,f1899,f99162]) ).
thf(f14900,plain,
( ! [X0: int,X1: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8)) )
| ~ spl54_32
| ~ spl54_218 ),
inference(trivial_inequality_removal,[],[f7748]) ).
thf(f7748,plain,
( ! [X0: int,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),sK8)) ) )
| ~ spl54_32
| ~ spl54_218 ),
inference(superposition,[],[f4636,f1901]) ).
thf(f99157,plain,
( spl54_872
| ~ spl54_32
| ~ spl54_219
| ~ spl54_254 ),
inference(avatar_split_clause,[],[f7644,f5625,f4639,f1899,f99155]) ).
thf(f99155,plain,
( spl54_872
<=> ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_872])]) ).
thf(f7644,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0)),sK8) )
| ~ spl54_32
| ~ spl54_219
| ~ spl54_254 ),
inference(forward_demodulation,[],[f6398,f6434]) ).
thf(f6434,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),sK8) )
| ~ spl54_32
| ~ spl54_219 ),
inference(trivial_inequality_removal,[],[f5298]) ).
thf(f5298,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),sK8) ) )
| ~ spl54_32
| ~ spl54_219 ),
inference(superposition,[],[f4640,f1901]) ).
thf(f6398,plain,
( ! [X0: nat,X1: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_32
| ~ spl54_254 ),
inference(trivial_inequality_removal,[],[f5632]) ).
thf(f5632,plain,
( ! [X0: nat,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),sK8)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_254 ),
inference(superposition,[],[f5626,f1901]) ).
thf(f99153,plain,
( spl54_871
| ~ spl54_89 ),
inference(avatar_split_clause,[],[f2299,f2288,f99151]) ).
thf(f99151,plain,
( spl54_871
<=> ! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,vAPP(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o)),bCOMB,vNOT),vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))),vAPP(sTfun(product_prod_a_a,$o),a,sK47,vAPP(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o)),bCOMB,vNOT),vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_871])]) ).
thf(f2288,plain,
( spl54_89
<=> ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK47,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_89])]) ).
thf(f2299,plain,
( ! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,vAPP(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o)),bCOMB,vNOT),vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))),vAPP(sTfun(product_prod_a_a,$o),a,sK47,vAPP(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o)),bCOMB,vNOT),vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))) = X0 )
| ~ spl54_89 ),
inference(leibniz_equality_elimination,[],[f2289]) ).
thf(f2289,plain,
( ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK47,X0))) )
| ( $true = vAPP(product_prod_a_a,$o,X0,X1) ) )
| ~ spl54_89 ),
inference(avatar_component_clause,[],[f2288]) ).
thf(f98259,plain,
( spl54_370
| ~ spl54_17
| ~ spl54_78
| ~ spl54_141
| ~ spl54_295
| ~ spl54_368
| ~ spl54_568
| ~ spl54_658
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_822
| ~ spl54_843
| ~ spl54_848
| ~ spl54_865 ),
inference(avatar_split_clause,[],[f97895,f97138,f95463,f95133,f93451,f86417,f42130,f41848,f41125,f28173,f16886,f9549,f3336,f2187,f1824,f16940]) ).
thf(f93451,plain,
( spl54_822
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_822])]) ).
thf(f97138,plain,
( spl54_865
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_865])]) ).
thf(f97895,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_141
| ~ spl54_295
| ~ spl54_368
| ~ spl54_568
| ~ spl54_658
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_822
| ~ spl54_843
| ~ spl54_848
| ~ spl54_865 ),
inference(forward_demodulation,[],[f97894,f94437]) ).
thf(f97894,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_141
| ~ spl54_295
| ~ spl54_368
| ~ spl54_568
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_822
| ~ spl54_843
| ~ spl54_848
| ~ spl54_865 ),
inference(forward_demodulation,[],[f97893,f35104]) ).
thf(f97893,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_17
| ~ spl54_78
| ~ spl54_141
| ~ spl54_368
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_822
| ~ spl54_843
| ~ spl54_848
| ~ spl54_865 ),
inference(forward_demodulation,[],[f97892,f97278]) ).
thf(f97278,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_78
| ~ spl54_141
| ~ spl54_368
| ~ spl54_673
| ~ spl54_691
| ~ spl54_771
| ~ spl54_843
| ~ spl54_848
| ~ spl54_865 ),
inference(forward_demodulation,[],[f97277,f95819]) ).
thf(f97277,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_141
| ~ spl54_691
| ~ spl54_865 ),
inference(forward_demodulation,[],[f97183,f42132]) ).
thf(f97183,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8)) )
| ~ spl54_141
| ~ spl54_865 ),
inference(trivial_inequality_removal,[],[f97179]) ).
thf(f97179,plain,
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8)) )
| ~ spl54_141
| ~ spl54_865 ),
inference(superposition,[],[f97139,f3338]) ).
thf(f97139,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) ) )
| ~ spl54_865 ),
inference(avatar_component_clause,[],[f97138]) ).
thf(f97892,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_17
| ~ spl54_368
| ~ spl54_822 ),
inference(forward_demodulation,[],[f93557,f16888]) ).
thf(f93557,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_17
| ~ spl54_822 ),
inference(trivial_inequality_removal,[],[f93477]) ).
thf(f93477,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_17
| ~ spl54_822 ),
inference(superposition,[],[f93452,f1826]) ).
thf(f93452,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_822 ),
inference(avatar_component_clause,[],[f93451]) ).
thf(f98258,plain,
( spl54_870
| ~ spl54_88 ),
inference(avatar_split_clause,[],[f2291,f2284,f98256]) ).
thf(f98256,plain,
( spl54_870
<=> ! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,vAPP(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o)),bCOMB,vNOT),vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))),vAPP(sTfun(product_prod_a_a,$o),a,sK45,vAPP(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o)),bCOMB,vNOT),vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_870])]) ).
thf(f2284,plain,
( spl54_88
<=> ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK45,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_88])]) ).
thf(f2291,plain,
( ! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,vAPP(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o)),bCOMB,vNOT),vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))),vAPP(sTfun(product_prod_a_a,$o),a,sK45,vAPP(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod_a_a,$o),sTfun(product_prod_a_a,$o)),bCOMB,vNOT),vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))) = X0 )
| ~ spl54_88 ),
inference(leibniz_equality_elimination,[],[f2285]) ).
thf(f2285,plain,
( ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK45,X0))) )
| ( $true = vAPP(product_prod_a_a,$o,X0,X1) ) )
| ~ spl54_88 ),
inference(avatar_component_clause,[],[f2284]) ).
thf(f98253,plain,
( spl54_869
| ~ spl54_49
| ~ spl54_860 ),
inference(avatar_split_clause,[],[f97293,f97107,f2008,f98251]) ).
thf(f97107,plain,
( spl54_860
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_860])]) ).
thf(f97293,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_860 ),
inference(forward_demodulation,[],[f97108,f2010]) ).
thf(f97108,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_860 ),
inference(avatar_component_clause,[],[f97107]) ).
thf(f98248,plain,
( spl54_868
| ~ spl54_49
| ~ spl54_861 ),
inference(avatar_split_clause,[],[f97292,f97113,f2008,f98246]) ).
thf(f97113,plain,
( spl54_861
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_861])]) ).
thf(f97292,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_861 ),
inference(forward_demodulation,[],[f97114,f2010]) ).
thf(f97114,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_861 ),
inference(avatar_component_clause,[],[f97113]) ).
thf(f98243,plain,
( spl54_867
| ~ spl54_49
| ~ spl54_864 ),
inference(avatar_split_clause,[],[f97289,f97132,f2008,f98241]) ).
thf(f97132,plain,
( spl54_864
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_864])]) ).
thf(f97289,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_864 ),
inference(forward_demodulation,[],[f97133,f2010]) ).
thf(f97133,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_864 ),
inference(avatar_component_clause,[],[f97132]) ).
thf(f98094,plain,
( ~ spl54_866
| ~ spl54_368
| spl54_659 ),
inference(avatar_split_clause,[],[f97684,f41162,f16886,f98091]) ).
thf(f97684,plain,
( ( sK8 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,sK8)),sK8) )
| ~ spl54_368
| spl54_659 ),
inference(forward_demodulation,[],[f41163,f16888]) ).
thf(f41163,plain,
( ( sK8 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| spl54_659 ),
inference(avatar_component_clause,[],[f41162]) ).
thf(f97848,plain,
( spl54_370
| ~ spl54_368
| ~ spl54_413
| ~ spl54_420
| ~ spl54_658 ),
inference(avatar_split_clause,[],[f97090,f41125,f18231,f18186,f16886,f16940]) ).
thf(f18186,plain,
( spl54_413
<=> ( sK8 = vAPP(a,a,sK37,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_413])]) ).
thf(f18231,plain,
( spl54_420
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_420])]) ).
thf(f97090,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_368
| ~ spl54_413
| ~ spl54_420
| ~ spl54_658 ),
inference(forward_demodulation,[],[f18236,f94437]) ).
thf(f18236,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_368
| ~ spl54_413
| ~ spl54_420 ),
inference(forward_demodulation,[],[f18235,f18188]) ).
thf(f18188,plain,
( ( sK8 = vAPP(a,a,sK37,sK8) )
| ~ spl54_413 ),
inference(avatar_component_clause,[],[f18186]) ).
thf(f18235,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,sK8)),sK8) )
| ~ spl54_368
| ~ spl54_420 ),
inference(forward_demodulation,[],[f18233,f16888]) ).
thf(f18233,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_420 ),
inference(avatar_component_clause,[],[f18231]) ).
thf(f97279,plain,
( spl54_370
| ~ spl54_141
| ~ spl54_151
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_656
| ~ spl54_658
| ~ spl54_666
| ~ spl54_667
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837 ),
inference(avatar_split_clause,[],[f97002,f94189,f86413,f41848,f41364,f41325,f41125,f41083,f18486,f18480,f16886,f3466,f3336,f16940]) ).
thf(f41083,plain,
( spl54_656
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_656])]) ).
thf(f86413,plain,
( spl54_770
<=> ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_770])]) ).
thf(f97002,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_141
| ~ spl54_151
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_656
| ~ spl54_658
| ~ spl54_666
| ~ spl54_667
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837 ),
inference(forward_demodulation,[],[f96111,f94437]) ).
thf(f96111,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_151
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_656
| ~ spl54_666
| ~ spl54_667
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837 ),
inference(forward_demodulation,[],[f18890,f94899]) ).
thf(f94899,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_656
| ~ spl54_666
| ~ spl54_667
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837 ),
inference(forward_demodulation,[],[f94898,f41085]) ).
thf(f41085,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) )
| ~ spl54_656 ),
inference(avatar_component_clause,[],[f41083]) ).
thf(f94898,plain,
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8)) )
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_666
| ~ spl54_667
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837 ),
inference(forward_demodulation,[],[f94897,f41365]) ).
thf(f94897,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),sK8)) )
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_666
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837 ),
inference(forward_demodulation,[],[f94896,f41849]) ).
thf(f94896,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8)) )
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_666
| ~ spl54_770
| ~ spl54_837 ),
inference(forward_demodulation,[],[f94895,f16888]) ).
thf(f94895,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_442
| ~ spl54_443
| ~ spl54_666
| ~ spl54_770
| ~ spl54_837 ),
inference(forward_demodulation,[],[f94894,f41619]) ).
thf(f94894,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8) )
| ~ spl54_442
| ~ spl54_770
| ~ spl54_837 ),
inference(forward_demodulation,[],[f94827,f86414]) ).
thf(f86414,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_770 ),
inference(avatar_component_clause,[],[f86413]) ).
thf(f94827,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) )
| ~ spl54_442
| ~ spl54_837 ),
inference(trivial_inequality_removal,[],[f94783]) ).
thf(f94783,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),sK8) ) )
| ~ spl54_442
| ~ spl54_837 ),
inference(superposition,[],[f94190,f18481]) ).
thf(f97140,plain,
( spl54_865
| ~ spl54_49
| ~ spl54_141
| ~ spl54_151
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_656
| ~ spl54_658
| ~ spl54_666
| ~ spl54_667
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837
| ~ spl54_864 ),
inference(avatar_split_clause,[],[f97136,f97132,f94189,f86413,f41848,f41364,f41325,f41125,f41083,f18486,f18480,f16886,f3466,f3336,f2008,f97138]) ).
thf(f97136,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) ) )
| ~ spl54_49
| ~ spl54_141
| ~ spl54_151
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_656
| ~ spl54_658
| ~ spl54_666
| ~ spl54_667
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837
| ~ spl54_864 ),
inference(forward_demodulation,[],[f97135,f2010]) ).
thf(f97135,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_141
| ~ spl54_151
| ~ spl54_368
| ~ spl54_442
| ~ spl54_443
| ~ spl54_656
| ~ spl54_658
| ~ spl54_666
| ~ spl54_667
| ~ spl54_673
| ~ spl54_770
| ~ spl54_837
| ~ spl54_864 ),
inference(forward_demodulation,[],[f97133,f97002]) ).
thf(f97134,plain,
( spl54_864
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_221 ),
inference(avatar_split_clause,[],[f4688,f4671,f3223,f1834,f1811,f97132]) ).
thf(f4688,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_221 ),
inference(forward_demodulation,[],[f4687,f3242]) ).
thf(f4687,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_221 ),
inference(forward_demodulation,[],[f4685,f1813]) ).
thf(f4685,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_221 ),
inference(trivial_inequality_removal,[],[f4680]) ).
thf(f4680,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_221 ),
inference(superposition,[],[f4672,f1836]) ).
thf(f97127,plain,
( spl54_863
| ~ spl54_18
| ~ spl54_213 ),
inference(avatar_split_clause,[],[f4592,f4560,f1829,f97125]) ).
thf(f4592,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_213 ),
inference(trivial_inequality_removal,[],[f4585]) ).
thf(f4585,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_213 ),
inference(superposition,[],[f4561,f1831]) ).
thf(f97121,plain,
( spl54_862
| ~ spl54_18
| ~ spl54_212 ),
inference(avatar_split_clause,[],[f4583,f4556,f1829,f97119]) ).
thf(f4583,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_212 ),
inference(trivial_inequality_removal,[],[f4576]) ).
thf(f4576,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_212 ),
inference(superposition,[],[f4557,f1831]) ).
thf(f97115,plain,
( spl54_861
| ~ spl54_19
| ~ spl54_212 ),
inference(avatar_split_clause,[],[f4582,f4556,f1834,f97113]) ).
thf(f4582,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_212 ),
inference(trivial_inequality_removal,[],[f4577]) ).
thf(f4577,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_212 ),
inference(superposition,[],[f4557,f1836]) ).
thf(f97109,plain,
( spl54_860
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_211 ),
inference(avatar_split_clause,[],[f4574,f4552,f3223,f1834,f1811,f97107]) ).
thf(f4574,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_211 ),
inference(forward_demodulation,[],[f4572,f3242]) ).
thf(f4572,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_211 ),
inference(trivial_inequality_removal,[],[f4567]) ).
thf(f4567,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_211 ),
inference(superposition,[],[f4553,f1836]) ).
thf(f97103,plain,
( spl54_859
| ~ spl54_18
| ~ spl54_211 ),
inference(avatar_split_clause,[],[f4573,f4552,f1829,f97101]) ).
thf(f4573,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_211 ),
inference(trivial_inequality_removal,[],[f4566]) ).
thf(f4566,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_211 ),
inference(superposition,[],[f4553,f1831]) ).
thf(f97099,plain,
( spl54_858
| ~ spl54_2
| ~ spl54_199 ),
inference(avatar_split_clause,[],[f4179,f4160,f1725,f97097]) ).
thf(f97097,plain,
( spl54_858
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_858])]) ).
thf(f4160,plain,
( spl54_199
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_199])]) ).
thf(f4179,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_2
| ~ spl54_199 ),
inference(trivial_inequality_removal,[],[f4178]) ).
thf(f4178,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_2
| ~ spl54_199 ),
inference(superposition,[],[f4161,f1726]) ).
thf(f4161,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) )
| ~ spl54_199 ),
inference(avatar_component_clause,[],[f4160]) ).
thf(f97095,plain,
( spl54_857
| ~ spl54_2
| ~ spl54_198 ),
inference(avatar_split_clause,[],[f4175,f4156,f1725,f97093]) ).
thf(f97093,plain,
( spl54_857
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_857])]) ).
thf(f4175,plain,
( ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_2
| ~ spl54_198 ),
inference(trivial_inequality_removal,[],[f4174]) ).
thf(f4174,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_2
| ~ spl54_198 ),
inference(superposition,[],[f4157,f1726]) ).
thf(f96976,plain,
( spl54_370
| ~ spl54_129
| ~ spl54_283
| ~ spl54_362
| ~ spl54_368
| ~ spl54_492
| ~ spl54_667
| ~ spl54_848 ),
inference(avatar_split_clause,[],[f95812,f95463,f41364,f19465,f16886,f14472,f6164,f3223,f16940]) ).
thf(f19465,plain,
( spl54_492
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_492])]) ).
thf(f95812,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_129
| ~ spl54_283
| ~ spl54_362
| ~ spl54_368
| ~ spl54_492
| ~ spl54_667
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95811,f41365]) ).
thf(f95811,plain,
( ! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) )
| ~ spl54_129
| ~ spl54_283
| ~ spl54_362
| ~ spl54_368
| ~ spl54_492
| ~ spl54_667
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95810,f19467]) ).
thf(f19467,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_492 ),
inference(avatar_component_clause,[],[f19465]) ).
thf(f95810,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_129
| ~ spl54_283
| ~ spl54_362
| ~ spl54_368
| ~ spl54_667
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95809,f7053]) ).
thf(f7053,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_129
| ~ spl54_283 ),
inference(superposition,[],[f3224,f6166]) ).
thf(f95809,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_362
| ~ spl54_368
| ~ spl54_667
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95484,f41365]) ).
thf(f95484,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_362
| ~ spl54_368
| ~ spl54_848 ),
inference(forward_demodulation,[],[f95468,f16888]) ).
thf(f95468,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_362
| ~ spl54_848 ),
inference(superposition,[],[f95464,f14474]) ).
thf(f96731,plain,
( spl54_856
| ~ spl54_49
| ~ spl54_854 ),
inference(avatar_split_clause,[],[f95806,f95802,f2008,f96729]) ).
thf(f96729,plain,
( spl54_856
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_856])]) ).
thf(f95802,plain,
( spl54_854
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_854])]) ).
thf(f95806,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) = X0 ) )
| ~ spl54_49
| ~ spl54_854 ),
inference(forward_demodulation,[],[f95805,f2010]) ).
thf(f95805,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_854 ),
inference(forward_demodulation,[],[f95803,f2010]) ).
thf(f95803,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_854 ),
inference(avatar_component_clause,[],[f95802]) ).
thf(f96727,plain,
( spl54_855
| ~ spl54_49
| ~ spl54_853 ),
inference(avatar_split_clause,[],[f95800,f95796,f2008,f96725]) ).
thf(f96725,plain,
( spl54_855
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_855])]) ).
thf(f95796,plain,
( spl54_853
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_853])]) ).
thf(f95800,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0)) = X0 ) )
| ~ spl54_49
| ~ spl54_853 ),
inference(forward_demodulation,[],[f95799,f2010]) ).
thf(f95799,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_853 ),
inference(forward_demodulation,[],[f95797,f2010]) ).
thf(f95797,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_853 ),
inference(avatar_component_clause,[],[f95796]) ).
thf(f96416,plain,
( spl54_776
| ~ spl54_49
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656
| ~ spl54_815 ),
inference(avatar_split_clause,[],[f95962,f93409,f41083,f27864,f17732,f3336,f2008,f86459]) ).
thf(f95962,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) ) )
| ~ spl54_49
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656
| ~ spl54_815 ),
inference(forward_demodulation,[],[f93412,f2010]) ).
thf(f93412,plain,
( ! [X0: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656
| ~ spl54_815 ),
inference(forward_demodulation,[],[f93410,f91858]) ).
thf(f91858,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656 ),
inference(forward_demodulation,[],[f27909,f41085]) ).
thf(f96255,plain,
( spl54_777
| ~ spl54_49
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656
| ~ spl54_817 ),
inference(avatar_split_clause,[],[f95961,f93421,f41083,f27864,f17732,f3336,f2008,f86464]) ).
thf(f86464,plain,
( spl54_777
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_777])]) ).
thf(f95961,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) )
| ~ spl54_49
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656
| ~ spl54_817 ),
inference(forward_demodulation,[],[f93424,f2010]) ).
thf(f93424,plain,
( ! [X0: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656
| ~ spl54_817 ),
inference(forward_demodulation,[],[f93422,f91858]) ).
thf(f95807,plain,
( ~ spl54_452
| ~ spl54_389
| spl54_760 ),
inference(avatar_split_clause,[],[f93432,f50040,f17732,f18679]) ).
thf(f50040,plain,
( spl54_760
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_760])]) ).
thf(f93432,plain,
( ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_389
| spl54_760 ),
inference(superposition,[],[f50042,f17734]) ).
thf(f50042,plain,
( ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,sK8)) )
| spl54_760 ),
inference(avatar_component_clause,[],[f50040]) ).
thf(f95804,plain,
( spl54_854
| ~ spl54_2
| ~ spl54_196 ),
inference(avatar_split_clause,[],[f4145,f4127,f1725,f95802]) ).
thf(f4127,plain,
( spl54_196
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_196])]) ).
thf(f4145,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_196 ),
inference(trivial_inequality_removal,[],[f4144]) ).
thf(f4144,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_196 ),
inference(superposition,[],[f4128,f1726]) ).
thf(f4128,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_196 ),
inference(avatar_component_clause,[],[f4127]) ).
thf(f95798,plain,
( spl54_853
| ~ spl54_2
| ~ spl54_195 ),
inference(avatar_split_clause,[],[f4135,f4123,f1725,f95796]) ).
thf(f4123,plain,
( spl54_195
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_195])]) ).
thf(f4135,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_195 ),
inference(trivial_inequality_removal,[],[f4134]) ).
thf(f4134,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_195 ),
inference(superposition,[],[f4124,f1726]) ).
thf(f4124,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_195 ),
inference(avatar_component_clause,[],[f4123]) ).
thf(f95528,plain,
( spl54_852
| ~ spl54_49
| ~ spl54_850 ),
inference(avatar_split_clause,[],[f95520,f95517,f2008,f95526]) ).
thf(f95517,plain,
( spl54_850
<=> ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_850])]) ).
thf(f95520,plain,
( ! [X0: int,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_850 ),
inference(forward_demodulation,[],[f95518,f2010]) ).
thf(f95518,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_850 ),
inference(avatar_component_clause,[],[f95517]) ).
thf(f95524,plain,
( spl54_851
| ~ spl54_49
| ~ spl54_849 ),
inference(avatar_split_clause,[],[f95515,f95512,f2008,f95522]) ).
thf(f95512,plain,
( spl54_849
<=> ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_849])]) ).
thf(f95515,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_849 ),
inference(forward_demodulation,[],[f95513,f2010]) ).
thf(f95513,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_849 ),
inference(avatar_component_clause,[],[f95512]) ).
thf(f95519,plain,
( spl54_850
| ~ spl54_19
| ~ spl54_70
| ~ spl54_232 ),
inference(avatar_split_clause,[],[f4945,f4759,f2152,f1834,f95517]) ).
thf(f4945,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_70
| ~ spl54_232 ),
inference(forward_demodulation,[],[f4943,f2153]) ).
thf(f4943,plain,
( ! [X0: int,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_232 ),
inference(trivial_inequality_removal,[],[f4936]) ).
thf(f4936,plain,
( ! [X0: int,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_232 ),
inference(superposition,[],[f4760,f1836]) ).
thf(f95514,plain,
( spl54_849
| ~ spl54_19
| ~ spl54_68
| ~ spl54_230 ),
inference(avatar_split_clause,[],[f4781,f4751,f2144,f1834,f95512]) ).
thf(f4781,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_68
| ~ spl54_230 ),
inference(forward_demodulation,[],[f4779,f2145]) ).
thf(f4779,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_230 ),
inference(trivial_inequality_removal,[],[f4774]) ).
thf(f4774,plain,
( ! [X0: nat,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_230 ),
inference(superposition,[],[f4752,f1836]) ).
thf(f95465,plain,
( spl54_848
| ~ spl54_129
| ~ spl54_164 ),
inference(avatar_split_clause,[],[f3724,f3720,f3223,f95463]) ).
thf(f3724,plain,
( ! [X0: nat,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1))),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ~ spl54_129
| ~ spl54_164 ),
inference(superposition,[],[f3721,f3224]) ).
thf(f95190,plain,
( spl54_847
| ~ spl54_2
| ~ spl54_194 ),
inference(avatar_split_clause,[],[f4118,f4088,f1725,f95188]) ).
thf(f95188,plain,
( spl54_847
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_847])]) ).
thf(f4088,plain,
( spl54_194
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_194])]) ).
thf(f4118,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_194 ),
inference(trivial_inequality_removal,[],[f4117]) ).
thf(f4117,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_194 ),
inference(superposition,[],[f4089,f1726]) ).
thf(f4089,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_194 ),
inference(avatar_component_clause,[],[f4088]) ).
thf(f95186,plain,
( spl54_846
| ~ spl54_2
| ~ spl54_193 ),
inference(avatar_split_clause,[],[f4109,f4020,f1725,f95184]) ).
thf(f95184,plain,
( spl54_846
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_846])]) ).
thf(f4020,plain,
( spl54_193
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_193])]) ).
thf(f4109,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_193 ),
inference(trivial_inequality_removal,[],[f4108]) ).
thf(f4108,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_193 ),
inference(superposition,[],[f4021,f1726]) ).
thf(f4021,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_193 ),
inference(avatar_component_clause,[],[f4020]) ).
thf(f95182,plain,
( spl54_845
| ~ spl54_2
| ~ spl54_192 ),
inference(avatar_split_clause,[],[f4100,f4016,f1725,f95180]) ).
thf(f95180,plain,
( spl54_845
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_845])]) ).
thf(f4016,plain,
( spl54_192
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_192])]) ).
thf(f4100,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_192 ),
inference(trivial_inequality_removal,[],[f4099]) ).
thf(f4099,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_192 ),
inference(superposition,[],[f4017,f1726]) ).
thf(f4017,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) )
| ~ spl54_192 ),
inference(avatar_component_clause,[],[f4016]) ).
thf(f95178,plain,
( spl54_844
| ~ spl54_2
| ~ spl54_190 ),
inference(avatar_split_clause,[],[f4093,f4008,f1725,f95176]) ).
thf(f95176,plain,
( spl54_844
<=> ! [X2: a,X0: a,X1: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_844])]) ).
thf(f4008,plain,
( spl54_190
<=> ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_190])]) ).
thf(f4093,plain,
( ! [X2: a,X0: a,X1: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_190 ),
inference(trivial_inequality_removal,[],[f4092]) ).
thf(f4092,plain,
( ! [X2: a,X0: a,X1: partia96731725t_unit] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X0),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_190 ),
inference(superposition,[],[f4009,f1726]) ).
thf(f4009,plain,
( ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) )
| ~ spl54_190 ),
inference(avatar_component_clause,[],[f4008]) ).
thf(f95135,plain,
( spl54_843
| ~ spl54_49
| ~ spl54_841 ),
inference(avatar_split_clause,[],[f95126,f95123,f2008,f95133]) ).
thf(f95123,plain,
( spl54_841
<=> ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_841])]) ).
thf(f95126,plain,
( ! [X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_841 ),
inference(forward_demodulation,[],[f95124,f2010]) ).
thf(f95124,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_841 ),
inference(avatar_component_clause,[],[f95123]) ).
thf(f95131,plain,
( ~ spl54_842
| ~ spl54_368
| spl54_736 ),
inference(avatar_split_clause,[],[f94442,f42762,f16886,f95128]) ).
thf(f95128,plain,
( spl54_842
<=> ( sK8 = vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_842])]) ).
thf(f42762,plain,
( spl54_736
<=> ( sK8 = vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_736])]) ).
thf(f94442,plain,
( ( sK8 != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r) )
| ~ spl54_368
| spl54_736 ),
inference(superposition,[],[f42764,f16888]) ).
thf(f42764,plain,
( ( sK8 != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) )
| spl54_736 ),
inference(avatar_component_clause,[],[f42762]) ).
thf(f95125,plain,
( spl54_841
| ~ spl54_2
| ~ spl54_188 ),
inference(avatar_split_clause,[],[f3995,f3988,f1725,f95123]) ).
thf(f3988,plain,
( spl54_188
<=> ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_188])]) ).
thf(f3995,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_188 ),
inference(trivial_inequality_removal,[],[f3994]) ).
thf(f3994,plain,
( ! [X0: a,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_188 ),
inference(superposition,[],[f3989,f1726]) ).
thf(f3989,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) )
| ~ spl54_188 ),
inference(avatar_component_clause,[],[f3988]) ).
thf(f94764,plain,
( spl54_840
| ~ spl54_129
| ~ spl54_452
| ~ spl54_834 ),
inference(avatar_split_clause,[],[f94035,f94032,f18679,f3223,f94762]) ).
thf(f94762,plain,
( spl54_840
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_840])]) ).
thf(f94035,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_129
| ~ spl54_452
| ~ spl54_834 ),
inference(forward_demodulation,[],[f94033,f18784]) ).
thf(f18784,plain,
( ! [X0: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) )
| ~ spl54_129
| ~ spl54_452 ),
inference(superposition,[],[f3224,f18681]) ).
thf(f18681,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_452 ),
inference(avatar_component_clause,[],[f18679]) ).
thf(f94399,plain,
( spl54_368
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656 ),
inference(avatar_split_clause,[],[f91858,f41083,f27864,f17732,f3336,f16886]) ).
thf(f94199,plain,
( spl54_839
| ~ spl54_49
| ~ spl54_827 ),
inference(avatar_split_clause,[],[f94006,f94003,f2008,f94197]) ).
thf(f94197,plain,
( spl54_839
<=> ! [X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_839])]) ).
thf(f94003,plain,
( spl54_827
<=> ! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_827])]) ).
thf(f94006,plain,
( ! [X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_49
| ~ spl54_827 ),
inference(forward_demodulation,[],[f94004,f2010]) ).
thf(f94004,plain,
( ! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_827 ),
inference(avatar_component_clause,[],[f94003]) ).
thf(f94195,plain,
( spl54_838
| ~ spl54_49
| ~ spl54_826 ),
inference(avatar_split_clause,[],[f94001,f93998,f2008,f94193]) ).
thf(f94193,plain,
( spl54_838
<=> ! [X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_838])]) ).
thf(f93998,plain,
( spl54_826
<=> ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_826])]) ).
thf(f94001,plain,
( ! [X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_49
| ~ spl54_826 ),
inference(forward_demodulation,[],[f93999,f2010]) ).
thf(f93999,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_826 ),
inference(avatar_component_clause,[],[f93998]) ).
thf(f94191,plain,
( spl54_837
| ~ spl54_32
| ~ spl54_49
| ~ spl54_212 ),
inference(avatar_split_clause,[],[f15906,f4556,f2008,f1899,f94189]) ).
thf(f15906,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_212 ),
inference(forward_demodulation,[],[f14898,f2010]) ).
thf(f14898,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_212 ),
inference(trivial_inequality_removal,[],[f7746]) ).
thf(f7746,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_212 ),
inference(superposition,[],[f4557,f1901]) ).
thf(f94044,plain,
( spl54_836
| ~ spl54_452
| ~ spl54_835 ),
inference(avatar_split_clause,[],[f94040,f94037,f18679,f94042]) ).
thf(f94040,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_452
| ~ spl54_835 ),
inference(forward_demodulation,[],[f94038,f18681]) ).
thf(f94039,plain,
( spl54_835
| ~ spl54_32
| ~ spl54_49
| ~ spl54_213 ),
inference(avatar_split_clause,[],[f15905,f4560,f2008,f1899,f94037]) ).
thf(f15905,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_213 ),
inference(forward_demodulation,[],[f14899,f2010]) ).
thf(f14899,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_213 ),
inference(trivial_inequality_removal,[],[f7747]) ).
thf(f7747,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_213 ),
inference(superposition,[],[f4561,f1901]) ).
thf(f94034,plain,
( spl54_834
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_216 ),
inference(avatar_split_clause,[],[f15658,f4613,f2008,f1899,f1766,f94032]) ).
thf(f15658,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_216 ),
inference(trivial_inequality_removal,[],[f15657]) ).
thf(f15657,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_216 ),
inference(forward_demodulation,[],[f15656,f1768]) ).
thf(f15656,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_216 ),
inference(forward_demodulation,[],[f7819,f2010]) ).
thf(f7819,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_216 ),
inference(trivial_inequality_removal,[],[f7794]) ).
thf(f7794,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_216 ),
inference(superposition,[],[f4614,f1901]) ).
thf(f94030,plain,
( spl54_833
| ~ spl54_2
| ~ spl54_187 ),
inference(avatar_split_clause,[],[f3982,f3902,f1725,f94028]) ).
thf(f94028,plain,
( spl54_833
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_833])]) ).
thf(f3902,plain,
( spl54_187
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_187])]) ).
thf(f3982,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_187 ),
inference(trivial_inequality_removal,[],[f3981]) ).
thf(f3981,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_187 ),
inference(superposition,[],[f3903,f1726]) ).
thf(f3903,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_187 ),
inference(avatar_component_clause,[],[f3902]) ).
thf(f94026,plain,
( spl54_832
| ~ spl54_2
| ~ spl54_186 ),
inference(avatar_split_clause,[],[f3974,f3898,f1725,f94024]) ).
thf(f94024,plain,
( spl54_832
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_832])]) ).
thf(f3898,plain,
( spl54_186
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_186])]) ).
thf(f3974,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_186 ),
inference(trivial_inequality_removal,[],[f3973]) ).
thf(f3973,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_186 ),
inference(superposition,[],[f3899,f1726]) ).
thf(f3899,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_186 ),
inference(avatar_component_clause,[],[f3898]) ).
thf(f94022,plain,
( spl54_831
| ~ spl54_2
| ~ spl54_185 ),
inference(avatar_split_clause,[],[f3952,f3894,f1725,f94020]) ).
thf(f94020,plain,
( spl54_831
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_831])]) ).
thf(f3894,plain,
( spl54_185
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_185])]) ).
thf(f3952,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_185 ),
inference(trivial_inequality_removal,[],[f3951]) ).
thf(f3951,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_185 ),
inference(superposition,[],[f3895,f1726]) ).
thf(f3895,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_185 ),
inference(avatar_component_clause,[],[f3894]) ).
thf(f94018,plain,
( spl54_830
| ~ spl54_2
| ~ spl54_184 ),
inference(avatar_split_clause,[],[f3943,f3890,f1725,f94016]) ).
thf(f94016,plain,
( spl54_830
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_830])]) ).
thf(f3890,plain,
( spl54_184
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_184])]) ).
thf(f3943,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_184 ),
inference(trivial_inequality_removal,[],[f3942]) ).
thf(f3942,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_184 ),
inference(superposition,[],[f3891,f1726]) ).
thf(f3891,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_184 ),
inference(avatar_component_clause,[],[f3890]) ).
thf(f94014,plain,
( spl54_829
| ~ spl54_2
| ~ spl54_182 ),
inference(avatar_split_clause,[],[f3935,f3882,f1725,f94012]) ).
thf(f94012,plain,
( spl54_829
<=> ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_829])]) ).
thf(f3882,plain,
( spl54_182
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_182])]) ).
thf(f3935,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_182 ),
inference(trivial_inequality_removal,[],[f3934]) ).
thf(f3934,plain,
( ! [X2: a,X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X2),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_182 ),
inference(superposition,[],[f3883,f1726]) ).
thf(f3883,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) )
| ~ spl54_182 ),
inference(avatar_component_clause,[],[f3882]) ).
thf(f94010,plain,
( spl54_828
| ~ spl54_2
| ~ spl54_181 ),
inference(avatar_split_clause,[],[f3930,f3878,f1725,f94008]) ).
thf(f94008,plain,
( spl54_828
<=> ! [X2: a,X0: a,X1: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_828])]) ).
thf(f3878,plain,
( spl54_181
<=> ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_181])]) ).
thf(f3930,plain,
( ! [X2: a,X0: a,X1: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_181 ),
inference(trivial_inequality_removal,[],[f3929]) ).
thf(f3929,plain,
( ! [X2: a,X0: a,X1: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X2),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_181 ),
inference(superposition,[],[f3879,f1726]) ).
thf(f3879,plain,
( ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) )
| ~ spl54_181 ),
inference(avatar_component_clause,[],[f3878]) ).
thf(f94005,plain,
( spl54_827
| ~ spl54_2
| ~ spl54_180 ),
inference(avatar_split_clause,[],[f3921,f3874,f1725,f94003]) ).
thf(f3874,plain,
( spl54_180
<=> ! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_180])]) ).
thf(f3921,plain,
( ! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_180 ),
inference(trivial_inequality_removal,[],[f3920]) ).
thf(f3920,plain,
( ! [X0: a,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_180 ),
inference(superposition,[],[f3875,f1726]) ).
thf(f3875,plain,
( ! [X0: a,X1: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_180 ),
inference(avatar_component_clause,[],[f3874]) ).
thf(f94000,plain,
( spl54_826
| ~ spl54_2
| ~ spl54_179 ),
inference(avatar_split_clause,[],[f3909,f3870,f1725,f93998]) ).
thf(f3870,plain,
( spl54_179
<=> ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_179])]) ).
thf(f3909,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_179 ),
inference(trivial_inequality_removal,[],[f3908]) ).
thf(f3908,plain,
( ! [X0: a,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_179 ),
inference(superposition,[],[f3871,f1726]) ).
thf(f3871,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_179 ),
inference(avatar_component_clause,[],[f3870]) ).
thf(f93465,plain,
( spl54_825
| ~ spl54_49
| ~ spl54_820 ),
inference(avatar_split_clause,[],[f93445,f93442,f2008,f93463]) ).
thf(f93442,plain,
( spl54_820
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_820])]) ).
thf(f93445,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) )
| ~ spl54_49
| ~ spl54_820 ),
inference(forward_demodulation,[],[f93443,f2010]) ).
thf(f93443,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_820 ),
inference(avatar_component_clause,[],[f93442]) ).
thf(f93461,plain,
( spl54_824
| ~ spl54_49
| ~ spl54_819 ),
inference(avatar_split_clause,[],[f93440,f93437,f2008,f93459]) ).
thf(f93459,plain,
( spl54_824
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_824])]) ).
thf(f93437,plain,
( spl54_819
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_819])]) ).
thf(f93440,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_819 ),
inference(forward_demodulation,[],[f93438,f2010]) ).
thf(f93438,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_819 ),
inference(avatar_component_clause,[],[f93437]) ).
thf(f93457,plain,
( spl54_823
| ~ spl54_49
| ~ spl54_818 ),
inference(avatar_split_clause,[],[f93431,f93428,f2008,f93455]) ).
thf(f93428,plain,
( spl54_818
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_818])]) ).
thf(f93431,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_818 ),
inference(forward_demodulation,[],[f93429,f2010]) ).
thf(f93429,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_818 ),
inference(avatar_component_clause,[],[f93428]) ).
thf(f93453,plain,
( spl54_822
| ~ spl54_49
| ~ spl54_816 ),
inference(avatar_split_clause,[],[f93419,f93416,f2008,f93451]) ).
thf(f93416,plain,
( spl54_816
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_816])]) ).
thf(f93419,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) )
| ~ spl54_49
| ~ spl54_816 ),
inference(forward_demodulation,[],[f93417,f2010]) ).
thf(f93417,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_816 ),
inference(avatar_component_clause,[],[f93416]) ).
thf(f93449,plain,
( spl54_821
| ~ spl54_49
| ~ spl54_814 ),
inference(avatar_split_clause,[],[f93407,f93404,f2008,f93447]) ).
thf(f93447,plain,
( spl54_821
<=> ! [X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_821])]) ).
thf(f93404,plain,
( spl54_814
<=> ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_814])]) ).
thf(f93407,plain,
( ! [X0: a,X1: nat] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) )
| ~ spl54_49
| ~ spl54_814 ),
inference(forward_demodulation,[],[f93405,f2010]) ).
thf(f93405,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_814 ),
inference(avatar_component_clause,[],[f93404]) ).
thf(f93444,plain,
( spl54_820
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_222 ),
inference(avatar_split_clause,[],[f4702,f4675,f3223,f1834,f1811,f93442]) ).
thf(f4702,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_222 ),
inference(forward_demodulation,[],[f4701,f3242]) ).
thf(f4701,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_222 ),
inference(forward_demodulation,[],[f4700,f3224]) ).
thf(f4700,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_222 ),
inference(forward_demodulation,[],[f4698,f1813]) ).
thf(f4698,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_222 ),
inference(trivial_inequality_removal,[],[f4693]) ).
thf(f4693,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_222 ),
inference(superposition,[],[f4676,f1836]) ).
thf(f93439,plain,
( spl54_819
| ~ spl54_14
| ~ spl54_19
| ~ spl54_213 ),
inference(avatar_split_clause,[],[f4593,f4560,f1834,f1811,f93437]) ).
thf(f4593,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_213 ),
inference(forward_demodulation,[],[f4591,f1813]) ).
thf(f4591,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_213 ),
inference(trivial_inequality_removal,[],[f4586]) ).
thf(f4586,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_213 ),
inference(superposition,[],[f4561,f1836]) ).
thf(f93430,plain,
( spl54_818
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_196 ),
inference(avatar_split_clause,[],[f4149,f4127,f3223,f1834,f1811,f93428]) ).
thf(f4149,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_196 ),
inference(forward_demodulation,[],[f4147,f3242]) ).
thf(f4147,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_196 ),
inference(trivial_inequality_removal,[],[f4142]) ).
thf(f4142,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_196 ),
inference(superposition,[],[f4128,f1836]) ).
thf(f93423,plain,
( spl54_817
| ~ spl54_18
| ~ spl54_196 ),
inference(avatar_split_clause,[],[f4148,f4127,f1829,f93421]) ).
thf(f4148,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_196 ),
inference(trivial_inequality_removal,[],[f4141]) ).
thf(f4141,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_196 ),
inference(superposition,[],[f4128,f1831]) ).
thf(f93418,plain,
( spl54_816
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_195 ),
inference(avatar_split_clause,[],[f4139,f4123,f3223,f1834,f1811,f93416]) ).
thf(f4139,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_129
| ~ spl54_195 ),
inference(forward_demodulation,[],[f4137,f3242]) ).
thf(f4137,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_195 ),
inference(trivial_inequality_removal,[],[f4132]) ).
thf(f4132,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_195 ),
inference(superposition,[],[f4124,f1836]) ).
thf(f93411,plain,
( spl54_815
| ~ spl54_18
| ~ spl54_195 ),
inference(avatar_split_clause,[],[f4138,f4123,f1829,f93409]) ).
thf(f4138,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_195 ),
inference(trivial_inequality_removal,[],[f4131]) ).
thf(f4131,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_195 ),
inference(superposition,[],[f4124,f1831]) ).
thf(f93406,plain,
( spl54_814
| ~ spl54_2
| ~ spl54_178 ),
inference(avatar_split_clause,[],[f3863,f3856,f1725,f93404]) ).
thf(f3856,plain,
( spl54_178
<=> ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_178])]) ).
thf(f3863,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_178 ),
inference(trivial_inequality_removal,[],[f3862]) ).
thf(f3862,plain,
( ! [X0: a,X1: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_178 ),
inference(superposition,[],[f3857,f1726]) ).
thf(f3857,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) )
| ~ spl54_178 ),
inference(avatar_component_clause,[],[f3856]) ).
thf(f93197,plain,
( spl54_813
| ~ spl54_49
| ~ spl54_809 ),
inference(avatar_split_clause,[],[f92325,f92321,f2008,f93195]) ).
thf(f93195,plain,
( spl54_813
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_813])]) ).
thf(f92321,plain,
( spl54_809
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_809])]) ).
thf(f92325,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) ) )
| ~ spl54_49
| ~ spl54_809 ),
inference(forward_demodulation,[],[f92324,f2010]) ).
thf(f92324,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_809 ),
inference(forward_demodulation,[],[f92322,f2010]) ).
thf(f92322,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_809 ),
inference(avatar_component_clause,[],[f92321]) ).
thf(f92860,plain,
( spl54_370
| ~ spl54_420
| ~ spl54_659 ),
inference(avatar_split_clause,[],[f41239,f41162,f18231,f16940]) ).
thf(f41239,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_420
| ~ spl54_659 ),
inference(superposition,[],[f18233,f41164]) ).
thf(f92383,plain,
( spl54_812
| ~ spl54_368
| ~ spl54_418
| ~ spl54_492
| ~ spl54_657 ),
inference(avatar_split_clause,[],[f92343,f41088,f19465,f18216,f16886,f92379]) ).
thf(f92379,plain,
( spl54_812
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK36,sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_812])]) ).
thf(f18216,plain,
( spl54_418
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_418])]) ).
thf(f92343,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK36,sK8)) )
| ~ spl54_368
| ~ spl54_418
| ~ spl54_492
| ~ spl54_657 ),
inference(forward_demodulation,[],[f18220,f41100]) ).
thf(f41100,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_492
| ~ spl54_657 ),
inference(superposition,[],[f41090,f19467]) ).
thf(f18220,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK36,sK8)) )
| ~ spl54_368
| ~ spl54_418 ),
inference(forward_demodulation,[],[f18218,f16888]) ).
thf(f18218,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_418 ),
inference(avatar_component_clause,[],[f18216]) ).
thf(f92382,plain,
( ~ spl54_812
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656
| spl54_660 ),
inference(avatar_split_clause,[],[f92340,f41233,f41083,f27864,f17732,f3336,f92379]) ).
thf(f41233,plain,
( spl54_660
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_660])]) ).
thf(f92340,plain,
( ( sK8 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK36,sK8)) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_536
| ~ spl54_656
| spl54_660 ),
inference(forward_demodulation,[],[f41234,f91858]) ).
thf(f41234,plain,
( ( sK8 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| spl54_660 ),
inference(avatar_component_clause,[],[f41233]) ).
thf(f92342,plain,
( ~ spl54_657
| ~ spl54_141
| ~ spl54_389
| ~ spl54_406
| ~ spl54_536
| ~ spl54_656
| spl54_660 ),
inference(avatar_split_clause,[],[f92341,f41233,f41083,f27864,f17909,f17732,f3336,f41088]) ).
thf(f17909,plain,
( spl54_406
<=> ( sK8 = vAPP(a,a,sK36,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_406])]) ).
thf(f92341,plain,
( ( sK8 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_406
| ~ spl54_536
| ~ spl54_656
| spl54_660 ),
inference(forward_demodulation,[],[f92340,f17911]) ).
thf(f17911,plain,
( ( sK8 = vAPP(a,a,sK36,sK8) )
| ~ spl54_406 ),
inference(avatar_component_clause,[],[f17909]) ).
thf(f92338,plain,
( spl54_370
| ~ spl54_418
| ~ spl54_660 ),
inference(avatar_split_clause,[],[f41274,f41233,f18216,f16940]) ).
thf(f41274,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_418
| ~ spl54_660 ),
inference(superposition,[],[f18218,f41235]) ).
thf(f41235,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_660 ),
inference(avatar_component_clause,[],[f41233]) ).
thf(f92337,plain,
( spl54_811
| ~ spl54_49
| ~ spl54_808 ),
inference(avatar_split_clause,[],[f92319,f92315,f2008,f92335]) ).
thf(f92335,plain,
( spl54_811
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_811])]) ).
thf(f92315,plain,
( spl54_808
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_808])]) ).
thf(f92319,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) )
| ~ spl54_49
| ~ spl54_808 ),
inference(forward_demodulation,[],[f92318,f2010]) ).
thf(f92318,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_808 ),
inference(forward_demodulation,[],[f92316,f2010]) ).
thf(f92316,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_808 ),
inference(avatar_component_clause,[],[f92315]) ).
thf(f92329,plain,
( spl54_810
| ~ spl54_18
| ~ spl54_188 ),
inference(avatar_split_clause,[],[f3998,f3988,f1829,f92327]) ).
thf(f3998,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_188 ),
inference(trivial_inequality_removal,[],[f3991]) ).
thf(f3991,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_18
| ~ spl54_188 ),
inference(superposition,[],[f3989,f1831]) ).
thf(f92323,plain,
( spl54_809
| ~ spl54_2
| ~ spl54_177 ),
inference(avatar_split_clause,[],[f3851,f3836,f1725,f92321]) ).
thf(f3836,plain,
( spl54_177
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_177])]) ).
thf(f3851,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_177 ),
inference(trivial_inequality_removal,[],[f3850]) ).
thf(f3850,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_177 ),
inference(superposition,[],[f3837,f1726]) ).
thf(f3837,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_177 ),
inference(avatar_component_clause,[],[f3836]) ).
thf(f92317,plain,
( spl54_808
| ~ spl54_2
| ~ spl54_176 ),
inference(avatar_split_clause,[],[f3843,f3832,f1725,f92315]) ).
thf(f3832,plain,
( spl54_176
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_176])]) ).
thf(f3843,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_176 ),
inference(trivial_inequality_removal,[],[f3842]) ).
thf(f3842,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_176 ),
inference(superposition,[],[f3833,f1726]) ).
thf(f3833,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_176 ),
inference(avatar_component_clause,[],[f3832]) ).
thf(f92294,plain,
( spl54_807
| ~ spl54_49
| ~ spl54_806 ),
inference(avatar_split_clause,[],[f92290,f92287,f2008,f92292]) ).
thf(f92292,plain,
( spl54_807
<=> ! [X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_807])]) ).
thf(f92287,plain,
( spl54_806
<=> ! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_806])]) ).
thf(f92290,plain,
( ! [X0: a,X1: int] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) ) )
| ~ spl54_49
| ~ spl54_806 ),
inference(forward_demodulation,[],[f92288,f2010]) ).
thf(f92288,plain,
( ! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_806 ),
inference(avatar_component_clause,[],[f92287]) ).
thf(f92289,plain,
( spl54_806
| ~ spl54_2
| ~ spl54_174 ),
inference(avatar_split_clause,[],[f3817,f3810,f1725,f92287]) ).
thf(f3817,plain,
( ! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_174 ),
inference(trivial_inequality_removal,[],[f3816]) ).
thf(f3816,plain,
( ! [X0: a,X1: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_174 ),
inference(superposition,[],[f3811,f1726]) ).
thf(f92065,plain,
( ~ spl54_370
| ~ spl54_399
| spl54_401 ),
inference(avatar_split_clause,[],[f19837,f17791,f17780,f16940]) ).
thf(f17780,plain,
( spl54_399
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_399])]) ).
thf(f17791,plain,
( spl54_401
<=> ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_401])]) ).
thf(f19837,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != sK8 )
| ~ spl54_399
| spl54_401 ),
inference(superposition,[],[f17792,f17782]) ).
thf(f17782,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) )
| ~ spl54_399 ),
inference(avatar_component_clause,[],[f17780]) ).
thf(f17792,plain,
( ( sK8 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) )
| spl54_401 ),
inference(avatar_component_clause,[],[f17791]) ).
thf(f92064,plain,
( spl54_805
| ~ spl54_49
| ~ spl54_796 ),
inference(avatar_split_clause,[],[f91125,f91120,f2008,f92062]) ).
thf(f92062,plain,
( spl54_805
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_805])]) ).
thf(f91120,plain,
( spl54_796
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_796])]) ).
thf(f91125,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_796 ),
inference(forward_demodulation,[],[f91124,f2010]) ).
thf(f91124,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_796 ),
inference(forward_demodulation,[],[f91123,f2010]) ).
thf(f91123,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_796 ),
inference(forward_demodulation,[],[f91121,f2010]) ).
thf(f91121,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_796 ),
inference(avatar_component_clause,[],[f91120]) ).
thf(f92060,plain,
( spl54_804
| ~ spl54_49
| ~ spl54_794 ),
inference(avatar_split_clause,[],[f91112,f91107,f2008,f92058]) ).
thf(f92058,plain,
( spl54_804
<=> ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_804])]) ).
thf(f91107,plain,
( spl54_794
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_794])]) ).
thf(f91112,plain,
( ! [X0: a,X1: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_794 ),
inference(forward_demodulation,[],[f91111,f2010]) ).
thf(f91111,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_794 ),
inference(forward_demodulation,[],[f91110,f2010]) ).
thf(f91110,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_794 ),
inference(forward_demodulation,[],[f91108,f2010]) ).
thf(f91108,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_794 ),
inference(avatar_component_clause,[],[f91107]) ).
thf(f91945,plain,
( spl54_803
| ~ spl54_49
| ~ spl54_764 ),
inference(avatar_split_clause,[],[f91713,f86192,f2008,f91943]) ).
thf(f91943,plain,
( spl54_803
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_803])]) ).
thf(f86192,plain,
( spl54_764
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_764])]) ).
thf(f91713,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) )
| ~ spl54_49
| ~ spl54_764 ),
inference(forward_demodulation,[],[f86193,f2010]) ).
thf(f86193,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_764 ),
inference(avatar_component_clause,[],[f86192]) ).
thf(f91940,plain,
( spl54_802
| ~ spl54_49
| ~ spl54_766 ),
inference(avatar_split_clause,[],[f91712,f86203,f2008,f91938]) ).
thf(f91938,plain,
( spl54_802
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_802])]) ).
thf(f86203,plain,
( spl54_766
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_766])]) ).
thf(f91712,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) )
| ~ spl54_49
| ~ spl54_766 ),
inference(forward_demodulation,[],[f86204,f2010]) ).
thf(f86204,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_766 ),
inference(avatar_component_clause,[],[f86203]) ).
thf(f91935,plain,
( spl54_801
| ~ spl54_49
| ~ spl54_692 ),
inference(avatar_split_clause,[],[f91765,f42144,f2008,f91933]) ).
thf(f91933,plain,
( spl54_801
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_801])]) ).
thf(f42144,plain,
( spl54_692
<=> ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_692])]) ).
thf(f91765,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) )
| ~ spl54_49
| ~ spl54_692 ),
inference(forward_demodulation,[],[f91764,f2010]) ).
thf(f91764,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) )
| ~ spl54_49
| ~ spl54_692 ),
inference(forward_demodulation,[],[f42145,f2010]) ).
thf(f42145,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) )
| ~ spl54_692 ),
inference(avatar_component_clause,[],[f42144]) ).
thf(f91930,plain,
( spl54_800
| ~ spl54_49
| ~ spl54_694 ),
inference(avatar_split_clause,[],[f91758,f42276,f2008,f91928]) ).
thf(f91928,plain,
( spl54_800
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_800])]) ).
thf(f42276,plain,
( spl54_694
<=> ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_694])]) ).
thf(f91758,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) )
| ~ spl54_49
| ~ spl54_694 ),
inference(forward_demodulation,[],[f91757,f2010]) ).
thf(f91757,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) )
| ~ spl54_49
| ~ spl54_694 ),
inference(forward_demodulation,[],[f42277,f2010]) ).
thf(f42277,plain,
( ! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) )
| ~ spl54_694 ),
inference(avatar_component_clause,[],[f42276]) ).
thf(f91925,plain,
( spl54_799
| ~ spl54_49
| ~ spl54_698 ),
inference(avatar_split_clause,[],[f42430,f42426,f2008,f91923]) ).
thf(f91923,plain,
( spl54_799
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_799])]) ).
thf(f42426,plain,
( spl54_698
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_698])]) ).
thf(f42430,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 ) )
| ~ spl54_49
| ~ spl54_698 ),
inference(forward_demodulation,[],[f42429,f2010]) ).
thf(f42429,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 ) )
| ~ spl54_49
| ~ spl54_698 ),
inference(forward_demodulation,[],[f42427,f2010]) ).
thf(f42427,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 ) )
| ~ spl54_698 ),
inference(avatar_component_clause,[],[f42426]) ).
thf(f91920,plain,
( spl54_798
| ~ spl54_49
| ~ spl54_696 ),
inference(avatar_split_clause,[],[f42353,f42349,f2008,f91918]) ).
thf(f91918,plain,
( spl54_798
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_798])]) ).
thf(f42349,plain,
( spl54_696
<=> ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_696])]) ).
thf(f42353,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 ) )
| ~ spl54_49
| ~ spl54_696 ),
inference(forward_demodulation,[],[f42352,f2010]) ).
thf(f42352,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 ) )
| ~ spl54_49
| ~ spl54_696 ),
inference(forward_demodulation,[],[f42350,f2010]) ).
thf(f42350,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 ) )
| ~ spl54_696 ),
inference(avatar_component_clause,[],[f42349]) ).
thf(f91619,plain,
( ~ spl54_141
| spl54_368
| ~ spl54_33
| ~ spl54_49
| ~ spl54_370
| ~ spl54_388
| ~ spl54_786 ),
inference(avatar_split_clause,[],[f91279,f91075,f17679,f16940,f2008,f1903,f16886,f3336]) ).
thf(f1903,plain,
( spl54_33
<=> ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_33])]) ).
thf(f17679,plain,
( spl54_388
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_388])]) ).
thf(f91075,plain,
( spl54_786
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_786])]) ).
thf(f91279,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_33
| ~ spl54_49
| ~ spl54_370
| ~ spl54_388
| ~ spl54_786 ),
inference(forward_demodulation,[],[f91278,f16942]) ).
thf(f91278,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_33
| ~ spl54_49
| ~ spl54_370
| ~ spl54_388
| ~ spl54_786 ),
inference(trivial_inequality_removal,[],[f91277]) ).
thf(f91277,plain,
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_33
| ~ spl54_49
| ~ spl54_370
| ~ spl54_388
| ~ spl54_786 ),
inference(forward_demodulation,[],[f91276,f1905]) ).
thf(f1905,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $true )
| ~ spl54_33 ),
inference(avatar_component_clause,[],[f1903]) ).
thf(f91276,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_388
| ~ spl54_786 ),
inference(forward_demodulation,[],[f91275,f16942]) ).
thf(f91275,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_49
| ~ spl54_388
| ~ spl54_786 ),
inference(forward_demodulation,[],[f91250,f2010]) ).
thf(f91250,plain,
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_388
| ~ spl54_786 ),
inference(trivial_inequality_removal,[],[f91249]) ).
thf(f91249,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_388
| ~ spl54_786 ),
inference(duplicate_literal_removal,[],[f91217]) ).
thf(f91217,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_388
| ~ spl54_786 ),
inference(superposition,[],[f91076,f17681]) ).
thf(f17681,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_388 ),
inference(avatar_component_clause,[],[f17679]) ).
thf(f91076,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = X2 ) )
| ~ spl54_786 ),
inference(avatar_component_clause,[],[f91075]) ).
thf(f91129,plain,
( spl54_797
| ~ spl54_2
| ~ spl54_172 ),
inference(avatar_split_clause,[],[f3805,f3759,f1725,f91127]) ).
thf(f91127,plain,
( spl54_797
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_797])]) ).
thf(f3759,plain,
( spl54_172
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_172])]) ).
thf(f3805,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_172 ),
inference(trivial_inequality_removal,[],[f3804]) ).
thf(f3804,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_172 ),
inference(superposition,[],[f3760,f1726]) ).
thf(f3760,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_172 ),
inference(avatar_component_clause,[],[f3759]) ).
thf(f91122,plain,
( spl54_796
| ~ spl54_2
| ~ spl54_171 ),
inference(avatar_split_clause,[],[f3796,f3755,f1725,f91120]) ).
thf(f3755,plain,
( spl54_171
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_171])]) ).
thf(f3796,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_171 ),
inference(trivial_inequality_removal,[],[f3795]) ).
thf(f3795,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_171 ),
inference(superposition,[],[f3756,f1726]) ).
thf(f3756,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_171 ),
inference(avatar_component_clause,[],[f3755]) ).
thf(f91117,plain,
( spl54_795
| ~ spl54_49
| ~ spl54_93
| ~ spl54_208 ),
inference(avatar_split_clause,[],[f15474,f4264,f2329,f2008,f91114]) ).
thf(f91114,plain,
( spl54_795
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(a,a,sK36,sK8))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_795])]) ).
thf(f2329,plain,
( spl54_93
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_93])]) ).
thf(f4264,plain,
( spl54_208
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_208])]) ).
thf(f15474,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(a,a,sK36,sK8))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_93
| ~ spl54_208 ),
inference(forward_demodulation,[],[f4912,f2010]) ).
thf(f4912,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(a,a,sK36,sK8))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_93
| ~ spl54_208 ),
inference(trivial_inequality_removal,[],[f4783]) ).
thf(f4783,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(a,a,sK36,sK8))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_93
| ~ spl54_208 ),
inference(superposition,[],[f2330,f4266]) ).
thf(f4266,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_208 ),
inference(avatar_component_clause,[],[f4264]) ).
thf(f2330,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_93 ),
inference(avatar_component_clause,[],[f2329]) ).
thf(f91109,plain,
( spl54_794
| ~ spl54_2
| ~ spl54_170 ),
inference(avatar_split_clause,[],[f3788,f3751,f1725,f91107]) ).
thf(f3751,plain,
( spl54_170
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_170])]) ).
thf(f3788,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_170 ),
inference(trivial_inequality_removal,[],[f3787]) ).
thf(f3787,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_170 ),
inference(superposition,[],[f3752,f1726]) ).
thf(f3752,plain,
( ! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_170 ),
inference(avatar_component_clause,[],[f3751]) ).
thf(f91105,plain,
( spl54_793
| ~ spl54_2
| ~ spl54_169 ),
inference(avatar_split_clause,[],[f3780,f3747,f1725,f91103]) ).
thf(f91103,plain,
( spl54_793
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_793])]) ).
thf(f3747,plain,
( spl54_169
<=> ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_169])]) ).
thf(f3780,plain,
( ! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_169 ),
inference(trivial_inequality_removal,[],[f3779]) ).
thf(f3779,plain,
( ! [X0: a,X1: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_169 ),
inference(superposition,[],[f3748,f1726]) ).
thf(f3748,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_169 ),
inference(avatar_component_clause,[],[f3747]) ).
thf(f91101,plain,
spl54_792,
inference(avatar_split_clause,[],[f1584,f91099]) ).
thf(f91099,plain,
( spl54_792
<=> ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_792])]) ).
thf(f1584,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != X2 ) ),
inference(equality_proxy_clausification,[],[f1583]) ).
thf(f1583,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) ) ),
inference(equality_proxy_clausification,[],[f1579]) ).
thf(f1579,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) ) ),
inference(binary_proxy_clausification,[],[f1347]) ).
thf(f1347,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f873]) ).
thf(f873,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(flattening,[],[f872]) ).
thf(f872,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(ennf_transformation,[],[f496]) ).
thf(f496,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) ) ) ) ),
inference(fool_elimination,[],[f495]) ).
thf(f495,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = X1 )
= ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = X2 ) ) ) ) ),
inference(rectify,[],[f210]) ).
thf(f210,axiom,
! [X36: partia96731725t_unit,X7: a,X0: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X7),X0) = X7 )
= ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X36) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_group_Ol__cancel__one) ).
thf(f91097,plain,
spl54_791,
inference(avatar_split_clause,[],[f1582,f91095]) ).
thf(f91095,plain,
( spl54_791
<=> ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_791])]) ).
thf(f1582,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = X2 ) ),
inference(equality_proxy_clausification,[],[f1581]) ).
thf(f1581,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) ) ),
inference(equality_proxy_clausification,[],[f1580]) ).
thf(f1580,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) ) ),
inference(binary_proxy_clausification,[],[f1347]) ).
thf(f91093,plain,
spl54_790,
inference(avatar_split_clause,[],[f1578,f91091]) ).
thf(f91091,plain,
( spl54_790
<=> ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_790])]) ).
thf(f1578,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) != X1 ) ),
inference(equality_proxy_clausification,[],[f1577]) ).
thf(f1577,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),X1) ) ),
inference(equality_proxy_clausification,[],[f1573]) ).
thf(f1573,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),X1) ) ),
inference(binary_proxy_clausification,[],[f1348]) ).
thf(f1348,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f875]) ).
thf(f875,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(flattening,[],[f874]) ).
thf(f874,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(ennf_transformation,[],[f498]) ).
thf(f498,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),X1) ) ) ) ),
inference(fool_elimination,[],[f497]) ).
thf(f497,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = X1 )
= ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = X2 ) ) ) ) ),
inference(rectify,[],[f208]) ).
thf(f208,axiom,
! [X36: partia96731725t_unit,X7: a,X0: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X0),X7) = X7 )
= ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X36) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_group_Or__cancel__one) ).
thf(f91089,plain,
spl54_789,
inference(avatar_split_clause,[],[f1576,f91087]) ).
thf(f91087,plain,
( spl54_789
<=> ! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_789])]) ).
thf(f1576,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) = X1 ) ),
inference(equality_proxy_clausification,[],[f1575]) ).
thf(f1575,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),X1) ) ),
inference(equality_proxy_clausification,[],[f1574]) ).
thf(f1574,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1)),X1) ) ),
inference(binary_proxy_clausification,[],[f1348]) ).
thf(f91085,plain,
spl54_788,
inference(avatar_split_clause,[],[f1560,f91083]) ).
thf(f91083,plain,
( spl54_788
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_788])]) ).
thf(f1560,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != X2 ) ),
inference(equality_proxy_clausification,[],[f1559]) ).
thf(f1559,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) ) ),
inference(equality_proxy_clausification,[],[f1555]) ).
thf(f1555,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) ) ),
inference(binary_proxy_clausification,[],[f1355]) ).
thf(f1355,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f889]) ).
thf(f889,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(flattening,[],[f888]) ).
thf(f888,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(ennf_transformation,[],[f512]) ).
thf(f512,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) ) ) ) ),
inference(fool_elimination,[],[f511]) ).
thf(f511,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = X1 )
= ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = X2 ) ) ) ) ),
inference(rectify,[],[f211]) ).
thf(f211,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X0: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X7),X0) = X7 )
= ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_group_Ol__cancel__one) ).
thf(f91081,plain,
spl54_787,
inference(avatar_split_clause,[],[f1558,f91079]) ).
thf(f91079,plain,
( spl54_787
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_787])]) ).
thf(f1558,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = X2 ) ),
inference(equality_proxy_clausification,[],[f1557]) ).
thf(f1557,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) ) ),
inference(equality_proxy_clausification,[],[f1556]) ).
thf(f1556,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) ) ),
inference(binary_proxy_clausification,[],[f1355]) ).
thf(f91077,plain,
spl54_786,
inference(avatar_split_clause,[],[f1554,f91075]) ).
thf(f1554,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) != X1 ) ),
inference(equality_proxy_clausification,[],[f1553]) ).
thf(f1553,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),X1) ) ),
inference(equality_proxy_clausification,[],[f1549]) ).
thf(f1549,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),X1) ) ),
inference(binary_proxy_clausification,[],[f1356]) ).
thf(f1356,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f891]) ).
thf(f891,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(flattening,[],[f890]) ).
thf(f890,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(ennf_transformation,[],[f514]) ).
thf(f514,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),X1) ) ) ) ),
inference(fool_elimination,[],[f513]) ).
thf(f513,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) = X1 )
= ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = X2 ) ) ) ) ),
inference(rectify,[],[f205]) ).
thf(f205,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X0: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X0),X7) = X7 )
= ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_group_Or__cancel__one_H) ).
thf(f91073,plain,
spl54_785,
inference(avatar_split_clause,[],[f1552,f91071]) ).
thf(f91071,plain,
( spl54_785
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_785])]) ).
thf(f1552,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) = X1 ) ),
inference(equality_proxy_clausification,[],[f1551]) ).
thf(f1551,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),X1) ) ),
inference(equality_proxy_clausification,[],[f1550]) ).
thf(f1550,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1)),X1) ) ),
inference(binary_proxy_clausification,[],[f1356]) ).
thf(f91068,plain,
( spl54_784
| ~ spl54_49
| ~ spl54_94
| ~ spl54_238 ),
inference(avatar_split_clause,[],[f15232,f5004,f2333,f2008,f91065]) ).
thf(f91065,plain,
( spl54_784
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(a,a,sK37,sK8))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_784])]) ).
thf(f2333,plain,
( spl54_94
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_94])]) ).
thf(f5004,plain,
( spl54_238
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_238])]) ).
thf(f15232,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(a,a,sK37,sK8))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_94
| ~ spl54_238 ),
inference(forward_demodulation,[],[f5825,f2010]) ).
thf(f5825,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(a,a,sK37,sK8))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_94
| ~ spl54_238 ),
inference(trivial_inequality_removal,[],[f5668]) ).
thf(f5668,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(a,a,sK37,sK8))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_94
| ~ spl54_238 ),
inference(superposition,[],[f2334,f5006]) ).
thf(f5006,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_238 ),
inference(avatar_component_clause,[],[f5004]) ).
thf(f2334,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_94 ),
inference(avatar_component_clause,[],[f2333]) ).
thf(f86802,plain,
( spl54_783
| ~ spl54_36
| ~ spl54_37
| ~ spl54_112
| ~ spl54_114
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3207,f3141,f2495,f2487,f1922,f1918,f86800]) ).
thf(f86800,plain,
( spl54_783
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_783])]) ).
thf(f1918,plain,
( spl54_36
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,uminus_uminus_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_36])]) ).
thf(f1922,plain,
( spl54_37
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_37])]) ).
thf(f2487,plain,
( spl54_112
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_112])]) ).
thf(f2495,plain,
( spl54_114
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_114])]) ).
thf(f3141,plain,
( spl54_127
<=> ! [X2: int,X1: int,X3: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_127])]) ).
thf(f3207,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X0)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_112
| ~ spl54_114
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3206,f1965]) ).
thf(f1965,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) )
| ~ spl54_36
| ~ spl54_37 ),
inference(superposition,[],[f1923,f1919]) ).
thf(f1919,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,uminus_uminus_int,X1)) )
| ~ spl54_36 ),
inference(avatar_component_clause,[],[f1918]) ).
thf(f1923,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) )
| ~ spl54_37 ),
inference(avatar_component_clause,[],[f1922]) ).
thf(f3206,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) )
| ~ spl54_112
| ~ spl54_114
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3178,f2496]) ).
thf(f2496,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) )
| ~ spl54_114 ),
inference(avatar_component_clause,[],[f2495]) ).
thf(f3178,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) )
| ~ spl54_112
| ~ spl54_127 ),
inference(superposition,[],[f2488,f3142]) ).
thf(f3142,plain,
( ! [X2: int,X3: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ~ spl54_127 ),
inference(avatar_component_clause,[],[f3141]) ).
thf(f2488,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ~ spl54_112 ),
inference(avatar_component_clause,[],[f2487]) ).
thf(f86798,plain,
( spl54_782
| ~ spl54_107
| ~ spl54_109
| ~ spl54_115
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3205,f3141,f2500,f2475,f2467,f86796]) ).
thf(f86796,plain,
( spl54_782
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_782])]) ).
thf(f2467,plain,
( spl54_107
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_107])]) ).
thf(f2475,plain,
( spl54_109
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_109])]) ).
thf(f2500,plain,
( spl54_115
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_115])]) ).
thf(f3205,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3))) )
| ~ spl54_107
| ~ spl54_109
| ~ spl54_115
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3204,f2501]) ).
thf(f2501,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) )
| ~ spl54_115 ),
inference(avatar_component_clause,[],[f2500]) ).
thf(f3204,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2))) )
| ~ spl54_107
| ~ spl54_109
| ~ spl54_115
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3203,f2468]) ).
thf(f2468,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) )
| ~ spl54_107 ),
inference(avatar_component_clause,[],[f2467]) ).
thf(f3203,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X3)) )
| ~ spl54_109
| ~ spl54_115
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3177,f2501]) ).
thf(f3177,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X3) )
| ~ spl54_109
| ~ spl54_127 ),
inference(superposition,[],[f2476,f3142]) ).
thf(f2476,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) )
| ~ spl54_109 ),
inference(avatar_component_clause,[],[f2475]) ).
thf(f86794,plain,
( spl54_781
| ~ spl54_107
| ~ spl54_110
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3198,f3141,f2479,f2467,f86792]) ).
thf(f86792,plain,
( spl54_781
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_781])]) ).
thf(f2479,plain,
( spl54_110
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_110])]) ).
thf(f3198,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_107
| ~ spl54_110
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3174,f2480]) ).
thf(f2480,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ~ spl54_110 ),
inference(avatar_component_clause,[],[f2479]) ).
thf(f3174,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X3) )
| ~ spl54_107
| ~ spl54_127 ),
inference(superposition,[],[f2468,f3142]) ).
thf(f86582,plain,
( spl54_780
| ~ spl54_129
| ~ spl54_452
| ~ spl54_777 ),
inference(avatar_split_clause,[],[f86467,f86464,f18679,f3223,f86580]) ).
thf(f86580,plain,
( spl54_780
<=> ! [X0: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_780])]) ).
thf(f86467,plain,
( ! [X0: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_129
| ~ spl54_452
| ~ spl54_777 ),
inference(forward_demodulation,[],[f86465,f18784]) ).
thf(f86465,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) )
| ~ spl54_777 ),
inference(avatar_component_clause,[],[f86464]) ).
thf(f86578,plain,
( spl54_779
| ~ spl54_129
| ~ spl54_452
| ~ spl54_776 ),
inference(avatar_split_clause,[],[f86462,f86459,f18679,f3223,f86576]) ).
thf(f86576,plain,
( spl54_779
<=> ! [X0: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_779])]) ).
thf(f86462,plain,
( ! [X0: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_129
| ~ spl54_452
| ~ spl54_776 ),
inference(forward_demodulation,[],[f86460,f18784]) ).
thf(f86573,plain,
( spl54_778
| ~ spl54_49
| ~ spl54_93
| ~ spl54_238 ),
inference(avatar_split_clause,[],[f15231,f5004,f2329,f2008,f86570]) ).
thf(f86570,plain,
( spl54_778
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(a,a,sK37,sK8))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_778])]) ).
thf(f15231,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(a,a,sK37,sK8))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_93
| ~ spl54_238 ),
inference(forward_demodulation,[],[f5826,f2010]) ).
thf(f5826,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(a,a,sK37,sK8))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_93
| ~ spl54_238 ),
inference(trivial_inequality_removal,[],[f5667]) ).
thf(f5667,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(a,a,sK37,sK8))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_93
| ~ spl54_238 ),
inference(superposition,[],[f2330,f5006]) ).
thf(f86466,plain,
( spl54_777
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_203 ),
inference(avatar_split_clause,[],[f15655,f4194,f2008,f1899,f1766,f86464]) ).
thf(f15655,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_203 ),
inference(trivial_inequality_removal,[],[f15654]) ).
thf(f15654,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_203 ),
inference(forward_demodulation,[],[f15653,f1768]) ).
thf(f15653,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_203 ),
inference(forward_demodulation,[],[f7820,f2010]) ).
thf(f7820,plain,
( ! [X0: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_203 ),
inference(trivial_inequality_removal,[],[f7793]) ).
thf(f7793,plain,
( ! [X0: a] :
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_203 ),
inference(superposition,[],[f4195,f1901]) ).
thf(f86461,plain,
( spl54_776
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_202 ),
inference(avatar_split_clause,[],[f15652,f4190,f2008,f1899,f1766,f86459]) ).
thf(f15652,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_202 ),
inference(trivial_inequality_removal,[],[f15651]) ).
thf(f15651,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_202 ),
inference(forward_demodulation,[],[f15650,f1768]) ).
thf(f15650,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_202 ),
inference(forward_demodulation,[],[f7821,f2010]) ).
thf(f7821,plain,
( ! [X0: a] :
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_202 ),
inference(trivial_inequality_removal,[],[f7792]) ).
thf(f7792,plain,
( ! [X0: a] :
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),sK8)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_202 ),
inference(superposition,[],[f4191,f1901]) ).
thf(f86457,plain,
( spl54_775
| ~ spl54_78
| ~ spl54_169 ),
inference(avatar_split_clause,[],[f3782,f3747,f2187,f86455]) ).
thf(f86455,plain,
( spl54_775
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_775])]) ).
thf(f3782,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_78
| ~ spl54_169 ),
inference(trivial_inequality_removal,[],[f3777]) ).
thf(f3777,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_78
| ~ spl54_169 ),
inference(superposition,[],[f3748,f2189]) ).
thf(f86453,plain,
( spl54_774
| ~ spl54_35
| ~ spl54_134 ),
inference(avatar_split_clause,[],[f3310,f3298,f1914,f86451]) ).
thf(f86451,plain,
( spl54_774
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,sK9,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,a,sK10,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_774])]) ).
thf(f3298,plain,
( spl54_134
<=> ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,a,sK10,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_134])]) ).
thf(f3310,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia96731725t_unit,a,sK9,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))),vAPP(partia96731725t_unit,a,sK10,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ) )
| ~ spl54_35
| ~ spl54_134 ),
inference(superposition,[],[f3299,f1915]) ).
thf(f3299,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,a,sK10,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_134 ),
inference(avatar_component_clause,[],[f3298]) ).
thf(f86449,plain,
( spl54_773
| ~ spl54_34
| ~ spl54_134 ),
inference(avatar_split_clause,[],[f3309,f3298,f1910,f86447]) ).
thf(f86447,plain,
( spl54_773
<=> ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,a,sK10,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_773])]) ).
thf(f3309,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))),vAPP(partia96731725t_unit,a,sK10,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ) )
| ~ spl54_34
| ~ spl54_134 ),
inference(superposition,[],[f3299,f1911]) ).
thf(f86424,plain,
( spl54_772
| ~ spl54_49
| ~ spl54_92
| ~ spl54_294 ),
inference(avatar_split_clause,[],[f9739,f7242,f2325,f2008,f86421]) ).
thf(f86421,plain,
( spl54_772
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_772])]) ).
thf(f2325,plain,
( spl54_92
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_92])]) ).
thf(f9739,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_92
| ~ spl54_294 ),
inference(forward_demodulation,[],[f9735,f2010]) ).
thf(f9735,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_92
| ~ spl54_294 ),
inference(trivial_inequality_removal,[],[f9720]) ).
thf(f9720,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_92
| ~ spl54_294 ),
inference(superposition,[],[f2326,f7244]) ).
thf(f2326,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_92 ),
inference(avatar_component_clause,[],[f2325]) ).
thf(f86419,plain,
( spl54_771
| ~ spl54_18
| ~ spl54_178
| ~ spl54_179 ),
inference(avatar_split_clause,[],[f3913,f3870,f3856,f1829,f86417]) ).
thf(f3913,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_178
| ~ spl54_179 ),
inference(forward_demodulation,[],[f3912,f3866]) ).
thf(f3866,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_178 ),
inference(trivial_inequality_removal,[],[f3859]) ).
thf(f3859,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_18
| ~ spl54_178 ),
inference(superposition,[],[f3857,f1831]) ).
thf(f3912,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_179 ),
inference(trivial_inequality_removal,[],[f3905]) ).
thf(f3905,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_18
| ~ spl54_179 ),
inference(superposition,[],[f3871,f1831]) ).
thf(f86415,plain,
( spl54_770
| ~ spl54_18
| ~ spl54_178 ),
inference(avatar_split_clause,[],[f3866,f3856,f1829,f86413]) ).
thf(f86220,plain,
( spl54_769
| ~ spl54_49
| ~ spl54_767 ),
inference(avatar_split_clause,[],[f86212,f86209,f2008,f86218]) ).
thf(f86218,plain,
( spl54_769
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_769])]) ).
thf(f86209,plain,
( spl54_767
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_767])]) ).
thf(f86212,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) ) )
| ~ spl54_49
| ~ spl54_767 ),
inference(forward_demodulation,[],[f86210,f2010]) ).
thf(f86210,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_767 ),
inference(avatar_component_clause,[],[f86209]) ).
thf(f86216,plain,
( spl54_768
| ~ spl54_49
| ~ spl54_765 ),
inference(avatar_split_clause,[],[f86201,f86198,f2008,f86214]) ).
thf(f86214,plain,
( spl54_768
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_768])]) ).
thf(f86198,plain,
( spl54_765
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_765])]) ).
thf(f86201,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) ) )
| ~ spl54_49
| ~ spl54_765 ),
inference(forward_demodulation,[],[f86199,f2010]) ).
thf(f86199,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_765 ),
inference(avatar_component_clause,[],[f86198]) ).
thf(f86211,plain,
( spl54_767
| ~ spl54_18
| ~ spl54_177 ),
inference(avatar_split_clause,[],[f3854,f3836,f1829,f86209]) ).
thf(f3854,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_177 ),
inference(trivial_inequality_removal,[],[f3847]) ).
thf(f3847,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_177 ),
inference(superposition,[],[f3837,f1831]) ).
thf(f86205,plain,
( spl54_766
| ~ spl54_19
| ~ spl54_177 ),
inference(avatar_split_clause,[],[f3853,f3836,f1834,f86203]) ).
thf(f3853,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_177 ),
inference(trivial_inequality_removal,[],[f3848]) ).
thf(f3848,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_177 ),
inference(superposition,[],[f3837,f1836]) ).
thf(f86200,plain,
( spl54_765
| ~ spl54_18
| ~ spl54_176 ),
inference(avatar_split_clause,[],[f3846,f3832,f1829,f86198]) ).
thf(f3846,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_176 ),
inference(trivial_inequality_removal,[],[f3839]) ).
thf(f3839,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_176 ),
inference(superposition,[],[f3833,f1831]) ).
thf(f86194,plain,
( spl54_764
| ~ spl54_19
| ~ spl54_176 ),
inference(avatar_split_clause,[],[f3845,f3832,f1834,f86192]) ).
thf(f3845,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_176 ),
inference(trivial_inequality_removal,[],[f3840]) ).
thf(f3840,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_176 ),
inference(superposition,[],[f3833,f1836]) ).
thf(f86189,plain,
( spl54_763
| ~ spl54_49
| ~ spl54_91
| ~ spl54_294 ),
inference(avatar_split_clause,[],[f9738,f7242,f2321,f2008,f86186]) ).
thf(f86186,plain,
( spl54_763
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_763])]) ).
thf(f2321,plain,
( spl54_91
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_91])]) ).
thf(f9738,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_91
| ~ spl54_294 ),
inference(forward_demodulation,[],[f9736,f2010]) ).
thf(f9736,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_91
| ~ spl54_294 ),
inference(trivial_inequality_removal,[],[f9719]) ).
thf(f9719,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_91
| ~ spl54_294 ),
inference(superposition,[],[f2322,f7244]) ).
thf(f2322,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_91 ),
inference(avatar_component_clause,[],[f2321]) ).
thf(f76392,plain,
( spl54_762
| ~ spl54_49
| ~ spl54_292 ),
inference(avatar_split_clause,[],[f9670,f7089,f2008,f76389]) ).
thf(f76389,plain,
( spl54_762
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_762])]) ).
thf(f7089,plain,
( spl54_292
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_292])]) ).
thf(f9670,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_292 ),
inference(superposition,[],[f7091,f2010]) ).
thf(f7091,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_292 ),
inference(avatar_component_clause,[],[f7089]) ).
thf(f63417,plain,
( spl54_761
| ~ spl54_49
| ~ spl54_289 ),
inference(avatar_split_clause,[],[f9668,f7075,f2008,f63414]) ).
thf(f63414,plain,
( spl54_761
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_761])]) ).
thf(f7075,plain,
( spl54_289
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_289])]) ).
thf(f9668,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_289 ),
inference(superposition,[],[f7077,f2010]) ).
thf(f7077,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_289 ),
inference(avatar_component_clause,[],[f7075]) ).
thf(f50043,plain,
( ~ spl54_760
| spl54_389
| ~ spl54_447
| ~ spl54_512 ),
inference(avatar_split_clause,[],[f42699,f20568,f18555,f17732,f50040]) ).
thf(f18555,plain,
( spl54_447
<=> ! [X0: a] :
( ( sK8 = X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) != sK8 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_447])]) ).
thf(f20568,plain,
( spl54_512
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_512])]) ).
thf(f42699,plain,
( ( sK8 = vAPP(a,a,sK32,sK8) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,sK8)) )
| ~ spl54_447
| ~ spl54_512 ),
inference(trivial_inequality_removal,[],[f42674]) ).
thf(f42674,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,sK32,sK8) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,sK8)) )
| ~ spl54_447
| ~ spl54_512 ),
inference(superposition,[],[f18556,f20570]) ).
thf(f20570,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_512 ),
inference(avatar_component_clause,[],[f20568]) ).
thf(f18556,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = X0 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) != sK8 ) )
| ~ spl54_447 ),
inference(avatar_component_clause,[],[f18555]) ).
thf(f42858,plain,
( spl54_759
| ~ spl54_74
| ~ spl54_106
| ~ spl54_144 ),
inference(avatar_split_clause,[],[f3425,f3350,f2463,f2170,f42856]) ).
thf(f42856,plain,
( spl54_759
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_759])]) ).
thf(f2170,plain,
( spl54_74
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,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,suc,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_74])]) ).
thf(f2463,plain,
( spl54_106
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_106])]) ).
thf(f3350,plain,
( spl54_144
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_144])]) ).
thf(f3425,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X2),X3))) )
| ~ spl54_74
| ~ spl54_106
| ~ spl54_144 ),
inference(forward_demodulation,[],[f3424,f3351]) ).
thf(f3351,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)) )
| ~ spl54_144 ),
inference(avatar_component_clause,[],[f3350]) ).
thf(f3424,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3))) )
| ~ spl54_74
| ~ spl54_106
| ~ spl54_144 ),
inference(forward_demodulation,[],[f3415,f2171]) ).
thf(f2171,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,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,suc,X0)),X1) )
| ~ spl54_74 ),
inference(avatar_component_clause,[],[f2170]) ).
thf(f3415,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X2)),X3)) )
| ~ spl54_106
| ~ spl54_144 ),
inference(superposition,[],[f2464,f3351]) ).
thf(f2464,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
| ~ spl54_106 ),
inference(avatar_component_clause,[],[f2463]) ).
thf(f42854,plain,
( spl54_758
| ~ spl54_36
| ~ spl54_112
| ~ spl54_114
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3209,f3141,f2495,f2487,f1918,f42852]) ).
thf(f42852,plain,
( spl54_758
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_758])]) ).
thf(f3209,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_36
| ~ spl54_112
| ~ spl54_114
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3208,f1919]) ).
thf(f3208,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,uminus_uminus_int,X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_112
| ~ spl54_114
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3179,f2496]) ).
thf(f3179,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,uminus_uminus_int,X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_112
| ~ spl54_127 ),
inference(superposition,[],[f2488,f3142]) ).
thf(f42850,plain,
( ~ spl54_757
| spl54_400
| ~ spl54_447
| ~ spl54_506 ),
inference(avatar_split_clause,[],[f31171,f20347,f18555,f17786,f42847]) ).
thf(f31171,plain,
( ( sK8 = vAPP(a,a,sK33,sK8) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK8)) )
| ~ spl54_447
| ~ spl54_506 ),
inference(trivial_inequality_removal,[],[f31164]) ).
thf(f31164,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,sK33,sK8) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK8)) )
| ~ spl54_447
| ~ spl54_506 ),
inference(superposition,[],[f18556,f20349]) ).
thf(f42845,plain,
( spl54_756
| ~ spl54_39
| ~ spl54_103
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3197,f3141,f2450,f1933,f42843]) ).
thf(f42843,plain,
( spl54_756
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_756])]) ).
thf(f1933,plain,
( spl54_39
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_39])]) ).
thf(f2450,plain,
( spl54_103
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_103])]) ).
thf(f3197,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_39
| ~ spl54_103
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3173,f1934]) ).
thf(f1934,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) )
| ~ spl54_39 ),
inference(avatar_component_clause,[],[f1933]) ).
thf(f3173,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_103
| ~ spl54_127 ),
inference(superposition,[],[f2451,f3142]) ).
thf(f2451,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) )
| ~ spl54_103 ),
inference(avatar_component_clause,[],[f2450]) ).
thf(f42841,plain,
( spl54_755
| ~ spl54_39
| ~ spl54_103
| ~ spl54_110
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3196,f3141,f2479,f2450,f1933,f42839]) ).
thf(f42839,plain,
( spl54_755
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_755])]) ).
thf(f3196,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0)) )
| ~ spl54_39
| ~ spl54_103
| ~ spl54_110
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3195,f2480]) ).
thf(f3195,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0)) )
| ~ spl54_39
| ~ spl54_103
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3172,f1934]) ).
thf(f3172,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X3)) )
| ~ spl54_103
| ~ spl54_127 ),
inference(superposition,[],[f2451,f3142]) ).
thf(f42837,plain,
( spl54_754
| ~ spl54_39
| ~ spl54_85
| ~ spl54_109
| ~ spl54_111
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3188,f3141,f2483,f2475,f2242,f1933,f42835]) ).
thf(f42835,plain,
( spl54_754
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_754])]) ).
thf(f2242,plain,
( spl54_85
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,uminus_uminus_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_85])]) ).
thf(f2483,plain,
( spl54_111
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_111])]) ).
thf(f3188,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3))) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_109
| ~ spl54_111
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3187,f2476]) ).
thf(f3187,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X3)) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_109
| ~ spl54_111
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3159,f2789]) ).
thf(f2789,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_109 ),
inference(forward_demodulation,[],[f2788,f1934]) ).
thf(f2788,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),X2)) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_109 ),
inference(forward_demodulation,[],[f2761,f1934]) ).
thf(f2761,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),X2) )
| ~ spl54_85
| ~ spl54_109 ),
inference(superposition,[],[f2476,f2243]) ).
thf(f2243,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,uminus_uminus_int,X0)) )
| ~ spl54_85 ),
inference(avatar_component_clause,[],[f2242]) ).
thf(f3159,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X3)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_111
| ~ spl54_127 ),
inference(superposition,[],[f3142,f2484]) ).
thf(f2484,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ~ spl54_111 ),
inference(avatar_component_clause,[],[f2483]) ).
thf(f42833,plain,
( spl54_753
| ~ spl54_39
| ~ spl54_85
| ~ spl54_109
| ~ spl54_112
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3186,f3141,f2487,f2475,f2242,f1933,f42831]) ).
thf(f42831,plain,
( spl54_753
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_753])]) ).
thf(f3186,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_109
| ~ spl54_112
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3158,f2789]) ).
thf(f3158,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X3)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) )
| ~ spl54_112
| ~ spl54_127 ),
inference(superposition,[],[f3142,f2488]) ).
thf(f42829,plain,
( spl54_752
| ~ spl54_39
| ~ spl54_85
| ~ spl54_103
| ~ spl54_109
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3185,f3141,f2475,f2450,f2242,f1933,f42827]) ).
thf(f42827,plain,
( spl54_752
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_752])]) ).
thf(f3185,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_103
| ~ spl54_109
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3157,f2789]) ).
thf(f3157,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X3)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) )
| ~ spl54_103
| ~ spl54_127 ),
inference(superposition,[],[f3142,f2451]) ).
thf(f42825,plain,
( spl54_751
| ~ spl54_39
| ~ spl54_85
| ~ spl54_107
| ~ spl54_109
| ~ spl54_115
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3184,f3141,f2500,f2475,f2467,f2242,f1933,f42823]) ).
thf(f42823,plain,
( spl54_751
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_751])]) ).
thf(f3184,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_107
| ~ spl54_109
| ~ spl54_115
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3183,f2501]) ).
thf(f3183,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)),X3)) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_107
| ~ spl54_109
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3156,f2789]) ).
thf(f3156,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X3)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) )
| ~ spl54_107
| ~ spl54_127 ),
inference(superposition,[],[f3142,f2468]) ).
thf(f42821,plain,
( spl54_750
| ~ spl54_37
| ~ spl54_115
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3180,f3141,f2500,f1922,f42819]) ).
thf(f42819,plain,
( spl54_750
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_750])]) ).
thf(f3180,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) )
| ~ spl54_37
| ~ spl54_115
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3153,f2501]) ).
thf(f3153,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) )
| ~ spl54_37
| ~ spl54_127 ),
inference(superposition,[],[f3142,f1923]) ).
thf(f42817,plain,
( spl54_749
| ~ spl54_110
| ~ spl54_112
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3024,f2500,f2487,f2479,f42815]) ).
thf(f42815,plain,
( spl54_749
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_749])]) ).
thf(f3024,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1)) )
| ~ spl54_110
| ~ spl54_112
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2995,f2480]) ).
thf(f2995,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) )
| ~ spl54_112
| ~ spl54_115 ),
inference(superposition,[],[f2488,f2501]) ).
thf(f42813,plain,
( spl54_748
| ~ spl54_109
| ~ spl54_110
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3023,f2500,f2479,f2475,f42811]) ).
thf(f42811,plain,
( spl54_748
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_748])]) ).
thf(f3023,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2))) )
| ~ spl54_109
| ~ spl54_110
| ~ spl54_115 ),
inference(forward_demodulation,[],[f3022,f2480]) ).
thf(f3022,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3)) )
| ~ spl54_109
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2994,f2501]) ).
thf(f2994,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),X3) )
| ~ spl54_109
| ~ spl54_115 ),
inference(superposition,[],[f2476,f2501]) ).
thf(f42809,plain,
( spl54_747
| ~ spl54_103
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3018,f2500,f2450,f42807]) ).
thf(f42807,plain,
( spl54_747
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_747])]) ).
thf(f3018,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) )
| ~ spl54_103
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2989,f2501]) ).
thf(f2989,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X3)) )
| ~ spl54_103
| ~ spl54_115 ),
inference(superposition,[],[f2451,f2501]) ).
thf(f42805,plain,
( spl54_746
| ~ spl54_108
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3015,f2500,f2471,f42803]) ).
thf(f42803,plain,
( spl54_746
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_746])]) ).
thf(f2471,plain,
( spl54_108
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_108])]) ).
thf(f3015,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) )
| ~ spl54_108
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2982,f2501]) ).
thf(f2982,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X3)) )
| ~ spl54_108
| ~ spl54_115 ),
inference(superposition,[],[f2501,f2472]) ).
thf(f2472,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ~ spl54_108 ),
inference(avatar_component_clause,[],[f2471]) ).
thf(f42801,plain,
( spl54_745
| ~ spl54_110
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3010,f2500,f2479,f42799]) ).
thf(f42799,plain,
( spl54_745
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_745])]) ).
thf(f3010,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1))) )
| ~ spl54_110
| ~ spl54_115 ),
inference(forward_demodulation,[],[f3009,f2501]) ).
thf(f3009,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)),X1)) )
| ~ spl54_110
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2977,f2480]) ).
thf(f2977,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) )
| ~ spl54_110
| ~ spl54_115 ),
inference(superposition,[],[f2501,f2480]) ).
thf(f42797,plain,
( spl54_744
| ~ spl54_110
| ~ spl54_111
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3008,f2500,f2483,f2479,f42795]) ).
thf(f42795,plain,
( spl54_744
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_744])]) ).
thf(f3008,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1))) )
| ~ spl54_110
| ~ spl54_111
| ~ spl54_115 ),
inference(forward_demodulation,[],[f3007,f2501]) ).
thf(f3007,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)),X1)) )
| ~ spl54_110
| ~ spl54_111
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2976,f2480]) ).
thf(f2976,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) )
| ~ spl54_111
| ~ spl54_115 ),
inference(superposition,[],[f2501,f2484]) ).
thf(f42793,plain,
( spl54_743
| ~ spl54_107
| ~ spl54_112
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3006,f2500,f2487,f2467,f42791]) ).
thf(f42791,plain,
( spl54_743
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_743])]) ).
thf(f3006,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1))) )
| ~ spl54_107
| ~ spl54_112
| ~ spl54_115 ),
inference(forward_demodulation,[],[f3005,f2501]) ).
thf(f3005,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1))) )
| ~ spl54_107
| ~ spl54_112
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2975,f2468]) ).
thf(f2975,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)),X3)) )
| ~ spl54_112
| ~ spl54_115 ),
inference(superposition,[],[f2501,f2488]) ).
thf(f42789,plain,
( spl54_742
| ~ spl54_107
| ~ spl54_110
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3002,f2500,f2479,f2467,f42787]) ).
thf(f42787,plain,
( spl54_742
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_742])]) ).
thf(f3002,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3))) )
| ~ spl54_107
| ~ spl54_110
| ~ spl54_115 ),
inference(forward_demodulation,[],[f3001,f2480]) ).
thf(f3001,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)),X1)) )
| ~ spl54_107
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2973,f2468]) ).
thf(f2973,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3)) )
| ~ spl54_107
| ~ spl54_115 ),
inference(superposition,[],[f2501,f2468]) ).
thf(f42785,plain,
( spl54_741
| ~ spl54_108
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f2992,f2500,f2471,f42783]) ).
thf(f42783,plain,
( spl54_741
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_741])]) ).
thf(f2992,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) )
| ~ spl54_108
| ~ spl54_115 ),
inference(superposition,[],[f2472,f2501]) ).
thf(f42781,plain,
( spl54_740
| ~ spl54_114
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f2984,f2500,f2495,f42779]) ).
thf(f42779,plain,
( spl54_740
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_740])]) ).
thf(f2984,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) )
| ~ spl54_114
| ~ spl54_115 ),
inference(superposition,[],[f2501,f2496]) ).
thf(f42777,plain,
( spl54_739
| ~ spl54_109
| ~ spl54_110
| ~ spl54_114
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f2965,f2500,f2495,f2479,f2475,f42775]) ).
thf(f42775,plain,
( spl54_739
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_739])]) ).
thf(f2965,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3))) )
| ~ spl54_109
| ~ spl54_110
| ~ spl54_114
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2964,f2501]) ).
thf(f2964,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1))) )
| ~ spl54_109
| ~ spl54_110
| ~ spl54_114
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2963,f2480]) ).
thf(f2963,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)),X3)) )
| ~ spl54_109
| ~ spl54_114
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2944,f2501]) ).
thf(f2944,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) )
| ~ spl54_109
| ~ spl54_114 ),
inference(superposition,[],[f2476,f2496]) ).
thf(f42773,plain,
( spl54_738
| ~ spl54_103
| ~ spl54_110
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2960,f2495,f2479,f2450,f42771]) ).
thf(f42771,plain,
( spl54_738
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_738])]) ).
thf(f2960,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)) )
| ~ spl54_103
| ~ spl54_110
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2939,f2480]) ).
thf(f2939,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)) )
| ~ spl54_103
| ~ spl54_114 ),
inference(superposition,[],[f2451,f2496]) ).
thf(f42769,plain,
( spl54_737
| ~ spl54_107
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2941,f2495,f2467,f42767]) ).
thf(f42767,plain,
( spl54_737
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_737])]) ).
thf(f2941,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) )
| ~ spl54_107
| ~ spl54_114 ),
inference(superposition,[],[f2468,f2496]) ).
thf(f42765,plain,
( spl54_368
| ~ spl54_736
| ~ spl54_17
| ~ spl54_141
| ~ spl54_370
| ~ spl54_526
| ~ spl54_695 ),
inference(avatar_split_clause,[],[f42335,f42283,f20628,f16940,f3336,f1824,f42762,f16886]) ).
thf(f20628,plain,
( spl54_526
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_526])]) ).
thf(f42283,plain,
( spl54_695
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_695])]) ).
thf(f42335,plain,
( ( sK8 != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_370
| ~ spl54_526
| ~ spl54_695 ),
inference(trivial_inequality_removal,[],[f42334]) ).
thf(f42334,plain,
( ( $true != $true )
| ( sK8 != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_17
| ~ spl54_141
| ~ spl54_370
| ~ spl54_526
| ~ spl54_695 ),
inference(forward_demodulation,[],[f42333,f3338]) ).
thf(f42333,plain,
( ( sK8 != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_370
| ~ spl54_526
| ~ spl54_695 ),
inference(inner_rewriting,[],[f42332]) ).
thf(f42332,plain,
( ( sK8 != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_370
| ~ spl54_526
| ~ spl54_695 ),
inference(trivial_inequality_removal,[],[f42331]) ).
thf(f42331,plain,
( ( $true != $true )
| ( sK8 != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_370
| ~ spl54_526
| ~ spl54_695 ),
inference(forward_demodulation,[],[f42330,f1826]) ).
thf(f42330,plain,
( ( sK8 != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_370
| ~ spl54_526
| ~ spl54_695 ),
inference(forward_demodulation,[],[f42298,f16942]) ).
thf(f42298,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_526
| ~ spl54_695 ),
inference(superposition,[],[f42284,f20630]) ).
thf(f20630,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_526 ),
inference(avatar_component_clause,[],[f20628]) ).
thf(f42284,plain,
( ! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_695 ),
inference(avatar_component_clause,[],[f42283]) ).
thf(f42760,plain,
( spl54_735
| ~ spl54_103
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2940,f2495,f2450,f42758]) ).
thf(f42758,plain,
( spl54_735
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_735])]) ).
thf(f2940,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) )
| ~ spl54_103
| ~ spl54_114 ),
inference(superposition,[],[f2451,f2496]) ).
thf(f42756,plain,
( spl54_734
| ~ spl54_110
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2928,f2495,f2479,f42754]) ).
thf(f42754,plain,
( spl54_734
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_734])]) ).
thf(f2928,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) )
| ~ spl54_110
| ~ spl54_114 ),
inference(superposition,[],[f2496,f2480]) ).
thf(f42752,plain,
( spl54_733
| ~ spl54_111
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2927,f2495,f2483,f42750]) ).
thf(f42750,plain,
( spl54_733
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_733])]) ).
thf(f2927,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_111
| ~ spl54_114 ),
inference(superposition,[],[f2496,f2484]) ).
thf(f42748,plain,
( spl54_732
| ~ spl54_107
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2924,f2495,f2467,f42746]) ).
thf(f42746,plain,
( spl54_732
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_732])]) ).
thf(f2924,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) )
| ~ spl54_107
| ~ spl54_114 ),
inference(superposition,[],[f2496,f2468]) ).
thf(f42744,plain,
( spl54_731
| ~ spl54_105
| ~ spl54_106
| ~ spl54_113 ),
inference(avatar_split_clause,[],[f2921,f2491,f2463,f2459,f42742]) ).
thf(f42742,plain,
( spl54_731
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_731])]) ).
thf(f2459,plain,
( spl54_105
<=> ! [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,[spl54_105])]) ).
thf(f2491,plain,
( spl54_113
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_113])]) ).
thf(f2921,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),X3))) )
| ~ spl54_105
| ~ spl54_106
| ~ spl54_113 ),
inference(forward_demodulation,[],[f2920,f2460]) ).
thf(f2460,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) )
| ~ spl54_105 ),
inference(avatar_component_clause,[],[f2459]) ).
thf(f2920,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)),X3)) )
| ~ spl54_106
| ~ spl54_113 ),
inference(forward_demodulation,[],[f2911,f2464]) ).
thf(f2911,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))),X3) )
| ~ spl54_106
| ~ spl54_113 ),
inference(superposition,[],[f2464,f2492]) ).
thf(f2492,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) )
| ~ spl54_113 ),
inference(avatar_component_clause,[],[f2491]) ).
thf(f42740,plain,
( spl54_730
| ~ spl54_106
| ~ spl54_113 ),
inference(avatar_split_clause,[],[f2917,f2491,f2463,f42738]) ).
thf(f42738,plain,
( spl54_730
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X3),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_730])]) ).
thf(f2917,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X3),X2))) )
| ~ spl54_106
| ~ spl54_113 ),
inference(forward_demodulation,[],[f2908,f2464]) ).
thf(f2908,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) )
| ~ spl54_106
| ~ spl54_113 ),
inference(superposition,[],[f2492,f2464]) ).
thf(f42736,plain,
( spl54_729
| ~ spl54_105
| ~ spl54_106
| ~ spl54_113 ),
inference(avatar_split_clause,[],[f2916,f2491,f2463,f2459,f42734]) ).
thf(f42734,plain,
( spl54_729
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_729])]) ).
thf(f2916,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),X3))) )
| ~ spl54_105
| ~ spl54_106
| ~ spl54_113 ),
inference(forward_demodulation,[],[f2915,f2460]) ).
thf(f2915,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)),X3)) )
| ~ spl54_106
| ~ spl54_113 ),
inference(forward_demodulation,[],[f2907,f2464]) ).
thf(f2907,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))),X3) )
| ~ spl54_113 ),
inference(superposition,[],[f2492,f2492]) ).
thf(f42732,plain,
( spl54_728
| ~ spl54_109
| ~ spl54_110
| ~ spl54_111
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2900,f2487,f2483,f2479,f2475,f42730]) ).
thf(f42730,plain,
( spl54_728
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_728])]) ).
thf(f2900,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3))) )
| ~ spl54_109
| ~ spl54_110
| ~ spl54_111
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2899,f2476]) ).
thf(f2899,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) )
| ~ spl54_110
| ~ spl54_111
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2882,f2480]) ).
thf(f2882,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X3) )
| ~ spl54_111
| ~ spl54_112 ),
inference(superposition,[],[f2484,f2488]) ).
thf(f42728,plain,
( spl54_727
| ~ spl54_107
| ~ spl54_109
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2888,f2487,f2475,f2467,f42726]) ).
thf(f42726,plain,
( spl54_727
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_727])]) ).
thf(f2888,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X1)) )
| ~ spl54_107
| ~ spl54_109
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2858,f2468]) ).
thf(f2858,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) )
| ~ spl54_109
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2476]) ).
thf(f42724,plain,
( spl54_726
| ~ spl54_108
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2875,f2487,f2471,f42722]) ).
thf(f42722,plain,
( spl54_726
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_726])]) ).
thf(f2875,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_108
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2472]) ).
thf(f42663,plain,
( spl54_725
| ~ spl54_109
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2868,f2487,f2475,f42661]) ).
thf(f42661,plain,
( spl54_725
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_725])]) ).
thf(f2868,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_109
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2476]) ).
thf(f42659,plain,
( spl54_724
| ~ spl54_108
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2865,f2487,f2471,f42657]) ).
thf(f42657,plain,
( spl54_724
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_724])]) ).
thf(f2865,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_108
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2472]) ).
thf(f42655,plain,
( spl54_723
| ~ spl54_110
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2855,f2483,f2479,f42653]) ).
thf(f42653,plain,
( spl54_723
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_723])]) ).
thf(f2855,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_110
| ~ spl54_111 ),
inference(forward_demodulation,[],[f2839,f2480]) ).
thf(f2839,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X3) )
| ~ spl54_110
| ~ spl54_111 ),
inference(superposition,[],[f2480,f2484]) ).
thf(f42651,plain,
( spl54_722
| ~ spl54_109
| ~ spl54_110
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2850,f2483,f2479,f2475,f42649]) ).
thf(f42649,plain,
( spl54_722
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_722])]) ).
thf(f2850,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X1))) )
| ~ spl54_109
| ~ spl54_110
| ~ spl54_111 ),
inference(forward_demodulation,[],[f2849,f2476]) ).
thf(f2849,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)),X1)) )
| ~ spl54_110
| ~ spl54_111 ),
inference(forward_demodulation,[],[f2834,f2480]) ).
thf(f2834,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) )
| ~ spl54_110
| ~ spl54_111 ),
inference(superposition,[],[f2484,f2480]) ).
thf(f42647,plain,
( spl54_721
| ~ spl54_110
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2848,f2483,f2479,f42645]) ).
thf(f42645,plain,
( spl54_721
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_721])]) ).
thf(f2848,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_110
| ~ spl54_111 ),
inference(forward_demodulation,[],[f2833,f2480]) ).
thf(f2833,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X3) )
| ~ spl54_111 ),
inference(superposition,[],[f2484,f2484]) ).
thf(f42643,plain,
( spl54_720
| ~ spl54_107
| ~ spl54_110
| ~ spl54_111
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2845,f2495,f2483,f2479,f2467,f42641]) ).
thf(f42641,plain,
( spl54_720
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_720])]) ).
thf(f2845,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X3))) )
| ~ spl54_107
| ~ spl54_110
| ~ spl54_111
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2831,f2821]) ).
thf(f2821,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) )
| ~ spl54_107
| ~ spl54_110
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2820,f2496]) ).
thf(f2820,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) )
| ~ spl54_107
| ~ spl54_110 ),
inference(forward_demodulation,[],[f2810,f2480]) ).
thf(f2810,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) )
| ~ spl54_107
| ~ spl54_110 ),
inference(superposition,[],[f2480,f2468]) ).
thf(f2831,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3)) )
| ~ spl54_107
| ~ spl54_111 ),
inference(superposition,[],[f2484,f2468]) ).
thf(f42639,plain,
( spl54_719
| ~ spl54_110 ),
inference(avatar_split_clause,[],[f2823,f2479,f42637]) ).
thf(f42637,plain,
( spl54_719
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_719])]) ).
thf(f2823,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) )
| ~ spl54_110 ),
inference(forward_demodulation,[],[f2812,f2480]) ).
thf(f2812,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X3) )
| ~ spl54_110 ),
inference(superposition,[],[f2480,f2480]) ).
thf(f42635,plain,
( spl54_718
| ~ spl54_107
| ~ spl54_110
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2821,f2495,f2479,f2467,f42633]) ).
thf(f42633,plain,
( spl54_718
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_718])]) ).
thf(f42631,plain,
( spl54_717
| ~ spl54_103
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2798,f2475,f2450,f42629]) ).
thf(f42629,plain,
( spl54_717
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_717])]) ).
thf(f2798,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X3))) )
| ~ spl54_103
| ~ spl54_109 ),
inference(forward_demodulation,[],[f2772,f2476]) ).
thf(f2772,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X3)) )
| ~ spl54_103
| ~ spl54_109 ),
inference(superposition,[],[f2451,f2476]) ).
thf(f42627,plain,
( spl54_716
| ~ spl54_108
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2791,f2475,f2471,f42625]) ).
thf(f42625,plain,
( spl54_716
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_716])]) ).
thf(f2791,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X3))) )
| ~ spl54_108
| ~ spl54_109 ),
inference(forward_demodulation,[],[f2764,f2476]) ).
thf(f2764,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X3)) )
| ~ spl54_108
| ~ spl54_109 ),
inference(superposition,[],[f2476,f2472]) ).
thf(f42623,plain,
( spl54_715
| ~ spl54_108
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2775,f2475,f2471,f42621]) ).
thf(f42621,plain,
( spl54_715
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_715])]) ).
thf(f2775,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),X2)) )
| ~ spl54_108
| ~ spl54_109 ),
inference(superposition,[],[f2472,f2476]) ).
thf(f42619,plain,
( spl54_714
| ~ spl54_103
| ~ spl54_107
| ~ spl54_108 ),
inference(avatar_split_clause,[],[f2743,f2471,f2467,f2450,f42617]) ).
thf(f42617,plain,
( spl54_714
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_714])]) ).
thf(f2743,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)) )
| ~ spl54_103
| ~ spl54_107
| ~ spl54_108 ),
inference(forward_demodulation,[],[f2707,f2468]) ).
thf(f2707,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X3) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)) )
| ~ spl54_103
| ~ spl54_108 ),
inference(superposition,[],[f2451,f2472]) ).
thf(f42615,plain,
( spl54_713
| ~ spl54_107
| ~ spl54_108 ),
inference(avatar_split_clause,[],[f2709,f2471,f2467,f42613]) ).
thf(f42613,plain,
( spl54_713
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_713])]) ).
thf(f2709,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X3) )
| ~ spl54_107
| ~ spl54_108 ),
inference(superposition,[],[f2468,f2472]) ).
thf(f42611,plain,
( spl54_712
| ~ spl54_103
| ~ spl54_108 ),
inference(avatar_split_clause,[],[f2708,f2471,f2450,f42609]) ).
thf(f42609,plain,
( spl54_712
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_712])]) ).
thf(f2708,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X3)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_103
| ~ spl54_108 ),
inference(superposition,[],[f2451,f2472]) ).
thf(f42607,plain,
( spl54_711
| ~ spl54_108 ),
inference(avatar_split_clause,[],[f2686,f2471,f42605]) ).
thf(f42605,plain,
( spl54_711
<=> ! [X0: int,X3: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_711])]) ).
thf(f2686,plain,
( ! [X2: int,X3: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_108 ),
inference(superposition,[],[f2472,f2472]) ).
thf(f42603,plain,
( spl54_710
| ~ spl54_102
| ~ spl54_105
| ~ spl54_106 ),
inference(avatar_split_clause,[],[f2643,f2463,f2459,f2446,f42601]) ).
thf(f42601,plain,
( spl54_710
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_710])]) ).
thf(f2446,plain,
( spl54_102
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,[spl54_102])]) ).
thf(f2643,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3))) )
| ~ spl54_102
| ~ spl54_105
| ~ spl54_106 ),
inference(forward_demodulation,[],[f2642,f2460]) ).
thf(f2642,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3)) )
| ~ spl54_102
| ~ spl54_106 ),
inference(forward_demodulation,[],[f2637,f2464]) ).
thf(f2637,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X3) )
| ~ spl54_102
| ~ spl54_106 ),
inference(superposition,[],[f2464,f2447]) ).
thf(f2447,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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)) )
| ~ spl54_102 ),
inference(avatar_component_clause,[],[f2446]) ).
thf(f42599,plain,
( spl54_709
| ~ spl54_101
| ~ spl54_105 ),
inference(avatar_split_clause,[],[f2628,f2459,f2442,f42597]) ).
thf(f42597,plain,
( spl54_709
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_709])]) ).
thf(f2442,plain,
( spl54_101
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,[spl54_101])]) ).
thf(f2628,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X3))) )
| ~ spl54_101
| ~ spl54_105 ),
inference(forward_demodulation,[],[f2606,f2460]) ).
thf(f2606,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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)),X3)) )
| ~ spl54_101
| ~ spl54_105 ),
inference(superposition,[],[f2443,f2460]) ).
thf(f2443,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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)) )
| ~ spl54_101 ),
inference(avatar_component_clause,[],[f2442]) ).
thf(f42595,plain,
( spl54_708
| ~ spl54_104
| ~ spl54_105 ),
inference(avatar_split_clause,[],[f2622,f2459,f2454,f42593]) ).
thf(f42593,plain,
( spl54_708
<=> ! [X0: nat,X3: nat,X2: 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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_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))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_708])]) ).
thf(f2454,plain,
( spl54_104
<=> ! [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,[spl54_104])]) ).
thf(f2622,plain,
( ! [X2: nat,X3: 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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X3))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_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))),X3) )
| ~ spl54_104
| ~ spl54_105 ),
inference(forward_demodulation,[],[f2599,f2460]) ).
thf(f2599,plain,
( ! [X2: nat,X3: 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,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_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))),X3) )
| ~ spl54_104
| ~ spl54_105 ),
inference(superposition,[],[f2460,f2455]) ).
thf(f2455,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)) )
| ~ spl54_104 ),
inference(avatar_component_clause,[],[f2454]) ).
thf(f42591,plain,
( spl54_707
| ~ spl54_104
| ~ spl54_105 ),
inference(avatar_split_clause,[],[f2610,f2459,f2454,f42589]) ).
thf(f42589,plain,
( spl54_707
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),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)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_707])]) ).
thf(f2610,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),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)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),X2)) )
| ~ spl54_104
| ~ spl54_105 ),
inference(superposition,[],[f2455,f2460]) ).
thf(f42587,plain,
( spl54_706
| ~ spl54_102
| ~ spl54_105 ),
inference(avatar_split_clause,[],[f2609,f2459,f2446,f42585]) ).
thf(f42585,plain,
( spl54_706
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),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,[spl54_706])]) ).
thf(f2609,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),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))) )
| ~ spl54_102
| ~ spl54_105 ),
inference(superposition,[],[f2447,f2460]) ).
thf(f42581,plain,
( spl54_368
| spl54_165
| ~ spl54_141
| ~ spl54_389
| ~ spl54_461
| ~ spl54_536 ),
inference(avatar_split_clause,[],[f27913,f27864,f18792,f17732,f3336,f3728,f16886]) ).
thf(f3728,plain,
( spl54_165
<=> ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_165])]) ).
thf(f18792,plain,
( spl54_461
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_461])]) ).
thf(f27913,plain,
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_461
| ~ spl54_536 ),
inference(forward_demodulation,[],[f27912,f17734]) ).
thf(f27912,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_461
| ~ spl54_536 ),
inference(trivial_inequality_removal,[],[f27911]) ).
thf(f27911,plain,
( ( $true = $false )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_141
| ~ spl54_389
| ~ spl54_461
| ~ spl54_536 ),
inference(forward_demodulation,[],[f27910,f3338]) ).
thf(f27910,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_389
| ~ spl54_461
| ~ spl54_536 ),
inference(forward_demodulation,[],[f27893,f17734]) ).
thf(f27893,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,sK32,sK8) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_461
| ~ spl54_536 ),
inference(superposition,[],[f27865,f18793]) ).
thf(f18793,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) = X0 )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_461 ),
inference(avatar_component_clause,[],[f18792]) ).
thf(f42580,plain,
( spl54_705
| ~ spl54_102
| ~ spl54_105 ),
inference(avatar_split_clause,[],[f2608,f2459,f2446,f42578]) ).
thf(f42578,plain,
( spl54_705
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X3),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_705])]) ).
thf(f2608,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X3),X2)) )
| ~ spl54_102
| ~ spl54_105 ),
inference(superposition,[],[f2447,f2460]) ).
thf(f42576,plain,
( spl54_704
| ~ spl54_102
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2576,f2454,f2446,f42574]) ).
thf(f42574,plain,
( spl54_704
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X3),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),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,[spl54_704])]) ).
thf(f2576,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X3),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),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))) )
| ~ spl54_102
| ~ spl54_104 ),
inference(superposition,[],[f2447,f2455]) ).
thf(f42572,plain,
( spl54_703
| ~ spl54_102
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2575,f2454,f2446,f42570]) ).
thf(f42570,plain,
( spl54_703
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_703])]) ).
thf(f2575,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) )
| ~ spl54_102
| ~ spl54_104 ),
inference(superposition,[],[f2447,f2455]) ).
thf(f42568,plain,
( spl54_702
| ~ spl54_101
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2574,f2454,f2442,f42566]) ).
thf(f42566,plain,
( spl54_702
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3)),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,[spl54_702])]) ).
thf(f2574,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X3)),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))) )
| ~ spl54_101
| ~ spl54_104 ),
inference(superposition,[],[f2443,f2455]) ).
thf(f42564,plain,
( spl54_701
| ~ spl54_101
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2573,f2454,f2442,f42562]) ).
thf(f42562,plain,
( spl54_701
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_701])]) ).
thf(f2573,plain,
( ! [X2: nat,X3: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),X3)) )
| ~ spl54_101
| ~ spl54_104 ),
inference(superposition,[],[f2443,f2455]) ).
thf(f42560,plain,
( spl54_700
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2562,f2454,f42558]) ).
thf(f42558,plain,
( spl54_700
<=> ! [X0: nat,X3: nat,X2: 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,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),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,[spl54_700])]) ).
thf(f2562,plain,
( ! [X2: nat,X3: 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,X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X3),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))) )
| ~ spl54_104 ),
inference(superposition,[],[f2455,f2455]) ).
thf(f42435,plain,
( spl54_699
| ~ spl54_49
| ~ spl54_370
| ~ spl54_698 ),
inference(avatar_split_clause,[],[f42431,f42426,f16940,f2008,f42433]) ).
thf(f42433,plain,
( spl54_699
<=> ! [X0: a,X1: a] :
( ( sK8 != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_699])]) ).
thf(f42431,plain,
( ! [X0: a,X1: a] :
( ( sK8 != X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_698 ),
inference(forward_demodulation,[],[f42430,f16942]) ).
thf(f42428,plain,
spl54_698,
inference(avatar_split_clause,[],[f1656,f42426]) ).
thf(f1656,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 ) ),
inference(equality_proxy_clausification,[],[f1655]) ).
thf(f1655,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) ) ),
inference(equality_proxy_clausification,[],[f1651]) ).
thf(f1651,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) ) ),
inference(binary_proxy_clausification,[],[f1287]) ).
thf(f1287,plain,
! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f827]) ).
thf(f827,plain,
! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f826]) ).
thf(f826,plain,
! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f446]) ).
thf(f446,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) ) ) ),
inference(fool_elimination,[],[f445]) ).
thf(f445,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) = X0 )
= ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 ) ) ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
! [X7: a,X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X7) = X7 )
= ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add_Or__cancel__one) ).
thf(f42358,plain,
( spl54_697
| ~ spl54_49
| ~ spl54_370
| ~ spl54_696 ),
inference(avatar_split_clause,[],[f42354,f42349,f16940,f2008,f42356]) ).
thf(f42356,plain,
( spl54_697
<=> ! [X0: a,X1: a] :
( ( sK8 = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_697])]) ).
thf(f42354,plain,
( ! [X0: a,X1: a] :
( ( sK8 = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_696 ),
inference(forward_demodulation,[],[f42353,f16942]) ).
thf(f42351,plain,
spl54_696,
inference(avatar_split_clause,[],[f1654,f42349]) ).
thf(f1654,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 ) ),
inference(equality_proxy_clausification,[],[f1653]) ).
thf(f1653,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) != X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) ) ),
inference(equality_proxy_clausification,[],[f1652]) ).
thf(f1652,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) ) ),
inference(binary_proxy_clausification,[],[f1287]) ).
thf(f42285,plain,
( spl54_695
| ~ spl54_49
| ~ spl54_370
| ~ spl54_694 ),
inference(avatar_split_clause,[],[f42281,f42276,f16940,f2008,f42283]) ).
thf(f42281,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_694 ),
inference(forward_demodulation,[],[f42280,f2010]) ).
thf(f42280,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_694 ),
inference(forward_demodulation,[],[f42279,f2010]) ).
thf(f42279,plain,
( ! [X0: a,X1: a] :
( ( sK8 = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) )
| ~ spl54_370
| ~ spl54_694 ),
inference(forward_demodulation,[],[f42277,f16942]) ).
thf(f42278,plain,
spl54_694,
inference(avatar_split_clause,[],[f1650,f42276]) ).
thf(f1650,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X0 ) ),
inference(equality_proxy_clausification,[],[f1649]) ).
thf(f1649,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1645]) ).
thf(f1645,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1288]) ).
thf(f1288,plain,
! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f829]) ).
thf(f829,plain,
! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f828]) ).
thf(f828,plain,
! [X0: a,X1: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f448]) ).
thf(f448,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X0) ) ) ),
inference(fool_elimination,[],[f447]) ).
thf(f447,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 )
= ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X1 ) ) ) ),
inference(rectify,[],[f53]) ).
thf(f53,axiom,
! [X7: a,X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X0) = X7 )
= ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add_Ol__cancel__one_H) ).
thf(f42153,plain,
( spl54_693
| ~ spl54_49
| ~ spl54_370
| ~ spl54_692 ),
inference(avatar_split_clause,[],[f42149,f42144,f16940,f2008,f42151]) ).
thf(f42151,plain,
( spl54_693
<=> ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_693])]) ).
thf(f42149,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 != X1 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_692 ),
inference(forward_demodulation,[],[f42148,f2010]) ).
thf(f42148,plain,
( ! [X0: a,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( sK8 != X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_692 ),
inference(forward_demodulation,[],[f42147,f2010]) ).
thf(f42147,plain,
( ! [X0: a,X1: a] :
( ( sK8 != X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) )
| ~ spl54_370
| ~ spl54_692 ),
inference(forward_demodulation,[],[f42145,f16942]) ).
thf(f42146,plain,
spl54_692,
inference(avatar_split_clause,[],[f1648,f42144]) ).
thf(f1648,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X0 ) ),
inference(equality_proxy_clausification,[],[f1647]) ).
thf(f1647,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X0) ) ),
inference(equality_proxy_clausification,[],[f1646]) ).
thf(f1646,plain,
! [X0: a,X1: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X0) ) ),
inference(binary_proxy_clausification,[],[f1288]) ).
thf(f42133,plain,
( spl54_691
| ~ spl54_129
| ~ spl54_164
| ~ spl54_452
| ~ spl54_667 ),
inference(avatar_split_clause,[],[f41940,f41364,f18679,f3720,f3223,f42130]) ).
thf(f41940,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) )
| ~ spl54_129
| ~ spl54_164
| ~ spl54_452
| ~ spl54_667 ),
inference(forward_demodulation,[],[f41939,f41365]) ).
thf(f41939,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),sK8),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) )
| ~ spl54_129
| ~ spl54_164
| ~ spl54_452
| ~ spl54_667 ),
inference(forward_demodulation,[],[f41932,f18784]) ).
thf(f41932,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_164
| ~ spl54_667 ),
inference(superposition,[],[f3721,f41365]) ).
thf(f42025,plain,
( spl54_690
| ~ spl54_32
| ~ spl54_188 ),
inference(avatar_split_clause,[],[f14894,f3988,f1899,f42023]) ).
thf(f42023,plain,
( spl54_690
<=> ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_690])]) ).
thf(f14894,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_32
| ~ spl54_188 ),
inference(trivial_inequality_removal,[],[f7742]) ).
thf(f7742,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_188 ),
inference(superposition,[],[f3989,f1901]) ).
thf(f42021,plain,
( spl54_689
| ~ spl54_18
| ~ spl54_174
| ~ spl54_180 ),
inference(avatar_split_clause,[],[f3925,f3874,f3810,f1829,f42019]) ).
thf(f42019,plain,
( spl54_689
<=> ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_689])]) ).
thf(f3925,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_174
| ~ spl54_180 ),
inference(forward_demodulation,[],[f3924,f3820]) ).
thf(f3924,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_180 ),
inference(trivial_inequality_removal,[],[f3917]) ).
thf(f3917,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) )
| ~ spl54_18
| ~ spl54_180 ),
inference(superposition,[],[f3875,f1831]) ).
thf(f42017,plain,
( spl54_688
| ~ spl54_18
| ~ spl54_174 ),
inference(avatar_split_clause,[],[f3820,f3810,f1829,f42015]) ).
thf(f42013,plain,
spl54_687,
inference(avatar_split_clause,[],[f1660,f42011]) ).
thf(f42011,plain,
( spl54_687
<=> ! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X0) )
| ( $false = vAPP(product_prod_a_a,$o,X0,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) )
| ( $false = vAPP(product_prod_a_a,$o,X1,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_687])]) ).
thf(f1660,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X0) )
| ( $false = vAPP(product_prod_a_a,$o,X0,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) )
| ( $false = vAPP(product_prod_a_a,$o,X1,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1247]) ).
thf(f1247,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X0) )
| ( vAPP(product_prod_a_a,$o,X0,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) != vAPP(product_prod_a_a,$o,X1,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) ) ),
inference(cnf_transformation,[],[f1091]) ).
thf(f1091,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X0) )
| ( vAPP(product_prod_a_a,$o,X0,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) != vAPP(product_prod_a_a,$o,X1,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f765,f1090]) ).
thf(f1090,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ? [X2: product_prod_a_a] : ( vAPP(product_prod_a_a,$o,X0,X2) != vAPP(product_prod_a_a,$o,X1,X2) )
=> ( vAPP(product_prod_a_a,$o,X0,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) != vAPP(product_prod_a_a,$o,X1,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f765,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X0) )
| ? [X2: product_prod_a_a] : ( vAPP(product_prod_a_a,$o,X0,X2) != vAPP(product_prod_a_a,$o,X1,X2) ) ),
inference(ennf_transformation,[],[f688]) ).
thf(f688,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ! [X2: product_prod_a_a] : ( vAPP(product_prod_a_a,$o,X0,X2) = vAPP(product_prod_a_a,$o,X1,X2) )
=> ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X0) ) ),
inference(rectify,[],[f51]) ).
thf(f51,axiom,
! [X20: product_prod_a_a > $o,X23: product_prod_a_a > $o] :
( ! [X17: product_prod_a_a] : ( vAPP(product_prod_a_a,$o,X20,X17) = vAPP(product_prod_a_a,$o,X23,X17) )
=> ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X20) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Collect__cong) ).
thf(f42009,plain,
spl54_686,
inference(avatar_split_clause,[],[f1659,f42007]) ).
thf(f42007,plain,
( spl54_686
<=> ! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X0) )
| ( $true = vAPP(product_prod_a_a,$o,X0,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) )
| ( $true = vAPP(product_prod_a_a,$o,X1,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_686])]) ).
thf(f1659,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a > $o] :
( ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1) = vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X0) )
| ( $true = vAPP(product_prod_a_a,$o,X0,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) )
| ( $true = vAPP(product_prod_a_a,$o,X1,vAPP(sTfun(product_prod_a_a,$o),product_prod_a_a,vAPP(sTfun(product_prod_a_a,$o),sTfun(sTfun(product_prod_a_a,$o),product_prod_a_a),sK42,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1247]) ).
thf(f42005,plain,
spl54_685,
inference(avatar_split_clause,[],[f1658,f42003]) ).
thf(f42003,plain,
( spl54_685
<=> ! [X0: a > $o,X1: a > $o] :
( ( vAPP(sTfun(a,$o),set_a,collect_a,X1) = vAPP(sTfun(a,$o),set_a,collect_a,X0) )
| ( $false = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) )
| ( $false = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_685])]) ).
thf(f1658,plain,
! [X0: a > $o,X1: a > $o] :
( ( vAPP(sTfun(a,$o),set_a,collect_a,X1) = vAPP(sTfun(a,$o),set_a,collect_a,X0) )
| ( $false = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) )
| ( $false = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1248]) ).
thf(f1248,plain,
! [X0: a > $o,X1: a > $o] :
( ( vAPP(sTfun(a,$o),set_a,collect_a,X1) = vAPP(sTfun(a,$o),set_a,collect_a,X0) )
| ( vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) ) ),
inference(cnf_transformation,[],[f1093]) ).
thf(f1093,plain,
! [X0: a > $o,X1: a > $o] :
( ( vAPP(sTfun(a,$o),set_a,collect_a,X1) = vAPP(sTfun(a,$o),set_a,collect_a,X0) )
| ( vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f766,f1092]) ).
thf(f1092,plain,
! [X0: a > $o,X1: a > $o] :
( ? [X2: a] : ( vAPP(a,$o,X0,X2) != vAPP(a,$o,X1,X2) )
=> ( vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) != vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) ) ),
introduced(choice_axiom,[]) ).
thf(f766,plain,
! [X0: a > $o,X1: a > $o] :
( ( vAPP(sTfun(a,$o),set_a,collect_a,X1) = vAPP(sTfun(a,$o),set_a,collect_a,X0) )
| ? [X2: a] : ( vAPP(a,$o,X0,X2) != vAPP(a,$o,X1,X2) ) ),
inference(ennf_transformation,[],[f689]) ).
thf(f689,plain,
! [X0: a > $o,X1: a > $o] :
( ! [X2: a] : ( vAPP(a,$o,X0,X2) = vAPP(a,$o,X1,X2) )
=> ( vAPP(sTfun(a,$o),set_a,collect_a,X1) = vAPP(sTfun(a,$o),set_a,collect_a,X0) ) ),
inference(rectify,[],[f50]) ).
thf(f50,axiom,
! [X20: a > $o,X23: a > $o] :
( ! [X17: a] : ( vAPP(a,$o,X20,X17) = vAPP(a,$o,X23,X17) )
=> ( vAPP(sTfun(a,$o),set_a,collect_a,X20) = vAPP(sTfun(a,$o),set_a,collect_a,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__cong) ).
thf(f41997,plain,
spl54_684,
inference(avatar_split_clause,[],[f1657,f41995]) ).
thf(f41995,plain,
( spl54_684
<=> ! [X0: a > $o,X1: a > $o] :
( ( vAPP(sTfun(a,$o),set_a,collect_a,X1) = vAPP(sTfun(a,$o),set_a,collect_a,X0) )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) )
| ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_684])]) ).
thf(f1657,plain,
! [X0: a > $o,X1: a > $o] :
( ( vAPP(sTfun(a,$o),set_a,collect_a,X1) = vAPP(sTfun(a,$o),set_a,collect_a,X0) )
| ( $true = vAPP(a,$o,X0,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) )
| ( $true = vAPP(a,$o,X1,vAPP(sTfun(a,$o),a,vAPP(sTfun(a,$o),sTfun(sTfun(a,$o),a),sK43,X1),X0)) ) ),
inference(binary_proxy_clausification,[],[f1248]) ).
thf(f41950,plain,
( spl54_683
| ~ spl54_32
| ~ spl54_180 ),
inference(avatar_split_clause,[],[f14893,f3874,f1899,f41948]) ).
thf(f41948,plain,
( spl54_683
<=> ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_683])]) ).
thf(f14893,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_32
| ~ spl54_180 ),
inference(trivial_inequality_removal,[],[f7741]) ).
thf(f7741,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_32
| ~ spl54_180 ),
inference(superposition,[],[f3875,f1901]) ).
thf(f41944,plain,
( spl54_682
| ~ spl54_32
| ~ spl54_179 ),
inference(avatar_split_clause,[],[f14892,f3870,f1899,f41942]) ).
thf(f14892,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_32
| ~ spl54_179 ),
inference(trivial_inequality_removal,[],[f7740]) ).
thf(f7740,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_32
| ~ spl54_179 ),
inference(superposition,[],[f3871,f1901]) ).
thf(f41928,plain,
( spl54_681
| ~ spl54_2
| ~ spl54_163 ),
inference(avatar_split_clause,[],[f3709,f3658,f1725,f41926]) ).
thf(f41926,plain,
( spl54_681
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X0),X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_681])]) ).
thf(f3658,plain,
( spl54_163
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_163])]) ).
thf(f3709,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X0),X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_163 ),
inference(trivial_inequality_removal,[],[f3708]) ).
thf(f3708,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X0),X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_163 ),
inference(superposition,[],[f3659,f1726]) ).
thf(f3659,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),X1) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_163 ),
inference(avatar_component_clause,[],[f3658]) ).
thf(f41924,plain,
( spl54_680
| ~ spl54_2
| ~ spl54_162 ),
inference(avatar_split_clause,[],[f3700,f3654,f1725,f41922]) ).
thf(f41922,plain,
( spl54_680
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_680])]) ).
thf(f3654,plain,
( spl54_162
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_162])]) ).
thf(f3700,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_162 ),
inference(trivial_inequality_removal,[],[f3699]) ).
thf(f3699,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_162 ),
inference(superposition,[],[f3655,f1726]) ).
thf(f3655,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X1) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_162 ),
inference(avatar_component_clause,[],[f3654]) ).
thf(f41920,plain,
( spl54_679
| ~ spl54_2
| ~ spl54_161 ),
inference(avatar_split_clause,[],[f3691,f3650,f1725,f41918]) ).
thf(f41918,plain,
( spl54_679
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_679])]) ).
thf(f3650,plain,
( spl54_161
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_161])]) ).
thf(f3691,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_161 ),
inference(trivial_inequality_removal,[],[f3690]) ).
thf(f3690,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_161 ),
inference(superposition,[],[f3651,f1726]) ).
thf(f3651,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_161 ),
inference(avatar_component_clause,[],[f3650]) ).
thf(f41916,plain,
( spl54_678
| ~ spl54_2
| ~ spl54_160 ),
inference(avatar_split_clause,[],[f3680,f3646,f1725,f41914]) ).
thf(f41914,plain,
( spl54_678
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X0),X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_678])]) ).
thf(f3646,plain,
( spl54_160
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_160])]) ).
thf(f3680,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X0),X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_160 ),
inference(trivial_inequality_removal,[],[f3679]) ).
thf(f3679,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X0),X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_160 ),
inference(superposition,[],[f3647,f1726]) ).
thf(f3647,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),X1) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) )
| ~ spl54_160 ),
inference(avatar_component_clause,[],[f3646]) ).
thf(f41912,plain,
( spl54_677
| ~ spl54_2
| ~ spl54_159 ),
inference(avatar_split_clause,[],[f3669,f3642,f1725,f41910]) ).
thf(f41910,plain,
( spl54_677
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X0),X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_677])]) ).
thf(f3642,plain,
( spl54_159
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_159])]) ).
thf(f3669,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X0),X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_159 ),
inference(trivial_inequality_removal,[],[f3668]) ).
thf(f3668,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X0),X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_159 ),
inference(superposition,[],[f3643,f1726]) ).
thf(f3643,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) )
| ~ spl54_159 ),
inference(avatar_component_clause,[],[f3642]) ).
thf(f41908,plain,
( spl54_676
| ~ spl54_2
| ~ spl54_158 ),
inference(avatar_split_clause,[],[f3664,f3638,f1725,f41906]) ).
thf(f41906,plain,
( spl54_676
<=> ! [X0: a,X1: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X0),X1)),X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_676])]) ).
thf(f3638,plain,
( spl54_158
<=> ! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_158])]) ).
thf(f3664,plain,
( ! [X0: a,X1: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X0),X1)),X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_158 ),
inference(trivial_inequality_removal,[],[f3663]) ).
thf(f3663,plain,
( ! [X0: a,X1: partia96731725t_unit] :
( ( $true != $true )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X0),X1)),X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_158 ),
inference(superposition,[],[f3639,f1726]) ).
thf(f3639,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),X1) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) )
| ~ spl54_158 ),
inference(avatar_component_clause,[],[f3638]) ).
thf(f41904,plain,
( spl54_675
| ~ spl54_2
| ~ spl54_157 ),
inference(avatar_split_clause,[],[f3662,f3634,f1725,f41902]) ).
thf(f41902,plain,
( spl54_675
<=> ! [X0: a,X1: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X0),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X0),X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_675])]) ).
thf(f3634,plain,
( spl54_157
<=> ! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_157])]) ).
thf(f3662,plain,
( ! [X0: a,X1: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X0),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X0),X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_157 ),
inference(trivial_inequality_removal,[],[f3661]) ).
thf(f3661,plain,
( ! [X0: a,X1: partia96731725t_unit] :
( ( $true != $true )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X1),X0),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X0),X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_157 ),
inference(superposition,[],[f3635,f1726]) ).
thf(f3635,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) )
| ~ spl54_157 ),
inference(avatar_component_clause,[],[f3634]) ).
thf(f41854,plain,
( spl54_674
| ~ spl54_32
| ~ spl54_178 ),
inference(avatar_split_clause,[],[f14891,f3856,f1899,f41852]) ).
thf(f14891,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_32
| ~ spl54_178 ),
inference(trivial_inequality_removal,[],[f7739]) ).
thf(f7739,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_178 ),
inference(superposition,[],[f3857,f1901]) ).
thf(f41850,plain,
( spl54_673
| ~ spl54_70
| ~ spl54_370 ),
inference(avatar_split_clause,[],[f16952,f16940,f2152,f41848]) ).
thf(f16952,plain,
( ! [X0: int] : ( sK8 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) )
| ~ spl54_70
| ~ spl54_370 ),
inference(superposition,[],[f2153,f16942]) ).
thf(f41844,plain,
( spl54_672
| ~ spl54_32
| ~ spl54_178
| ~ spl54_179 ),
inference(avatar_split_clause,[],[f5204,f3870,f3856,f1899,f41842]) ).
thf(f5204,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_32
| ~ spl54_178
| ~ spl54_179 ),
inference(forward_demodulation,[],[f4508,f4509]) ).
thf(f4509,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) )
| ~ spl54_32
| ~ spl54_178 ),
inference(trivial_inequality_removal,[],[f4446]) ).
thf(f4446,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) ) )
| ~ spl54_32
| ~ spl54_178 ),
inference(superposition,[],[f3857,f1901]) ).
thf(f4508,plain,
( ! [X0: nat] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_32
| ~ spl54_179 ),
inference(trivial_inequality_removal,[],[f4447]) ).
thf(f4447,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_32
| ~ spl54_179 ),
inference(superposition,[],[f3871,f1901]) ).
thf(f41840,plain,
( spl54_671
| ~ spl54_78
| ~ spl54_120 ),
inference(avatar_split_clause,[],[f3098,f3069,f2187,f41837]) ).
thf(f41837,plain,
( spl54_671
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_671])]) ).
thf(f3098,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_78
| ~ spl54_120 ),
inference(trivial_inequality_removal,[],[f3095]) ).
thf(f3095,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_78
| ~ spl54_120 ),
inference(superposition,[],[f3070,f2189]) ).
thf(f41835,plain,
( spl54_670
| ~ spl54_78
| ~ spl54_119 ),
inference(avatar_split_clause,[],[f3092,f3065,f2187,f41832]) ).
thf(f41832,plain,
( spl54_670
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_670])]) ).
thf(f3065,plain,
( spl54_119
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_119])]) ).
thf(f3092,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_78
| ~ spl54_119 ),
inference(trivial_inequality_removal,[],[f3089]) ).
thf(f3089,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))) )
| ~ spl54_78
| ~ spl54_119 ),
inference(superposition,[],[f3066,f2189]) ).
thf(f3066,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) ) )
| ~ spl54_119 ),
inference(avatar_component_clause,[],[f3065]) ).
thf(f41467,plain,
( spl54_669
| ~ spl54_49
| ~ spl54_662 ),
inference(avatar_split_clause,[],[f41306,f41302,f2008,f41465]) ).
thf(f41465,plain,
( spl54_669
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_669])]) ).
thf(f41302,plain,
( spl54_662
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_662])]) ).
thf(f41306,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_662 ),
inference(forward_demodulation,[],[f41305,f2010]) ).
thf(f41305,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_49
| ~ spl54_662 ),
inference(forward_demodulation,[],[f41303,f2010]) ).
thf(f41303,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_662 ),
inference(avatar_component_clause,[],[f41302]) ).
thf(f41463,plain,
( spl54_668
| ~ spl54_49
| ~ spl54_661 ),
inference(avatar_split_clause,[],[f41300,f41296,f2008,f41461]) ).
thf(f41461,plain,
( spl54_668
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_668])]) ).
thf(f41296,plain,
( spl54_661
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_661])]) ).
thf(f41300,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_661 ),
inference(forward_demodulation,[],[f41299,f2010]) ).
thf(f41299,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_49
| ~ spl54_661 ),
inference(forward_demodulation,[],[f41297,f2010]) ).
thf(f41297,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_661 ),
inference(avatar_component_clause,[],[f41296]) ).
thf(f41366,plain,
( spl54_667
| ~ spl54_68
| ~ spl54_370 ),
inference(avatar_split_clause,[],[f16951,f16940,f2144,f41364]) ).
thf(f16951,plain,
( ! [X0: nat] : ( sK8 = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8) )
| ~ spl54_68
| ~ spl54_370 ),
inference(superposition,[],[f2145,f16942]) ).
thf(f41327,plain,
( spl54_666
| ~ spl54_32
| ~ spl54_49
| ~ spl54_177 ),
inference(avatar_split_clause,[],[f15910,f3836,f2008,f1899,f41325]) ).
thf(f15910,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_177 ),
inference(forward_demodulation,[],[f14890,f2010]) ).
thf(f14890,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_177 ),
inference(trivial_inequality_removal,[],[f7738]) ).
thf(f7738,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_32
| ~ spl54_177 ),
inference(superposition,[],[f3837,f1901]) ).
thf(f41323,plain,
( spl54_665
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_193 ),
inference(avatar_split_clause,[],[f15648,f4020,f2008,f1899,f1761,f41321]) ).
thf(f15648,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_193 ),
inference(trivial_inequality_removal,[],[f15647]) ).
thf(f15647,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_193 ),
inference(forward_demodulation,[],[f15646,f1763]) ).
thf(f15646,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_193 ),
inference(forward_demodulation,[],[f7823,f2010]) ).
thf(f7823,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_193 ),
inference(trivial_inequality_removal,[],[f7790]) ).
thf(f7790,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_193 ),
inference(superposition,[],[f4021,f1901]) ).
thf(f41317,plain,
( spl54_664
| ~ spl54_18
| ~ spl54_172 ),
inference(avatar_split_clause,[],[f3808,f3759,f1829,f41315]) ).
thf(f41315,plain,
( spl54_664
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_664])]) ).
thf(f3808,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_172 ),
inference(trivial_inequality_removal,[],[f3801]) ).
thf(f3801,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_172 ),
inference(superposition,[],[f3760,f1831]) ).
thf(f41310,plain,
( spl54_663
| ~ spl54_19
| ~ spl54_172 ),
inference(avatar_split_clause,[],[f3807,f3759,f1834,f41308]) ).
thf(f41308,plain,
( spl54_663
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_663])]) ).
thf(f3807,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_172 ),
inference(trivial_inequality_removal,[],[f3802]) ).
thf(f3802,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_172 ),
inference(superposition,[],[f3760,f1836]) ).
thf(f41304,plain,
( spl54_662
| ~ spl54_18
| ~ spl54_171 ),
inference(avatar_split_clause,[],[f3799,f3755,f1829,f41302]) ).
thf(f3799,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_171 ),
inference(trivial_inequality_removal,[],[f3792]) ).
thf(f3792,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_171 ),
inference(superposition,[],[f3756,f1831]) ).
thf(f41298,plain,
( spl54_661
| ~ spl54_18
| ~ spl54_170 ),
inference(avatar_split_clause,[],[f3791,f3751,f1829,f41296]) ).
thf(f3791,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_170 ),
inference(trivial_inequality_removal,[],[f3784]) ).
thf(f3784,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_18
| ~ spl54_170 ),
inference(superposition,[],[f3752,f1831]) ).
thf(f41236,plain,
( spl54_660
| ~ spl54_370
| ~ spl54_418 ),
inference(avatar_split_clause,[],[f19041,f18216,f16940,f41233]) ).
thf(f19041,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_370
| ~ spl54_418 ),
inference(forward_demodulation,[],[f18218,f16942]) ).
thf(f41166,plain,
( ~ spl54_370
| ~ spl54_14
| spl54_542 ),
inference(avatar_split_clause,[],[f28086,f27925,f1811,f16940]) ).
thf(f27925,plain,
( spl54_542
<=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_542])]) ).
thf(f28086,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != sK8 )
| ~ spl54_14
| spl54_542 ),
inference(superposition,[],[f27927,f1813]) ).
thf(f27927,plain,
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) != sK8 )
| spl54_542 ),
inference(avatar_component_clause,[],[f27925]) ).
thf(f41165,plain,
( spl54_659
| ~ spl54_370
| ~ spl54_420 ),
inference(avatar_split_clause,[],[f19040,f18231,f16940,f41162]) ).
thf(f19040,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_370
| ~ spl54_420 ),
inference(forward_demodulation,[],[f18233,f16942]) ).
thf(f41128,plain,
( spl54_658
| ~ spl54_370
| ~ spl54_384 ),
inference(avatar_split_clause,[],[f17657,f17653,f16940,f41125]) ).
thf(f17657,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ~ spl54_370
| ~ spl54_384 ),
inference(forward_demodulation,[],[f17655,f16942]) ).
thf(f41091,plain,
( spl54_657
| ~ spl54_370
| ~ spl54_413
| ~ spl54_419 ),
inference(avatar_split_clause,[],[f18229,f18224,f18186,f16940,f41088]) ).
thf(f18224,plain,
( spl54_419
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_419])]) ).
thf(f18229,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_370
| ~ spl54_413
| ~ spl54_419 ),
inference(forward_demodulation,[],[f18228,f18188]) ).
thf(f18228,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,sK8)),sK8) )
| ~ spl54_370
| ~ spl54_419 ),
inference(forward_demodulation,[],[f18226,f16942]) ).
thf(f18226,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_419 ),
inference(avatar_component_clause,[],[f18224]) ).
thf(f41086,plain,
( spl54_656
| ~ spl54_370
| ~ spl54_388 ),
inference(avatar_split_clause,[],[f17683,f17679,f16940,f41083]) ).
thf(f17683,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),sK8) )
| ~ spl54_370
| ~ spl54_388 ),
inference(forward_demodulation,[],[f17681,f16942]) ).
thf(f41036,plain,
( spl54_370
| ~ spl54_399
| ~ spl54_401 ),
inference(avatar_split_clause,[],[f19183,f17791,f17780,f16940]) ).
thf(f19183,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_399
| ~ spl54_401 ),
inference(forward_demodulation,[],[f17782,f17793]) ).
thf(f17793,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) )
| ~ spl54_401 ),
inference(avatar_component_clause,[],[f17791]) ).
thf(f40841,plain,
( spl54_165
| spl54_370
| ~ spl54_455
| ~ spl54_492 ),
inference(avatar_split_clause,[],[f19479,f19465,f18694,f16940,f3728]) ).
thf(f18694,plain,
( spl54_455
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_455])]) ).
thf(f19479,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_455
| ~ spl54_492 ),
inference(superposition,[],[f19467,f18695]) ).
thf(f18695,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = X0 )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_455 ),
inference(avatar_component_clause,[],[f18694]) ).
thf(f40838,plain,
( spl54_655
| ~ spl54_19
| ~ spl54_170 ),
inference(avatar_split_clause,[],[f3790,f3751,f1834,f40836]) ).
thf(f40836,plain,
( spl54_655
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_655])]) ).
thf(f3790,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_170 ),
inference(trivial_inequality_removal,[],[f3785]) ).
thf(f3785,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_19
| ~ spl54_170 ),
inference(superposition,[],[f3752,f1836]) ).
thf(f40834,plain,
( spl54_654
| ~ spl54_17
| ~ spl54_169 ),
inference(avatar_split_clause,[],[f3783,f3747,f1824,f40832]) ).
thf(f40832,plain,
( spl54_654
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_654])]) ).
thf(f3783,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_169 ),
inference(trivial_inequality_removal,[],[f3776]) ).
thf(f3776,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_169 ),
inference(superposition,[],[f3748,f1826]) ).
thf(f40830,plain,
( spl54_653
| ~ spl54_2
| ~ spl54_156 ),
inference(avatar_split_clause,[],[f3631,f3626,f1725,f40828]) ).
thf(f40828,plain,
( spl54_653
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_653])]) ).
thf(f3626,plain,
( spl54_156
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_156])]) ).
thf(f3631,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_156 ),
inference(trivial_inequality_removal,[],[f3630]) ).
thf(f3630,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_156 ),
inference(superposition,[],[f3627,f1726]) ).
thf(f3627,plain,
( ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) ) )
| ~ spl54_156 ),
inference(avatar_component_clause,[],[f3626]) ).
thf(f39430,plain,
( spl54_652
| ~ spl54_36
| ~ spl54_37
| ~ spl54_85
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2892,f2487,f2242,f1922,f1918,f39428]) ).
thf(f39428,plain,
( spl54_652
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_652])]) ).
thf(f2892,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_85
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2862,f1965]) ).
thf(f2862,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_85
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2243]) ).
thf(f39425,plain,
( spl54_651
| ~ spl54_36
| ~ spl54_37
| ~ spl54_86
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2891,f2487,f2246,f1922,f1918,f39423]) ).
thf(f39423,plain,
( spl54_651
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_651])]) ).
thf(f2246,plain,
( spl54_86
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,uminus_uminus_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_86])]) ).
thf(f2891,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_86
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2861,f1965]) ).
thf(f2861,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_86
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2247]) ).
thf(f2247,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,uminus_uminus_int,X1)) )
| ~ spl54_86 ),
inference(avatar_component_clause,[],[f2246]) ).
thf(f39421,plain,
( spl54_650
| ~ spl54_84
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2873,f2487,f2238,f39419]) ).
thf(f39419,plain,
( spl54_650
<=> ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(nat,int,semiri2019852685at_int,X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1))),vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_650])]) ).
thf(f2238,plain,
( spl54_84
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(nat,int,semiri2019852685at_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_84])]) ).
thf(f2873,plain,
( ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(nat,int,semiri2019852685at_int,X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1))),vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_84
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2239]) ).
thf(f2239,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(nat,int,semiri2019852685at_int,X1)) )
| ~ spl54_84 ),
inference(avatar_component_clause,[],[f2238]) ).
thf(f39417,plain,
( spl54_649
| ~ spl54_84
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2863,f2487,f2238,f39415]) ).
thf(f39415,plain,
( spl54_649
<=> ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,X0)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_649])]) ).
thf(f2863,plain,
( ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,X0)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1))) )
| ~ spl54_84
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2239]) ).
thf(f39413,plain,
( spl54_648
| ~ spl54_84
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2762,f2475,f2238,f39411]) ).
thf(f39411,plain,
( spl54_648
<=> ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_648])]) ).
thf(f2762,plain,
( ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X1)),X2)) )
| ~ spl54_84
| ~ spl54_109 ),
inference(superposition,[],[f2476,f2239]) ).
thf(f39409,plain,
( spl54_647
| ~ spl54_84
| ~ spl54_108 ),
inference(avatar_split_clause,[],[f2684,f2471,f2238,f39407]) ).
thf(f39407,plain,
( spl54_647
<=> ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_647])]) ).
thf(f2684,plain,
( ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_84
| ~ spl54_108 ),
inference(superposition,[],[f2472,f2239]) ).
thf(f39405,plain,
( spl54_646
| ~ spl54_84
| ~ spl54_107 ),
inference(avatar_split_clause,[],[f2653,f2467,f2238,f39403]) ).
thf(f39403,plain,
( spl54_646
<=> ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_646])]) ).
thf(f2653,plain,
( ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1))) )
| ~ spl54_84
| ~ spl54_107 ),
inference(superposition,[],[f2468,f2239]) ).
thf(f39401,plain,
( spl54_645
| ~ spl54_83
| ~ spl54_105 ),
inference(avatar_split_clause,[],[f2596,f2459,f2234,f39399]) ).
thf(f39399,plain,
( spl54_645
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X1)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_645])]) ).
thf(f2234,plain,
( spl54_83
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,semiri1382578993at_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,semiri1382578993at_nat,X0)),vAPP(nat,nat,semiri1382578993at_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_83])]) ).
thf(f2596,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X1)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X2) )
| ~ spl54_83
| ~ spl54_105 ),
inference(superposition,[],[f2460,f2235]) ).
thf(f2235,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,semiri1382578993at_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,semiri1382578993at_nat,X0)),vAPP(nat,nat,semiri1382578993at_nat,X1)) )
| ~ spl54_83 ),
inference(avatar_component_clause,[],[f2234]) ).
thf(f39397,plain,
( spl54_644
| ~ spl54_83
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2560,f2454,f2234,f39395]) ).
thf(f39395,plain,
( spl54_644
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,X1))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_644])]) ).
thf(f2560,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,X1))) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_83
| ~ spl54_104 ),
inference(superposition,[],[f2455,f2235]) ).
thf(f39393,plain,
( spl54_643
| ~ spl54_84
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2537,f2450,f2238,f39391]) ).
thf(f39391,plain,
( spl54_643
<=> ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),X2)),vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_643])]) ).
thf(f2537,plain,
( ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(nat,int,semiri2019852685at_int,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),X2)),vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_84
| ~ spl54_103 ),
inference(superposition,[],[f2451,f2239]) ).
thf(f39389,plain,
( spl54_642
| ~ spl54_84
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2530,f2450,f2238,f39387]) ).
thf(f39387,plain,
( spl54_642
<=> ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_642])]) ).
thf(f2530,plain,
( ! [X2: int,X0: nat,X1: nat] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),X2)) )
| ~ spl54_84
| ~ spl54_103 ),
inference(superposition,[],[f2451,f2239]) ).
thf(f39385,plain,
( spl54_641
| ~ spl54_83
| ~ spl54_102 ),
inference(avatar_split_clause,[],[f2517,f2446,f2234,f39383]) ).
thf(f39383,plain,
( spl54_641
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,X1))),vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_641])]) ).
thf(f2517,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,X1))),vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_83
| ~ spl54_102 ),
inference(superposition,[],[f2447,f2235]) ).
thf(f39381,plain,
( spl54_640
| ~ spl54_83
| ~ spl54_102 ),
inference(avatar_split_clause,[],[f2514,f2446,f2234,f39379]) ).
thf(f39379,plain,
( spl54_640
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_nat,X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_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),vAPP(nat,nat,semiri1382578993at_nat,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_640])]) ).
thf(f2514,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_nat,X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_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),vAPP(nat,nat,semiri1382578993at_nat,X1))) )
| ~ spl54_83
| ~ spl54_102 ),
inference(superposition,[],[f2447,f2235]) ).
thf(f39377,plain,
( spl54_639
| ~ spl54_83
| ~ spl54_101 ),
inference(avatar_split_clause,[],[f2507,f2442,f2234,f39375]) ).
thf(f39375,plain,
( spl54_639
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X0)),X2)),vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_639])]) ).
thf(f2507,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),vAPP(nat,nat,semiri1382578993at_nat,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X0)),X2)),vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_83
| ~ spl54_101 ),
inference(superposition,[],[f2443,f2235]) ).
thf(f39373,plain,
( ~ spl54_637
| spl54_638
| ~ spl54_447
| ~ spl54_491 ),
inference(avatar_split_clause,[],[f19450,f19410,f18555,f39370,f39366]) ).
thf(f39366,plain,
( spl54_637
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_637])]) ).
thf(f39370,plain,
( spl54_638
<=> ( sK8 = vAPP(a,a,sK33,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_638])]) ).
thf(f19410,plain,
( spl54_491
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_491])]) ).
thf(f19450,plain,
( ( sK8 = vAPP(a,a,sK33,sK7) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK7)) )
| ~ spl54_447
| ~ spl54_491 ),
inference(trivial_inequality_removal,[],[f19449]) ).
thf(f19449,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,sK33,sK7) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK33,sK7)) )
| ~ spl54_447
| ~ spl54_491 ),
inference(superposition,[],[f18556,f19412]) ).
thf(f19412,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_491 ),
inference(avatar_component_clause,[],[f19410]) ).
thf(f39364,plain,
( spl54_636
| ~ spl54_83
| ~ spl54_101 ),
inference(avatar_split_clause,[],[f2504,f2442,f2234,f39362]) ).
thf(f39362,plain,
( spl54_636
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_nat,X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_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,semiri1382578993at_nat,X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_636])]) ).
thf(f2504,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_nat,X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_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,semiri1382578993at_nat,X0)),X2)) )
| ~ spl54_83
| ~ spl54_101 ),
inference(superposition,[],[f2443,f2235]) ).
thf(f39342,plain,
( spl54_635
| ~ spl54_633
| ~ spl54_634 ),
inference(avatar_split_clause,[],[f39338,f39335,f39319,f39340]) ).
thf(f39335,plain,
( spl54_634
<=> ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_634])]) ).
thf(f39338,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) )
| ~ spl54_633
| ~ spl54_634 ),
inference(forward_demodulation,[],[f39336,f39320]) ).
thf(f39336,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) )
| ~ spl54_634 ),
inference(avatar_component_clause,[],[f39335]) ).
thf(f39337,plain,
( spl54_634
| ~ spl54_32
| ~ spl54_174 ),
inference(avatar_split_clause,[],[f14888,f3810,f1899,f39335]) ).
thf(f14888,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) )
| ~ spl54_32
| ~ spl54_174 ),
inference(trivial_inequality_removal,[],[f7736]) ).
thf(f7736,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) ) )
| ~ spl54_32
| ~ spl54_174 ),
inference(superposition,[],[f3811,f1901]) ).
thf(f39321,plain,
( spl54_633
| ~ spl54_452
| ~ spl54_632 ),
inference(avatar_split_clause,[],[f39317,f39314,f18679,f39319]) ).
thf(f39317,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) )
| ~ spl54_452
| ~ spl54_632 ),
inference(forward_demodulation,[],[f39315,f18681]) ).
thf(f39316,plain,
( spl54_632
| ~ spl54_32
| ~ spl54_174
| ~ spl54_180 ),
inference(avatar_split_clause,[],[f3928,f3874,f3810,f1899,f39314]) ).
thf(f3928,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_32
| ~ spl54_174
| ~ spl54_180 ),
inference(forward_demodulation,[],[f3922,f3818]) ).
thf(f3818,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) )
| ~ spl54_32
| ~ spl54_174 ),
inference(trivial_inequality_removal,[],[f3815]) ).
thf(f3815,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X0)),sK8) ) )
| ~ spl54_32
| ~ spl54_174 ),
inference(superposition,[],[f3811,f1901]) ).
thf(f3922,plain,
( ! [X0: int] : ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_32
| ~ spl54_180 ),
inference(trivial_inequality_removal,[],[f3919]) ).
thf(f3919,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) )
| ~ spl54_32
| ~ spl54_180 ),
inference(superposition,[],[f3875,f1901]) ).
thf(f39312,plain,
( spl54_631
| ~ spl54_2
| ~ spl54_155 ),
inference(avatar_split_clause,[],[f3621,f3603,f1725,f39310]) ).
thf(f39310,plain,
( spl54_631
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_631])]) ).
thf(f3603,plain,
( spl54_155
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_155])]) ).
thf(f3621,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_155 ),
inference(trivial_inequality_removal,[],[f3620]) ).
thf(f3620,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_155 ),
inference(superposition,[],[f3604,f1726]) ).
thf(f3604,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_155 ),
inference(avatar_component_clause,[],[f3603]) ).
thf(f39308,plain,
( spl54_630
| ~ spl54_2
| ~ spl54_154 ),
inference(avatar_split_clause,[],[f3613,f3599,f1725,f39306]) ).
thf(f39306,plain,
( spl54_630
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_630])]) ).
thf(f3599,plain,
( spl54_154
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_154])]) ).
thf(f3613,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_154 ),
inference(trivial_inequality_removal,[],[f3612]) ).
thf(f3612,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_154 ),
inference(superposition,[],[f3600,f1726]) ).
thf(f3600,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_154 ),
inference(avatar_component_clause,[],[f3599]) ).
thf(f39006,plain,
( spl54_629
| ~ spl54_49
| ~ spl54_622 ),
inference(avatar_split_clause,[],[f38977,f38974,f2008,f39004]) ).
thf(f38974,plain,
( spl54_622
<=> ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_622])]) ).
thf(f38977,plain,
( ! [X0: nat,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),X1) ) )
| ~ spl54_49
| ~ spl54_622 ),
inference(forward_demodulation,[],[f38975,f2010]) ).
thf(f38975,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_622 ),
inference(avatar_component_clause,[],[f38974]) ).
thf(f39002,plain,
( spl54_628
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_186 ),
inference(avatar_split_clause,[],[f15642,f3898,f2008,f1899,f1766,f39000]) ).
thf(f39000,plain,
( spl54_628
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_628])]) ).
thf(f15642,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_186 ),
inference(trivial_inequality_removal,[],[f15641]) ).
thf(f15641,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_186 ),
inference(forward_demodulation,[],[f15640,f1768]) ).
thf(f15640,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_186 ),
inference(forward_demodulation,[],[f15639,f2010]) ).
thf(f15639,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_186 ),
inference(forward_demodulation,[],[f7826,f2010]) ).
thf(f7826,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_186 ),
inference(trivial_inequality_removal,[],[f7787]) ).
thf(f7787,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_186 ),
inference(superposition,[],[f3899,f1901]) ).
thf(f38997,plain,
( spl54_627
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_184 ),
inference(avatar_split_clause,[],[f15588,f3890,f2008,f1899,f1761,f38995]) ).
thf(f38995,plain,
( spl54_627
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_627])]) ).
thf(f15588,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_184 ),
inference(trivial_inequality_removal,[],[f15587]) ).
thf(f15587,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_49
| ~ spl54_184 ),
inference(forward_demodulation,[],[f15586,f1763]) ).
thf(f15586,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_184 ),
inference(forward_demodulation,[],[f15585,f2010]) ).
thf(f15585,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_184 ),
inference(forward_demodulation,[],[f7552,f2010]) ).
thf(f7552,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_184 ),
inference(trivial_inequality_removal,[],[f5322]) ).
thf(f5322,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true ) )
| ~ spl54_32
| ~ spl54_184 ),
inference(superposition,[],[f3891,f1901]) ).
thf(f38993,plain,
( spl54_626
| ~ spl54_2
| ~ spl54_284 ),
inference(avatar_split_clause,[],[f7133,f6197,f1725,f38991]) ).
thf(f38991,plain,
( spl54_626
<=> ! [X0: a,X1: int] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_626])]) ).
thf(f6197,plain,
( spl54_284
<=> ! [X0: a,X1: int] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_284])]) ).
thf(f7133,plain,
( ! [X0: a,X1: int] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_284 ),
inference(trivial_inequality_removal,[],[f7132]) ).
thf(f7132,plain,
( ! [X0: a,X1: int] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_284 ),
inference(superposition,[],[f6198,f1726]) ).
thf(f6198,plain,
( ! [X0: a,X1: int] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_284 ),
inference(avatar_component_clause,[],[f6197]) ).
thf(f38989,plain,
( spl54_625
| ~ spl54_2
| ~ spl54_239 ),
inference(avatar_split_clause,[],[f6756,f5033,f1725,f38987]) ).
thf(f38987,plain,
( spl54_625
<=> ! [X0: a,X1: nat] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_625])]) ).
thf(f5033,plain,
( spl54_239
<=> ! [X0: a,X1: nat] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_239])]) ).
thf(f6756,plain,
( ! [X0: a,X1: nat] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_239 ),
inference(trivial_inequality_removal,[],[f6755]) ).
thf(f6755,plain,
( ! [X0: a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_239 ),
inference(superposition,[],[f5034,f1726]) ).
thf(f5034,plain,
( ! [X0: a,X1: nat] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_239 ),
inference(avatar_component_clause,[],[f5033]) ).
thf(f38985,plain,
( spl54_624
| ~ spl54_2
| ~ spl54_209 ),
inference(avatar_split_clause,[],[f5411,f4299,f1725,f38983]) ).
thf(f38983,plain,
( spl54_624
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_624])]) ).
thf(f4299,plain,
( spl54_209
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_209])]) ).
thf(f5411,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_209 ),
inference(trivial_inequality_removal,[],[f5410]) ).
thf(f5410,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_209 ),
inference(superposition,[],[f4300,f1726]) ).
thf(f4300,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) ) )
| ~ spl54_209 ),
inference(avatar_component_clause,[],[f4299]) ).
thf(f38981,plain,
( spl54_623
| ~ spl54_2
| ~ spl54_151 ),
inference(avatar_split_clause,[],[f4543,f3466,f1725,f38979]) ).
thf(f38979,plain,
( spl54_623
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_623])]) ).
thf(f4543,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_151 ),
inference(trivial_inequality_removal,[],[f4542]) ).
thf(f4542,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_151 ),
inference(superposition,[],[f3467,f1726]) ).
thf(f38976,plain,
( spl54_622
| ~ spl54_207 ),
inference(avatar_split_clause,[],[f4262,f4245,f38974]) ).
thf(f4245,plain,
( spl54_207
<=> ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)),X0) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_207])]) ).
thf(f4262,plain,
( ! [X0: nat,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_207 ),
inference(equality_resolution,[],[f4246]) ).
thf(f4246,plain,
( ! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_207 ),
inference(avatar_component_clause,[],[f4245]) ).
thf(f38970,plain,
( spl54_621
| ~ spl54_2
| ~ spl54_150 ),
inference(avatar_split_clause,[],[f3585,f3460,f1725,f38968]) ).
thf(f38968,plain,
( spl54_621
<=> ! [X0: a,X1: int] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_621])]) ).
thf(f3460,plain,
( spl54_150
<=> ! [X0: a,X1: int] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_150])]) ).
thf(f3585,plain,
( ! [X0: a,X1: int] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_150 ),
inference(trivial_inequality_removal,[],[f3584]) ).
thf(f3584,plain,
( ! [X0: a,X1: int] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_150 ),
inference(superposition,[],[f3461,f1726]) ).
thf(f3461,plain,
( ! [X0: a,X1: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_150 ),
inference(avatar_component_clause,[],[f3460]) ).
thf(f38964,plain,
( spl54_620
| ~ spl54_2
| ~ spl54_149 ),
inference(avatar_split_clause,[],[f3576,f3454,f1725,f38962]) ).
thf(f38962,plain,
( spl54_620
<=> ! [X0: a,X1: nat] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_620])]) ).
thf(f3454,plain,
( spl54_149
<=> ! [X0: a,X1: nat] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_149])]) ).
thf(f3576,plain,
( ! [X0: a,X1: nat] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_149 ),
inference(trivial_inequality_removal,[],[f3575]) ).
thf(f3575,plain,
( ! [X0: a,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_149 ),
inference(superposition,[],[f3455,f1726]) ).
thf(f3455,plain,
( ! [X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_149 ),
inference(avatar_component_clause,[],[f3454]) ).
thf(f38959,plain,
( spl54_619
| ~ spl54_2
| ~ spl54_148 ),
inference(avatar_split_clause,[],[f3567,f3449,f1725,f38957]) ).
thf(f38957,plain,
( spl54_619
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_619])]) ).
thf(f3449,plain,
( spl54_148
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_148])]) ).
thf(f3567,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_148 ),
inference(trivial_inequality_removal,[],[f3566]) ).
thf(f3566,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_148 ),
inference(superposition,[],[f3450,f1726]) ).
thf(f3450,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) ) )
| ~ spl54_148 ),
inference(avatar_component_clause,[],[f3449]) ).
thf(f38954,plain,
( spl54_618
| ~ spl54_2
| ~ spl54_147 ),
inference(avatar_split_clause,[],[f3558,f3444,f1725,f38952]) ).
thf(f38952,plain,
( spl54_618
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_618])]) ).
thf(f3444,plain,
( spl54_147
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_147])]) ).
thf(f3558,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_147 ),
inference(trivial_inequality_removal,[],[f3557]) ).
thf(f3557,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_147 ),
inference(superposition,[],[f3445,f1726]) ).
thf(f3445,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_147 ),
inference(avatar_component_clause,[],[f3444]) ).
thf(f38946,plain,
( ~ spl54_616
| spl54_617
| ~ spl54_447
| ~ spl54_490 ),
inference(avatar_split_clause,[],[f19425,f19405,f18555,f38943,f38939]) ).
thf(f38939,plain,
( spl54_616
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_616])]) ).
thf(f38943,plain,
( spl54_617
<=> ( sK8 = vAPP(a,a,sK32,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_617])]) ).
thf(f19425,plain,
( ( sK8 = vAPP(a,a,sK32,sK7) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,sK7)) )
| ~ spl54_447
| ~ spl54_490 ),
inference(trivial_inequality_removal,[],[f19424]) ).
thf(f19424,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,sK32,sK7) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK32,sK7)) )
| ~ spl54_447
| ~ spl54_490 ),
inference(superposition,[],[f18556,f19407]) ).
thf(f19407,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_490 ),
inference(avatar_component_clause,[],[f19405]) ).
thf(f38937,plain,
( spl54_615
| ~ spl54_2
| spl54_146 ),
inference(avatar_split_clause,[],[f3442,f3437,f1725,f38934]) ).
thf(f3437,plain,
( spl54_146
<=> ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_146])]) ).
thf(f3442,plain,
( ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ~ spl54_2
| spl54_146 ),
inference(trivial_inequality_removal,[],[f3441]) ).
thf(f3441,plain,
( ( $true != $true )
| ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ~ spl54_2
| spl54_146 ),
inference(superposition,[],[f3439,f1726]) ).
thf(f3439,plain,
( ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| spl54_146 ),
inference(avatar_component_clause,[],[f3437]) ).
thf(f35341,plain,
( spl54_614
| ~ spl54_74
| ~ spl54_113
| ~ spl54_144 ),
inference(avatar_split_clause,[],[f3420,f3350,f2491,f2170,f35339]) ).
thf(f35339,plain,
( spl54_614
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_614])]) ).
thf(f3420,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))) )
| ~ spl54_74
| ~ spl54_113
| ~ spl54_144 ),
inference(forward_demodulation,[],[f3412,f2171]) ).
thf(f3412,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X2)),X1)) )
| ~ spl54_113
| ~ spl54_144 ),
inference(superposition,[],[f3351,f2492]) ).
thf(f35337,plain,
( spl54_613
| ~ spl54_2
| ~ spl54_143 ),
inference(avatar_split_clause,[],[f3406,f3346,f1725,f35335]) ).
thf(f35335,plain,
( spl54_613
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_613])]) ).
thf(f3346,plain,
( spl54_143
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_143])]) ).
thf(f3406,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_143 ),
inference(trivial_inequality_removal,[],[f3405]) ).
thf(f3405,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_143 ),
inference(superposition,[],[f3347,f1726]) ).
thf(f3347,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_143 ),
inference(avatar_component_clause,[],[f3346]) ).
thf(f35333,plain,
( spl54_612
| ~ spl54_2
| ~ spl54_142 ),
inference(avatar_split_clause,[],[f3391,f3342,f1725,f35331]) ).
thf(f35331,plain,
( spl54_612
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_612])]) ).
thf(f3342,plain,
( spl54_142
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_142])]) ).
thf(f3391,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f3390]) ).
thf(f3390,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_142 ),
inference(superposition,[],[f3343,f1726]) ).
thf(f3343,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_142 ),
inference(avatar_component_clause,[],[f3342]) ).
thf(f35329,plain,
( spl54_611
| ~ spl54_2
| ~ spl54_140 ),
inference(avatar_split_clause,[],[f3376,f3332,f1725,f35327]) ).
thf(f35327,plain,
( spl54_611
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_611])]) ).
thf(f3332,plain,
( spl54_140
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_140])]) ).
thf(f3376,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_140 ),
inference(trivial_inequality_removal,[],[f3375]) ).
thf(f3375,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_140 ),
inference(superposition,[],[f3333,f1726]) ).
thf(f3333,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) )
| ~ spl54_140 ),
inference(avatar_component_clause,[],[f3332]) ).
thf(f35325,plain,
( spl54_610
| ~ spl54_2
| ~ spl54_139 ),
inference(avatar_split_clause,[],[f3361,f3328,f1725,f35323]) ).
thf(f35323,plain,
( spl54_610
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_610])]) ).
thf(f3328,plain,
( spl54_139
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_139])]) ).
thf(f3361,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_139 ),
inference(trivial_inequality_removal,[],[f3360]) ).
thf(f3360,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_139 ),
inference(superposition,[],[f3329,f1726]) ).
thf(f3329,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) )
| ~ spl54_139 ),
inference(avatar_component_clause,[],[f3328]) ).
thf(f35321,plain,
( spl54_609
| ~ spl54_2
| ~ spl54_138 ),
inference(avatar_split_clause,[],[f3356,f3324,f1725,f35319]) ).
thf(f35319,plain,
( spl54_609
<=> ! [X0: a,X1: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X0),X1)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_609])]) ).
thf(f3324,plain,
( spl54_138
<=> ! [X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_138])]) ).
thf(f3356,plain,
( ! [X0: a,X1: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X0),X1)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_138 ),
inference(trivial_inequality_removal,[],[f3355]) ).
thf(f3355,plain,
( ! [X0: a,X1: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X0),X1)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_138 ),
inference(superposition,[],[f3325,f1726]) ).
thf(f3325,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) )
| ~ spl54_138 ),
inference(avatar_component_clause,[],[f3324]) ).
thf(f35317,plain,
( spl54_608
| ~ spl54_2
| ~ spl54_137 ),
inference(avatar_split_clause,[],[f3354,f3320,f1725,f35315]) ).
thf(f35315,plain,
( spl54_608
<=> ! [X0: a,X1: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X0),X1)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_608])]) ).
thf(f3320,plain,
( spl54_137
<=> ! [X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_137])]) ).
thf(f3354,plain,
( ! [X0: a,X1: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X0),X1)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_137 ),
inference(trivial_inequality_removal,[],[f3353]) ).
thf(f3353,plain,
( ! [X0: a,X1: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X0),X1)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X1)) ) )
| ~ spl54_2
| ~ spl54_137 ),
inference(superposition,[],[f3321,f1726]) ).
thf(f3321,plain,
( ! [X0: partia96731725t_unit,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) )
| ~ spl54_137 ),
inference(avatar_component_clause,[],[f3320]) ).
thf(f35313,plain,
( spl54_607
| ~ spl54_79
| ~ spl54_85
| ~ spl54_109
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3193,f3141,f2475,f2242,f2200,f35311]) ).
thf(f35311,plain,
( spl54_607
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_607])]) ).
thf(f2200,plain,
( spl54_79
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_79])]) ).
thf(f3193,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_79
| ~ spl54_85
| ~ spl54_109
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3192,f2476]) ).
thf(f3192,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) )
| ~ spl54_79
| ~ spl54_85
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3191,f2201]) ).
thf(f2201,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ~ spl54_79 ),
inference(avatar_component_clause,[],[f2200]) ).
thf(f3191,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ~ spl54_79
| ~ spl54_85
| ~ spl54_127 ),
inference(forward_demodulation,[],[f3161,f2243]) ).
thf(f3161,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X2)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_79
| ~ spl54_127 ),
inference(superposition,[],[f3142,f2201]) ).
thf(f35308,plain,
( spl54_606
| ~ spl54_40
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3171,f3141,f1937,f35306]) ).
thf(f35306,plain,
( spl54_606
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_606])]) ).
thf(f1937,plain,
( spl54_40
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_40])]) ).
thf(f3171,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))) )
| ~ spl54_40
| ~ spl54_127 ),
inference(superposition,[],[f1938,f3142]) ).
thf(f1938,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = X1 )
| ~ spl54_40 ),
inference(avatar_component_clause,[],[f1937]) ).
thf(f35304,plain,
( ~ spl54_604
| spl54_605
| ~ spl54_371
| ~ spl54_447 ),
inference(avatar_split_clause,[],[f19390,f18555,f16944,f35301,f35297]) ).
thf(f35297,plain,
( spl54_604
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK34,sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_604])]) ).
thf(f35301,plain,
( spl54_605
<=> ( sK8 = vAPP(a,a,sK34,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_605])]) ).
thf(f16944,plain,
( spl54_371
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_371])]) ).
thf(f19390,plain,
( ( sK8 = vAPP(a,a,sK34,sK8) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK34,sK8)) )
| ~ spl54_371
| ~ spl54_447 ),
inference(trivial_inequality_removal,[],[f19389]) ).
thf(f19389,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,sK34,sK8) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK34,sK8)) )
| ~ spl54_371
| ~ spl54_447 ),
inference(superposition,[],[f18556,f16946]) ).
thf(f16946,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_371 ),
inference(avatar_component_clause,[],[f16944]) ).
thf(f35294,plain,
( spl54_603
| ~ spl54_36
| ~ spl54_85
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2897,f2487,f2242,f1918,f35292]) ).
thf(f35292,plain,
( spl54_603
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_603])]) ).
thf(f2897,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) )
| ~ spl54_36
| ~ spl54_85
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2872,f1919]) ).
thf(f2872,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,uminus_uminus_int,X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) )
| ~ spl54_85
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2243]) ).
thf(f35289,plain,
( spl54_602
| ~ spl54_36
| ~ spl54_86
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2896,f2487,f2246,f1918,f35287]) ).
thf(f35287,plain,
( spl54_602
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_602])]) ).
thf(f2896,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_36
| ~ spl54_86
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2871,f1919]) ).
thf(f2871,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,uminus_uminus_int,X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_86
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2247]) ).
thf(f35285,plain,
( spl54_601
| ~ spl54_36
| ~ spl54_37
| ~ spl54_79
| ~ spl54_109
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2852,f2483,f2475,f2200,f1922,f1918,f35283]) ).
thf(f35283,plain,
( spl54_601
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_601])]) ).
thf(f2852,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0))) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_79
| ~ spl54_109
| ~ spl54_111 ),
inference(forward_demodulation,[],[f2851,f2476]) ).
thf(f2851,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_79
| ~ spl54_111 ),
inference(forward_demodulation,[],[f2835,f1965]) ).
thf(f2835,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ~ spl54_79
| ~ spl54_111 ),
inference(superposition,[],[f2484,f2201]) ).
thf(f35280,plain,
( spl54_600
| ~ spl54_36
| ~ spl54_39
| ~ spl54_86
| ~ spl54_108
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2733,f2495,f2471,f2246,f1933,f1918,f35278]) ).
thf(f35278,plain,
( spl54_600
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_600])]) ).
thf(f2733,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_36
| ~ spl54_39
| ~ spl54_86
| ~ spl54_108
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2694,f2723]) ).
thf(f2723,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_36
| ~ spl54_39
| ~ spl54_86
| ~ spl54_108
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2722,f1919]) ).
thf(f2722,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_39
| ~ spl54_86
| ~ spl54_108
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2682,f2721]) ).
thf(f2721,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ~ spl54_39
| ~ spl54_108
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2680,f2496]) ).
thf(f2680,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ~ spl54_39
| ~ spl54_108 ),
inference(superposition,[],[f2472,f1934]) ).
thf(f2682,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_86
| ~ spl54_108 ),
inference(superposition,[],[f2472,f2247]) ).
thf(f2694,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_86
| ~ spl54_108 ),
inference(superposition,[],[f2472,f2247]) ).
thf(f35275,plain,
( spl54_599
| ~ spl54_36
| ~ spl54_39
| ~ spl54_85
| ~ spl54_86
| ~ spl54_108
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2724,f2495,f2471,f2246,f2242,f1933,f1918,f35273]) ).
thf(f35273,plain,
( spl54_599
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_599])]) ).
thf(f2724,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ~ spl54_36
| ~ spl54_39
| ~ spl54_85
| ~ spl54_86
| ~ spl54_108
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2683,f2723]) ).
thf(f2683,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) )
| ~ spl54_85
| ~ spl54_108 ),
inference(superposition,[],[f2472,f2243]) ).
thf(f35271,plain,
( spl54_598
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_85
| ~ spl54_107
| ~ spl54_109
| ~ spl54_110 ),
inference(avatar_split_clause,[],[f2672,f2479,f2475,f2467,f2242,f1933,f1922,f1918,f35269]) ).
thf(f35269,plain,
( spl54_598
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),X2) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_598])]) ).
thf(f2672,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),X2) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_85
| ~ spl54_107
| ~ spl54_109
| ~ spl54_110 ),
inference(forward_demodulation,[],[f2671,f2476]) ).
thf(f2671,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),X2) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),X1)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_85
| ~ spl54_107
| ~ spl54_110 ),
inference(forward_demodulation,[],[f2670,f1965]) ).
thf(f2670,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_107
| ~ spl54_110 ),
inference(forward_demodulation,[],[f2652,f2666]) ).
thf(f2666,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) )
| ~ spl54_39
| ~ spl54_107
| ~ spl54_110 ),
inference(forward_demodulation,[],[f2649,f2480]) ).
thf(f2649,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) )
| ~ spl54_39
| ~ spl54_107 ),
inference(superposition,[],[f2468,f1934]) ).
thf(f2652,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_85
| ~ spl54_107 ),
inference(superposition,[],[f2468,f2243]) ).
thf(f35267,plain,
( spl54_597
| ~ spl54_75
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2587,f2454,f2174,f35265]) ).
thf(f35265,plain,
( spl54_597
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_597])]) ).
thf(f2174,plain,
( spl54_75
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,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,suc,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_75])]) ).
thf(f2587,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))) )
| ~ spl54_75
| ~ spl54_104 ),
inference(forward_demodulation,[],[f2586,f2175]) ).
thf(f2175,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,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,suc,X1)) )
| ~ spl54_75 ),
inference(avatar_component_clause,[],[f2174]) ).
thf(f2586,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,suc,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,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))) )
| ~ spl54_75
| ~ spl54_104 ),
inference(forward_demodulation,[],[f2561,f2175]) ).
thf(f2561,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,suc,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,X2),vAPP(nat,nat,suc,X1))) )
| ~ spl54_75
| ~ spl54_104 ),
inference(superposition,[],[f2455,f2175]) ).
thf(f35263,plain,
( spl54_596
| ~ spl54_74
| ~ spl54_75
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2585,f2454,f2174,f2170,f35261]) ).
thf(f35261,plain,
( spl54_596
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_596])]) ).
thf(f2585,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_74
| ~ spl54_75
| ~ spl54_104 ),
inference(forward_demodulation,[],[f2559,f2175]) ).
thf(f2559,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_74
| ~ spl54_104 ),
inference(superposition,[],[f2455,f2171]) ).
thf(f35259,plain,
( spl54_595
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_85
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2550,f2450,f2242,f1933,f1922,f1918,f35257]) ).
thf(f35257,plain,
( spl54_595
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_595])]) ).
thf(f2550,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_85
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2549,f1965]) ).
thf(f2549,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2529,f1934]) ).
thf(f2529,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X2)) )
| ~ spl54_85
| ~ spl54_103 ),
inference(superposition,[],[f2451,f2243]) ).
thf(f35255,plain,
( spl54_594
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_86
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2548,f2450,f2246,f1933,f1922,f1918,f35253]) ).
thf(f35253,plain,
( spl54_594
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_594])]) ).
thf(f2548,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_86
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2547,f1965]) ).
thf(f2547,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) )
| ~ spl54_39
| ~ spl54_86
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2528,f1934]) ).
thf(f2528,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X2)) )
| ~ spl54_86
| ~ spl54_103 ),
inference(superposition,[],[f2451,f2247]) ).
thf(f35251,plain,
( spl54_593
| ~ spl54_75
| ~ spl54_102 ),
inference(avatar_split_clause,[],[f2523,f2446,f2174,f35249]) ).
thf(f35249,plain,
( spl54_593
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_593])]) ).
thf(f2523,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1))) )
| ~ spl54_75
| ~ spl54_102 ),
inference(forward_demodulation,[],[f2515,f2175]) ).
thf(f2515,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,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),vAPP(nat,nat,suc,X1))) )
| ~ spl54_75
| ~ spl54_102 ),
inference(superposition,[],[f2447,f2175]) ).
thf(f35247,plain,
( spl54_592
| ~ spl54_74
| ~ spl54_102 ),
inference(avatar_split_clause,[],[f2516,f2446,f2170,f35245]) ).
thf(f35245,plain,
( spl54_592
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_592])]) ).
thf(f2516,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_74
| ~ spl54_102 ),
inference(superposition,[],[f2447,f2171]) ).
thf(f35243,plain,
( spl54_591
| ~ spl54_74
| ~ spl54_102 ),
inference(avatar_split_clause,[],[f2513,f2446,f2170,f35241]) ).
thf(f35241,plain,
( spl54_591
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,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,[spl54_591])]) ).
thf(f2513,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,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)) )
| ~ spl54_74
| ~ spl54_102 ),
inference(superposition,[],[f2447,f2171]) ).
thf(f35239,plain,
( spl54_590
| ~ spl54_74
| ~ spl54_101 ),
inference(avatar_split_clause,[],[f2511,f2442,f2170,f35237]) ).
thf(f35237,plain,
( spl54_590
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_590])]) ).
thf(f2511,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2))) )
| ~ spl54_74
| ~ spl54_101 ),
inference(forward_demodulation,[],[f2503,f2171]) ).
thf(f2503,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,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,suc,X0)),X2)) )
| ~ spl54_74
| ~ spl54_101 ),
inference(superposition,[],[f2443,f2171]) ).
thf(f35235,plain,
( spl54_589
| ~ spl54_75
| ~ spl54_101 ),
inference(avatar_split_clause,[],[f2508,f2442,f2174,f35233]) ).
thf(f35233,plain,
( spl54_589
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),vAPP(nat,nat,suc,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_589])]) ).
thf(f2508,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X2),vAPP(nat,nat,suc,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X2)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_75
| ~ spl54_101 ),
inference(superposition,[],[f2443,f2175]) ).
thf(f35231,plain,
( spl54_588
| ~ spl54_75
| ~ spl54_101 ),
inference(avatar_split_clause,[],[f2505,f2442,f2174,f35229]) ).
thf(f35229,plain,
( spl54_588
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,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,[spl54_588])]) ).
thf(f2505,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,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)) )
| ~ spl54_75
| ~ spl54_101 ),
inference(superposition,[],[f2443,f2175]) ).
thf(f35219,plain,
( spl54_587
| ~ spl54_2
| ~ spl54_136 ),
inference(avatar_split_clause,[],[f3318,f3306,f1725,f35217]) ).
thf(f35217,plain,
( spl54_587
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,a,sK26,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_587])]) ).
thf(f3306,plain,
( spl54_136
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,a,sK26,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_136])]) ).
thf(f3318,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,a,sK26,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_2
| ~ spl54_136 ),
inference(trivial_inequality_removal,[],[f3317]) ).
thf(f3317,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,a,sK26,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_2
| ~ spl54_136 ),
inference(superposition,[],[f3307,f1726]) ).
thf(f3307,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,a,sK26,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) )
| ~ spl54_136 ),
inference(avatar_component_clause,[],[f3306]) ).
thf(f35215,plain,
( spl54_586
| ~ spl54_2
| ~ spl54_135 ),
inference(avatar_split_clause,[],[f3315,f3302,f1725,f35213]) ).
thf(f35213,plain,
( spl54_586
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,a,sK19,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_586])]) ).
thf(f3302,plain,
( spl54_135
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,a,sK19,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_135])]) ).
thf(f3315,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,a,sK19,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_2
| ~ spl54_135 ),
inference(trivial_inequality_removal,[],[f3314]) ).
thf(f3314,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,a,sK19,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_2
| ~ spl54_135 ),
inference(superposition,[],[f3303,f1726]) ).
thf(f3303,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,a,sK19,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) )
| ~ spl54_135 ),
inference(avatar_component_clause,[],[f3302]) ).
thf(f35211,plain,
( spl54_585
| ~ spl54_2
| ~ spl54_134 ),
inference(avatar_split_clause,[],[f3312,f3298,f1725,f35209]) ).
thf(f35209,plain,
( spl54_585
<=> ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,a,sK10,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_585])]) ).
thf(f3312,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,a,sK10,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_2
| ~ spl54_134 ),
inference(trivial_inequality_removal,[],[f3311]) ).
thf(f3311,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,a,sK10,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_2
| ~ spl54_134 ),
inference(superposition,[],[f3299,f1726]) ).
thf(f35207,plain,
( spl54_584
| ~ spl54_72 ),
inference(avatar_split_clause,[],[f2164,f2160,f35205]) ).
thf(f35205,plain,
( spl54_584
<=> ! [X0: set_a,X1: set_a] :
( ( X0 = X1 )
| ( vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0) != vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_584])]) ).
thf(f2160,plain,
( spl54_72
<=> ! [X0: set_a] : ( vAPP(sTfun(a,$o),set_a,collect_a,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_72])]) ).
thf(f2164,plain,
( ! [X0: set_a,X1: set_a] :
( ( X0 = X1 )
| ( vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0) != vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X1) ) )
| ~ spl54_72 ),
inference(constrained_superposition,[],[f2161,f2161]) ).
thf(f2161,plain,
( ! [X0: set_a] : ( vAPP(sTfun(a,$o),set_a,collect_a,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0)) = X0 )
| ~ spl54_72 ),
inference(avatar_component_clause,[],[f2160]) ).
thf(f35203,plain,
( spl54_583
| ~ spl54_71 ),
inference(avatar_split_clause,[],[f2163,f2156,f35201]) ).
thf(f35201,plain,
( spl54_583
<=> ! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( X0 = X1 )
| ( vAPP(set_Product_prod_a_a,sTfun(product_prod_a_a,$o),vAPP(sTfun(product_prod_a_a,sTfun(set_Product_prod_a_a,$o)),sTfun(set_Product_prod_a_a,sTfun(product_prod_a_a,$o)),cCOMB,member449909584od_a_a),X0) != vAPP(set_Product_prod_a_a,sTfun(product_prod_a_a,$o),vAPP(sTfun(product_prod_a_a,sTfun(set_Product_prod_a_a,$o)),sTfun(set_Product_prod_a_a,sTfun(product_prod_a_a,$o)),cCOMB,member449909584od_a_a),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_583])]) ).
thf(f2156,plain,
( spl54_71
<=> ! [X0: set_Product_prod_a_a] : ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,vAPP(set_Product_prod_a_a,sTfun(product_prod_a_a,$o),vAPP(sTfun(product_prod_a_a,sTfun(set_Product_prod_a_a,$o)),sTfun(set_Product_prod_a_a,sTfun(product_prod_a_a,$o)),cCOMB,member449909584od_a_a),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_71])]) ).
thf(f2163,plain,
( ! [X0: set_Product_prod_a_a,X1: set_Product_prod_a_a] :
( ( X0 = X1 )
| ( vAPP(set_Product_prod_a_a,sTfun(product_prod_a_a,$o),vAPP(sTfun(product_prod_a_a,sTfun(set_Product_prod_a_a,$o)),sTfun(set_Product_prod_a_a,sTfun(product_prod_a_a,$o)),cCOMB,member449909584od_a_a),X0) != vAPP(set_Product_prod_a_a,sTfun(product_prod_a_a,$o),vAPP(sTfun(product_prod_a_a,sTfun(set_Product_prod_a_a,$o)),sTfun(set_Product_prod_a_a,sTfun(product_prod_a_a,$o)),cCOMB,member449909584od_a_a),X1) ) )
| ~ spl54_71 ),
inference(constrained_superposition,[],[f2157,f2157]) ).
thf(f2157,plain,
( ! [X0: set_Product_prod_a_a] : ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,vAPP(set_Product_prod_a_a,sTfun(product_prod_a_a,$o),vAPP(sTfun(product_prod_a_a,sTfun(set_Product_prod_a_a,$o)),sTfun(set_Product_prod_a_a,sTfun(product_prod_a_a,$o)),cCOMB,member449909584od_a_a),X0)) = X0 )
| ~ spl54_71 ),
inference(avatar_component_clause,[],[f2156]) ).
thf(f35179,plain,
( ~ spl54_581
| spl54_582
| ~ spl54_369
| ~ spl54_447 ),
inference(avatar_split_clause,[],[f19365,f18555,f16890,f35176,f35172]) ).
thf(f35172,plain,
( spl54_581
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK35,sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_581])]) ).
thf(f35176,plain,
( spl54_582
<=> ( sK8 = vAPP(a,a,sK35,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_582])]) ).
thf(f16890,plain,
( spl54_369
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_369])]) ).
thf(f19365,plain,
( ( sK8 = vAPP(a,a,sK35,sK8) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK35,sK8)) )
| ~ spl54_369
| ~ spl54_447 ),
inference(trivial_inequality_removal,[],[f19364]) ).
thf(f19364,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,sK35,sK8) )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,sK35,sK8)) )
| ~ spl54_369
| ~ spl54_447 ),
inference(superposition,[],[f18556,f16892]) ).
thf(f16892,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_369 ),
inference(avatar_component_clause,[],[f16890]) ).
thf(f35170,plain,
( spl54_580
| ~ spl54_2
| ~ spl54_133 ),
inference(avatar_split_clause,[],[f3271,f3239,f1725,f35168]) ).
thf(f35168,plain,
( spl54_580
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_580])]) ).
thf(f3239,plain,
( spl54_133
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_133])]) ).
thf(f3271,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_133 ),
inference(trivial_inequality_removal,[],[f3270]) ).
thf(f3270,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_133 ),
inference(superposition,[],[f3240,f1726]) ).
thf(f3240,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_133 ),
inference(avatar_component_clause,[],[f3239]) ).
thf(f35166,plain,
( spl54_579
| ~ spl54_2
| ~ spl54_132 ),
inference(avatar_split_clause,[],[f3263,f3235,f1725,f35164]) ).
thf(f35164,plain,
( spl54_579
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_579])]) ).
thf(f3235,plain,
( spl54_132
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_132])]) ).
thf(f3263,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_132 ),
inference(trivial_inequality_removal,[],[f3262]) ).
thf(f3262,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_132 ),
inference(superposition,[],[f3236,f1726]) ).
thf(f3236,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X1) = X1 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_132 ),
inference(avatar_component_clause,[],[f3235]) ).
thf(f35162,plain,
( spl54_578
| ~ spl54_2
| ~ spl54_131 ),
inference(avatar_split_clause,[],[f3255,f3231,f1725,f35160]) ).
thf(f35160,plain,
( spl54_578
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_578])]) ).
thf(f3231,plain,
( spl54_131
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_131])]) ).
thf(f3255,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_131 ),
inference(trivial_inequality_removal,[],[f3254]) ).
thf(f3254,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)),X0) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_131 ),
inference(superposition,[],[f3232,f1726]) ).
thf(f3232,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_131 ),
inference(avatar_component_clause,[],[f3231]) ).
thf(f35158,plain,
( spl54_577
| ~ spl54_2
| ~ spl54_130 ),
inference(avatar_split_clause,[],[f3247,f3227,f1725,f35156]) ).
thf(f35156,plain,
( spl54_577
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_577])]) ).
thf(f3227,plain,
( spl54_130
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_130])]) ).
thf(f3247,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_130 ),
inference(trivial_inequality_removal,[],[f3246]) ).
thf(f3246,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X1)) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_130 ),
inference(superposition,[],[f3228,f1726]) ).
thf(f3228,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) = X1 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_130 ),
inference(avatar_component_clause,[],[f3227]) ).
thf(f31292,plain,
( ~ spl54_576
| spl54_368
| ~ spl54_17
| ~ spl54_447 ),
inference(avatar_split_clause,[],[f18577,f18555,f1824,f16886,f31289]) ).
thf(f18577,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) != sK8 )
| ~ spl54_17
| ~ spl54_447 ),
inference(trivial_inequality_removal,[],[f18558]) ).
thf(f18558,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) != sK8 )
| ~ spl54_17
| ~ spl54_447 ),
inference(superposition,[],[f18556,f1826]) ).
thf(f31287,plain,
( spl54_575
| ~ spl54_18
| ~ spl54_33
| ~ spl54_160 ),
inference(avatar_split_clause,[],[f30940,f3646,f1903,f1829,f31284]) ).
thf(f31284,plain,
( spl54_575
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_575])]) ).
thf(f30940,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_33
| ~ spl54_160 ),
inference(trivial_inequality_removal,[],[f30939]) ).
thf(f30939,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_33
| ~ spl54_160 ),
inference(forward_demodulation,[],[f3683,f1905]) ).
thf(f3683,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_160 ),
inference(trivial_inequality_removal,[],[f3676]) ).
thf(f3676,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_160 ),
inference(superposition,[],[f3647,f1831]) ).
thf(f31282,plain,
( spl54_574
| ~ spl54_19
| ~ spl54_33
| ~ spl54_160 ),
inference(avatar_split_clause,[],[f30938,f3646,f1903,f1834,f31279]) ).
thf(f30938,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_33
| ~ spl54_160 ),
inference(trivial_inequality_removal,[],[f30937]) ).
thf(f30937,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_33
| ~ spl54_160 ),
inference(forward_demodulation,[],[f3682,f1905]) ).
thf(f3682,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_160 ),
inference(trivial_inequality_removal,[],[f3677]) ).
thf(f3677,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_160 ),
inference(superposition,[],[f3647,f1836]) ).
thf(f31277,plain,
( spl54_573
| ~ spl54_18
| ~ spl54_33
| ~ spl54_159 ),
inference(avatar_split_clause,[],[f30936,f3642,f1903,f1829,f31274]) ).
thf(f31274,plain,
( spl54_573
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_573])]) ).
thf(f30936,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)) )
| ~ spl54_18
| ~ spl54_33
| ~ spl54_159 ),
inference(trivial_inequality_removal,[],[f30935]) ).
thf(f30935,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)) )
| ~ spl54_18
| ~ spl54_33
| ~ spl54_159 ),
inference(forward_demodulation,[],[f3672,f1905]) ).
thf(f3672,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_159 ),
inference(trivial_inequality_removal,[],[f3665]) ).
thf(f3665,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_159 ),
inference(superposition,[],[f3643,f1831]) ).
thf(f31272,plain,
( spl54_572
| ~ spl54_19
| ~ spl54_33
| ~ spl54_159 ),
inference(avatar_split_clause,[],[f30934,f3642,f1903,f1834,f31269]) ).
thf(f30934,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)) )
| ~ spl54_19
| ~ spl54_33
| ~ spl54_159 ),
inference(trivial_inequality_removal,[],[f30933]) ).
thf(f30933,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)) )
| ~ spl54_19
| ~ spl54_33
| ~ spl54_159 ),
inference(forward_demodulation,[],[f3671,f1905]) ).
thf(f3671,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_159 ),
inference(trivial_inequality_removal,[],[f3666]) ).
thf(f3666,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_159 ),
inference(superposition,[],[f3643,f1836]) ).
thf(f31229,plain,
( spl54_571
| ~ spl54_32
| ~ spl54_33
| ~ spl54_159 ),
inference(avatar_split_clause,[],[f30928,f3642,f1903,f1899,f31226]) ).
thf(f31226,plain,
( spl54_571
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_571])]) ).
thf(f30928,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)) )
| ~ spl54_32
| ~ spl54_33
| ~ spl54_159 ),
inference(trivial_inequality_removal,[],[f30927]) ).
thf(f30927,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)) )
| ~ spl54_32
| ~ spl54_33
| ~ spl54_159 ),
inference(forward_demodulation,[],[f7546,f1905]) ).
thf(f7546,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_159 ),
inference(trivial_inequality_removal,[],[f5316]) ).
thf(f5316,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_159 ),
inference(superposition,[],[f3643,f1901]) ).
thf(f31224,plain,
( spl54_570
| ~ spl54_32
| ~ spl54_33
| ~ spl54_160 ),
inference(avatar_split_clause,[],[f30926,f3646,f1903,f1899,f31221]) ).
thf(f31221,plain,
( spl54_570
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_570])]) ).
thf(f30926,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),sK8) )
| ~ spl54_32
| ~ spl54_33
| ~ spl54_160 ),
inference(trivial_inequality_removal,[],[f30925]) ).
thf(f30925,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),sK8) )
| ~ spl54_32
| ~ spl54_33
| ~ spl54_160 ),
inference(forward_demodulation,[],[f7547,f1905]) ).
thf(f7547,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_160 ),
inference(trivial_inequality_removal,[],[f5317]) ).
thf(f5317,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_160 ),
inference(superposition,[],[f3647,f1901]) ).
thf(f31186,plain,
( spl54_363
| ~ spl54_49
| ~ spl54_426 ),
inference(avatar_split_clause,[],[f30918,f18279,f2008,f14477]) ).
thf(f14477,plain,
( spl54_363
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_363])]) ).
thf(f18279,plain,
( spl54_426
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_426])]) ).
thf(f30918,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_426 ),
inference(forward_demodulation,[],[f18281,f2010]) ).
thf(f18281,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_426 ),
inference(avatar_component_clause,[],[f18279]) ).
thf(f31021,plain,
( spl54_569
| ~ spl54_32
| ~ spl54_33
| ~ spl54_49
| ~ spl54_139 ),
inference(avatar_split_clause,[],[f30932,f3328,f2008,f1903,f1899,f31018]) ).
thf(f31018,plain,
( spl54_569
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_569])]) ).
thf(f30932,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_33
| ~ spl54_49
| ~ spl54_139 ),
inference(trivial_inequality_removal,[],[f30931]) ).
thf(f30931,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_33
| ~ spl54_49
| ~ spl54_139 ),
inference(forward_demodulation,[],[f15611,f1905]) ).
thf(f15611,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_139 ),
inference(forward_demodulation,[],[f7540,f2010]) ).
thf(f7540,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_139 ),
inference(trivial_inequality_removal,[],[f5310]) ).
thf(f5310,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_139 ),
inference(superposition,[],[f3329,f1901]) ).
thf(f30983,plain,
( spl54_429
| ~ spl54_32
| ~ spl54_33
| ~ spl54_49
| ~ spl54_140 ),
inference(avatar_split_clause,[],[f30930,f3332,f2008,f1903,f1899,f18299]) ).
thf(f18299,plain,
( spl54_429
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_429])]) ).
thf(f30930,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_33
| ~ spl54_49
| ~ spl54_140 ),
inference(trivial_inequality_removal,[],[f30929]) ).
thf(f30929,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_33
| ~ spl54_49
| ~ spl54_140 ),
inference(forward_demodulation,[],[f15609,f1905]) ).
thf(f15609,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_140 ),
inference(forward_demodulation,[],[f7541,f2010]) ).
thf(f7541,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_140 ),
inference(trivial_inequality_removal,[],[f5311]) ).
thf(f5311,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_140 ),
inference(superposition,[],[f3333,f1901]) ).
thf(f30924,plain,
( ~ spl54_33
| ~ spl54_2
| ~ spl54_32
| ~ spl54_49
| ~ spl54_140
| spl54_429 ),
inference(avatar_split_clause,[],[f30893,f18299,f3332,f2008,f1899,f1725,f1903]) ).
thf(f30893,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_2
| ~ spl54_32
| ~ spl54_49
| ~ spl54_140
| spl54_429 ),
inference(trivial_inequality_removal,[],[f30892]) ).
thf(f30892,plain,
( ( $true = $false )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_2
| ~ spl54_32
| ~ spl54_49
| ~ spl54_140
| spl54_429 ),
inference(forward_demodulation,[],[f16693,f18304]) ).
thf(f18304,plain,
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_2
| spl54_429 ),
inference(trivial_inequality_removal,[],[f18303]) ).
thf(f18303,plain,
( ( $true != $true )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_2
| spl54_429 ),
inference(superposition,[],[f18301,f1726]) ).
thf(f18301,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| spl54_429 ),
inference(avatar_component_clause,[],[f18299]) ).
thf(f16693,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_140 ),
inference(forward_demodulation,[],[f14534,f2010]) ).
thf(f14534,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_140 ),
inference(trivial_inequality_removal,[],[f3524]) ).
thf(f3524,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_140 ),
inference(superposition,[],[f3333,f1901]) ).
thf(f30856,plain,
( ~ spl54_506
| ~ spl54_49
| ~ spl54_128
| ~ spl54_141
| ~ spl54_537 ),
inference(avatar_split_clause,[],[f28129,f27868,f3336,f3211,f2008,f20347]) ).
thf(f3211,plain,
( spl54_128
<=> ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_128])]) ).
thf(f27868,plain,
( spl54_537
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_537])]) ).
thf(f28129,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_141
| ~ spl54_537 ),
inference(trivial_inequality_removal,[],[f28128]) ).
thf(f28128,plain,
( ( $true = $false )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_141
| ~ spl54_537 ),
inference(forward_demodulation,[],[f27963,f3338]) ).
thf(f27963,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_537 ),
inference(forward_demodulation,[],[f27941,f2010]) ).
thf(f27941,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_128
| ~ spl54_537 ),
inference(trivial_inequality_removal,[],[f27940]) ).
thf(f27940,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_128
| ~ spl54_537 ),
inference(superposition,[],[f3212,f27869]) ).
thf(f27869,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_537 ),
inference(avatar_component_clause,[],[f27868]) ).
thf(f3212,plain,
( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_128 ),
inference(avatar_component_clause,[],[f3211]) ).
thf(f28175,plain,
( spl54_568
| ~ spl54_14
| ~ spl54_129 ),
inference(avatar_split_clause,[],[f3242,f3223,f1811,f28173]) ).
thf(f28171,plain,
( spl54_567
| ~ spl54_29
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3170,f3141,f1881,f28169]) ).
thf(f28169,plain,
( spl54_567
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_567])]) ).
thf(f1881,plain,
( spl54_29
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_29])]) ).
thf(f3170,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) )
| ~ spl54_29
| ~ spl54_127 ),
inference(superposition,[],[f1882,f3142]) ).
thf(f1882,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X1) = X0 )
| ~ spl54_29 ),
inference(avatar_component_clause,[],[f1881]) ).
thf(f28167,plain,
( spl54_566
| ~ spl54_28
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3169,f3141,f1877,f28165]) ).
thf(f28165,plain,
( spl54_566
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,uminus_uminus_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_566])]) ).
thf(f1877,plain,
( spl54_28
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_28])]) ).
thf(f3169,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,uminus_uminus_int,X0)) )
| ~ spl54_28
| ~ spl54_127 ),
inference(superposition,[],[f1878,f3142]) ).
thf(f1878,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X0) = X1 )
| ~ spl54_28 ),
inference(avatar_component_clause,[],[f1877]) ).
thf(f28163,plain,
( spl54_565
| ~ spl54_2
| ~ spl54_126 ),
inference(avatar_split_clause,[],[f3148,f3137,f1725,f28161]) ).
thf(f28161,plain,
( spl54_565
<=> ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_565])]) ).
thf(f3137,plain,
( spl54_126
<=> ! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_126])]) ).
thf(f3148,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_126 ),
inference(trivial_inequality_removal,[],[f3147]) ).
thf(f3147,plain,
( ! [X0: a,X1: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X1),X0)) = X0 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X1) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1)) ) )
| ~ spl54_2
| ~ spl54_126 ),
inference(superposition,[],[f3138,f1726]) ).
thf(f3138,plain,
( ! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) = X1 )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_126 ),
inference(avatar_component_clause,[],[f3137]) ).
thf(f28159,plain,
( spl54_564
| ~ spl54_39
| ~ spl54_79
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3011,f2500,f2200,f1933,f28157]) ).
thf(f28157,plain,
( spl54_564
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_564])]) ).
thf(f3011,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) )
| ~ spl54_39
| ~ spl54_79
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2978,f1934]) ).
thf(f2978,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X2) )
| ~ spl54_79
| ~ spl54_115 ),
inference(superposition,[],[f2501,f2201]) ).
thf(f28155,plain,
( spl54_563
| ~ spl54_40
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2938,f2495,f1937,f28153]) ).
thf(f28153,plain,
( spl54_563
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_563])]) ).
thf(f2938,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) )
| ~ spl54_40
| ~ spl54_114 ),
inference(superposition,[],[f1938,f2496]) ).
thf(f28151,plain,
( spl54_562
| ~ spl54_36
| ~ spl54_37
| ~ spl54_40
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2890,f2487,f1937,f1922,f1918,f28149]) ).
thf(f28149,plain,
( spl54_562
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_562])]) ).
thf(f2890,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_40
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2860,f1965]) ).
thf(f2860,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_40
| ~ spl54_112 ),
inference(superposition,[],[f2488,f1938]) ).
thf(f28147,plain,
( spl54_561
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2889,f2487,f1933,f1922,f1918,f28145]) ).
thf(f28145,plain,
( spl54_561
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_561])]) ).
thf(f2889,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_39
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2859,f1965]) ).
thf(f2859,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ~ spl54_39
| ~ spl54_112 ),
inference(superposition,[],[f2488,f1934]) ).
thf(f28143,plain,
( spl54_560
| ~ spl54_37
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2840,f2483,f1922,f28141]) ).
thf(f28141,plain,
( spl54_560
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_560])]) ).
thf(f2840,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_37
| ~ spl54_111 ),
inference(superposition,[],[f1923,f2484]) ).
thf(f28139,plain,
( spl54_559
| ~ spl54_36
| ~ spl54_107
| ~ spl54_110 ),
inference(avatar_split_clause,[],[f2826,f2479,f2467,f1918,f28137]) ).
thf(f28137,plain,
( spl54_559
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_559])]) ).
thf(f2826,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_36
| ~ spl54_107
| ~ spl54_110 ),
inference(forward_demodulation,[],[f2814,f2468]) ).
thf(f2814,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_36
| ~ spl54_110 ),
inference(superposition,[],[f2480,f1919]) ).
thf(f28135,plain,
( spl54_558
| ~ spl54_37
| ~ spl54_110 ),
inference(avatar_split_clause,[],[f2816,f2479,f1922,f28133]) ).
thf(f28133,plain,
( spl54_558
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_558])]) ).
thf(f2816,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) )
| ~ spl54_37
| ~ spl54_110 ),
inference(superposition,[],[f1923,f2480]) ).
thf(f28127,plain,
( ~ spl54_141
| ~ spl54_49
| ~ spl54_128
| ~ spl54_400
| ~ spl54_537 ),
inference(avatar_split_clause,[],[f27966,f27868,f17786,f3211,f2008,f3336]) ).
thf(f27966,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_400
| ~ spl54_537 ),
inference(trivial_inequality_removal,[],[f27965]) ).
thf(f27965,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = $false )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_400
| ~ spl54_537 ),
inference(inner_rewriting,[],[f27964]) ).
thf(f27964,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_400
| ~ spl54_537 ),
inference(forward_demodulation,[],[f27963,f17788]) ).
thf(f28126,plain,
( spl54_557
| ~ spl54_39
| ~ spl54_85
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2789,f2475,f2242,f1933,f28124]) ).
thf(f28124,plain,
( spl54_557
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_557])]) ).
thf(f28122,plain,
( spl54_556
| ~ spl54_40
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2771,f2475,f1937,f28120]) ).
thf(f28120,plain,
( spl54_556
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_556])]) ).
thf(f2771,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) = X2 )
| ~ spl54_40
| ~ spl54_109 ),
inference(superposition,[],[f1938,f2476]) ).
thf(f28118,plain,
( spl54_555
| ~ spl54_39
| ~ spl54_108
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2721,f2495,f2471,f1933,f28116]) ).
thf(f28116,plain,
( spl54_555
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_555])]) ).
thf(f28114,plain,
( spl54_554
| ~ spl54_40
| ~ spl54_108 ),
inference(avatar_split_clause,[],[f2681,f2471,f1937,f28112]) ).
thf(f28112,plain,
( spl54_554
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_554])]) ).
thf(f2681,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_40
| ~ spl54_108 ),
inference(superposition,[],[f2472,f1938]) ).
thf(f28110,plain,
( spl54_553
| ~ spl54_39
| ~ spl54_107
| ~ spl54_110 ),
inference(avatar_split_clause,[],[f2666,f2479,f2467,f1933,f28108]) ).
thf(f28108,plain,
( spl54_553
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_553])]) ).
thf(f28106,plain,
( spl54_552
| ~ spl54_40
| ~ spl54_107 ),
inference(avatar_split_clause,[],[f2650,f2467,f1937,f28104]) ).
thf(f28104,plain,
( spl54_552
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_552])]) ).
thf(f2650,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_40
| ~ spl54_107 ),
inference(superposition,[],[f2468,f1938]) ).
thf(f28102,plain,
( spl54_551
| ~ spl54_36
| ~ spl54_39
| ~ spl54_85
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2557,f2450,f2242,f1933,f1918,f28100]) ).
thf(f28100,plain,
( spl54_551
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_551])]) ).
thf(f2557,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) )
| ~ spl54_36
| ~ spl54_39
| ~ spl54_85
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2556,f1919]) ).
thf(f2556,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,uminus_uminus_int,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) )
| ~ spl54_39
| ~ spl54_85
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2536,f1934]) ).
thf(f2536,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,uminus_uminus_int,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X2)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) )
| ~ spl54_85
| ~ spl54_103 ),
inference(superposition,[],[f2451,f2243]) ).
thf(f28098,plain,
( spl54_550
| ~ spl54_36
| ~ spl54_39
| ~ spl54_86
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2555,f2450,f2246,f1933,f1918,f28096]) ).
thf(f28096,plain,
( spl54_550
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_550])]) ).
thf(f2555,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_36
| ~ spl54_39
| ~ spl54_86
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2554,f1919]) ).
thf(f2554,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,uminus_uminus_int,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_39
| ~ spl54_86
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2535,f1934]) ).
thf(f2535,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,uminus_uminus_int,X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X2)),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_86
| ~ spl54_103 ),
inference(superposition,[],[f2451,f2247]) ).
thf(f28094,plain,
( spl54_549
| ~ spl54_37
| ~ spl54_86 ),
inference(avatar_split_clause,[],[f2278,f2246,f1922,f28092]) ).
thf(f28092,plain,
( spl54_549
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_549])]) ).
thf(f2278,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0))) )
| ~ spl54_37
| ~ spl54_86 ),
inference(forward_demodulation,[],[f2277,f1714]) ).
thf(f1714,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) ),
inference(forward_demodulation,[],[f1309,f1308]) ).
thf(f1308,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ),
inference(cnf_transformation,[],[f179]) ).
thf(f179,axiom,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_diff__diff__eq2) ).
thf(f1309,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) ),
inference(cnf_transformation,[],[f178]) ).
thf(f178,axiom,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_add__diff__eq) ).
thf(f2277,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))) )
| ~ spl54_37
| ~ spl54_86 ),
inference(forward_demodulation,[],[f2267,f1454]) ).
thf(f1454,plain,
! [X2: int,X3: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ),
inference(equality_resolution,[],[f1405]) ).
thf(f1405,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2) != X0 ) ),
inference(cnf_transformation,[],[f972]) ).
thf(f972,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2) != X0 ) ),
inference(ennf_transformation,[],[f714]) ).
thf(f714,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2) = X0 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X3),X2)) ) ),
inference(rectify,[],[f263]) ).
thf(f263,axiom,
! [X44: int,X30: int,X1: int,X0: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X30),X1) = X44 )
=> ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X44) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X30)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_group__cancel_Osub2) ).
thf(f2267,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X2)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) )
| ~ spl54_37
| ~ spl54_86 ),
inference(superposition,[],[f2247,f1923]) ).
thf(f28090,plain,
( spl54_548
| ~ spl54_37
| ~ spl54_85 ),
inference(avatar_split_clause,[],[f2263,f2242,f1922,f28088]) ).
thf(f28088,plain,
( spl54_548
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,uminus_uminus_int,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_548])]) ).
thf(f2263,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,uminus_uminus_int,X2)) )
| ~ spl54_37
| ~ spl54_85 ),
inference(forward_demodulation,[],[f2262,f1313]) ).
thf(f1313,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ),
inference(cnf_transformation,[],[f181]) ).
thf(f181,axiom,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_diff__add__eq__diff__diff__swap) ).
thf(f2262,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,uminus_uminus_int,X2)) )
| ~ spl54_37
| ~ spl54_85 ),
inference(forward_demodulation,[],[f2261,f1923]) ).
thf(f2261,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,uminus_uminus_int,X2)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0))) )
| ~ spl54_37
| ~ spl54_85 ),
inference(forward_demodulation,[],[f2254,f1714]) ).
thf(f2254,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,uminus_uminus_int,X2)) )
| ~ spl54_37
| ~ spl54_85 ),
inference(superposition,[],[f2243,f1923]) ).
thf(f28085,plain,
( spl54_547
| ~ spl54_37
| ~ spl54_79 ),
inference(avatar_split_clause,[],[f2210,f2200,f1922,f28083]) ).
thf(f28083,plain,
( spl54_547
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_547])]) ).
thf(f2210,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) )
| ~ spl54_37
| ~ spl54_79 ),
inference(forward_demodulation,[],[f2209,f1716]) ).
thf(f1716,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) ),
inference(forward_demodulation,[],[f1316,f1308]) ).
thf(f1316,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) ),
inference(cnf_transformation,[],[f180]) ).
thf(f180,axiom,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_diff__add__eq) ).
thf(f2209,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ~ spl54_37
| ~ spl54_79 ),
inference(forward_demodulation,[],[f2203,f1313]) ).
thf(f2203,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),X2) )
| ~ spl54_37
| ~ spl54_79 ),
inference(superposition,[],[f2201,f1923]) ).
thf(f27982,plain,
( spl54_546
| ~ spl54_49
| ~ spl54_541 ),
inference(avatar_split_clause,[],[f27890,f27887,f2008,f27980]) ).
thf(f27980,plain,
( spl54_546
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_546])]) ).
thf(f27887,plain,
( spl54_541
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_541])]) ).
thf(f27890,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) ) )
| ~ spl54_49
| ~ spl54_541 ),
inference(forward_demodulation,[],[f27888,f2010]) ).
thf(f27888,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_541 ),
inference(avatar_component_clause,[],[f27887]) ).
thf(f27978,plain,
( spl54_545
| ~ spl54_49
| ~ spl54_540 ),
inference(avatar_split_clause,[],[f27885,f27882,f2008,f27976]) ).
thf(f27976,plain,
( spl54_545
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_545])]) ).
thf(f27882,plain,
( spl54_540
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_540])]) ).
thf(f27885,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) ) )
| ~ spl54_49
| ~ spl54_540 ),
inference(forward_demodulation,[],[f27883,f2010]) ).
thf(f27883,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_540 ),
inference(avatar_component_clause,[],[f27882]) ).
thf(f27974,plain,
( spl54_544
| ~ spl54_49
| ~ spl54_539 ),
inference(avatar_split_clause,[],[f27880,f27877,f2008,f27972]) ).
thf(f27972,plain,
( spl54_544
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_544])]) ).
thf(f27877,plain,
( spl54_539
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_539])]) ).
thf(f27880,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) )
| ~ spl54_49
| ~ spl54_539 ),
inference(forward_demodulation,[],[f27878,f2010]) ).
thf(f27878,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_539 ),
inference(avatar_component_clause,[],[f27877]) ).
thf(f27970,plain,
( spl54_543
| ~ spl54_49
| ~ spl54_538 ),
inference(avatar_split_clause,[],[f27875,f27872,f2008,f27968]) ).
thf(f27968,plain,
( spl54_543
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_543])]) ).
thf(f27872,plain,
( spl54_538
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_538])]) ).
thf(f27875,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_538 ),
inference(forward_demodulation,[],[f27873,f2010]) ).
thf(f27873,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_538 ),
inference(avatar_component_clause,[],[f27872]) ).
thf(f27928,plain,
( ~ spl54_542
| spl54_370
| ~ spl54_294
| ~ spl54_447 ),
inference(avatar_split_clause,[],[f18576,f18555,f7242,f16940,f27925]) ).
thf(f18576,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) != sK8 )
| ~ spl54_294
| ~ spl54_447 ),
inference(trivial_inequality_removal,[],[f18559]) ).
thf(f18559,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) != sK8 )
| ~ spl54_294
| ~ spl54_447 ),
inference(superposition,[],[f18556,f7244]) ).
thf(f27889,plain,
( spl54_541
| ~ spl54_2
| ~ spl54_124 ),
inference(avatar_split_clause,[],[f3132,f3085,f1725,f27887]) ).
thf(f3085,plain,
( spl54_124
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_124])]) ).
thf(f3132,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_124 ),
inference(trivial_inequality_removal,[],[f3131]) ).
thf(f3131,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_124 ),
inference(superposition,[],[f3086,f1726]) ).
thf(f3086,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) ) )
| ~ spl54_124 ),
inference(avatar_component_clause,[],[f3085]) ).
thf(f27884,plain,
( spl54_540
| ~ spl54_2
| ~ spl54_123 ),
inference(avatar_split_clause,[],[f3124,f3081,f1725,f27882]) ).
thf(f3081,plain,
( spl54_123
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_123])]) ).
thf(f3124,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_123 ),
inference(trivial_inequality_removal,[],[f3123]) ).
thf(f3123,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_123 ),
inference(superposition,[],[f3082,f1726]) ).
thf(f3082,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) ) )
| ~ spl54_123 ),
inference(avatar_component_clause,[],[f3081]) ).
thf(f27879,plain,
( spl54_539
| ~ spl54_2
| ~ spl54_122 ),
inference(avatar_split_clause,[],[f3116,f3077,f1725,f27877]) ).
thf(f3077,plain,
( spl54_122
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_122])]) ).
thf(f3116,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_122 ),
inference(trivial_inequality_removal,[],[f3115]) ).
thf(f3115,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_122 ),
inference(superposition,[],[f3078,f1726]) ).
thf(f3078,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) )
| ~ spl54_122 ),
inference(avatar_component_clause,[],[f3077]) ).
thf(f27874,plain,
( spl54_538
| ~ spl54_2
| ~ spl54_121 ),
inference(avatar_split_clause,[],[f3108,f3073,f1725,f27872]) ).
thf(f3073,plain,
( spl54_121
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_121])]) ).
thf(f3108,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_121 ),
inference(trivial_inequality_removal,[],[f3107]) ).
thf(f3107,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_121 ),
inference(superposition,[],[f3074,f1726]) ).
thf(f3074,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) )
| ~ spl54_121 ),
inference(avatar_component_clause,[],[f3073]) ).
thf(f27870,plain,
( spl54_537
| ~ spl54_2
| ~ spl54_120 ),
inference(avatar_split_clause,[],[f3097,f3069,f1725,f27868]) ).
thf(f3097,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_120 ),
inference(trivial_inequality_removal,[],[f3096]) ).
thf(f3096,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_120 ),
inference(superposition,[],[f3070,f1726]) ).
thf(f27866,plain,
( spl54_536
| ~ spl54_2
| ~ spl54_119 ),
inference(avatar_split_clause,[],[f3091,f3065,f1725,f27864]) ).
thf(f3091,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_119 ),
inference(trivial_inequality_removal,[],[f3090]) ).
thf(f3090,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_119 ),
inference(superposition,[],[f3066,f1726]) ).
thf(f27796,plain,
( spl54_535
| ~ spl54_49
| ~ spl54_533 ),
inference(avatar_split_clause,[],[f27684,f27680,f2008,f27794]) ).
thf(f27794,plain,
( spl54_535
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_535])]) ).
thf(f27680,plain,
( spl54_533
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_533])]) ).
thf(f27684,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 ) )
| ~ spl54_49
| ~ spl54_533 ),
inference(forward_demodulation,[],[f27683,f2010]) ).
thf(f27683,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_533 ),
inference(forward_demodulation,[],[f27681,f2010]) ).
thf(f27681,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_533 ),
inference(avatar_component_clause,[],[f27680]) ).
thf(f27688,plain,
( spl54_534
| ~ spl54_49
| ~ spl54_532 ),
inference(avatar_split_clause,[],[f27678,f27674,f2008,f27686]) ).
thf(f27686,plain,
( spl54_534
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_534])]) ).
thf(f27674,plain,
( spl54_532
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_532])]) ).
thf(f27678,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) )
| ~ spl54_49
| ~ spl54_532 ),
inference(forward_demodulation,[],[f27677,f2010]) ).
thf(f27677,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_532 ),
inference(forward_demodulation,[],[f27675,f2010]) ).
thf(f27675,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_532 ),
inference(avatar_component_clause,[],[f27674]) ).
thf(f27682,plain,
( spl54_533
| ~ spl54_2
| ~ spl54_118 ),
inference(avatar_split_clause,[],[f3061,f3046,f1725,f27680]) ).
thf(f3046,plain,
( spl54_118
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_118])]) ).
thf(f3061,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_118 ),
inference(trivial_inequality_removal,[],[f3060]) ).
thf(f3060,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_118 ),
inference(superposition,[],[f3047,f1726]) ).
thf(f3047,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 ) )
| ~ spl54_118 ),
inference(avatar_component_clause,[],[f3046]) ).
thf(f27676,plain,
( spl54_532
| ~ spl54_2
| ~ spl54_117 ),
inference(avatar_split_clause,[],[f3054,f3042,f1725,f27674]) ).
thf(f3042,plain,
( spl54_117
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_117])]) ).
thf(f3054,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_117 ),
inference(trivial_inequality_removal,[],[f3053]) ).
thf(f3053,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_117 ),
inference(superposition,[],[f3043,f1726]) ).
thf(f3043,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) )
| ~ spl54_117 ),
inference(avatar_component_clause,[],[f3042]) ).
thf(f27634,plain,
( spl54_531
| ~ spl54_49
| ~ spl54_530 ),
inference(avatar_split_clause,[],[f27630,f27626,f2008,f27632]) ).
thf(f27632,plain,
( spl54_531
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_531])]) ).
thf(f27626,plain,
( spl54_530
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_530])]) ).
thf(f27630,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_530 ),
inference(forward_demodulation,[],[f27629,f2010]) ).
thf(f27629,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_530 ),
inference(forward_demodulation,[],[f27627,f2010]) ).
thf(f27627,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_530 ),
inference(avatar_component_clause,[],[f27626]) ).
thf(f27628,plain,
( spl54_530
| ~ spl54_2
| ~ spl54_116 ),
inference(avatar_split_clause,[],[f3036,f3029,f1725,f27626]) ).
thf(f3029,plain,
( spl54_116
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_116])]) ).
thf(f3036,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_116 ),
inference(trivial_inequality_removal,[],[f3035]) ).
thf(f3035,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_116 ),
inference(superposition,[],[f3030,f1726]) ).
thf(f3030,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_116 ),
inference(avatar_component_clause,[],[f3029]) ).
thf(f27506,plain,
( spl54_529
| ~ spl54_27
| ~ spl54_471 ),
inference(avatar_split_clause,[],[f21928,f18852,f1873,f27504]) ).
thf(f27504,plain,
( spl54_529
<=> ! [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,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_529])]) ).
thf(f1873,plain,
( spl54_27
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_27])]) ).
thf(f18852,plain,
( spl54_471
<=> ! [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),minus_minus_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,[spl54_471])]) ).
thf(f21928,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,X1),X0) )
| ~ spl54_27
| ~ spl54_471 ),
inference(superposition,[],[f18853,f1874]) ).
thf(f1874,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) = X1 )
| ~ spl54_27 ),
inference(avatar_component_clause,[],[f1873]) ).
thf(f18853,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),minus_minus_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) )
| ~ spl54_471 ),
inference(avatar_component_clause,[],[f18852]) ).
thf(f21687,plain,
( spl54_528
| ~ spl54_29
| ~ spl54_281 ),
inference(avatar_split_clause,[],[f6925,f6152,f1881,f21685]) ).
thf(f21685,plain,
( spl54_528
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_528])]) ).
thf(f6152,plain,
( spl54_281
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_281])]) ).
thf(f6925,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X1)) = X0 )
| ~ spl54_29
| ~ spl54_281 ),
inference(superposition,[],[f6153,f1882]) ).
thf(f6153,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X1)) = X0 )
| ~ spl54_281 ),
inference(avatar_component_clause,[],[f6152]) ).
thf(f20636,plain,
( spl54_527
| ~ spl54_5
| ~ spl54_19
| ~ spl54_163 ),
inference(avatar_split_clause,[],[f3716,f3658,f1834,f1766,f20633]) ).
thf(f20633,plain,
( spl54_527
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_527])]) ).
thf(f3716,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_5
| ~ spl54_19
| ~ spl54_163 ),
inference(trivial_inequality_removal,[],[f3715]) ).
thf(f3715,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_5
| ~ spl54_19
| ~ spl54_163 ),
inference(forward_demodulation,[],[f3711,f1768]) ).
thf(f3711,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_163 ),
inference(trivial_inequality_removal,[],[f3706]) ).
thf(f3706,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_163 ),
inference(superposition,[],[f3659,f1836]) ).
thf(f20631,plain,
( spl54_526
| ~ spl54_5
| ~ spl54_18
| ~ spl54_163 ),
inference(avatar_split_clause,[],[f3714,f3658,f1829,f1766,f20628]) ).
thf(f3714,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_18
| ~ spl54_163 ),
inference(trivial_inequality_removal,[],[f3713]) ).
thf(f3713,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_18
| ~ spl54_163 ),
inference(forward_demodulation,[],[f3712,f1768]) ).
thf(f3712,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_163 ),
inference(trivial_inequality_removal,[],[f3705]) ).
thf(f3705,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_163 ),
inference(superposition,[],[f3659,f1831]) ).
thf(f20626,plain,
( spl54_525
| ~ spl54_18
| ~ spl54_148 ),
inference(avatar_split_clause,[],[f3570,f3449,f1829,f20623]) ).
thf(f3570,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_148 ),
inference(trivial_inequality_removal,[],[f3563]) ).
thf(f3563,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_148 ),
inference(superposition,[],[f3450,f1831]) ).
thf(f20621,plain,
( spl54_524
| ~ spl54_18
| ~ spl54_147 ),
inference(avatar_split_clause,[],[f3561,f3444,f1829,f20618]) ).
thf(f20618,plain,
( spl54_524
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_524])]) ).
thf(f3561,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_147 ),
inference(trivial_inequality_removal,[],[f3554]) ).
thf(f3554,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_147 ),
inference(superposition,[],[f3445,f1831]) ).
thf(f20616,plain,
( spl54_523
| ~ spl54_28
| ~ spl54_281 ),
inference(avatar_split_clause,[],[f6924,f6152,f1877,f20614]) ).
thf(f20614,plain,
( spl54_523
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X0)),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_523])]) ).
thf(f6924,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X0)),X1) = X1 )
| ~ spl54_28
| ~ spl54_281 ),
inference(superposition,[],[f6153,f1878]) ).
thf(f20612,plain,
( spl54_522
| ~ spl54_36
| ~ spl54_37
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f3013,f2500,f1922,f1918,f20610]) ).
thf(f20610,plain,
( spl54_522
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_522])]) ).
thf(f3013,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_115 ),
inference(forward_demodulation,[],[f3012,f1919]) ).
thf(f3012,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2979,f1965]) ).
thf(f2979,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X2)) )
| ~ spl54_36
| ~ spl54_115 ),
inference(superposition,[],[f2501,f1919]) ).
thf(f20608,plain,
( spl54_521
| ~ spl54_28
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f2986,f2500,f1877,f20606]) ).
thf(f20606,plain,
( spl54_521
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_521])]) ).
thf(f2986,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = X2 )
| ~ spl54_28
| ~ spl54_115 ),
inference(superposition,[],[f1878,f2501]) ).
thf(f20604,plain,
( spl54_520
| ~ spl54_28
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f2971,f2500,f1877,f20602]) ).
thf(f20602,plain,
( spl54_520
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_520])]) ).
thf(f2971,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) )
| ~ spl54_28
| ~ spl54_115 ),
inference(superposition,[],[f2501,f1878]) ).
thf(f20600,plain,
( spl54_519
| ~ spl54_30
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2931,f2495,f1885,f20598]) ).
thf(f20598,plain,
( spl54_519
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_519])]) ).
thf(f1885,plain,
( spl54_30
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_30])]) ).
thf(f2931,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1)) = X0 )
| ~ spl54_30
| ~ spl54_114 ),
inference(superposition,[],[f2496,f1886]) ).
thf(f1886,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X1) = X0 )
| ~ spl54_30 ),
inference(avatar_component_clause,[],[f1885]) ).
thf(f20596,plain,
( spl54_518
| ~ spl54_106
| ~ spl54_113 ),
inference(avatar_split_clause,[],[f2910,f2491,f2463,f20594]) ).
thf(f20594,plain,
( spl54_518
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_518])]) ).
thf(f2910,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X2),X1)) )
| ~ spl54_106
| ~ spl54_113 ),
inference(superposition,[],[f2492,f2464]) ).
thf(f20592,plain,
( spl54_517
| ~ spl54_27
| ~ spl54_113 ),
inference(avatar_split_clause,[],[f2904,f2491,f1873,f20590]) ).
thf(f20590,plain,
( spl54_517
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_517])]) ).
thf(f2904,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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),X0)) )
| ~ spl54_27
| ~ spl54_113 ),
inference(superposition,[],[f2492,f1874]) ).
thf(f20588,plain,
( spl54_516
| ~ spl54_31
| ~ spl54_112
| ~ spl54_114 ),
inference(avatar_split_clause,[],[f2898,f2495,f2487,f1889,f20586]) ).
thf(f20586,plain,
( spl54_516
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_516])]) ).
thf(f1889,plain,
( spl54_31
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_31])]) ).
thf(f2898,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1))),X1) )
| ~ spl54_31
| ~ spl54_112
| ~ spl54_114 ),
inference(forward_demodulation,[],[f2874,f2496]) ).
thf(f2874,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0))),X1) )
| ~ spl54_31
| ~ spl54_112 ),
inference(superposition,[],[f2488,f1890]) ).
thf(f1890,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) = X1 )
| ~ spl54_31 ),
inference(avatar_component_clause,[],[f1889]) ).
thf(f20584,plain,
( spl54_515
| ~ spl54_36
| ~ spl54_39
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2894,f2487,f1933,f1918,f20582]) ).
thf(f20582,plain,
( spl54_515
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_515])]) ).
thf(f2894,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) )
| ~ spl54_36
| ~ spl54_39
| ~ spl54_112 ),
inference(forward_demodulation,[],[f2869,f1919]) ).
thf(f2869,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,uminus_uminus_int,X0)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) )
| ~ spl54_39
| ~ spl54_112 ),
inference(superposition,[],[f2488,f1934]) ).
thf(f20580,plain,
( spl54_514
| ~ spl54_31
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2885,f2487,f1889,f20578]) ).
thf(f20578,plain,
( spl54_514
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_514])]) ).
thf(f2885,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2)) )
| ~ spl54_31
| ~ spl54_112 ),
inference(superposition,[],[f1890,f2488]) ).
thf(f20576,plain,
( spl54_513
| ~ spl54_30
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2842,f2483,f1885,f20574]) ).
thf(f20574,plain,
( spl54_513
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_513])]) ).
thf(f2842,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X2) )
| ~ spl54_30
| ~ spl54_111 ),
inference(superposition,[],[f1886,f2484]) ).
thf(f20571,plain,
( spl54_512
| ~ spl54_49
| ~ spl54_91
| ~ spl54_141 ),
inference(avatar_split_clause,[],[f15566,f3336,f2321,f2008,f20568]) ).
thf(f15566,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_91
| ~ spl54_141 ),
inference(forward_demodulation,[],[f3768,f2010]) ).
thf(f3768,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_91
| ~ spl54_141 ),
inference(trivial_inequality_removal,[],[f3765]) ).
thf(f3765,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_91
| ~ spl54_141 ),
inference(superposition,[],[f2322,f3338]) ).
thf(f20566,plain,
( spl54_511
| ~ spl54_31
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2841,f2483,f1889,f20564]) ).
thf(f20564,plain,
( spl54_511
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_511])]) ).
thf(f2841,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))) )
| ~ spl54_31
| ~ spl54_111 ),
inference(superposition,[],[f1890,f2484]) ).
thf(f20450,plain,
( spl54_510
| ~ spl54_49
| ~ spl54_458 ),
inference(avatar_split_clause,[],[f19289,f18750,f2008,f20448]) ).
thf(f20448,plain,
( spl54_510
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_510])]) ).
thf(f18750,plain,
( spl54_458
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_458])]) ).
thf(f19289,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 ) )
| ~ spl54_49
| ~ spl54_458 ),
inference(forward_demodulation,[],[f18751,f2010]) ).
thf(f18751,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_458 ),
inference(avatar_component_clause,[],[f18750]) ).
thf(f20446,plain,
( spl54_509
| ~ spl54_49
| ~ spl54_454 ),
inference(avatar_split_clause,[],[f19267,f18688,f2008,f20444]) ).
thf(f20444,plain,
( spl54_509
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_509])]) ).
thf(f18688,plain,
( spl54_454
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_454])]) ).
thf(f19267,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 ) )
| ~ spl54_49
| ~ spl54_454 ),
inference(forward_demodulation,[],[f18689,f2010]) ).
thf(f18689,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_454 ),
inference(avatar_component_clause,[],[f18688]) ).
thf(f20442,plain,
( spl54_508
| ~ spl54_49
| ~ spl54_456 ),
inference(avatar_split_clause,[],[f19014,f18725,f2008,f20440]) ).
thf(f20440,plain,
( spl54_508
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_508])]) ).
thf(f18725,plain,
( spl54_456
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_456])]) ).
thf(f19014,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 ) )
| ~ spl54_49
| ~ spl54_456 ),
inference(forward_demodulation,[],[f18726,f2010]) ).
thf(f18726,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_456 ),
inference(avatar_component_clause,[],[f18725]) ).
thf(f20438,plain,
( spl54_507
| ~ spl54_49
| ~ spl54_460 ),
inference(avatar_split_clause,[],[f18971,f18786,f2008,f20436]) ).
thf(f20436,plain,
( spl54_507
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_507])]) ).
thf(f18786,plain,
( spl54_460
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_460])]) ).
thf(f18971,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 ) )
| ~ spl54_49
| ~ spl54_460 ),
inference(forward_demodulation,[],[f18787,f2010]) ).
thf(f18787,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_460 ),
inference(avatar_component_clause,[],[f18786]) ).
thf(f20350,plain,
( spl54_506
| ~ spl54_49
| ~ spl54_92
| ~ spl54_141 ),
inference(avatar_split_clause,[],[f15565,f3336,f2325,f2008,f20347]) ).
thf(f15565,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_92
| ~ spl54_141 ),
inference(forward_demodulation,[],[f3769,f2010]) ).
thf(f3769,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_92
| ~ spl54_141 ),
inference(trivial_inequality_removal,[],[f3764]) ).
thf(f3764,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_92
| ~ spl54_141 ),
inference(superposition,[],[f2326,f3338]) ).
thf(f20284,plain,
( spl54_505
| ~ spl54_49
| ~ spl54_448 ),
inference(avatar_split_clause,[],[f19266,f18580,f2008,f20282]) ).
thf(f20282,plain,
( spl54_505
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_505])]) ).
thf(f18580,plain,
( spl54_448
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_448])]) ).
thf(f19266,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 ) )
| ~ spl54_49
| ~ spl54_448 ),
inference(forward_demodulation,[],[f18581,f2010]) ).
thf(f18581,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 ) )
| ~ spl54_448 ),
inference(avatar_component_clause,[],[f18580]) ).
thf(f20280,plain,
( spl54_504
| ~ spl54_49
| ~ spl54_446 ),
inference(avatar_split_clause,[],[f19265,f18548,f2008,f20278]) ).
thf(f20278,plain,
( spl54_504
<=> ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_504])]) ).
thf(f18548,plain,
( spl54_446
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_446])]) ).
thf(f19265,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) )
| ~ spl54_49
| ~ spl54_446 ),
inference(forward_demodulation,[],[f18549,f2010]) ).
thf(f18549,plain,
( ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) )
| ~ spl54_446 ),
inference(avatar_component_clause,[],[f18548]) ).
thf(f20231,plain,
( spl54_503
| ~ spl54_2
| spl54_487 ),
inference(avatar_split_clause,[],[f20224,f19315,f1725,f20228]) ).
thf(f19315,plain,
( spl54_487
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_487])]) ).
thf(f20224,plain,
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_2
| spl54_487 ),
inference(trivial_inequality_removal,[],[f20223]) ).
thf(f20223,plain,
( ( $true != $true )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_2
| spl54_487 ),
inference(superposition,[],[f19316,f1726]) ).
thf(f19316,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| spl54_487 ),
inference(avatar_component_clause,[],[f19315]) ).
thf(f20167,plain,
( ~ spl54_490
| ~ spl54_488
| ~ spl54_496 ),
inference(avatar_split_clause,[],[f19606,f19576,f19345,f19405]) ).
thf(f19936,plain,
( spl54_502
| ~ spl54_151
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19335,f19315,f3466,f19933]) ).
thf(f19933,plain,
( spl54_502
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK7),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_502])]) ).
thf(f19335,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK7),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7)) )
| ~ spl54_151
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19324]) ).
thf(f19324,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK7),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7)) )
| ~ spl54_151
| ~ spl54_487 ),
inference(superposition,[],[f3467,f19317]) ).
thf(f19317,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_487 ),
inference(avatar_component_clause,[],[f19315]) ).
thf(f19896,plain,
( spl54_501
| ~ spl54_209
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19333,f19315,f4299,f19893]) ).
thf(f19893,plain,
( spl54_501
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7)),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_501])]) ).
thf(f19333,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7)),sK7) )
| ~ spl54_209
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19326]) ).
thf(f19326,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7)),sK7) )
| ~ spl54_209
| ~ spl54_487 ),
inference(superposition,[],[f4300,f19317]) ).
thf(f19891,plain,
( spl54_500
| ~ spl54_239
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19332,f19315,f5033,f19889]) ).
thf(f19889,plain,
( spl54_500
<=> ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_500])]) ).
thf(f19332,plain,
( ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_239
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19327]) ).
thf(f19327,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_239
| ~ spl54_487 ),
inference(superposition,[],[f5034,f19317]) ).
thf(f19887,plain,
( spl54_499
| ~ spl54_284
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19331,f19315,f6197,f19885]) ).
thf(f19885,plain,
( spl54_499
<=> ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_499])]) ).
thf(f19331,plain,
( ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_284
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19328]) ).
thf(f19328,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_284
| ~ spl54_487 ),
inference(superposition,[],[f6198,f19317]) ).
thf(f19835,plain,
( spl54_498
| ~ spl54_49
| ~ spl54_398 ),
inference(avatar_split_clause,[],[f17777,f17773,f2008,f19832]) ).
thf(f17773,plain,
( spl54_398
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_398])]) ).
thf(f17777,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_398 ),
inference(forward_demodulation,[],[f17775,f2010]) ).
thf(f17775,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_398 ),
inference(avatar_component_clause,[],[f17773]) ).
thf(f19830,plain,
( spl54_497
| ~ spl54_49
| ~ spl54_397 ),
inference(avatar_split_clause,[],[f17770,f17766,f2008,f19827]) ).
thf(f17766,plain,
( spl54_397
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_397])]) ).
thf(f17770,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_397 ),
inference(forward_demodulation,[],[f17768,f2010]) ).
thf(f17768,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_397 ),
inference(avatar_component_clause,[],[f17766]) ).
thf(f19815,plain,
( spl54_386
| ~ spl54_311
| ~ spl54_416 ),
inference(avatar_split_clause,[],[f19042,f18202,f9806,f17667]) ).
thf(f17667,plain,
( spl54_386
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_386])]) ).
thf(f18202,plain,
( spl54_416
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_416])]) ).
thf(f19042,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_311
| ~ spl54_416 ),
inference(forward_demodulation,[],[f18204,f9808]) ).
thf(f18204,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_416 ),
inference(avatar_component_clause,[],[f18202]) ).
thf(f19666,plain,
( ~ spl54_432
| ~ spl54_49
| spl54_428 ),
inference(avatar_split_clause,[],[f18296,f18292,f2008,f18319]) ).
thf(f18292,plain,
( spl54_428
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_428])]) ).
thf(f18296,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| spl54_428 ),
inference(forward_demodulation,[],[f18293,f2010]) ).
thf(f18293,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| spl54_428 ),
inference(avatar_component_clause,[],[f18292]) ).
thf(f19663,plain,
( ~ spl54_427
| ~ spl54_49
| spl54_425 ),
inference(avatar_split_clause,[],[f18276,f18272,f2008,f18286]) ).
thf(f18272,plain,
( spl54_425
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_425])]) ).
thf(f18276,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| spl54_425 ),
inference(forward_demodulation,[],[f18273,f2010]) ).
thf(f18273,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| spl54_425 ),
inference(avatar_component_clause,[],[f18272]) ).
thf(f19579,plain,
( spl54_496
| ~ spl54_119
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19337,f19315,f3065,f19576]) ).
thf(f19337,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),vAPP(a,a,sK32,sK7)) )
| ~ spl54_119
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19322]) ).
thf(f19322,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),vAPP(a,a,sK32,sK7)) )
| ~ spl54_119
| ~ spl54_487 ),
inference(superposition,[],[f3066,f19317]) ).
thf(f19574,plain,
( spl54_495
| ~ spl54_120
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19336,f19315,f3069,f19571]) ).
thf(f19571,plain,
( spl54_495
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK7)),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_495])]) ).
thf(f19336,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK7)),sK7) )
| ~ spl54_120
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19323]) ).
thf(f19323,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,sK7)),sK7) )
| ~ spl54_120
| ~ spl54_487 ),
inference(superposition,[],[f3070,f19317]) ).
thf(f19478,plain,
( spl54_494
| ~ spl54_49
| ~ spl54_411 ),
inference(avatar_split_clause,[],[f19313,f18119,f2008,f19475]) ).
thf(f19475,plain,
( spl54_494
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_494])]) ).
thf(f18119,plain,
( spl54_411
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_411])]) ).
thf(f19313,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_411 ),
inference(forward_demodulation,[],[f18121,f2010]) ).
thf(f18121,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_411 ),
inference(avatar_component_clause,[],[f18119]) ).
thf(f19473,plain,
( spl54_493
| ~ spl54_49
| ~ spl54_412 ),
inference(avatar_split_clause,[],[f19312,f18127,f2008,f19470]) ).
thf(f19470,plain,
( spl54_493
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_493])]) ).
thf(f18127,plain,
( spl54_412
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_412])]) ).
thf(f19312,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_412 ),
inference(forward_demodulation,[],[f18129,f2010]) ).
thf(f18129,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_412 ),
inference(avatar_component_clause,[],[f18127]) ).
thf(f19468,plain,
( spl54_492
| ~ spl54_373
| ~ spl54_406 ),
inference(avatar_split_clause,[],[f19237,f17909,f16982,f19465]) ).
thf(f16982,plain,
( spl54_373
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK36,sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_373])]) ).
thf(f19237,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),sK8) )
| ~ spl54_373
| ~ spl54_406 ),
inference(forward_demodulation,[],[f16984,f17911]) ).
thf(f16984,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK36,sK8)) )
| ~ spl54_373 ),
inference(avatar_component_clause,[],[f16982]) ).
thf(f19413,plain,
( spl54_491
| ~ spl54_49
| ~ spl54_92
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19343,f19315,f2325,f2008,f19410]) ).
thf(f19343,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_92
| ~ spl54_487 ),
inference(forward_demodulation,[],[f19338,f2010]) ).
thf(f19338,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK7)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_92
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19321]) ).
thf(f19321,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,sK7)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_92
| ~ spl54_487 ),
inference(superposition,[],[f2326,f19317]) ).
thf(f19408,plain,
( spl54_490
| ~ spl54_49
| ~ spl54_91
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19342,f19315,f2321,f2008,f19405]) ).
thf(f19342,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_91
| ~ spl54_487 ),
inference(forward_demodulation,[],[f19339,f2010]) ).
thf(f19339,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_91
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19320]) ).
thf(f19320,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,sK7)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_91
| ~ spl54_487 ),
inference(superposition,[],[f2322,f19317]) ).
thf(f19353,plain,
( ~ spl54_489
| spl54_372
| ~ spl54_447
| ~ spl54_487 ),
inference(avatar_split_clause,[],[f19330,f19315,f18555,f16977,f19350]) ).
thf(f19350,plain,
( spl54_489
<=> ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_489])]) ).
thf(f16977,plain,
( spl54_372
<=> ( sK7 = sK8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_372])]) ).
thf(f19330,plain,
( ( sK7 = sK8 )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7) )
| ~ spl54_447
| ~ spl54_487 ),
inference(trivial_inequality_removal,[],[f19329]) ).
thf(f19329,plain,
( ( $true != $true )
| ( sK7 = sK8 )
| ( sK8 != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK7) )
| ~ spl54_447
| ~ spl54_487 ),
inference(superposition,[],[f18556,f19317]) ).
thf(f19347,plain,
( spl54_410
| spl54_488
| ~ spl54_25
| ~ spl54_49 ),
inference(avatar_split_clause,[],[f19098,f2008,f1864,f19345,f18115]) ).
thf(f1864,plain,
( spl54_25
<=> ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_25])]) ).
thf(f19098,plain,
( ! [X1: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),X1) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) )
| ~ spl54_25
| ~ spl54_49 ),
inference(forward_demodulation,[],[f19086,f2010]) ).
thf(f19086,plain,
( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) )
| ~ spl54_25 ),
inference(trivial_inequality_removal,[],[f19085]) ).
thf(f19085,plain,
( ! [X1: a] :
( ( $true = $false )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) )
| ~ spl54_25 ),
inference(forward_demodulation,[],[f1130,f1866]) ).
thf(f1866,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $false )
| ~ spl54_25 ),
inference(avatar_component_clause,[],[f1864]) ).
thf(f1130,plain,
! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK7),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) ),
inference(cnf_transformation,[],[f1024]) ).
thf(f19318,plain,
( spl54_410
| spl54_487
| ~ spl54_25
| ~ spl54_49 ),
inference(avatar_split_clause,[],[f19091,f2008,f1864,f19315,f18115]) ).
thf(f19091,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_25
| ~ spl54_49 ),
inference(trivial_inequality_removal,[],[f19090]) ).
thf(f19090,plain,
( ( $true = $false )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_25
| ~ spl54_49 ),
inference(forward_demodulation,[],[f17634,f1866]) ).
thf(f19242,plain,
( spl54_368
| ~ spl54_293
| ~ spl54_376
| ~ spl54_410 ),
inference(avatar_split_clause,[],[f19232,f18115,f17002,f7094,f16886]) ).
thf(f17002,plain,
( spl54_376
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_376])]) ).
thf(f19232,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_293
| ~ spl54_376
| ~ spl54_410 ),
inference(forward_demodulation,[],[f19231,f7096]) ).
thf(f19231,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_376
| ~ spl54_410 ),
inference(forward_demodulation,[],[f17004,f18117]) ).
thf(f17004,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_376 ),
inference(avatar_component_clause,[],[f17002]) ).
thf(f19239,plain,
( spl54_370
| ~ spl54_399
| ~ spl54_401 ),
inference(avatar_split_clause,[],[f19183,f17791,f17780,f16940]) ).
thf(f19097,plain,
( spl54_368
| ~ spl54_370
| ~ spl54_410 ),
inference(avatar_split_clause,[],[f19043,f18115,f16940,f16886]) ).
thf(f19043,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_370
| ~ spl54_410 ),
inference(forward_demodulation,[],[f18117,f16942]) ).
thf(f18945,plain,
( ~ spl54_141
| ~ spl54_49
| ~ spl54_128
| ~ spl54_365
| ~ spl54_368 ),
inference(avatar_split_clause,[],[f17598,f16886,f16781,f3211,f2008,f3336]) ).
thf(f17598,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_365
| ~ spl54_368 ),
inference(trivial_inequality_removal,[],[f17597]) ).
thf(f17597,plain,
( ( sK8 != sK8 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_365
| ~ spl54_368 ),
inference(forward_demodulation,[],[f16818,f16888]) ).
thf(f16818,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_365 ),
inference(inner_rewriting,[],[f16817]) ).
thf(f16817,plain,
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ~ spl54_49
| ~ spl54_128
| ~ spl54_365 ),
inference(forward_demodulation,[],[f16812,f2010]) ).
thf(f16812,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ~ spl54_128
| ~ spl54_365 ),
inference(superposition,[],[f3212,f16783]) ).
thf(f18944,plain,
( spl54_486
| ~ spl54_110
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2837,f2483,f2479,f18942]) ).
thf(f18942,plain,
( spl54_486
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_486])]) ).
thf(f2837,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ~ spl54_110
| ~ spl54_111 ),
inference(superposition,[],[f2484,f2480]) ).
thf(f18940,plain,
( spl54_485
| ~ spl54_29
| ~ spl54_111 ),
inference(avatar_split_clause,[],[f2830,f2483,f1881,f18938]) ).
thf(f18938,plain,
( spl54_485
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_485])]) ).
thf(f2830,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ~ spl54_29
| ~ spl54_111 ),
inference(superposition,[],[f2484,f1882]) ).
thf(f18936,plain,
( spl54_484
| ~ spl54_30
| ~ spl54_110 ),
inference(avatar_split_clause,[],[f2818,f2479,f1885,f18934]) ).
thf(f18934,plain,
( spl54_484
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_484])]) ).
thf(f2818,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))),X2) )
| ~ spl54_30
| ~ spl54_110 ),
inference(superposition,[],[f1886,f2480]) ).
thf(f18932,plain,
( spl54_483
| ~ spl54_31
| ~ spl54_110 ),
inference(avatar_split_clause,[],[f2817,f2479,f1889,f18930]) ).
thf(f18930,plain,
( spl54_483
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_483])]) ).
thf(f2817,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1))) )
| ~ spl54_31
| ~ spl54_110 ),
inference(superposition,[],[f1890,f2480]) ).
thf(f18928,plain,
( spl54_482
| ~ spl54_28
| ~ spl54_110 ),
inference(avatar_split_clause,[],[f2808,f2479,f1877,f18926]) ).
thf(f18926,plain,
( spl54_482
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_482])]) ).
thf(f2808,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)) )
| ~ spl54_28
| ~ spl54_110 ),
inference(superposition,[],[f2480,f1878]) ).
thf(f18924,plain,
( spl54_481
| ~ spl54_29
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2770,f2475,f1881,f18922]) ).
thf(f18922,plain,
( spl54_481
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_481])]) ).
thf(f2770,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),X2) )
| ~ spl54_29
| ~ spl54_109 ),
inference(superposition,[],[f1882,f2476]) ).
thf(f18920,plain,
( spl54_480
| ~ spl54_28
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2769,f2475,f1877,f18918]) ).
thf(f18918,plain,
( spl54_480
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_480])]) ).
thf(f2769,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = X2 )
| ~ spl54_28
| ~ spl54_109 ),
inference(superposition,[],[f1878,f2476]) ).
thf(f18916,plain,
( spl54_479
| ~ spl54_30
| ~ spl54_109 ),
inference(avatar_split_clause,[],[f2756,f2475,f1885,f18914]) ).
thf(f18914,plain,
( spl54_479
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_479])]) ).
thf(f2756,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) )
| ~ spl54_30
| ~ spl54_109 ),
inference(superposition,[],[f2476,f1886]) ).
thf(f18912,plain,
( spl54_478
| ~ spl54_29
| ~ spl54_108 ),
inference(avatar_split_clause,[],[f2705,f2471,f1881,f18910]) ).
thf(f18910,plain,
( spl54_478
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_478])]) ).
thf(f2705,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = X0 )
| ~ spl54_29
| ~ spl54_108 ),
inference(superposition,[],[f1882,f2472]) ).
thf(f18908,plain,
( spl54_477
| ~ spl54_28
| ~ spl54_108 ),
inference(avatar_split_clause,[],[f2704,f2471,f1877,f18906]) ).
thf(f18906,plain,
( spl54_477
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_477])]) ).
thf(f2704,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2))),X0) )
| ~ spl54_28
| ~ spl54_108 ),
inference(superposition,[],[f1878,f2472]) ).
thf(f18874,plain,
( spl54_476
| ~ spl54_30
| ~ spl54_107 ),
inference(avatar_split_clause,[],[f2663,f2467,f1885,f18872]) ).
thf(f18872,plain,
( spl54_476
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_476])]) ).
thf(f2663,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))),X2) )
| ~ spl54_30
| ~ spl54_107 ),
inference(superposition,[],[f1886,f2468]) ).
thf(f18870,plain,
( spl54_475
| ~ spl54_31
| ~ spl54_107 ),
inference(avatar_split_clause,[],[f2662,f2467,f1889,f18868]) ).
thf(f18868,plain,
( spl54_475
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_475])]) ).
thf(f2662,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1))) )
| ~ spl54_31
| ~ spl54_107 ),
inference(superposition,[],[f1890,f2468]) ).
thf(f18866,plain,
( spl54_474
| ~ spl54_31
| ~ spl54_107 ),
inference(avatar_split_clause,[],[f2654,f2467,f1889,f18864]) ).
thf(f18864,plain,
( spl54_474
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_474])]) ).
thf(f2654,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0))) )
| ~ spl54_31
| ~ spl54_107 ),
inference(superposition,[],[f2468,f1890]) ).
thf(f18862,plain,
( spl54_473
| ~ spl54_26
| ~ spl54_106 ),
inference(avatar_split_clause,[],[f2634,f2463,f1869,f18860]) ).
thf(f18860,plain,
( spl54_473
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_473])]) ).
thf(f1869,plain,
( spl54_26
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_26])]) ).
thf(f2634,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,X1),X2)) )
| ~ spl54_26
| ~ spl54_106 ),
inference(superposition,[],[f2464,f1870]) ).
thf(f1870,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) = X0 )
| ~ spl54_26 ),
inference(avatar_component_clause,[],[f1869]) ).
thf(f18858,plain,
( spl54_472
| ~ spl54_27
| ~ spl54_105 ),
inference(avatar_split_clause,[],[f2605,f2459,f1873,f18856]) ).
thf(f18856,plain,
( spl54_472
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_472])]) ).
thf(f2605,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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)) = X2 )
| ~ spl54_27
| ~ spl54_105 ),
inference(superposition,[],[f1874,f2460]) ).
thf(f18854,plain,
( spl54_471
| ~ spl54_26
| ~ spl54_105 ),
inference(avatar_split_clause,[],[f2604,f2459,f1869,f18852]) ).
thf(f2604,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),minus_minus_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) )
| ~ spl54_26
| ~ spl54_105 ),
inference(superposition,[],[f1870,f2460]) ).
thf(f18850,plain,
( spl54_470
| ~ spl54_27
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2572,f2454,f1873,f18848]) ).
thf(f18848,plain,
( spl54_470
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,[spl54_470])]) ).
thf(f2572,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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) )
| ~ spl54_27
| ~ spl54_104 ),
inference(superposition,[],[f1874,f2455]) ).
thf(f18846,plain,
( spl54_469
| ~ spl54_26
| ~ spl54_104 ),
inference(avatar_split_clause,[],[f2571,f2454,f1869,f18844]) ).
thf(f18844,plain,
( spl54_469
<=> ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_469])]) ).
thf(f2571,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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)) = X0 )
| ~ spl54_26
| ~ spl54_104 ),
inference(superposition,[],[f1870,f2455]) ).
thf(f18842,plain,
( spl54_468
| ~ spl54_30
| ~ spl54_103
| ~ spl54_115 ),
inference(avatar_split_clause,[],[f2551,f2500,f2450,f1885,f18840]) ).
thf(f18840,plain,
( spl54_468
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_468])]) ).
thf(f2551,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))),X0) )
| ~ spl54_30
| ~ spl54_103
| ~ spl54_115 ),
inference(forward_demodulation,[],[f2532,f2501]) ).
thf(f2532,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2)),X0) )
| ~ spl54_30
| ~ spl54_103 ),
inference(superposition,[],[f2451,f1886]) ).
thf(f18838,plain,
( spl54_467
| ~ spl54_39
| ~ spl54_40
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2546,f2450,f1937,f1933,f18836]) ).
thf(f18836,plain,
( spl54_467
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_467])]) ).
thf(f2546,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) )
| ~ spl54_39
| ~ spl54_40
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2527,f1934]) ).
thf(f2527,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X2)) )
| ~ spl54_40
| ~ spl54_103 ),
inference(superposition,[],[f2451,f1938]) ).
thf(f18834,plain,
( ~ spl54_22
| ~ spl54_368
| ~ spl54_11
| ~ spl54_370 ),
inference(avatar_split_clause,[],[f16966,f16940,f1793,f16886,f1847]) ).
thf(f16966,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| ~ spl54_11
| ~ spl54_370 ),
inference(superposition,[],[f1794,f16942]) ).
thf(f18833,plain,
( spl54_466
| ~ spl54_39
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2545,f2450,f1933,f18831]) ).
thf(f18831,plain,
( spl54_466
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_466])]) ).
thf(f2545,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X0)) )
| ~ spl54_39
| ~ spl54_103 ),
inference(forward_demodulation,[],[f2526,f1934]) ).
thf(f2526,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X2)) )
| ~ spl54_39
| ~ spl54_103 ),
inference(superposition,[],[f2451,f1934]) ).
thf(f18829,plain,
( spl54_465
| ~ spl54_30
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2543,f2450,f1885,f18827]) ).
thf(f18827,plain,
( spl54_465
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_465])]) ).
thf(f2543,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) )
| ~ spl54_30
| ~ spl54_103 ),
inference(superposition,[],[f1886,f2451]) ).
thf(f18825,plain,
( spl54_464
| ~ spl54_31
| ~ spl54_103 ),
inference(avatar_split_clause,[],[f2542,f2450,f1889,f18823]) ).
thf(f18823,plain,
( spl54_464
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_464])]) ).
thf(f2542,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)) )
| ~ spl54_31
| ~ spl54_103 ),
inference(superposition,[],[f1890,f2451]) ).
thf(f18821,plain,
( spl54_463
| ~ spl54_37
| ~ spl54_40 ),
inference(avatar_split_clause,[],[f1985,f1937,f1922,f18819]) ).
thf(f18819,plain,
( spl54_463
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_463])]) ).
thf(f1985,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2))) = X2 )
| ~ spl54_37
| ~ spl54_40 ),
inference(forward_demodulation,[],[f1976,f1716]) ).
thf(f1976,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2)) = X2 )
| ~ spl54_37
| ~ spl54_40 ),
inference(superposition,[],[f1938,f1923]) ).
thf(f18817,plain,
( spl54_462
| ~ spl54_37
| ~ spl54_39 ),
inference(avatar_split_clause,[],[f1969,f1933,f1922,f18815]) ).
thf(f18815,plain,
( spl54_462
<=> ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_462])]) ).
thf(f1969,plain,
( ! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),X2) )
| ~ spl54_37
| ~ spl54_39 ),
inference(superposition,[],[f1934,f1923]) ).
thf(f18794,plain,
( spl54_461
| ~ spl54_49
| ~ spl54_368
| ~ spl54_460 ),
inference(avatar_split_clause,[],[f18790,f18786,f16886,f2008,f18792]) ).
thf(f18790,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) = X0 ) )
| ~ spl54_49
| ~ spl54_368
| ~ spl54_460 ),
inference(forward_demodulation,[],[f18789,f2010]) ).
thf(f18789,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_368
| ~ spl54_460 ),
inference(forward_demodulation,[],[f18787,f16888]) ).
thf(f18788,plain,
( spl54_460
| ~ spl54_2
| ~ spl54_100 ),
inference(avatar_split_clause,[],[f2437,f2406,f1725,f18786]) ).
thf(f2406,plain,
( spl54_100
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_100])]) ).
thf(f2437,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_100 ),
inference(trivial_inequality_removal,[],[f2436]) ).
thf(f2436,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_100 ),
inference(superposition,[],[f2407,f1726]) ).
thf(f2407,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 ) )
| ~ spl54_100 ),
inference(avatar_component_clause,[],[f2406]) ).
thf(f18758,plain,
( spl54_459
| ~ spl54_49
| ~ spl54_370
| ~ spl54_458 ),
inference(avatar_split_clause,[],[f18754,f18750,f16940,f2008,f18756]) ).
thf(f18756,plain,
( spl54_459
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_459])]) ).
thf(f18754,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) = X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_458 ),
inference(forward_demodulation,[],[f18753,f2010]) ).
thf(f18753,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_370
| ~ spl54_458 ),
inference(forward_demodulation,[],[f18751,f16942]) ).
thf(f18752,plain,
( spl54_458
| ~ spl54_2
| ~ spl54_99 ),
inference(avatar_split_clause,[],[f2429,f2402,f1725,f18750]) ).
thf(f2402,plain,
( spl54_99
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_99])]) ).
thf(f2429,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_99 ),
inference(trivial_inequality_removal,[],[f2428]) ).
thf(f2428,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_99 ),
inference(superposition,[],[f2403,f1726]) ).
thf(f2403,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 ) )
| ~ spl54_99 ),
inference(avatar_component_clause,[],[f2402]) ).
thf(f18733,plain,
( spl54_457
| ~ spl54_49
| ~ spl54_368
| ~ spl54_456 ),
inference(avatar_split_clause,[],[f18729,f18725,f16886,f2008,f18731]) ).
thf(f18731,plain,
( spl54_457
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_457])]) ).
thf(f18729,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = X0 ) )
| ~ spl54_49
| ~ spl54_368
| ~ spl54_456 ),
inference(forward_demodulation,[],[f18728,f2010]) ).
thf(f18728,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),sK8) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_368
| ~ spl54_456 ),
inference(forward_demodulation,[],[f18726,f16888]) ).
thf(f18727,plain,
( spl54_456
| ~ spl54_2
| ~ spl54_98 ),
inference(avatar_split_clause,[],[f2421,f2397,f1725,f18725]) ).
thf(f2397,plain,
( spl54_98
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_98])]) ).
thf(f2421,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_98 ),
inference(trivial_inequality_removal,[],[f2420]) ).
thf(f2420,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_98 ),
inference(superposition,[],[f2398,f1726]) ).
thf(f2398,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 ) )
| ~ spl54_98 ),
inference(avatar_component_clause,[],[f2397]) ).
thf(f18696,plain,
( spl54_455
| ~ spl54_49
| ~ spl54_370
| ~ spl54_454 ),
inference(avatar_split_clause,[],[f18692,f18688,f16940,f2008,f18694]) ).
thf(f18692,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_454 ),
inference(forward_demodulation,[],[f18691,f2010]) ).
thf(f18691,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),sK8) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_370
| ~ spl54_454 ),
inference(forward_demodulation,[],[f18689,f16942]) ).
thf(f18690,plain,
( spl54_454
| ~ spl54_2
| ~ spl54_97 ),
inference(avatar_split_clause,[],[f2413,f2393,f1725,f18688]) ).
thf(f2393,plain,
( spl54_97
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_97])]) ).
thf(f2413,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_97 ),
inference(trivial_inequality_removal,[],[f2412]) ).
thf(f2412,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_97 ),
inference(superposition,[],[f2394,f1726]) ).
thf(f2394,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 ) )
| ~ spl54_97 ),
inference(avatar_component_clause,[],[f2393]) ).
thf(f18686,plain,
( spl54_453
| ~ spl54_89 ),
inference(avatar_split_clause,[],[f2306,f2288,f18684]) ).
thf(f18684,plain,
( spl54_453
<=> ! [X0: product_prod_a_a,X1: product_prod_a_a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))),vAPP(sTfun(product_prod_a_a,$o),a,sK47,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_453])]) ).
thf(f2306,plain,
( ! [X0: product_prod_a_a,X1: product_prod_a_a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))),vAPP(sTfun(product_prod_a_a,$o),a,sK47,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))) != X0 )
| ( X0 = X1 ) )
| ~ spl54_89 ),
inference(equality_proxy_clausification,[],[f2305]) ).
thf(f2305,plain,
( ! [X0: product_prod_a_a,X1: product_prod_a_a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))),vAPP(sTfun(product_prod_a_a,$o),a,sK47,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))) != X0 )
| ( $true = vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0),X1) ) )
| ~ spl54_89 ),
inference(equality_proxy_clausification,[],[f2302]) ).
thf(f2302,plain,
( ! [X0: product_prod_a_a,X1: product_prod_a_a] :
( ( $true != vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0),vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))),vAPP(sTfun(product_prod_a_a,$o),a,sK47,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))) )
| ( $true = vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0),X1) ) )
| ~ spl54_89 ),
inference(primitive_instantiation,[],[f2289]) ).
thf(f18682,plain,
( spl54_452
| ~ spl54_14
| ~ spl54_370 ),
inference(avatar_split_clause,[],[f16948,f16940,f1811,f18679]) ).
thf(f16948,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8) )
| ~ spl54_14
| ~ spl54_370 ),
inference(superposition,[],[f1813,f16942]) ).
thf(f18677,plain,
( spl54_451
| ~ spl54_88 ),
inference(avatar_split_clause,[],[f2298,f2284,f18675]) ).
thf(f18675,plain,
( spl54_451
<=> ! [X0: product_prod_a_a,X1: product_prod_a_a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))),vAPP(sTfun(product_prod_a_a,$o),a,sK45,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))) != X0 )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_451])]) ).
thf(f2298,plain,
( ! [X0: product_prod_a_a,X1: product_prod_a_a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))),vAPP(sTfun(product_prod_a_a,$o),a,sK45,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))) != X0 )
| ( X0 = X1 ) )
| ~ spl54_88 ),
inference(equality_proxy_clausification,[],[f2297]) ).
thf(f2297,plain,
( ! [X0: product_prod_a_a,X1: product_prod_a_a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))),vAPP(sTfun(product_prod_a_a,$o),a,sK45,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))) != X0 )
| ( $true = vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0),X1) ) )
| ~ spl54_88 ),
inference(equality_proxy_clausification,[],[f2294]) ).
thf(f2294,plain,
( ! [X0: product_prod_a_a,X1: product_prod_a_a] :
( ( $true != vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0),vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0))),vAPP(sTfun(product_prod_a_a,$o),a,sK45,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0)))) )
| ( $true = vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),X0),X1) ) )
| ~ spl54_88 ),
inference(primitive_instantiation,[],[f2285]) ).
thf(f18628,plain,
( spl54_450
| ~ spl54_2
| ~ spl54_96 ),
inference(avatar_split_clause,[],[f2387,f2379,f1725,f18626]) ).
thf(f18626,plain,
( spl54_450
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,X0))) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $false = vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_450])]) ).
thf(f2379,plain,
( spl54_96
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_96])]) ).
thf(f2387,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,X0))) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl54_2
| ~ spl54_96 ),
inference(trivial_inequality_removal,[],[f2386]) ).
thf(f2386,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,X0))) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $false = vAPP(nat,$o,X0,X1) ) )
| ~ spl54_2
| ~ spl54_96 ),
inference(superposition,[],[f2380,f1726]) ).
thf(f2380,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true != vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,X0))) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) )
| ~ spl54_96 ),
inference(avatar_component_clause,[],[f2379]) ).
thf(f18589,plain,
( spl54_449
| ~ spl54_49
| ~ spl54_370
| ~ spl54_448 ),
inference(avatar_split_clause,[],[f18585,f18580,f16940,f2008,f18587]) ).
thf(f18585,plain,
( ! [X0: a] :
( ( sK8 != X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) = sK8 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_448 ),
inference(forward_demodulation,[],[f18584,f16942]) ).
thf(f18584,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) = sK8 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_448 ),
inference(forward_demodulation,[],[f18583,f2010]) ).
thf(f18583,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) = sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 ) )
| ~ spl54_370
| ~ spl54_448 ),
inference(forward_demodulation,[],[f18581,f16942]) ).
thf(f18582,plain,
spl54_448,
inference(avatar_split_clause,[],[f1694,f18580]) ).
thf(f1694,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != X0 ) ),
inference(equality_proxy_clausification,[],[f1693]) ).
thf(f1693,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ),
inference(equality_proxy_clausification,[],[f1689]) ).
thf(f1689,plain,
! [X0: a] :
( ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ),
inference(binary_proxy_clausification,[],[f1200]) ).
thf(f1200,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f747]) ).
thf(f747,plain,
! [X0: a] :
( ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f354]) ).
thf(f354,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ),
inference(fool_elimination,[],[f353]) ).
thf(f353,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
= ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ) ),
inference(rectify,[],[f238]) ).
thf(f238,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7) )
= ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add_Oinv__eq__1__iff) ).
thf(f18557,plain,
( spl54_447
| ~ spl54_49
| ~ spl54_370
| ~ spl54_446 ),
inference(avatar_split_clause,[],[f18553,f18548,f16940,f2008,f18555]) ).
thf(f18553,plain,
( ! [X0: a] :
( ( sK8 = X0 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) != sK8 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_446 ),
inference(forward_demodulation,[],[f18552,f16942]) ).
thf(f18552,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) != sK8 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) )
| ~ spl54_49
| ~ spl54_370
| ~ spl54_446 ),
inference(forward_demodulation,[],[f18551,f2010]) ).
thf(f18551,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) != sK8 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) )
| ~ spl54_370
| ~ spl54_446 ),
inference(forward_demodulation,[],[f18549,f16942]) ).
thf(f18550,plain,
spl54_446,
inference(avatar_split_clause,[],[f1692,f18548]) ).
thf(f1692,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ),
inference(equality_proxy_clausification,[],[f1691]) ).
thf(f1691,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ),
inference(equality_proxy_clausification,[],[f1690]) ).
thf(f1690,plain,
! [X0: a] :
( ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( $true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ),
inference(binary_proxy_clausification,[],[f1200]) ).
thf(f18543,plain,
( spl54_445
| ~ spl54_49
| ~ spl54_444 ),
inference(avatar_split_clause,[],[f18539,f18536,f2008,f18541]) ).
thf(f18541,plain,
( spl54_445
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_445])]) ).
thf(f18536,plain,
( spl54_444
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_444])]) ).
thf(f18539,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 ) )
| ~ spl54_49
| ~ spl54_444 ),
inference(forward_demodulation,[],[f18537,f2010]) ).
thf(f18537,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_444 ),
inference(avatar_component_clause,[],[f18536]) ).
thf(f18538,plain,
( spl54_444
| ~ spl54_2
| ~ spl54_95 ),
inference(avatar_split_clause,[],[f2373,f2366,f1725,f18536]) ).
thf(f2366,plain,
( spl54_95
<=> ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_95])]) ).
thf(f2373,plain,
( ! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_95 ),
inference(trivial_inequality_removal,[],[f2372]) ).
thf(f2372,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_95 ),
inference(superposition,[],[f2367,f1726]) ).
thf(f2367,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 ) )
| ~ spl54_95 ),
inference(avatar_component_clause,[],[f2366]) ).
thf(f18488,plain,
( spl54_443
| ~ spl54_17
| ~ spl54_284 ),
inference(avatar_split_clause,[],[f7135,f6197,f1824,f18486]) ).
thf(f7135,plain,
( ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_284 ),
inference(trivial_inequality_removal,[],[f7129]) ).
thf(f7129,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_284 ),
inference(superposition,[],[f6198,f1826]) ).
thf(f18482,plain,
( spl54_442
| ~ spl54_17
| ~ spl54_239 ),
inference(avatar_split_clause,[],[f6758,f5033,f1824,f18480]) ).
thf(f6758,plain,
( ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_239 ),
inference(trivial_inequality_removal,[],[f6752]) ).
thf(f6752,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_17
| ~ spl54_239 ),
inference(superposition,[],[f5034,f1826]) ).
thf(f18477,plain,
( spl54_441
| ~ spl54_18
| ~ spl54_150 ),
inference(avatar_split_clause,[],[f3588,f3460,f1829,f18475]) ).
thf(f18475,plain,
( spl54_441
<=> ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_441])]) ).
thf(f3588,plain,
( ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_18
| ~ spl54_150 ),
inference(trivial_inequality_removal,[],[f3581]) ).
thf(f3581,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_18
| ~ spl54_150 ),
inference(superposition,[],[f3461,f1831]) ).
thf(f18472,plain,
( spl54_440
| ~ spl54_18
| ~ spl54_149 ),
inference(avatar_split_clause,[],[f3579,f3454,f1829,f18470]) ).
thf(f18470,plain,
( spl54_440
<=> ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_440])]) ).
thf(f3579,plain,
( ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_18
| ~ spl54_149 ),
inference(trivial_inequality_removal,[],[f3572]) ).
thf(f3572,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_18
| ~ spl54_149 ),
inference(superposition,[],[f3455,f1831]) ).
thf(f18467,plain,
( spl54_439
| ~ spl54_40
| ~ spl54_86 ),
inference(avatar_split_clause,[],[f2272,f2246,f1937,f18465]) ).
thf(f18465,plain,
( spl54_439
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_439])]) ).
thf(f2272,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_40
| ~ spl54_86 ),
inference(superposition,[],[f1938,f2247]) ).
thf(f18462,plain,
( spl54_438
| ~ spl54_40
| ~ spl54_85 ),
inference(avatar_split_clause,[],[f2258,f2242,f1937,f18460]) ).
thf(f18460,plain,
( spl54_438
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_438])]) ).
thf(f2258,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) )
| ~ spl54_40
| ~ spl54_85 ),
inference(superposition,[],[f1938,f2243]) ).
thf(f18458,plain,
( spl54_437
| ~ spl54_40
| ~ spl54_84 ),
inference(avatar_split_clause,[],[f2251,f2238,f1937,f18456]) ).
thf(f18456,plain,
( spl54_437
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_437])]) ).
thf(f2251,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X0))),vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))) )
| ~ spl54_40
| ~ spl54_84 ),
inference(superposition,[],[f1938,f2239]) ).
thf(f18339,plain,
( spl54_436
| ~ spl54_49
| ~ spl54_424 ),
inference(avatar_split_clause,[],[f18270,f18266,f2008,f18337]) ).
thf(f18337,plain,
( spl54_436
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_436])]) ).
thf(f18266,plain,
( spl54_424
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_424])]) ).
thf(f18270,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_424 ),
inference(forward_demodulation,[],[f18269,f2010]) ).
thf(f18269,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_424 ),
inference(forward_demodulation,[],[f18267,f2010]) ).
thf(f18267,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_424 ),
inference(avatar_component_clause,[],[f18266]) ).
thf(f18335,plain,
( spl54_435
| ~ spl54_49
| ~ spl54_423 ),
inference(avatar_split_clause,[],[f18264,f18260,f2008,f18333]) ).
thf(f18333,plain,
( spl54_435
<=> ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_435])]) ).
thf(f18260,plain,
( spl54_423
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_423])]) ).
thf(f18264,plain,
( ! [X0: a] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_423 ),
inference(forward_demodulation,[],[f18263,f2010]) ).
thf(f18263,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_49
| ~ spl54_423 ),
inference(forward_demodulation,[],[f18261,f2010]) ).
thf(f18261,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_423 ),
inference(avatar_component_clause,[],[f18260]) ).
thf(f18331,plain,
( spl54_434
| ~ spl54_49
| ~ spl54_422 ),
inference(avatar_split_clause,[],[f18258,f18255,f2008,f18329]) ).
thf(f18329,plain,
( spl54_434
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_434])]) ).
thf(f18255,plain,
( spl54_422
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_422])]) ).
thf(f18258,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_422 ),
inference(forward_demodulation,[],[f18256,f2010]) ).
thf(f18256,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_422 ),
inference(avatar_component_clause,[],[f18255]) ).
thf(f18327,plain,
( spl54_433
| ~ spl54_49
| ~ spl54_421 ),
inference(avatar_split_clause,[],[f18253,f18250,f2008,f18325]) ).
thf(f18325,plain,
( spl54_433
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_433])]) ).
thf(f18250,plain,
( spl54_421
<=> ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_421])]) ).
thf(f18253,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_421 ),
inference(forward_demodulation,[],[f18251,f2010]) ).
thf(f18251,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_421 ),
inference(avatar_component_clause,[],[f18250]) ).
thf(f18322,plain,
( ~ spl54_33
| spl54_432
| ~ spl54_19
| ~ spl54_49
| ~ spl54_140 ),
inference(avatar_split_clause,[],[f3384,f3332,f2008,f1834,f18319,f1903]) ).
thf(f3384,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_49
| ~ spl54_140 ),
inference(forward_demodulation,[],[f3377,f2010]) ).
thf(f3377,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_140 ),
inference(trivial_inequality_removal,[],[f3374]) ).
thf(f3374,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_140 ),
inference(superposition,[],[f3333,f1836]) ).
thf(f18316,plain,
( ~ spl54_33
| spl54_431
| ~ spl54_18
| ~ spl54_49
| ~ spl54_140 ),
inference(avatar_split_clause,[],[f3381,f3332,f2008,f1829,f18313,f1903]) ).
thf(f18313,plain,
( spl54_431
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_431])]) ).
thf(f3381,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_49
| ~ spl54_140 ),
inference(forward_demodulation,[],[f3378,f2010]) ).
thf(f3378,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_140 ),
inference(trivial_inequality_removal,[],[f3373]) ).
thf(f3373,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_140 ),
inference(superposition,[],[f3333,f1831]) ).
thf(f18309,plain,
( ~ spl54_33
| spl54_430
| ~ spl54_18
| ~ spl54_140 ),
inference(avatar_split_clause,[],[f3378,f3332,f1829,f18306,f1903]) ).
thf(f18306,plain,
( spl54_430
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_430])]) ).
thf(f18302,plain,
( ~ spl54_429
| ~ spl54_49
| ~ spl54_370
| spl54_428 ),
inference(avatar_split_clause,[],[f18297,f18292,f16940,f2008,f18299]) ).
thf(f18297,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_370
| spl54_428 ),
inference(forward_demodulation,[],[f18296,f16942]) ).
thf(f18295,plain,
( ~ spl54_33
| spl54_428
| ~ spl54_19
| ~ spl54_140 ),
inference(avatar_split_clause,[],[f3377,f3332,f1834,f18292,f1903]) ).
thf(f18289,plain,
( ~ spl54_33
| spl54_427
| ~ spl54_19
| ~ spl54_49
| ~ spl54_139 ),
inference(avatar_split_clause,[],[f3369,f3328,f2008,f1834,f18286,f1903]) ).
thf(f3369,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_49
| ~ spl54_139 ),
inference(forward_demodulation,[],[f3362,f2010]) ).
thf(f3362,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_139 ),
inference(trivial_inequality_removal,[],[f3359]) ).
thf(f3359,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_139 ),
inference(superposition,[],[f3329,f1836]) ).
thf(f18284,plain,
( ~ spl54_33
| spl54_363
| ~ spl54_18
| ~ spl54_49
| ~ spl54_139 ),
inference(avatar_split_clause,[],[f3366,f3328,f2008,f1829,f14477,f1903]) ).
thf(f3366,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_49
| ~ spl54_139 ),
inference(forward_demodulation,[],[f3363,f2010]) ).
thf(f3363,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_139 ),
inference(trivial_inequality_removal,[],[f3358]) ).
thf(f3358,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_139 ),
inference(superposition,[],[f3329,f1831]) ).
thf(f18282,plain,
( ~ spl54_33
| spl54_426
| ~ spl54_18
| ~ spl54_139 ),
inference(avatar_split_clause,[],[f3363,f3328,f1829,f18279,f1903]) ).
thf(f18275,plain,
( ~ spl54_33
| spl54_425
| ~ spl54_19
| ~ spl54_139 ),
inference(avatar_split_clause,[],[f3362,f3328,f1834,f18272,f1903]) ).
thf(f18268,plain,
( spl54_424
| ~ spl54_2
| ~ spl54_94 ),
inference(avatar_split_clause,[],[f2361,f2333,f1725,f18266]) ).
thf(f2361,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_94 ),
inference(trivial_inequality_removal,[],[f2360]) ).
thf(f2360,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_94 ),
inference(superposition,[],[f2334,f1726]) ).
thf(f18262,plain,
( spl54_423
| ~ spl54_2
| ~ spl54_93 ),
inference(avatar_split_clause,[],[f2353,f2329,f1725,f18260]) ).
thf(f2353,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_93 ),
inference(trivial_inequality_removal,[],[f2352]) ).
thf(f2352,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $false ) )
| ~ spl54_2
| ~ spl54_93 ),
inference(superposition,[],[f2330,f1726]) ).
thf(f18257,plain,
( spl54_422
| ~ spl54_2
| ~ spl54_92 ),
inference(avatar_split_clause,[],[f2346,f2325,f1725,f18255]) ).
thf(f2346,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_92 ),
inference(trivial_inequality_removal,[],[f2345]) ).
thf(f2345,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_92 ),
inference(superposition,[],[f2326,f1726]) ).
thf(f18252,plain,
( spl54_421
| ~ spl54_2
| ~ spl54_91 ),
inference(avatar_split_clause,[],[f2340,f2321,f1725,f18250]) ).
thf(f2340,plain,
( ! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_91 ),
inference(trivial_inequality_removal,[],[f2339]) ).
thf(f2339,plain,
( ! [X0: a] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_91 ),
inference(superposition,[],[f2322,f1726]) ).
thf(f18234,plain,
( spl54_420
| ~ spl54_18
| ~ spl54_124 ),
inference(avatar_split_clause,[],[f3135,f3085,f1829,f18231]) ).
thf(f3135,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_124 ),
inference(trivial_inequality_removal,[],[f3128]) ).
thf(f3128,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_124 ),
inference(superposition,[],[f3086,f1831]) ).
thf(f18227,plain,
( spl54_419
| ~ spl54_19
| ~ spl54_124 ),
inference(avatar_split_clause,[],[f3134,f3085,f1834,f18224]) ).
thf(f3134,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_124 ),
inference(trivial_inequality_removal,[],[f3129]) ).
thf(f3129,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_124 ),
inference(superposition,[],[f3086,f1836]) ).
thf(f18219,plain,
( spl54_418
| ~ spl54_18
| ~ spl54_123 ),
inference(avatar_split_clause,[],[f3127,f3081,f1829,f18216]) ).
thf(f3127,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_123 ),
inference(trivial_inequality_removal,[],[f3120]) ).
thf(f3120,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_123 ),
inference(superposition,[],[f3082,f1831]) ).
thf(f18212,plain,
( spl54_417
| ~ spl54_19
| ~ spl54_123 ),
inference(avatar_split_clause,[],[f3126,f3081,f1834,f18209]) ).
thf(f18209,plain,
( spl54_417
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_417])]) ).
thf(f3126,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_19
| ~ spl54_123 ),
inference(trivial_inequality_removal,[],[f3121]) ).
thf(f3121,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_19
| ~ spl54_123 ),
inference(superposition,[],[f3082,f1836]) ).
thf(f18205,plain,
( spl54_416
| ~ spl54_17
| ~ spl54_120 ),
inference(avatar_split_clause,[],[f3099,f3069,f1824,f18202]) ).
thf(f3099,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_120 ),
inference(trivial_inequality_removal,[],[f3094]) ).
thf(f3094,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_120 ),
inference(superposition,[],[f3070,f1826]) ).
thf(f18198,plain,
( spl54_415
| ~ spl54_17
| ~ spl54_119 ),
inference(avatar_split_clause,[],[f3093,f3065,f1824,f18195]) ).
thf(f18195,plain,
( spl54_415
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_415])]) ).
thf(f3093,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_17
| ~ spl54_119 ),
inference(trivial_inequality_removal,[],[f3088]) ).
thf(f3088,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_17
| ~ spl54_119 ),
inference(superposition,[],[f3066,f1826]) ).
thf(f18193,plain,
( spl54_414
| ~ spl54_2
| ~ spl54_90 ),
inference(avatar_split_clause,[],[f2316,f2308,f1725,f18191]) ).
thf(f18191,plain,
( spl54_414
<=> ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK53,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_414])]) ).
thf(f2316,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK53,X0)) ) )
| ~ spl54_2
| ~ spl54_90 ),
inference(trivial_inequality_removal,[],[f2315]) ).
thf(f2315,plain,
( ! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true != $true )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,X1) )
| ( $false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK53,X0)) ) )
| ~ spl54_2
| ~ spl54_90 ),
inference(superposition,[],[f2309,f1726]) ).
thf(f18189,plain,
( spl54_413
| ~ spl54_319
| ~ spl54_370 ),
inference(avatar_split_clause,[],[f16959,f16940,f9979,f18186]) ).
thf(f9979,plain,
( spl54_319
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_319])]) ).
thf(f16959,plain,
( ( sK8 = vAPP(a,a,sK37,sK8) )
| ~ spl54_319
| ~ spl54_370 ),
inference(superposition,[],[f9981,f16942]) ).
thf(f9981,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_319 ),
inference(avatar_component_clause,[],[f9979]) ).
thf(f18130,plain,
( spl54_410
| spl54_412
| ~ spl54_19
| ~ spl54_118 ),
inference(avatar_split_clause,[],[f3063,f3046,f1834,f18127,f18115]) ).
thf(f3063,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_19
| ~ spl54_118 ),
inference(trivial_inequality_removal,[],[f3058]) ).
thf(f3058,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_19
| ~ spl54_118 ),
inference(superposition,[],[f3047,f1836]) ).
thf(f18122,plain,
( spl54_410
| spl54_411
| ~ spl54_18
| ~ spl54_117 ),
inference(avatar_split_clause,[],[f3056,f3042,f1829,f18119,f18115]) ).
thf(f3056,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_18
| ~ spl54_117 ),
inference(trivial_inequality_removal,[],[f3050]) ).
thf(f3050,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
| ~ spl54_18
| ~ spl54_117 ),
inference(superposition,[],[f3043,f1831]) ).
thf(f18113,plain,
( spl54_409
| ~ spl54_96 ),
inference(avatar_split_clause,[],[f2390,f2379,f18111]) ).
thf(f18111,plain,
( spl54_409
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_409])]) ).
thf(f2390,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = X0 ) )
| ~ spl54_96 ),
inference(equality_proxy_clausification,[],[f2389]) ).
thf(f2389,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) )
| ~ spl54_96 ),
inference(equality_proxy_clausification,[],[f2388]) ).
thf(f2388,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) )
| ~ spl54_96 ),
inference(equality_proxy_clausification,[],[f2385]) ).
thf(f2385,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) )
| ~ spl54_96 ),
inference(primitive_instantiation,[],[f2380]) ).
thf(f18109,plain,
( spl54_408
| ~ spl54_2
| ~ spl54_89 ),
inference(avatar_split_clause,[],[f2304,f2288,f1725,f18107]) ).
thf(f18107,plain,
( spl54_408
<=> ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $false = vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK47,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_408])]) ).
thf(f2304,plain,
( ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $false = vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK47,X0))) ) )
| ~ spl54_2
| ~ spl54_89 ),
inference(trivial_inequality_removal,[],[f2303]) ).
thf(f2303,plain,
( ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true != $true )
| ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $false = vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK47,X0))) ) )
| ~ spl54_2
| ~ spl54_89 ),
inference(superposition,[],[f2289,f1726]) ).
thf(f18105,plain,
( spl54_407
| ~ spl54_2
| ~ spl54_88 ),
inference(avatar_split_clause,[],[f2296,f2284,f1725,f18103]) ).
thf(f18103,plain,
( spl54_407
<=> ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $false = vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK45,X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_407])]) ).
thf(f2296,plain,
( ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $false = vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK45,X0))) ) )
| ~ spl54_2
| ~ spl54_88 ),
inference(trivial_inequality_removal,[],[f2295]) ).
thf(f2295,plain,
( ! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true != $true )
| ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $false = vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK45,X0))) ) )
| ~ spl54_2
| ~ spl54_88 ),
inference(superposition,[],[f2285,f1726]) ).
thf(f17912,plain,
( spl54_406
| ~ spl54_312
| ~ spl54_370 ),
inference(avatar_split_clause,[],[f16958,f16940,f9933,f17909]) ).
thf(f9933,plain,
( spl54_312
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_312])]) ).
thf(f16958,plain,
( ( sK8 = vAPP(a,a,sK36,sK8) )
| ~ spl54_312
| ~ spl54_370 ),
inference(superposition,[],[f9935,f16942]) ).
thf(f9935,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_312 ),
inference(avatar_component_clause,[],[f9933]) ).
thf(f17842,plain,
( spl54_405
| ~ spl54_32
| ~ spl54_49
| ~ spl54_149 ),
inference(avatar_split_clause,[],[f15925,f3454,f2008,f1899,f17840]) ).
thf(f17840,plain,
( spl54_405
<=> ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_405])]) ).
thf(f15925,plain,
( ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_149 ),
inference(forward_demodulation,[],[f14883,f2010]) ).
thf(f14883,plain,
( ! [X0: nat] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_32
| ~ spl54_149 ),
inference(trivial_inequality_removal,[],[f7731]) ).
thf(f7731,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_32
| ~ spl54_149 ),
inference(superposition,[],[f3455,f1901]) ).
thf(f17837,plain,
( spl54_404
| ~ spl54_32
| ~ spl54_49
| ~ spl54_150 ),
inference(avatar_split_clause,[],[f15924,f3460,f2008,f1899,f17835]) ).
thf(f17835,plain,
( spl54_404
<=> ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_404])]) ).
thf(f15924,plain,
( ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_150 ),
inference(forward_demodulation,[],[f14884,f2010]) ).
thf(f14884,plain,
( ! [X0: int] : ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_32
| ~ spl54_150 ),
inference(trivial_inequality_removal,[],[f7732]) ).
thf(f7732,plain,
( ! [X0: int] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ~ spl54_32
| ~ spl54_150 ),
inference(superposition,[],[f3461,f1901]) ).
thf(f17831,plain,
( spl54_403
| ~ spl54_5
| ~ spl54_32
| ~ spl54_161 ),
inference(avatar_split_clause,[],[f15596,f3650,f1899,f1766,f17828]) ).
thf(f17828,plain,
( spl54_403
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_403])]) ).
thf(f15596,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_161 ),
inference(trivial_inequality_removal,[],[f15595]) ).
thf(f15595,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_161 ),
inference(forward_demodulation,[],[f7548,f1768]) ).
thf(f7548,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_161 ),
inference(trivial_inequality_removal,[],[f5318]) ).
thf(f5318,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_161 ),
inference(superposition,[],[f3651,f1901]) ).
thf(f17824,plain,
( spl54_402
| ~ spl54_5
| ~ spl54_32
| ~ spl54_162 ),
inference(avatar_split_clause,[],[f15594,f3654,f1899,f1766,f17821]) ).
thf(f17821,plain,
( spl54_402
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_402])]) ).
thf(f15594,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_162 ),
inference(trivial_inequality_removal,[],[f15593]) ).
thf(f15593,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_162 ),
inference(forward_demodulation,[],[f7549,f1768]) ).
thf(f7549,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_162 ),
inference(trivial_inequality_removal,[],[f5319]) ).
thf(f5319,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_162 ),
inference(superposition,[],[f3655,f1901]) ).
thf(f17794,plain,
( spl54_401
| ~ spl54_370
| ~ spl54_399 ),
inference(avatar_split_clause,[],[f17784,f17780,f16940,f17791]) ).
thf(f17784,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) )
| ~ spl54_370
| ~ spl54_399 ),
inference(forward_demodulation,[],[f17782,f16942]) ).
thf(f17789,plain,
( spl54_400
| ~ spl54_311
| ~ spl54_368 ),
inference(avatar_split_clause,[],[f16906,f16886,f9806,f17786]) ).
thf(f16906,plain,
( ( sK8 = vAPP(a,a,sK33,sK8) )
| ~ spl54_311
| ~ spl54_368 ),
inference(superposition,[],[f9808,f16888]) ).
thf(f17783,plain,
( spl54_399
| ~ spl54_5
| ~ spl54_32
| ~ spl54_163 ),
inference(avatar_split_clause,[],[f15592,f3658,f1899,f1766,f17780]) ).
thf(f15592,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_163 ),
inference(trivial_inequality_removal,[],[f15591]) ).
thf(f15591,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_163 ),
inference(forward_demodulation,[],[f7550,f1768]) ).
thf(f7550,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_163 ),
inference(trivial_inequality_removal,[],[f5320]) ).
thf(f5320,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_163 ),
inference(superposition,[],[f3659,f1901]) ).
thf(f17776,plain,
( spl54_398
| ~ spl54_78
| ~ spl54_92 ),
inference(avatar_split_clause,[],[f2347,f2325,f2187,f17773]) ).
thf(f2347,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_78
| ~ spl54_92 ),
inference(trivial_inequality_removal,[],[f2344]) ).
thf(f2344,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_78
| ~ spl54_92 ),
inference(superposition,[],[f2326,f2189]) ).
thf(f17769,plain,
( spl54_397
| ~ spl54_78
| ~ spl54_91 ),
inference(avatar_split_clause,[],[f2341,f2321,f2187,f17766]) ).
thf(f2341,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_78
| ~ spl54_91 ),
inference(trivial_inequality_removal,[],[f2338]) ).
thf(f2338,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_78
| ~ spl54_91 ),
inference(superposition,[],[f2322,f2189]) ).
thf(f17764,plain,
( spl54_396
| ~ spl54_28
| ~ spl54_85 ),
inference(avatar_split_clause,[],[f2260,f2242,f1877,f17762]) ).
thf(f17762,plain,
( spl54_396
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,uminus_uminus_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_396])]) ).
thf(f2260,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,uminus_uminus_int,X0)) )
| ~ spl54_28
| ~ spl54_85 ),
inference(superposition,[],[f1878,f2243]) ).
thf(f17760,plain,
( spl54_395
| ~ spl54_29
| ~ spl54_85 ),
inference(avatar_split_clause,[],[f2259,f2242,f1881,f17758]) ).
thf(f17758,plain,
( spl54_395
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,uminus_uminus_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_395])]) ).
thf(f2259,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))),vAPP(int,int,uminus_uminus_int,X1)) )
| ~ spl54_29
| ~ spl54_85 ),
inference(superposition,[],[f1882,f2243]) ).
thf(f17756,plain,
( spl54_394
| ~ spl54_28
| ~ spl54_84 ),
inference(avatar_split_clause,[],[f2253,f2238,f1877,f17754]) ).
thf(f17754,plain,
( spl54_394
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,int,semiri2019852685at_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_394])]) ).
thf(f2253,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,int,semiri2019852685at_int,X0)) )
| ~ spl54_28
| ~ spl54_84 ),
inference(superposition,[],[f1878,f2239]) ).
thf(f17752,plain,
( spl54_393
| ~ spl54_29
| ~ spl54_84 ),
inference(avatar_split_clause,[],[f2252,f2238,f1881,f17750]) ).
thf(f17750,plain,
( spl54_393
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,int,semiri2019852685at_int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_393])]) ).
thf(f2252,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,int,semiri2019852685at_int,X1)) )
| ~ spl54_29
| ~ spl54_84 ),
inference(superposition,[],[f1882,f2239]) ).
thf(f17748,plain,
( spl54_392
| ~ spl54_26
| ~ spl54_83 ),
inference(avatar_split_clause,[],[f2250,f2234,f1869,f17746]) ).
thf(f17746,plain,
( spl54_392
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,semiri1382578993at_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,semiri1382578993at_nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_392])]) ).
thf(f2250,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,semiri1382578993at_nat,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,semiri1382578993at_nat,X1)) )
| ~ spl54_26
| ~ spl54_83 ),
inference(superposition,[],[f1870,f2235]) ).
thf(f17744,plain,
( spl54_391
| ~ spl54_27
| ~ spl54_83 ),
inference(avatar_split_clause,[],[f2249,f2234,f1873,f17742]) ).
thf(f17742,plain,
( spl54_391
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,semiri1382578993at_nat,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,semiri1382578993at_nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_391])]) ).
thf(f2249,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,semiri1382578993at_nat,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,semiri1382578993at_nat,X0)) )
| ~ spl54_27
| ~ spl54_83 ),
inference(superposition,[],[f1874,f2235]) ).
thf(f17739,plain,
( spl54_390
| ~ spl54_2
| ~ spl54_82 ),
inference(avatar_split_clause,[],[f2230,f2224,f1725,f17737]) ).
thf(f17737,plain,
( spl54_390
<=> ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_390])]) ).
thf(f2224,plain,
( spl54_82
<=> ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_82])]) ).
thf(f2230,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_82 ),
inference(trivial_inequality_removal,[],[f2229]) ).
thf(f2229,plain,
( ! [X0: a] :
( ( $true != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_2
| ~ spl54_82 ),
inference(superposition,[],[f2225,f1726]) ).
thf(f2225,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ~ spl54_82 ),
inference(avatar_component_clause,[],[f2224]) ).
thf(f17735,plain,
( spl54_389
| ~ spl54_300
| ~ spl54_368 ),
inference(avatar_split_clause,[],[f16905,f16886,f9761,f17732]) ).
thf(f16905,plain,
( ( sK8 = vAPP(a,a,sK32,sK8) )
| ~ spl54_300
| ~ spl54_368 ),
inference(superposition,[],[f9763,f16888]) ).
thf(f17682,plain,
( spl54_388
| ~ spl54_19
| ~ spl54_121 ),
inference(avatar_split_clause,[],[f3110,f3073,f1834,f17679]) ).
thf(f3110,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_121 ),
inference(trivial_inequality_removal,[],[f3105]) ).
thf(f3105,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_121 ),
inference(superposition,[],[f3074,f1836]) ).
thf(f17676,plain,
( spl54_387
| ~ spl54_18
| ~ spl54_99 ),
inference(avatar_split_clause,[],[f2432,f2402,f1829,f17673]) ).
thf(f2432,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_99 ),
inference(trivial_inequality_removal,[],[f2425]) ).
thf(f2425,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_99 ),
inference(superposition,[],[f2403,f1831]) ).
thf(f17670,plain,
( spl54_386
| ~ spl54_18
| ~ spl54_98 ),
inference(avatar_split_clause,[],[f2424,f2397,f1829,f17667]) ).
thf(f2424,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_98 ),
inference(trivial_inequality_removal,[],[f2417]) ).
thf(f2417,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_98 ),
inference(superposition,[],[f2398,f1831]) ).
thf(f17663,plain,
( spl54_385
| ~ spl54_19
| ~ spl54_98 ),
inference(avatar_split_clause,[],[f2423,f2397,f1834,f17660]) ).
thf(f17660,plain,
( spl54_385
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_385])]) ).
thf(f2423,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_19
| ~ spl54_98 ),
inference(trivial_inequality_removal,[],[f2418]) ).
thf(f2418,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_19
| ~ spl54_98 ),
inference(superposition,[],[f2398,f1836]) ).
thf(f17656,plain,
( spl54_384
| ~ spl54_18
| ~ spl54_97 ),
inference(avatar_split_clause,[],[f2416,f2393,f1829,f17653]) ).
thf(f2416,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_18
| ~ spl54_97 ),
inference(trivial_inequality_removal,[],[f2409]) ).
thf(f2409,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_18
| ~ spl54_97 ),
inference(superposition,[],[f2394,f1831]) ).
thf(f17650,plain,
( spl54_383
| ~ spl54_19
| ~ spl54_97 ),
inference(avatar_split_clause,[],[f2415,f2393,f1834,f17647]) ).
thf(f17647,plain,
( spl54_383
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_383])]) ).
thf(f2415,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_97 ),
inference(trivial_inequality_removal,[],[f2410]) ).
thf(f2410,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_97 ),
inference(superposition,[],[f2394,f1836]) ).
thf(f17645,plain,
( spl54_382
| ~ spl54_96 ),
inference(avatar_split_clause,[],[f2391,f2379,f17643]) ).
thf(f17643,plain,
( spl54_382
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_382])]) ).
thf(f2391,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = X0 )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl54_96 ),
inference(equality_proxy_clausification,[],[f2382]) ).
thf(f2382,plain,
( ! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)) )
| ( vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0 ) )
| ~ spl54_96 ),
inference(leibniz_equality_elimination,[],[f2380]) ).
thf(f17595,plain,
( ~ spl54_368
| ~ spl54_11
| ~ spl54_22
| ~ spl54_370 ),
inference(avatar_split_clause,[],[f16973,f16940,f1847,f1793,f16886]) ).
thf(f16973,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ~ spl54_11
| ~ spl54_22
| ~ spl54_370 ),
inference(trivial_inequality_removal,[],[f16972]) ).
thf(f16972,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK8 )
| ~ spl54_11
| ~ spl54_22
| ~ spl54_370 ),
inference(forward_demodulation,[],[f16966,f1849]) ).
thf(f1849,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ~ spl54_22 ),
inference(avatar_component_clause,[],[f1847]) ).
thf(f17594,plain,
( spl54_381
| ~ spl54_90 ),
inference(avatar_split_clause,[],[f2319,f2308,f17592]) ).
thf(f17592,plain,
( spl54_381
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = X0 )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_381])]) ).
thf(f2319,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = X0 )
| ( X0 != X1 ) )
| ~ spl54_90 ),
inference(equality_proxy_clausification,[],[f2318]) ).
thf(f2318,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl54_90 ),
inference(equality_proxy_clausification,[],[f2317]) ).
thf(f2317,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl54_90 ),
inference(equality_proxy_clausification,[],[f2314]) ).
thf(f2314,plain,
( ! [X2: nat,X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK53,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) )
| ~ spl54_90 ),
inference(primitive_instantiation,[],[f2309]) ).
thf(f17030,plain,
( spl54_380
| ~ spl54_5
| ~ spl54_18
| ~ spl54_142 ),
inference(avatar_split_clause,[],[f3494,f3342,f1829,f1766,f17027]) ).
thf(f17027,plain,
( spl54_380
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_380])]) ).
thf(f3494,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_5
| ~ spl54_18
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f3493]) ).
thf(f3493,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_5
| ~ spl54_18
| ~ spl54_142 ),
inference(forward_demodulation,[],[f3393,f1768]) ).
thf(f3393,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f3388]) ).
thf(f3388,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_142 ),
inference(superposition,[],[f3343,f1831]) ).
thf(f17023,plain,
( spl54_379
| ~ spl54_5
| ~ spl54_19
| ~ spl54_142 ),
inference(avatar_split_clause,[],[f3492,f3342,f1834,f1766,f17020]) ).
thf(f17020,plain,
( spl54_379
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_379])]) ).
thf(f3492,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_5
| ~ spl54_19
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f3491]) ).
thf(f3491,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_5
| ~ spl54_19
| ~ spl54_142 ),
inference(forward_demodulation,[],[f3392,f1768]) ).
thf(f3392,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f3389]) ).
thf(f3389,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_142 ),
inference(superposition,[],[f3343,f1836]) ).
thf(f17017,plain,
( spl54_378
| ~ spl54_5
| ~ spl54_19
| ~ spl54_49
| ~ spl54_142 ),
inference(avatar_split_clause,[],[f3401,f3342,f2008,f1834,f1766,f17014]) ).
thf(f17014,plain,
( spl54_378
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_378])]) ).
thf(f3401,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_19
| ~ spl54_49
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f3400]) ).
thf(f3400,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_19
| ~ spl54_49
| ~ spl54_142 ),
inference(forward_demodulation,[],[f3399,f1768]) ).
thf(f3399,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_49
| ~ spl54_142 ),
inference(forward_demodulation,[],[f3392,f2010]) ).
thf(f17011,plain,
( spl54_377
| ~ spl54_5
| ~ spl54_18
| ~ spl54_49
| ~ spl54_142 ),
inference(avatar_split_clause,[],[f3398,f3342,f2008,f1829,f1766,f17008]) ).
thf(f17008,plain,
( spl54_377
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_377])]) ).
thf(f3398,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_18
| ~ spl54_49
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f3397]) ).
thf(f3397,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_18
| ~ spl54_49
| ~ spl54_142 ),
inference(forward_demodulation,[],[f3396,f1768]) ).
thf(f3396,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_18
| ~ spl54_49
| ~ spl54_142 ),
inference(forward_demodulation,[],[f3393,f2010]) ).
thf(f17005,plain,
( spl54_376
| ~ spl54_4
| ~ spl54_32
| ~ spl54_154 ),
inference(avatar_split_clause,[],[f15602,f3599,f1899,f1761,f17002]) ).
thf(f15602,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_154 ),
inference(trivial_inequality_removal,[],[f15601]) ).
thf(f15601,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_154 ),
inference(forward_demodulation,[],[f7544,f1763]) ).
thf(f7544,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_154 ),
inference(trivial_inequality_removal,[],[f5314]) ).
thf(f5314,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_154 ),
inference(superposition,[],[f3600,f1901]) ).
thf(f16999,plain,
( spl54_375
| ~ spl54_4
| ~ spl54_32
| ~ spl54_155 ),
inference(avatar_split_clause,[],[f15600,f3603,f1899,f1761,f16996]) ).
thf(f16996,plain,
( spl54_375
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_375])]) ).
thf(f15600,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_155 ),
inference(trivial_inequality_removal,[],[f15599]) ).
thf(f15599,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_155 ),
inference(forward_demodulation,[],[f7545,f1763]) ).
thf(f7545,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_155 ),
inference(trivial_inequality_removal,[],[f5315]) ).
thf(f5315,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_155 ),
inference(superposition,[],[f3604,f1901]) ).
thf(f16992,plain,
( spl54_374
| ~ spl54_32
| ~ spl54_124 ),
inference(avatar_split_clause,[],[f14880,f3085,f1899,f16989]) ).
thf(f16989,plain,
( spl54_374
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,sK8)),sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_374])]) ).
thf(f14880,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,sK8)),sK8) )
| ~ spl54_32
| ~ spl54_124 ),
inference(trivial_inequality_removal,[],[f7728]) ).
thf(f7728,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,sK8)),sK8) )
| ~ spl54_32
| ~ spl54_124 ),
inference(superposition,[],[f3086,f1901]) ).
thf(f16985,plain,
( spl54_373
| ~ spl54_32
| ~ spl54_123 ),
inference(avatar_split_clause,[],[f14879,f3081,f1899,f16982]) ).
thf(f14879,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK36,sK8)) )
| ~ spl54_32
| ~ spl54_123 ),
inference(trivial_inequality_removal,[],[f7727]) ).
thf(f7727,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(a,a,sK36,sK8)) )
| ~ spl54_32
| ~ spl54_123 ),
inference(superposition,[],[f3082,f1901]) ).
thf(f16980,plain,
( ~ spl54_372
| spl54_20
| ~ spl54_368 ),
inference(avatar_split_clause,[],[f16896,f16886,f1839,f16977]) ).
thf(f1839,plain,
( spl54_20
<=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_20])]) ).
thf(f16896,plain,
( ( sK7 != sK8 )
| spl54_20
| ~ spl54_368 ),
inference(superposition,[],[f1840,f16888]) ).
thf(f1840,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != sK7 )
| spl54_20 ),
inference(avatar_component_clause,[],[f1839]) ).
thf(f16947,plain,
( spl54_370
| spl54_371
| ~ spl54_32
| ~ spl54_49
| ~ spl54_117 ),
inference(avatar_split_clause,[],[f15928,f3042,f2008,f1899,f16944,f16940]) ).
thf(f15928,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_117 ),
inference(forward_demodulation,[],[f14875,f2010]) ).
thf(f14875,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_32
| ~ spl54_117 ),
inference(trivial_inequality_removal,[],[f7723]) ).
thf(f7723,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK8 )
| ~ spl54_32
| ~ spl54_117 ),
inference(superposition,[],[f3043,f1901]) ).
thf(f16893,plain,
( spl54_368
| spl54_369
| ~ spl54_32
| ~ spl54_49
| ~ spl54_118 ),
inference(avatar_split_clause,[],[f15926,f3046,f2008,f1899,f16890,f16886]) ).
thf(f15926,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_118 ),
inference(forward_demodulation,[],[f14876,f2010]) ).
thf(f14876,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_32
| ~ spl54_118 ),
inference(trivial_inequality_removal,[],[f7724]) ).
thf(f7724,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK8 )
| ~ spl54_32
| ~ spl54_118 ),
inference(superposition,[],[f3047,f1901]) ).
thf(f16832,plain,
( spl54_367
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_142 ),
inference(avatar_split_clause,[],[f15608,f3342,f2008,f1899,f1766,f16829]) ).
thf(f16829,plain,
( spl54_367
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_367])]) ).
thf(f15608,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f15607]) ).
thf(f15607,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_142 ),
inference(forward_demodulation,[],[f15606,f1768]) ).
thf(f15606,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_142 ),
inference(forward_demodulation,[],[f7542,f2010]) ).
thf(f7542,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_142 ),
inference(trivial_inequality_removal,[],[f5312]) ).
thf(f5312,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,sK8),r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_142 ),
inference(superposition,[],[f3343,f1901]) ).
thf(f16824,plain,
( spl54_366
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_143 ),
inference(avatar_split_clause,[],[f15605,f3346,f2008,f1899,f1766,f16821]) ).
thf(f15605,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_143 ),
inference(trivial_inequality_removal,[],[f15604]) ).
thf(f15604,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_49
| ~ spl54_143 ),
inference(forward_demodulation,[],[f15603,f1768]) ).
thf(f15603,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_143 ),
inference(forward_demodulation,[],[f7543,f2010]) ).
thf(f7543,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_143 ),
inference(trivial_inequality_removal,[],[f5313]) ).
thf(f5313,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_143 ),
inference(superposition,[],[f3347,f1901]) ).
thf(f16784,plain,
( spl54_365
| ~ spl54_4
| ~ spl54_32
| ~ spl54_132 ),
inference(avatar_split_clause,[],[f15616,f3235,f1899,f1761,f16781]) ).
thf(f15616,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_132 ),
inference(trivial_inequality_removal,[],[f15615]) ).
thf(f15615,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ~ spl54_4
| ~ spl54_32
| ~ spl54_132 ),
inference(forward_demodulation,[],[f7538,f1763]) ).
thf(f7538,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_132 ),
inference(trivial_inequality_removal,[],[f5308]) ).
thf(f5308,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_132 ),
inference(superposition,[],[f3236,f1901]) ).
thf(f16779,plain,
( spl54_364
| ~ spl54_5
| ~ spl54_32
| ~ spl54_133 ),
inference(avatar_split_clause,[],[f15614,f3239,f1899,f1766,f16776]) ).
thf(f15614,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_133 ),
inference(trivial_inequality_removal,[],[f15613]) ).
thf(f15613,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_133 ),
inference(forward_demodulation,[],[f7539,f1768]) ).
thf(f7539,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_133 ),
inference(trivial_inequality_removal,[],[f5309]) ).
thf(f5309,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),sK8) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_133 ),
inference(superposition,[],[f3240,f1901]) ).
thf(f16753,plain,
( spl54_141
| ~ spl54_32
| ~ spl54_49 ),
inference(avatar_split_clause,[],[f16746,f2008,f1899,f3336]) ).
thf(f16746,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_49 ),
inference(forward_demodulation,[],[f1901,f2010]) ).
thf(f16749,plain,
( ~ spl54_32
| ~ spl54_49
| ~ spl54_165 ),
inference(avatar_contradiction_clause,[],[f16748]) ).
thf(f16748,plain,
( $false
| ~ spl54_32
| ~ spl54_49
| ~ spl54_165 ),
inference(trivial_inequality_removal,[],[f16747]) ).
thf(f16747,plain,
( ( $true = $false )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_165 ),
inference(forward_demodulation,[],[f16746,f3730]) ).
thf(f3730,plain,
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_165 ),
inference(avatar_component_clause,[],[f3728]) ).
thf(f16722,plain,
( ~ spl54_32
| ~ spl54_49
| ~ spl54_165 ),
inference(avatar_contradiction_clause,[],[f16721]) ).
thf(f16721,plain,
( $false
| ~ spl54_32
| ~ spl54_49
| ~ spl54_165 ),
inference(trivial_inequality_removal,[],[f16720]) ).
thf(f16720,plain,
( ( $true = $false )
| ~ spl54_32
| ~ spl54_49
| ~ spl54_165 ),
inference(forward_demodulation,[],[f3277,f3730]) ).
thf(f3277,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_49 ),
inference(superposition,[],[f1901,f2010]) ).
thf(f15579,plain,
( ~ spl54_141
| ~ spl54_165 ),
inference(avatar_contradiction_clause,[],[f15578]) ).
thf(f15578,plain,
( $false
| ~ spl54_141
| ~ spl54_165 ),
inference(trivial_inequality_removal,[],[f15577]) ).
thf(f15577,plain,
( ( $true = $false )
| ~ spl54_141
| ~ spl54_165 ),
inference(forward_demodulation,[],[f3338,f3730]) ).
thf(f15574,plain,
( ~ spl54_49
| ~ spl54_82
| ~ spl54_141
| ~ spl54_165 ),
inference(avatar_contradiction_clause,[],[f15573]) ).
thf(f15573,plain,
( $false
| ~ spl54_49
| ~ spl54_82
| ~ spl54_141
| ~ spl54_165 ),
inference(trivial_inequality_removal,[],[f15572]) ).
thf(f15572,plain,
( ( $true = $false )
| ~ spl54_49
| ~ spl54_82
| ~ spl54_141
| ~ spl54_165 ),
inference(forward_demodulation,[],[f15571,f3730]) ).
thf(f15571,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_82
| ~ spl54_141 ),
inference(forward_demodulation,[],[f14971,f2010]) ).
thf(f14971,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_82
| ~ spl54_141 ),
inference(trivial_inequality_removal,[],[f3766]) ).
thf(f3766,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_82
| ~ spl54_141 ),
inference(superposition,[],[f2225,f3338]) ).
thf(f15570,plain,
( ~ spl54_49
| ~ spl54_82
| ~ spl54_141
| ~ spl54_165 ),
inference(avatar_contradiction_clause,[],[f15569]) ).
thf(f15569,plain,
( $false
| ~ spl54_49
| ~ spl54_82
| ~ spl54_141
| ~ spl54_165 ),
inference(trivial_inequality_removal,[],[f15568]) ).
thf(f15568,plain,
( ( $true = $false )
| ~ spl54_49
| ~ spl54_82
| ~ spl54_141
| ~ spl54_165 ),
inference(forward_demodulation,[],[f15567,f3730]) ).
thf(f15567,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_82
| ~ spl54_141 ),
inference(forward_demodulation,[],[f3767,f2010]) ).
thf(f3767,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_82
| ~ spl54_141 ),
inference(trivial_inequality_removal,[],[f3766]) ).
thf(f14480,plain,
( spl54_363
| ~ spl54_18
| ~ spl54_33
| ~ spl54_49
| ~ spl54_139 ),
inference(avatar_split_clause,[],[f3368,f3328,f2008,f1903,f1829,f14477]) ).
thf(f3368,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_33
| ~ spl54_49
| ~ spl54_139 ),
inference(trivial_inequality_removal,[],[f3367]) ).
thf(f3367,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_18
| ~ spl54_33
| ~ spl54_49
| ~ spl54_139 ),
inference(forward_demodulation,[],[f3366,f1905]) ).
thf(f14475,plain,
( spl54_362
| ~ spl54_18
| ~ spl54_95 ),
inference(avatar_split_clause,[],[f2376,f2366,f1829,f14472]) ).
thf(f2376,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_95 ),
inference(trivial_inequality_removal,[],[f2369]) ).
thf(f2369,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_18
| ~ spl54_95 ),
inference(superposition,[],[f2367,f1831]) ).
thf(f14470,plain,
( spl54_361
| ~ spl54_85
| ~ spl54_86 ),
inference(avatar_split_clause,[],[f2268,f2246,f2242,f14468]) ).
thf(f14468,plain,
( spl54_361
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_361])]) ).
thf(f2268,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ~ spl54_85
| ~ spl54_86 ),
inference(superposition,[],[f2247,f2243]) ).
thf(f14463,plain,
( spl54_360
| ~ spl54_78
| ~ spl54_82 ),
inference(avatar_split_clause,[],[f2231,f2224,f2187,f14460]) ).
thf(f14460,plain,
( spl54_360
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_360])]) ).
thf(f2231,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_78
| ~ spl54_82 ),
inference(trivial_inequality_removal,[],[f2228]) ).
thf(f2228,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_78
| ~ spl54_82 ),
inference(superposition,[],[f2225,f2189]) ).
thf(f14458,plain,
( spl54_359
| ~ spl54_36
| ~ spl54_37
| ~ spl54_79 ),
inference(avatar_split_clause,[],[f2212,f2200,f1922,f1918,f14456]) ).
thf(f14456,plain,
( spl54_359
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_359])]) ).
thf(f2212,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_79 ),
inference(forward_demodulation,[],[f2205,f1919]) ).
thf(f2205,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,uminus_uminus_int,X0)) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_37
| ~ spl54_79 ),
inference(superposition,[],[f1923,f2201]) ).
thf(f14453,plain,
( spl54_358
| ~ spl54_36
| ~ spl54_39
| ~ spl54_79 ),
inference(avatar_split_clause,[],[f2211,f2200,f1933,f1918,f14451]) ).
thf(f14451,plain,
( spl54_358
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,uminus_uminus_int,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_358])]) ).
thf(f2211,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_36
| ~ spl54_39
| ~ spl54_79 ),
inference(forward_demodulation,[],[f2204,f1934]) ).
thf(f2204,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,uminus_uminus_int,X1))) )
| ~ spl54_36
| ~ spl54_79 ),
inference(superposition,[],[f2201,f1919]) ).
thf(f14449,plain,
( spl54_357
| ~ spl54_30
| ~ spl54_79 ),
inference(avatar_split_clause,[],[f2207,f2200,f1885,f14447]) ).
thf(f14447,plain,
( spl54_357
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_357])]) ).
thf(f2207,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))),X1) )
| ~ spl54_30
| ~ spl54_79 ),
inference(superposition,[],[f1886,f2201]) ).
thf(f14445,plain,
( spl54_356
| ~ spl54_31
| ~ spl54_79 ),
inference(avatar_split_clause,[],[f2206,f2200,f1889,f14443]) ).
thf(f14443,plain,
( spl54_356
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_356])]) ).
thf(f2206,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1))) )
| ~ spl54_31
| ~ spl54_79 ),
inference(superposition,[],[f1890,f2201]) ).
thf(f14441,plain,
( spl54_355
| ~ spl54_26
| ~ spl54_75 ),
inference(avatar_split_clause,[],[f2195,f2174,f1869,f14439]) ).
thf(f14439,plain,
( spl54_355
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,suc,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_355])]) ).
thf(f2195,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,suc,X1)) = X0 )
| ~ spl54_26
| ~ spl54_75 ),
inference(superposition,[],[f1870,f2175]) ).
thf(f14437,plain,
( spl54_354
| ~ spl54_27
| ~ spl54_75 ),
inference(avatar_split_clause,[],[f2194,f2174,f1873,f14435]) ).
thf(f14435,plain,
( spl54_354
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_354])]) ).
thf(f2194,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X0) )
| ~ spl54_27
| ~ spl54_75 ),
inference(superposition,[],[f1874,f2175]) ).
thf(f14433,plain,
( spl54_353
| ~ spl54_26
| ~ spl54_74 ),
inference(avatar_split_clause,[],[f2192,f2170,f1869,f14431]) ).
thf(f14431,plain,
( spl54_353
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_353])]) ).
thf(f2192,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),X1) )
| ~ spl54_26
| ~ spl54_74 ),
inference(superposition,[],[f1870,f2171]) ).
thf(f14429,plain,
( spl54_352
| ~ spl54_27
| ~ spl54_74 ),
inference(avatar_split_clause,[],[f2191,f2170,f1873,f14427]) ).
thf(f14427,plain,
( spl54_352
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,suc,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_352])]) ).
thf(f2191,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1))),vAPP(nat,nat,suc,X0)) = X1 )
| ~ spl54_27
| ~ spl54_74 ),
inference(superposition,[],[f1874,f2171]) ).
thf(f14425,plain,
( spl54_351
| ~ spl54_40 ),
inference(avatar_split_clause,[],[f1979,f1937,f14423]) ).
thf(f14423,plain,
( spl54_351
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_351])]) ).
thf(f1979,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),X1) )
| ~ spl54_40 ),
inference(superposition,[],[f1938,f1938]) ).
thf(f14420,plain,
( spl54_350
| ~ spl54_49
| ~ spl54_238 ),
inference(avatar_split_clause,[],[f7183,f5004,f2008,f14417]) ).
thf(f14417,plain,
( spl54_350
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_350])]) ).
thf(f7183,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_238 ),
inference(superposition,[],[f5006,f2010]) ).
thf(f14414,plain,
( spl54_349
| ~ spl54_39
| ~ spl54_40 ),
inference(avatar_split_clause,[],[f1978,f1937,f1933,f14412]) ).
thf(f14412,plain,
( spl54_349
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_349])]) ).
thf(f1978,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X0))),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) = X1 )
| ~ spl54_39
| ~ spl54_40 ),
inference(superposition,[],[f1938,f1934]) ).
thf(f14410,plain,
( spl54_348
| ~ spl54_36
| ~ spl54_37 ),
inference(avatar_split_clause,[],[f1965,f1922,f1918,f14408]) ).
thf(f14408,plain,
( spl54_348
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_348])]) ).
thf(f14366,plain,
spl54_347,
inference(avatar_split_clause,[],[f1499,f14364]) ).
thf(f14364,plain,
( spl54_347
<=> ! [X0: a,X3: a,X2: a,X1: a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1) = vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3) )
| ( X1 != X3 )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_347])]) ).
thf(f1499,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1) = vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3) )
| ( X1 != X3 )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f1498]) ).
thf(f1498,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1) = vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3) )
| ( X1 != X3 )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f1497]) ).
thf(f1497,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1) = vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X3) )
| ( $false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1496]) ).
thf(f1496,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1) = vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2)),vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X3)) ) ),
inference(equality_proxy_clausification,[],[f1489]) ).
thf(f1489,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( $true = vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) )
| ( $false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2)),vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X3)) ) ),
inference(binary_proxy_clausification,[],[f1398]) ).
thf(f1398,plain,
! [X2: a,X3: a,X0: a,X1: a] : ( vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2)),vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X3)) ),
inference(cnf_transformation,[],[f596]) ).
thf(f596,plain,
! [X0: a,X1: a,X2: a,X3: a] : ( vAPP(product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(product_prod_a_a,$o),vEQ(product_prod_a_a),vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X0),X2)),vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X3)) ),
inference(fool_elimination,[],[f595]) ).
thf(f595,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1) = vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3) )
= ( X1 = X3 ) )
& ( X0 = X2 ) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X0: a,X1: a,X14: a,X15: a] :
( ( ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1) = vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X14),X15) )
= ( X1 = X15 ) )
& ( X0 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_old_Oprod_Oinject) ).
thf(f14362,plain,
spl54_346,
inference(avatar_split_clause,[],[f1477,f14360]) ).
thf(f14360,plain,
( spl54_346
<=> ! [X0: int,X3: int,X2: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) )
| ( X2 != X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_346])]) ).
thf(f1477,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) )
| ( X2 != X3 ) ),
inference(equality_proxy_clausification,[],[f1476]) ).
thf(f1476,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( X0 = X1 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X2),X3) ) ),
inference(equality_proxy_clausification,[],[f1472]) ).
thf(f1472,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X2),X3) ) ),
inference(binary_proxy_clausification,[],[f1406]) ).
thf(f1406,plain,
! [X2: int,X3: int,X0: int,X1: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X2),X3) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) ) ),
inference(cnf_transformation,[],[f973]) ).
thf(f973,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X2),X3) )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) ) ),
inference(ennf_transformation,[],[f600]) ).
thf(f600,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) )
=> ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X2),X3) ) ),
inference(fool_elimination,[],[f599]) ).
thf(f599,plain,
! [X0: int,X1: int,X2: int,X3: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X3) )
=> ( ( X0 = X1 )
= ( X2 = X3 ) ) ),
inference(rectify,[],[f174]) ).
thf(f174,axiom,
! [X0: int,X1: int,X2: int,X19: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X19) )
=> ( ( X0 = X1 )
= ( X2 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_diff__eq__diff__eq) ).
thf(f13397,plain,
( spl54_345
| ~ spl54_49
| ~ spl54_208 ),
inference(avatar_split_clause,[],[f7171,f4264,f2008,f13394]) ).
thf(f13394,plain,
( spl54_345
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_345])]) ).
thf(f7171,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,sK8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_49
| ~ spl54_208 ),
inference(superposition,[],[f4266,f2010]) ).
thf(f10512,plain,
( spl54_344
| ~ spl54_2
| ~ spl54_66 ),
inference(avatar_split_clause,[],[f2141,f2082,f1725,f10510]) ).
thf(f10510,plain,
( spl54_344
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_344])]) ).
thf(f2082,plain,
( spl54_66
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_66])]) ).
thf(f2141,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_66 ),
inference(trivial_inequality_removal,[],[f2140]) ).
thf(f2140,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_66 ),
inference(superposition,[],[f2083,f1726]) ).
thf(f2083,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_66 ),
inference(avatar_component_clause,[],[f2082]) ).
thf(f10508,plain,
( spl54_343
| ~ spl54_2
| ~ spl54_65 ),
inference(avatar_split_clause,[],[f2137,f2078,f1725,f10506]) ).
thf(f10506,plain,
( spl54_343
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_343])]) ).
thf(f2078,plain,
( spl54_65
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_65])]) ).
thf(f2137,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_65 ),
inference(trivial_inequality_removal,[],[f2136]) ).
thf(f2136,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_65 ),
inference(superposition,[],[f2079,f1726]) ).
thf(f2079,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_65 ),
inference(avatar_component_clause,[],[f2078]) ).
thf(f10503,plain,
( spl54_342
| ~ spl54_2
| ~ spl54_64 ),
inference(avatar_split_clause,[],[f2133,f2074,f1725,f10501]) ).
thf(f10501,plain,
( spl54_342
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_342])]) ).
thf(f2074,plain,
( spl54_64
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_64])]) ).
thf(f2133,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_64 ),
inference(trivial_inequality_removal,[],[f2132]) ).
thf(f2132,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_64 ),
inference(superposition,[],[f2075,f1726]) ).
thf(f2075,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_64 ),
inference(avatar_component_clause,[],[f2074]) ).
thf(f10499,plain,
( spl54_341
| ~ spl54_2
| ~ spl54_63 ),
inference(avatar_split_clause,[],[f2130,f2070,f1725,f10497]) ).
thf(f10497,plain,
( spl54_341
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_341])]) ).
thf(f2070,plain,
( spl54_63
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_63])]) ).
thf(f2130,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_63 ),
inference(trivial_inequality_removal,[],[f2129]) ).
thf(f2129,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_63 ),
inference(superposition,[],[f2071,f1726]) ).
thf(f2071,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_63 ),
inference(avatar_component_clause,[],[f2070]) ).
thf(f10495,plain,
( spl54_340
| ~ spl54_2
| ~ spl54_62 ),
inference(avatar_split_clause,[],[f2125,f2066,f1725,f10493]) ).
thf(f10493,plain,
( spl54_340
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_340])]) ).
thf(f2066,plain,
( spl54_62
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_62])]) ).
thf(f2125,plain,
( ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) )
| ~ spl54_2
| ~ spl54_62 ),
inference(trivial_inequality_removal,[],[f2124]) ).
thf(f2124,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) )
| ~ spl54_2
| ~ spl54_62 ),
inference(superposition,[],[f2067,f1726]) ).
thf(f2067,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_62 ),
inference(avatar_component_clause,[],[f2066]) ).
thf(f10491,plain,
( spl54_339
| ~ spl54_2
| ~ spl54_61 ),
inference(avatar_split_clause,[],[f2122,f2062,f1725,f10489]) ).
thf(f10489,plain,
( spl54_339
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK29,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_339])]) ).
thf(f2062,plain,
( spl54_61
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK29,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_61])]) ).
thf(f2122,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK29,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) )
| ~ spl54_2
| ~ spl54_61 ),
inference(trivial_inequality_removal,[],[f2121]) ).
thf(f2121,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK29,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) )
| ~ spl54_2
| ~ spl54_61 ),
inference(superposition,[],[f2063,f1726]) ).
thf(f2063,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK29,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_61 ),
inference(avatar_component_clause,[],[f2062]) ).
thf(f10487,plain,
( spl54_338
| ~ spl54_2
| ~ spl54_60 ),
inference(avatar_split_clause,[],[f2120,f2058,f1725,f10485]) ).
thf(f10485,plain,
( spl54_338
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_338])]) ).
thf(f2058,plain,
( spl54_60
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_60])]) ).
thf(f2120,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) )
| ~ spl54_2
| ~ spl54_60 ),
inference(trivial_inequality_removal,[],[f2119]) ).
thf(f2119,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) )
| ~ spl54_2
| ~ spl54_60 ),
inference(superposition,[],[f2059,f1726]) ).
thf(f2059,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_60 ),
inference(avatar_component_clause,[],[f2058]) ).
thf(f10483,plain,
( spl54_337
| ~ spl54_2
| ~ spl54_59 ),
inference(avatar_split_clause,[],[f2118,f2051,f1725,f10481]) ).
thf(f10481,plain,
( spl54_337
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_337])]) ).
thf(f2051,plain,
( spl54_59
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_59])]) ).
thf(f2118,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) )
| ~ spl54_2
| ~ spl54_59 ),
inference(trivial_inequality_removal,[],[f2117]) ).
thf(f2117,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) )
| ~ spl54_2
| ~ spl54_59 ),
inference(superposition,[],[f2052,f1726]) ).
thf(f2052,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_59 ),
inference(avatar_component_clause,[],[f2051]) ).
thf(f10479,plain,
( spl54_336
| ~ spl54_2
| ~ spl54_58 ),
inference(avatar_split_clause,[],[f2116,f2047,f1725,f10477]) ).
thf(f10477,plain,
( spl54_336
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK26,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_336])]) ).
thf(f2047,plain,
( spl54_58
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK26,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_58])]) ).
thf(f2116,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK26,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) )
| ~ spl54_2
| ~ spl54_58 ),
inference(trivial_inequality_removal,[],[f2115]) ).
thf(f2115,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK26,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) )
| ~ spl54_2
| ~ spl54_58 ),
inference(superposition,[],[f2048,f1726]) ).
thf(f2048,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK26,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_58 ),
inference(avatar_component_clause,[],[f2047]) ).
thf(f10475,plain,
( spl54_335
| ~ spl54_2
| ~ spl54_57 ),
inference(avatar_split_clause,[],[f2110,f2043,f1725,f10473]) ).
thf(f10473,plain,
( spl54_335
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_335])]) ).
thf(f2043,plain,
( spl54_57
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_57])]) ).
thf(f2110,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) )
| ~ spl54_2
| ~ spl54_57 ),
inference(trivial_inequality_removal,[],[f2109]) ).
thf(f2109,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) )
| ~ spl54_2
| ~ spl54_57 ),
inference(superposition,[],[f2044,f1726]) ).
thf(f2044,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_57 ),
inference(avatar_component_clause,[],[f2043]) ).
thf(f10471,plain,
( spl54_334
| ~ spl54_2
| ~ spl54_56 ),
inference(avatar_split_clause,[],[f2108,f2039,f1725,f10469]) ).
thf(f10469,plain,
( spl54_334
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK22,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_334])]) ).
thf(f2039,plain,
( spl54_56
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK22,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_56])]) ).
thf(f2108,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK22,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) )
| ~ spl54_2
| ~ spl54_56 ),
inference(trivial_inequality_removal,[],[f2107]) ).
thf(f2107,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK22,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) )
| ~ spl54_2
| ~ spl54_56 ),
inference(superposition,[],[f2040,f1726]) ).
thf(f2040,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK22,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_56 ),
inference(avatar_component_clause,[],[f2039]) ).
thf(f10467,plain,
( spl54_333
| ~ spl54_2
| ~ spl54_55 ),
inference(avatar_split_clause,[],[f2106,f2035,f1725,f10465]) ).
thf(f10465,plain,
( spl54_333
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_333])]) ).
thf(f2035,plain,
( spl54_55
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_55])]) ).
thf(f2106,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) )
| ~ spl54_2
| ~ spl54_55 ),
inference(trivial_inequality_removal,[],[f2105]) ).
thf(f2105,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) )
| ~ spl54_2
| ~ spl54_55 ),
inference(superposition,[],[f2036,f1726]) ).
thf(f2036,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_55 ),
inference(avatar_component_clause,[],[f2035]) ).
thf(f10462,plain,
( spl54_332
| ~ spl54_2
| ~ spl54_54 ),
inference(avatar_split_clause,[],[f2104,f2031,f1725,f10460]) ).
thf(f10460,plain,
( spl54_332
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_332])]) ).
thf(f2031,plain,
( spl54_54
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_54])]) ).
thf(f2104,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) )
| ~ spl54_2
| ~ spl54_54 ),
inference(trivial_inequality_removal,[],[f2103]) ).
thf(f2103,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) )
| ~ spl54_2
| ~ spl54_54 ),
inference(superposition,[],[f2032,f1726]) ).
thf(f2032,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_54 ),
inference(avatar_component_clause,[],[f2031]) ).
thf(f10458,plain,
( spl54_331
| ~ spl54_2
| ~ spl54_53 ),
inference(avatar_split_clause,[],[f2102,f2027,f1725,f10456]) ).
thf(f10456,plain,
( spl54_331
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK19,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_331])]) ).
thf(f2027,plain,
( spl54_53
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK19,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_53])]) ).
thf(f2102,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK19,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) )
| ~ spl54_2
| ~ spl54_53 ),
inference(trivial_inequality_removal,[],[f2101]) ).
thf(f2101,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK19,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) )
| ~ spl54_2
| ~ spl54_53 ),
inference(superposition,[],[f2028,f1726]) ).
thf(f2028,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK19,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_53 ),
inference(avatar_component_clause,[],[f2027]) ).
thf(f10454,plain,
( spl54_330
| ~ spl54_2
| ~ spl54_52 ),
inference(avatar_split_clause,[],[f2100,f2023,f1725,f10452]) ).
thf(f10452,plain,
( spl54_330
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_330])]) ).
thf(f2023,plain,
( spl54_52
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_52])]) ).
thf(f2100,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) )
| ~ spl54_2
| ~ spl54_52 ),
inference(trivial_inequality_removal,[],[f2099]) ).
thf(f2099,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) )
| ~ spl54_2
| ~ spl54_52 ),
inference(superposition,[],[f2024,f1726]) ).
thf(f2024,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_52 ),
inference(avatar_component_clause,[],[f2023]) ).
thf(f10450,plain,
( spl54_329
| ~ spl54_2
| ~ spl54_51 ),
inference(avatar_split_clause,[],[f2098,f2019,f1725,f10448]) ).
thf(f10448,plain,
( spl54_329
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_329])]) ).
thf(f2019,plain,
( spl54_51
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_51])]) ).
thf(f2098,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) )
| ~ spl54_2
| ~ spl54_51 ),
inference(trivial_inequality_removal,[],[f2097]) ).
thf(f2097,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) )
| ~ spl54_2
| ~ spl54_51 ),
inference(superposition,[],[f2020,f1726]) ).
thf(f2020,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_51 ),
inference(avatar_component_clause,[],[f2019]) ).
thf(f10446,plain,
( spl54_328
| ~ spl54_2
| ~ spl54_50 ),
inference(avatar_split_clause,[],[f2096,f2015,f1725,f10444]) ).
thf(f10444,plain,
( spl54_328
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_328])]) ).
thf(f2015,plain,
( spl54_50
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_50])]) ).
thf(f2096,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) )
| ~ spl54_2
| ~ spl54_50 ),
inference(trivial_inequality_removal,[],[f2095]) ).
thf(f2095,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) )
| ~ spl54_2
| ~ spl54_50 ),
inference(superposition,[],[f2016,f1726]) ).
thf(f2016,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ~ spl54_50 ),
inference(avatar_component_clause,[],[f2015]) ).
thf(f10442,plain,
( spl54_327
| ~ spl54_2
| ~ spl54_48 ),
inference(avatar_split_clause,[],[f2094,f2004,f1725,f10440]) ).
thf(f10440,plain,
( spl54_327
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK13,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_327])]) ).
thf(f2004,plain,
( spl54_48
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK13,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_48])]) ).
thf(f2094,plain,
( ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK13,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) )
| ~ spl54_2
| ~ spl54_48 ),
inference(trivial_inequality_removal,[],[f2093]) ).
thf(f2093,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK13,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) )
| ~ spl54_2
| ~ spl54_48 ),
inference(superposition,[],[f2005,f1726]) ).
thf(f2005,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK13,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_48 ),
inference(avatar_component_clause,[],[f2004]) ).
thf(f10438,plain,
( spl54_326
| ~ spl54_2
| ~ spl54_47 ),
inference(avatar_split_clause,[],[f2092,f2000,f1725,f10436]) ).
thf(f10436,plain,
( spl54_326
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_326])]) ).
thf(f2000,plain,
( spl54_47
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_47])]) ).
thf(f2092,plain,
( ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) )
| ~ spl54_2
| ~ spl54_47 ),
inference(trivial_inequality_removal,[],[f2091]) ).
thf(f2091,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) )
| ~ spl54_2
| ~ spl54_47 ),
inference(superposition,[],[f2001,f1726]) ).
thf(f2001,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_47 ),
inference(avatar_component_clause,[],[f2000]) ).
thf(f10434,plain,
( spl54_325
| ~ spl54_2
| ~ spl54_46 ),
inference(avatar_split_clause,[],[f2090,f1996,f1725,f10432]) ).
thf(f10432,plain,
( spl54_325
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_325])]) ).
thf(f1996,plain,
( spl54_46
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_46])]) ).
thf(f2090,plain,
( ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) )
| ~ spl54_2
| ~ spl54_46 ),
inference(trivial_inequality_removal,[],[f2089]) ).
thf(f2089,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP0,X0) ) )
| ~ spl54_2
| ~ spl54_46 ),
inference(superposition,[],[f1997,f1726]) ).
thf(f1997,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_46 ),
inference(avatar_component_clause,[],[f1996]) ).
thf(f10430,plain,
( spl54_324
| ~ spl54_2
| ~ spl54_45 ),
inference(avatar_split_clause,[],[f2088,f1992,f1725,f10428]) ).
thf(f10428,plain,
( spl54_324
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK10,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_324])]) ).
thf(f1992,plain,
( spl54_45
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK10,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_45])]) ).
thf(f2088,plain,
( ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK10,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_2
| ~ spl54_45 ),
inference(trivial_inequality_removal,[],[f2087]) ).
thf(f2087,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK10,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_2
| ~ spl54_45 ),
inference(superposition,[],[f1993,f1726]) ).
thf(f1993,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK10,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_45 ),
inference(avatar_component_clause,[],[f1992]) ).
thf(f10426,plain,
( spl54_323
| ~ spl54_2
| ~ spl54_44 ),
inference(avatar_split_clause,[],[f2086,f1988,f1725,f10424]) ).
thf(f10424,plain,
( spl54_323
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_323])]) ).
thf(f1988,plain,
( spl54_44
<=> ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_44])]) ).
thf(f2086,plain,
( ! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_2
| ~ spl54_44 ),
inference(trivial_inequality_removal,[],[f2085]) ).
thf(f2085,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $false = vAPP(partia96731725t_unit,$o,sP1,X0) ) )
| ~ spl54_2
| ~ spl54_44 ),
inference(superposition,[],[f1989,f1726]) ).
thf(f1989,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ~ spl54_44 ),
inference(avatar_component_clause,[],[f1988]) ).
thf(f9994,plain,
( spl54_322
| ~ spl54_31
| ~ spl54_127 ),
inference(avatar_split_clause,[],[f3164,f3141,f1889,f9992]) ).
thf(f9992,plain,
( spl54_322
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,uminus_uminus_int,X0))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_322])]) ).
thf(f3164,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,uminus_uminus_int,X0))) = X1 )
| ~ spl54_31
| ~ spl54_127 ),
inference(superposition,[],[f3142,f1890]) ).
thf(f9990,plain,
( spl54_321
| ~ spl54_28
| ~ spl54_40 ),
inference(avatar_split_clause,[],[f1984,f1937,f1877,f9988]) ).
thf(f9988,plain,
( spl54_321
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,uminus_uminus_int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_321])]) ).
thf(f1984,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,uminus_uminus_int,X0)) )
| ~ spl54_28
| ~ spl54_40 ),
inference(superposition,[],[f1878,f1938]) ).
thf(f9986,plain,
( spl54_320
| ~ spl54_28
| ~ spl54_39 ),
inference(avatar_split_clause,[],[f1972,f1933,f1877,f9984]) ).
thf(f9984,plain,
( spl54_320
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,uminus_uminus_int,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_320])]) ).
thf(f1972,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),vAPP(int,int,uminus_uminus_int,X0)) = X1 )
| ~ spl54_28
| ~ spl54_39 ),
inference(superposition,[],[f1878,f1934]) ).
thf(f9982,plain,
( spl54_319
| ~ spl54_19
| ~ spl54_97
| ~ spl54_124
| ~ spl54_291 ),
inference(avatar_split_clause,[],[f9174,f7084,f3085,f2393,f1834,f9979]) ).
thf(f7084,plain,
( spl54_291
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_291])]) ).
thf(f9174,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_97
| ~ spl54_124
| ~ spl54_291 ),
inference(forward_demodulation,[],[f9170,f3134]) ).
thf(f9170,plain,
( ( vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_97
| ~ spl54_291 ),
inference(trivial_inequality_removal,[],[f8993]) ).
thf(f8993,plain,
( ( $true != $true )
| ( vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_97
| ~ spl54_291 ),
inference(superposition,[],[f2394,f7086]) ).
thf(f7086,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_291 ),
inference(avatar_component_clause,[],[f7084]) ).
thf(f9977,plain,
( spl54_318
| ~ spl54_29
| ~ spl54_39 ),
inference(avatar_split_clause,[],[f1971,f1933,f1881,f9975]) ).
thf(f9975,plain,
( spl54_318
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_318])]) ).
thf(f1971,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)),X1) )
| ~ spl54_29
| ~ spl54_39 ),
inference(superposition,[],[f1882,f1934]) ).
thf(f9973,plain,
( spl54_317
| ~ spl54_29
| ~ spl54_37 ),
inference(avatar_split_clause,[],[f1964,f1922,f1881,f9971]) ).
thf(f9971,plain,
( spl54_317
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_317])]) ).
thf(f1964,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) )
| ~ spl54_29
| ~ spl54_37 ),
inference(superposition,[],[f1923,f1882]) ).
thf(f9969,plain,
( spl54_316
| ~ spl54_28
| ~ spl54_37 ),
inference(avatar_split_clause,[],[f1963,f1922,f1877,f9967]) ).
thf(f9967,plain,
( spl54_316
<=> ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_316])]) ).
thf(f1963,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) )
| ~ spl54_28
| ~ spl54_37 ),
inference(superposition,[],[f1923,f1878]) ).
thf(f9965,plain,
( spl54_315
| ~ spl54_30
| ~ spl54_36 ),
inference(avatar_split_clause,[],[f1959,f1918,f1885,f9963]) ).
thf(f9963,plain,
( spl54_315
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,uminus_uminus_int,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_315])]) ).
thf(f1959,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,uminus_uminus_int,X1)) = X0 )
| ~ spl54_30
| ~ spl54_36 ),
inference(superposition,[],[f1886,f1919]) ).
thf(f9961,plain,
( spl54_314
| ~ spl54_31
| ~ spl54_36 ),
inference(avatar_split_clause,[],[f1958,f1918,f1889,f9959]) ).
thf(f9959,plain,
( spl54_314
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_314])]) ).
thf(f1958,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = X0 )
| ~ spl54_31
| ~ spl54_36 ),
inference(superposition,[],[f1890,f1919]) ).
thf(f9956,plain,
( spl54_313
| ~ spl54_29
| ~ spl54_36 ),
inference(avatar_split_clause,[],[f1956,f1918,f1881,f9954]) ).
thf(f9954,plain,
( spl54_313
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,uminus_uminus_int,X1))),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_313])]) ).
thf(f1956,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,uminus_uminus_int,X1))),X1) = X0 )
| ~ spl54_29
| ~ spl54_36 ),
inference(superposition,[],[f1919,f1882]) ).
thf(f9936,plain,
( spl54_312
| ~ spl54_19
| ~ spl54_99
| ~ spl54_123
| ~ spl54_288 ),
inference(avatar_split_clause,[],[f8644,f7070,f3081,f2402,f1834,f9933]) ).
thf(f7070,plain,
( spl54_288
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_288])]) ).
thf(f8644,plain,
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_19
| ~ spl54_99
| ~ spl54_123
| ~ spl54_288 ),
inference(forward_demodulation,[],[f8638,f3126]) ).
thf(f8638,plain,
( ( vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_99
| ~ spl54_288 ),
inference(trivial_inequality_removal,[],[f8465]) ).
thf(f8465,plain,
( ( $true != $true )
| ( vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))) )
| ~ spl54_99
| ~ spl54_288 ),
inference(superposition,[],[f2403,f7072]) ).
thf(f7072,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_288 ),
inference(avatar_component_clause,[],[f7070]) ).
thf(f9809,plain,
( spl54_311
| ~ spl54_17
| ~ spl54_98
| ~ spl54_120
| ~ spl54_287 ),
inference(avatar_split_clause,[],[f8369,f7065,f3069,f2397,f1824,f9806]) ).
thf(f7065,plain,
( spl54_287
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_287])]) ).
thf(f8369,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_98
| ~ spl54_120
| ~ spl54_287 ),
inference(forward_demodulation,[],[f8364,f3099]) ).
thf(f8364,plain,
( ( vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_98
| ~ spl54_287 ),
inference(trivial_inequality_removal,[],[f8189]) ).
thf(f8189,plain,
( ( $true != $true )
| ( vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_98
| ~ spl54_287 ),
inference(superposition,[],[f2398,f7067]) ).
thf(f7067,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_287 ),
inference(avatar_component_clause,[],[f7065]) ).
thf(f9804,plain,
spl54_310,
inference(avatar_split_clause,[],[f1688,f9802]) ).
thf(f9802,plain,
( spl54_310
<=> ! [X0: product_prod_a_a,X1: product_prod_a_a > $o] :
( ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1)) )
| ( $true = vAPP(product_prod_a_a,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_310])]) ).
thf(f1688,plain,
! [X0: product_prod_a_a,X1: product_prod_a_a > $o] :
( ( $false = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1)) )
| ( $true = vAPP(product_prod_a_a,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1212]) ).
thf(f1212,plain,
! [X0: product_prod_a_a,X1: product_prod_a_a > $o] : ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1)) = vAPP(product_prod_a_a,$o,X1,X0) ),
inference(cnf_transformation,[],[f673]) ).
thf(f673,plain,
! [X0: product_prod_a_a,X1: product_prod_a_a > $o] : ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1)) = vAPP(product_prod_a_a,$o,X1,X0) ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
! [X0: product_prod_a_a,X20: product_prod_a_a > $o] : ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X20)) = vAPP(product_prod_a_a,$o,X20,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(f9800,plain,
spl54_309,
inference(avatar_split_clause,[],[f1687,f9798]) ).
thf(f9798,plain,
( spl54_309
<=> ! [X0: product_prod_a_a,X1: product_prod_a_a > $o] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1)) )
| ( $false = vAPP(product_prod_a_a,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_309])]) ).
thf(f1687,plain,
! [X0: product_prod_a_a,X1: product_prod_a_a > $o] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X0),vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,X1)) )
| ( $false = vAPP(product_prod_a_a,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1212]) ).
thf(f9796,plain,
spl54_308,
inference(avatar_split_clause,[],[f1686,f9794]) ).
thf(f9794,plain,
( spl54_308
<=> ! [X0: a,X1: a > $o] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) )
| ( $true = vAPP(a,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_308])]) ).
thf(f1686,plain,
! [X0: a,X1: a > $o] :
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) )
| ( $true = vAPP(a,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1213]) ).
thf(f1213,plain,
! [X0: a,X1: a > $o] : ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) = vAPP(a,$o,X1,X0) ),
inference(cnf_transformation,[],[f674]) ).
thf(f674,plain,
! [X0: a,X1: a > $o] : ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) = vAPP(a,$o,X1,X0) ),
inference(rectify,[],[f47]) ).
thf(f47,axiom,
! [X0: a,X20: a > $o] : ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X20)) = vAPP(a,$o,X20,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mem__Collect__eq) ).
thf(f9792,plain,
spl54_307,
inference(avatar_split_clause,[],[f1685,f9790]) ).
thf(f9790,plain,
( spl54_307
<=> ! [X0: a,X1: a > $o] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) )
| ( $false = vAPP(a,$o,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_307])]) ).
thf(f1685,plain,
! [X0: a,X1: a > $o] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(sTfun(a,$o),set_a,collect_a,X1)) )
| ( $false = vAPP(a,$o,X1,X0) ) ),
inference(binary_proxy_clausification,[],[f1213]) ).
thf(f9788,plain,
spl54_306,
inference(avatar_split_clause,[],[f1632,f9786]) ).
thf(f9786,plain,
( spl54_306
<=> ! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_306])]) ).
thf(f1632,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) != X1 ) ),
inference(equality_proxy_clausification,[],[f1631]) ).
thf(f1631,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = X0 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ) ),
inference(equality_proxy_clausification,[],[f1627]) ).
thf(f1627,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ) ),
inference(binary_proxy_clausification,[],[f1320]) ).
thf(f1320,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ),
inference(cnf_transformation,[],[f466]) ).
thf(f466,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ),
inference(fool_elimination,[],[f465]) ).
thf(f465,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = X0 )
= ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) = X1 ) ),
inference(rectify,[],[f177]) ).
thf(f177,axiom,
! [X0: int,X2: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X2),X1) = X0 )
= ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_eq__diff__eq) ).
thf(f9784,plain,
spl54_305,
inference(avatar_split_clause,[],[f1630,f9782]) ).
thf(f9782,plain,
( spl54_305
<=> ! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) != X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_305])]) ).
thf(f1630,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) != X0 )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) = X1 ) ),
inference(equality_proxy_clausification,[],[f1629]) ).
thf(f1629,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) != X0 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ) ),
inference(equality_proxy_clausification,[],[f1628]) ).
thf(f1628,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),X1) ) ),
inference(binary_proxy_clausification,[],[f1320]) ).
thf(f9780,plain,
spl54_304,
inference(avatar_split_clause,[],[f1620,f9778]) ).
thf(f9778,plain,
( spl54_304
<=> ! [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,[spl54_304])]) ).
thf(f1620,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,[],[f1619]) ).
thf(f1619,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,[],[f1615]) ).
thf(f1615,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,$o),vEQ(nat),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1322]) ).
thf(f1322,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$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,$o),vEQ(nat),X1),X2) ),
inference(cnf_transformation,[],[f468]) ).
thf(f468,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$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,[],[f149]) ).
thf(f149,axiom,
! [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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_add__left__cancel) ).
thf(f9776,plain,
spl54_303,
inference(avatar_split_clause,[],[f1618,f9774]) ).
thf(f9774,plain,
( spl54_303
<=> ! [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,[spl54_303])]) ).
thf(f1618,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,[],[f1617]) ).
thf(f1617,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,[],[f1616]) ).
thf(f1616,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,[],[f1322]) ).
thf(f9772,plain,
spl54_302,
inference(avatar_split_clause,[],[f1614,f9770]) ).
thf(f9770,plain,
( spl54_302
<=> ! [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,[spl54_302])]) ).
thf(f1614,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,[],[f1613]) ).
thf(f1613,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,[],[f1609]) ).
thf(f1609,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,$o),vEQ(nat),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1323]) ).
thf(f1323,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,$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,$o),vEQ(nat),X0),X2) ),
inference(cnf_transformation,[],[f470]) ).
thf(f470,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,$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,[],[f469]) ).
thf(f469,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,[],[f147]) ).
thf(f147,axiom,
! [X1: nat,X0: nat,X2: 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,X1),X0) )
= ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_add__right__cancel) ).
thf(f9768,plain,
spl54_301,
inference(avatar_split_clause,[],[f1612,f9766]) ).
thf(f9766,plain,
( spl54_301
<=> ! [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,[spl54_301])]) ).
thf(f1612,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,[],[f1611]) ).
thf(f1611,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,[],[f1610]) ).
thf(f1610,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,[],[f1323]) ).
thf(f9764,plain,
( spl54_300
| ~ spl54_17
| ~ spl54_100
| ~ spl54_119
| ~ spl54_286 ),
inference(avatar_split_clause,[],[f8098,f7060,f3065,f2406,f1824,f9761]) ).
thf(f7060,plain,
( spl54_286
<=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_286])]) ).
thf(f8098,plain,
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_17
| ~ spl54_100
| ~ spl54_119
| ~ spl54_286 ),
inference(forward_demodulation,[],[f8091,f3093]) ).
thf(f8091,plain,
( ( vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_100
| ~ spl54_286 ),
inference(trivial_inequality_removal,[],[f7920]) ).
thf(f7920,plain,
( ( $true != $true )
| ( vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))) )
| ~ spl54_100
| ~ spl54_286 ),
inference(superposition,[],[f2407,f7062]) ).
thf(f7062,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_286 ),
inference(avatar_component_clause,[],[f7060]) ).
thf(f9759,plain,
spl54_299,
inference(avatar_split_clause,[],[f1608,f9757]) ).
thf(f9757,plain,
( spl54_299
<=> ! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) )
| ( X0 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_299])]) ).
thf(f1608,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) )
| ( X0 != X2 ) ),
inference(equality_proxy_clausification,[],[f1607]) ).
thf(f1607,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f1603]) ).
thf(f1603,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1324]) ).
thf(f1324,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X2) ),
inference(cnf_transformation,[],[f472]) ).
thf(f472,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X2) ),
inference(fool_elimination,[],[f471]) ).
thf(f471,plain,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) )
= ( X0 = X2 ) ),
inference(rectify,[],[f160]) ).
thf(f160,axiom,
! [X1: int,X0: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) )
= ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_group__add__class_Oadd_Oright__cancel) ).
thf(f9755,plain,
spl54_298,
inference(avatar_split_clause,[],[f1606,f9753]) ).
thf(f9753,plain,
( spl54_298
<=> ! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_298])]) ).
thf(f1606,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) )
| ( X0 = X2 ) ),
inference(equality_proxy_clausification,[],[f1605]) ).
thf(f1605,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X2) ) ),
inference(equality_proxy_clausification,[],[f1604]) ).
thf(f1604,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X0),X2) ) ),
inference(binary_proxy_clausification,[],[f1324]) ).
thf(f9751,plain,
spl54_297,
inference(avatar_split_clause,[],[f1602,f9749]) ).
thf(f9749,plain,
( spl54_297
<=> ! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) )
| ( X1 != X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_297])]) ).
thf(f1602,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f1601]) ).
thf(f1601,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1597]) ).
thf(f1597,plain,
! [X2: int,X0: int,X1: int] :
( ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1325]) ).
thf(f1325,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X1),X2) ),
inference(cnf_transformation,[],[f473]) ).
thf(f473,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X1),X2) ),
inference(fool_elimination,[],[f161]) ).
thf(f161,axiom,
! [X0: int,X1: int,X2: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) )
= ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_add_Oleft__cancel) ).
thf(f9747,plain,
spl54_296,
inference(avatar_split_clause,[],[f1600,f9745]) ).
thf(f9745,plain,
( spl54_296
<=> ! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) )
| ( X1 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_296])]) ).
thf(f1600,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f1599]) ).
thf(f1599,plain,
! [X2: int,X0: int,X1: int] :
( ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X1),X2) ) ),
inference(equality_proxy_clausification,[],[f1598]) ).
thf(f1598,plain,
! [X2: int,X0: int,X1: int] :
( ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),X1),X2) ) ),
inference(binary_proxy_clausification,[],[f1325]) ).
thf(f9552,plain,
( spl54_295
| ~ spl54_32
| ~ spl54_97 ),
inference(avatar_split_clause,[],[f7600,f2393,f1899,f9549]) ).
thf(f7600,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_32
| ~ spl54_97 ),
inference(trivial_inequality_removal,[],[f6565]) ).
thf(f6565,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ~ spl54_32
| ~ spl54_97 ),
inference(superposition,[],[f2394,f1901]) ).
thf(f7907,plain,
( spl54_38
| spl54_49
| ~ spl54_183 ),
inference(avatar_split_clause,[],[f7638,f3886,f2008,f1926]) ).
thf(f1926,plain,
( spl54_38
<=> ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_38])]) ).
thf(f3886,plain,
( spl54_183
<=> ! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_183])]) ).
thf(f7638,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| spl54_49
| ~ spl54_183 ),
inference(trivial_inequality_removal,[],[f6760]) ).
thf(f6760,plain,
( ( vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) != vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| spl54_49
| ~ spl54_183 ),
inference(superposition,[],[f2009,f3887]) ).
thf(f3887,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) )
| ~ spl54_183 ),
inference(avatar_component_clause,[],[f3886]) ).
thf(f2009,plain,
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r) != vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) )
| spl54_49 ),
inference(avatar_component_clause,[],[f2008]) ).
thf(f7245,plain,
( spl54_294
| ~ spl54_5
| ~ spl54_14
| ~ spl54_19
| ~ spl54_49
| ~ spl54_143 ),
inference(avatar_split_clause,[],[f7120,f3346,f2008,f1834,f1811,f1766,f7242]) ).
thf(f7120,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_14
| ~ spl54_19
| ~ spl54_49
| ~ spl54_143 ),
inference(trivial_inequality_removal,[],[f7119]) ).
thf(f7119,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_5
| ~ spl54_14
| ~ spl54_19
| ~ spl54_49
| ~ spl54_143 ),
inference(forward_demodulation,[],[f6189,f1768]) ).
thf(f6189,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_14
| ~ spl54_19
| ~ spl54_49
| ~ spl54_143 ),
inference(forward_demodulation,[],[f3409,f1813]) ).
thf(f3409,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_49
| ~ spl54_143 ),
inference(forward_demodulation,[],[f3407,f2010]) ).
thf(f3407,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_143 ),
inference(trivial_inequality_removal,[],[f3404]) ).
thf(f3404,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_19
| ~ spl54_143 ),
inference(superposition,[],[f3347,f1836]) ).
thf(f7097,plain,
( spl54_293
| ~ spl54_32
| ~ spl54_98 ),
inference(avatar_split_clause,[],[f6404,f2397,f1899,f7094]) ).
thf(f6404,plain,
( ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_98 ),
inference(trivial_inequality_removal,[],[f5268]) ).
thf(f5268,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),sK8),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) )
| ~ spl54_32
| ~ spl54_98 ),
inference(superposition,[],[f2398,f1901]) ).
thf(f7092,plain,
( spl54_292
| ~ spl54_18
| ~ spl54_94 ),
inference(avatar_split_clause,[],[f2364,f2333,f1829,f7089]) ).
thf(f2364,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_18
| ~ spl54_94 ),
inference(trivial_inequality_removal,[],[f2357]) ).
thf(f2357,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_18
| ~ spl54_94 ),
inference(superposition,[],[f2334,f1831]) ).
thf(f7087,plain,
( spl54_291
| ~ spl54_19
| ~ spl54_94 ),
inference(avatar_split_clause,[],[f2363,f2333,f1834,f7084]) ).
thf(f2363,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_19
| ~ spl54_94 ),
inference(trivial_inequality_removal,[],[f2358]) ).
thf(f2358,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_19
| ~ spl54_94 ),
inference(superposition,[],[f2334,f1836]) ).
thf(f7082,plain,
( spl54_290
| ~ spl54_29
| ~ spl54_36
| ~ spl54_37
| ~ spl54_79
| ~ spl54_114
| ~ spl54_269 ),
inference(avatar_split_clause,[],[f6862,f6013,f2495,f2200,f1922,f1918,f1881,f7080]) ).
thf(f7080,plain,
( spl54_290
<=> ! [X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_290])]) ).
thf(f6013,plain,
( spl54_269
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_269])]) ).
thf(f6862,plain,
( ! [X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,uminus_uminus_int,X1)) = X1 )
| ~ spl54_29
| ~ spl54_36
| ~ spl54_37
| ~ spl54_79
| ~ spl54_114
| ~ spl54_269 ),
inference(forward_demodulation,[],[f6861,f1964]) ).
thf(f6861,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0))) = X1 )
| ~ spl54_36
| ~ spl54_79
| ~ spl54_114
| ~ spl54_269 ),
inference(forward_demodulation,[],[f6860,f1919]) ).
thf(f6860,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),vAPP(int,int,uminus_uminus_int,X0)))) = X1 )
| ~ spl54_79
| ~ spl54_114
| ~ spl54_269 ),
inference(forward_demodulation,[],[f6840,f2496]) ).
thf(f6840,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X1))) = X1 )
| ~ spl54_79
| ~ spl54_269 ),
inference(superposition,[],[f6014,f2201]) ).
thf(f6014,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = X1 )
| ~ spl54_269 ),
inference(avatar_component_clause,[],[f6013]) ).
thf(f7078,plain,
( spl54_289
| ~ spl54_18
| ~ spl54_93 ),
inference(avatar_split_clause,[],[f2356,f2329,f1829,f7075]) ).
thf(f2356,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_18
| ~ spl54_93 ),
inference(trivial_inequality_removal,[],[f2349]) ).
thf(f2349,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_18
| ~ spl54_93 ),
inference(superposition,[],[f2330,f1831]) ).
thf(f7073,plain,
( spl54_288
| ~ spl54_19
| ~ spl54_93 ),
inference(avatar_split_clause,[],[f2355,f2329,f1834,f7070]) ).
thf(f2355,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_19
| ~ spl54_93 ),
inference(trivial_inequality_removal,[],[f2350]) ).
thf(f2350,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,vAPP(partia1833973666xt_a_b,a,zero_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_19
| ~ spl54_93 ),
inference(superposition,[],[f2330,f1836]) ).
thf(f7068,plain,
( spl54_287
| ~ spl54_17
| ~ spl54_92 ),
inference(avatar_split_clause,[],[f2348,f2325,f1824,f7065]) ).
thf(f2348,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_17
| ~ spl54_92 ),
inference(trivial_inequality_removal,[],[f2343]) ).
thf(f2343,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_17
| ~ spl54_92 ),
inference(superposition,[],[f2326,f1826]) ).
thf(f7063,plain,
( spl54_286
| ~ spl54_17
| ~ spl54_91 ),
inference(avatar_split_clause,[],[f2342,f2321,f1824,f7060]) ).
thf(f2342,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_17
| ~ spl54_91 ),
inference(trivial_inequality_removal,[],[f2337]) ).
thf(f2337,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_17
| ~ spl54_91 ),
inference(superposition,[],[f2322,f1826]) ).
thf(f7058,plain,
( spl54_285
| ~ spl54_6
| ~ spl54_7
| ~ spl54_9
| ~ spl54_10
| ~ spl54_62 ),
inference(avatar_split_clause,[],[f2128,f2066,f1789,f1785,f1776,f1771,f7055]) ).
thf(f1771,plain,
( spl54_6
<=> ( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_6])]) ).
thf(f1776,plain,
( spl54_7
<=> ( vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_7])]) ).
thf(f1789,plain,
( spl54_10
<=> ! [X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_10])]) ).
thf(f2128,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))) )
| ~ spl54_6
| ~ spl54_7
| ~ spl54_9
| ~ spl54_10
| ~ spl54_62 ),
inference(forward_demodulation,[],[f2127,f1786]) ).
thf(f2127,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))),vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))) )
| ~ spl54_6
| ~ spl54_7
| ~ spl54_10
| ~ spl54_62 ),
inference(forward_demodulation,[],[f2126,f1803]) ).
thf(f1803,plain,
( ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) )
| ~ spl54_7
| ~ spl54_10 ),
inference(trivial_inequality_removal,[],[f1800]) ).
thf(f1800,plain,
( ( $true != $true )
| ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) )
| ~ spl54_7
| ~ spl54_10 ),
inference(superposition,[],[f1790,f1778]) ).
thf(f1778,plain,
( ( vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = $true )
| ~ spl54_7 ),
inference(avatar_component_clause,[],[f1776]) ).
thf(f1790,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) ) )
| ~ spl54_10 ),
inference(avatar_component_clause,[],[f1789]) ).
thf(f2126,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))) )
| ~ spl54_6
| ~ spl54_62 ),
inference(trivial_inequality_removal,[],[f2123]) ).
thf(f2123,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r))) )
| ~ spl54_6
| ~ spl54_62 ),
inference(superposition,[],[f2067,f1773]) ).
thf(f1773,plain,
( ( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = $true )
| ~ spl54_6 ),
inference(avatar_component_clause,[],[f1771]) ).
thf(f6880,plain,
( spl54_38
| spl54_49
| ~ spl54_183 ),
inference(avatar_split_clause,[],[f5202,f3886,f2008,f1926]) ).
thf(f5202,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| spl54_49
| ~ spl54_183 ),
inference(trivial_inequality_removal,[],[f4689]) ).
thf(f4689,plain,
( ( vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) != vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| spl54_49
| ~ spl54_183 ),
inference(superposition,[],[f2009,f3887]) ).
thf(f6199,plain,
( spl54_284
| ~ spl54_49
| ~ spl54_150 ),
inference(avatar_split_clause,[],[f3464,f3460,f2008,f6197]) ).
thf(f3464,plain,
( ! [X0: a,X1: int] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_150 ),
inference(forward_demodulation,[],[f3463,f2010]) ).
thf(f3463,plain,
( ! [X0: a,X1: int] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_49
| ~ spl54_150 ),
inference(forward_demodulation,[],[f3461,f2010]) ).
thf(f6167,plain,
( spl54_283
| ~ spl54_5
| ~ spl54_32
| ~ spl54_126 ),
inference(avatar_split_clause,[],[f5206,f3137,f1899,f1766,f6164]) ).
thf(f5206,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_126 ),
inference(trivial_inequality_removal,[],[f5205]) ).
thf(f5205,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ~ spl54_5
| ~ spl54_32
| ~ spl54_126 ),
inference(forward_demodulation,[],[f4503,f1768]) ).
thf(f4503,plain,
( ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_126 ),
inference(trivial_inequality_removal,[],[f4452]) ).
thf(f4452,plain,
( ( $true != $true )
| ( sK8 = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),sK8)) )
| ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) != $true )
| ~ spl54_32
| ~ spl54_126 ),
inference(superposition,[],[f3138,f1901]) ).
thf(f6162,plain,
( spl54_282
| ~ spl54_103
| ~ spl54_112 ),
inference(avatar_split_clause,[],[f2877,f2487,f2450,f6160]) ).
thf(f6160,plain,
( spl54_282
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_282])]) ).
thf(f2877,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X0) )
| ~ spl54_103
| ~ spl54_112 ),
inference(superposition,[],[f2488,f2451]) ).
thf(f6154,plain,
( spl54_281
| ~ spl54_29
| ~ spl54_107 ),
inference(avatar_split_clause,[],[f2656,f2467,f1881,f6152]) ).
thf(f2656,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X1)) = X0 )
| ~ spl54_29
| ~ spl54_107 ),
inference(superposition,[],[f2468,f1882]) ).
thf(f6150,plain,
spl54_280,
inference(avatar_split_clause,[],[f1707,f6147]) ).
thf(f6147,plain,
( spl54_280
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_280])]) ).
thf(f1707,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)),
inference(forward_demodulation,[],[f1706,f1696]) ).
thf(f1696,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4)),
inference(forward_demodulation,[],[f1115,f1113]) ).
thf(f1113,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)),
inference(cnf_transformation,[],[f7]) ).
thf(f7,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_f9) ).
thf(f1115,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),
inference(cnf_transformation,[],[f10]) ).
thf(f10,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_f10) ).
thf(f1706,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),
inference(forward_demodulation,[],[f1705,f1697]) ).
thf(f1697,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4)),
inference(forward_demodulation,[],[f1116,f1113]) ).
thf(f1116,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4))),
inference(cnf_transformation,[],[f9]) ).
thf(f9,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_092_060close_062) ).
thf(f1705,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4))),
inference(forward_demodulation,[],[f1121,f1113]) ).
thf(f1121,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4))),
inference(cnf_transformation,[],[f15]) ).
thf(f15,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_f7) ).
thf(f6138,plain,
spl54_279,
inference(avatar_split_clause,[],[f1699,f6135]) ).
thf(f6135,plain,
( spl54_279
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_279])]) ).
thf(f1699,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)),
inference(forward_demodulation,[],[f1118,f1113]) ).
thf(f1118,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),
inference(cnf_transformation,[],[f14]) ).
thf(f14,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_A_092_060otimes_062_Ar_H_H_J_A_092_060oplus_062_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_092_060close_062) ).
thf(f6132,plain,
spl54_278,
inference(avatar_split_clause,[],[f1701,f6129]) ).
thf(f6129,plain,
( spl54_278
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_278])]) ).
thf(f1701,plain,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),
inference(forward_demodulation,[],[f1700,f1113]) ).
thf(f1700,plain,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),
inference(forward_demodulation,[],[f1119,f1699]) ).
thf(f1119,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4))))) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r),
inference(cnf_transformation,[],[f20]) ).
thf(f20,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4))))) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_A_092_060otimes_062_Ar_H_H_J_A_092_060oplus_062_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_A_061_A_092_060zero_062_092_060close_062) ).
thf(f6120,plain,
spl54_277,
inference(avatar_split_clause,[],[f1698,f6117]) ).
thf(f6117,plain,
( spl54_277
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_277])]) ).
thf(f1698,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4))),
inference(forward_demodulation,[],[f1117,f1113]) ).
thf(f1117,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4))),
inference(cnf_transformation,[],[f13]) ).
thf(f13,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060otimes_062_Ar_H_H_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062) ).
thf(f6115,plain,
spl54_276,
inference(avatar_split_clause,[],[f1123,f6112]) ).
thf(f6112,plain,
( spl54_276
<=> ( a_minus_a_b = vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,a)),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,a)),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add_a_b))),a_inv_a_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_276])]) ).
thf(f1123,plain,
a_minus_a_b = vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,a)),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,a)),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add_a_b))),a_inv_a_b),
inference(cnf_transformation,[],[f290]) ).
thf(f290,plain,
a_minus_a_b = vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,a)),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,a)),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1833973666xt_a_b,sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(a,a))),sTfun(partia1833973666xt_a_b,sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add_a_b))),a_inv_a_b),
inference(fool_elimination,[],[f289]) ).
thf(f289,plain,
( a_minus_a_b
= ( ^ [X0: partia1833973666xt_a_b,X1: a,X2: a] : vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) ) ),
inference(rectify,[],[f244]) ).
thf(f244,axiom,
( a_minus_a_b
= ( ^ [X46: partia1833973666xt_a_b,X22: a,X47: a] : vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X46),X22),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X46),X47)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_a__minus__def) ).
thf(f6103,plain,
( spl54_275
| ~ spl54_101
| ~ spl54_102 ),
inference(avatar_split_clause,[],[f2519,f2446,f2442,f6101]) ).
thf(f6101,plain,
( spl54_275
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_275])]) ).
thf(f2519,plain,
( ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X0) )
| ~ spl54_101
| ~ spl54_102 ),
inference(superposition,[],[f2447,f2443]) ).
thf(f6092,plain,
spl54_274,
inference(avatar_split_clause,[],[f1697,f6089]) ).
thf(f6089,plain,
( spl54_274
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3)),r4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_274])]) ).
thf(f6087,plain,
spl54_273,
inference(avatar_split_clause,[],[f1696,f6084]) ).
thf(f6084,plain,
( spl54_273
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),r4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_273])]) ).
thf(f6069,plain,
spl54_272,
inference(avatar_split_clause,[],[f1427,f6067]) ).
thf(f6067,plain,
( spl54_272
<=> ! [X4: a,X0: partia1833973666xt_a_b,X3: a,X2: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X3)),X2)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3)),X4) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_272])]) ).
thf(f1427,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a,X4: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X3)),X2)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3)),X4) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f1012]) ).
thf(f1012,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a,X4: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X3)),X2)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3)),X4) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f1011]) ).
thf(f1011,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a,X4: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X3)),X2)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3)),X4) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f634]) ).
thf(f634,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a,X4: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X3)),X2)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3)),X4) ) ) ) ) ) ),
inference(fool_elimination,[],[f633]) ).
thf(f633,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a,X4: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X3)),X2)),X4) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3)),X4) ) ) ) ) ) ),
inference(rectify,[],[f118]) ).
thf(f118,axiom,
! [X36: partia1833973666xt_a_b,X0: a,X1: a,X2: a,X19: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X19),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),X0),X2)),X1)),X19) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X0),X1)),X2)),X19) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_abelian__group_Ofour__elem__comm) ).
thf(f6052,plain,
spl54_271,
inference(avatar_split_clause,[],[f1425,f6050]) ).
thf(f1425,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1008]) ).
thf(f1008,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f1007]) ).
thf(f1007,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f630]) ).
thf(f630,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2)),X3) ) ) ) ) ),
inference(fool_elimination,[],[f629]) ).
thf(f629,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2)),X3) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f37,axiom,
! [X0: a,X1: a,X2: a,X19: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X19),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X2)),X1)),X19) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2)),X19) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_four__elem__comm) ).
thf(f6032,plain,
spl54_270,
inference(avatar_split_clause,[],[f1426,f6030]) ).
thf(f1426,plain,
! [X2: a,X3: a,X0: a,X1: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ),
inference(cnf_transformation,[],[f1010]) ).
thf(f1010,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ),
inference(flattening,[],[f1009]) ).
thf(f1009,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ),
inference(ennf_transformation,[],[f632]) ).
thf(f632,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
=> ( ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
=> ( $true = vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ) ),
inference(fool_elimination,[],[f631]) ).
thf(f631,plain,
! [X0: a,X1: a,X2: a,X3: a] :
( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X0),X1)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel))
=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel))
=> vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X3: a,X4: a,X5: a,X6: a] :
( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X3),X4)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel))
=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X5),X6)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel))
=> vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X6),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X4),X5))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X4),X6))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_closed__rel__add) ).
thf(f6015,plain,
( spl54_269
| ~ spl54_28
| ~ spl54_30 ),
inference(avatar_split_clause,[],[f1895,f1885,f1877,f6013]) ).
thf(f1895,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = X1 )
| ~ spl54_28
| ~ spl54_30 ),
inference(superposition,[],[f1878,f1886]) ).
thf(f5998,plain,
spl54_268,
inference(avatar_split_clause,[],[f1421,f5996]) ).
thf(f1421,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f1000]) ).
thf(f1000,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f999]) ).
thf(f999,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f622]) ).
thf(f622,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) ) ) ) ) ),
inference(fool_elimination,[],[f621]) ).
thf(f621,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) ) ) ) ) ),
inference(rectify,[],[f68]) ).
thf(f68,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a,X9: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X7),X9)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X8),X9)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_semiring_Ol__distr) ).
thf(f5994,plain,
spl54_267,
inference(avatar_split_clause,[],[f1420,f5992]) ).
thf(f1420,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f998]) ).
thf(f998,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f997]) ).
thf(f997,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f620]) ).
thf(f620,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X2)) ) ) ) ) ),
inference(fool_elimination,[],[f619]) ).
thf(f619,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X2)) ) ) ) ) ),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a,X9: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X9),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X9),X7)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X9),X8)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_semiring_Or__distr) ).
thf(f5982,plain,
spl54_266,
inference(avatar_split_clause,[],[f1341,f5980]) ).
thf(f1341,plain,
! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ),
inference(cnf_transformation,[],[f861]) ).
thf(f861,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ),
inference(flattening,[],[f860]) ).
thf(f860,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ),
inference(ennf_transformation,[],[f484]) ).
thf(f484,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) ) ) ) ),
inference(fool_elimination,[],[f483]) ).
thf(f483,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) ) ) ) ),
inference(rectify,[],[f93]) ).
thf(f93,axiom,
! [X7: a,X8: a,X34: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),X7) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add_Ogroup__commutes__pow) ).
thf(f5952,plain,
spl54_265,
inference(avatar_split_clause,[],[f1392,f5950]) ).
thf(f1392,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f956]) ).
thf(f956,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f955]) ).
thf(f955,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f584]) ).
thf(f584,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) ) ) ) ),
inference(fool_elimination,[],[f583]) ).
thf(f583,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f18,axiom,
! [X7: a,X8: a,X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X9)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X8),X9)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_l__distr) ).
thf(f5948,plain,
spl54_264,
inference(avatar_split_clause,[],[f1391,f5946]) ).
thf(f1391,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f954]) ).
thf(f954,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f953]) ).
thf(f953,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f582]) ).
thf(f582,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X1)) ) ) ) ),
inference(fool_elimination,[],[f581]) ).
thf(f581,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X2),X1)) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f19,axiom,
! [X7: a,X8: a,X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X9),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X9),X7)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X9),X8)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_r__distr) ).
thf(f5944,plain,
( spl54_263
| ~ spl54_28
| ~ spl54_30 ),
inference(avatar_split_clause,[],[f1894,f1885,f1877,f5942]) ).
thf(f5942,plain,
( spl54_263
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_263])]) ).
thf(f1894,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) )
| ~ spl54_28
| ~ spl54_30 ),
inference(superposition,[],[f1886,f1878]) ).
thf(f5940,plain,
spl54_262,
inference(avatar_split_clause,[],[f1441,f5937]) ).
thf(f5937,plain,
( spl54_262
<=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_262])]) ).
thf(f1441,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(cnf_transformation,[],[f662]) ).
thf(f662,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(fool_elimination,[],[f661]) ).
thf(f661,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_f12) ).
thf(f5846,plain,
spl54_261,
inference(avatar_split_clause,[],[f1424,f5844]) ).
thf(f1424,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f1006]) ).
thf(f1006,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f1005]) ).
thf(f1005,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f628]) ).
thf(f628,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) ) ) ) ) ),
inference(fool_elimination,[],[f627]) ).
thf(f627,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) ) ) ) ) ),
inference(rectify,[],[f111]) ).
thf(f111,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a,X9: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X8),X9)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_abelian__groupE_I3_J) ).
thf(f5842,plain,
spl54_260,
inference(avatar_split_clause,[],[f1423,f5840]) ).
thf(f1423,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f1004]) ).
thf(f1004,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f1003]) ).
thf(f1003,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f626]) ).
thf(f626,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) ) ) ) ) ),
inference(fool_elimination,[],[f625]) ).
thf(f625,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) ) ) ) ) ),
inference(rectify,[],[f119]) ).
thf(f119,axiom,
! [X36: partia1833973666xt_a_b,X0: a,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X0),X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_abelian__group_Oright__inv__add) ).
thf(f5665,plain,
spl54_259,
inference(avatar_split_clause,[],[f1419,f5663]) ).
thf(f1419,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f996]) ).
thf(f996,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f995]) ).
thf(f995,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f618]) ).
thf(f618,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) ) ) ) ) ),
inference(fool_elimination,[],[f617]) ).
thf(f617,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) ) ) ) ) ),
inference(rectify,[],[f83]) ).
thf(f83,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a,X9: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X8),X9)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_semiring_Osemiring__simprules_I8_J) ).
thf(f5661,plain,
spl54_258,
inference(avatar_split_clause,[],[f1418,f5659]) ).
thf(f1418,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f994]) ).
thf(f994,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f993]) ).
thf(f993,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f616]) ).
thf(f616,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) ) ) ) ) ),
inference(fool_elimination,[],[f615]) ).
thf(f615,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) ) ) ) ) ),
inference(rectify,[],[f85]) ).
thf(f85,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a,X9: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X8),X9)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_semiring_Osemiring__simprules_I5_J) ).
thf(f5657,plain,
spl54_257,
inference(avatar_split_clause,[],[f1417,f5655]) ).
thf(f1417,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f992]) ).
thf(f992,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f991]) ).
thf(f991,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f614]) ).
thf(f614,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X3)) ) ) ) ) ),
inference(fool_elimination,[],[f613]) ).
thf(f613,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X3)) ) ) ) ) ),
inference(rectify,[],[f87]) ).
thf(f87,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a,X9: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X8),X9)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X9)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_semiring_Osemiring__simprules_I12_J) ).
thf(f5653,plain,
spl54_256,
inference(avatar_split_clause,[],[f1413,f5651]) ).
thf(f1413,plain,
! [X2: a,X3: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(cnf_transformation,[],[f984]) ).
thf(f984,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(flattening,[],[f983]) ).
thf(f983,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(ennf_transformation,[],[f606]) ).
thf(f606,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) ) ) ) ) ),
inference(fool_elimination,[],[f605]) ).
thf(f605,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: a] :
( vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) ) ) ) ) ),
inference(rectify,[],[f278]) ).
thf(f278,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a,X9: a] :
( vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X8),X9)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_comm__groupE_I3_J) ).
thf(f5649,plain,
spl54_255,
inference(avatar_split_clause,[],[f1411,f5647]) ).
thf(f1411,plain,
! [X2: a,X3: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(cnf_transformation,[],[f980]) ).
thf(f980,plain,
! [X0: partia96731725t_unit,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(flattening,[],[f979]) ).
thf(f979,plain,
! [X0: partia96731725t_unit,X1: a,X2: a,X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(ennf_transformation,[],[f602]) ).
thf(f602,plain,
! [X0: partia96731725t_unit,X1: a,X2: a,X3: a] :
( ( $true = vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) ) ) ) ) ),
inference(fool_elimination,[],[f601]) ).
thf(f601,plain,
! [X0: partia96731725t_unit,X1: a,X2: a,X3: a] :
( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) ) ) ) ) ),
inference(rectify,[],[f277]) ).
thf(f277,axiom,
! [X36: partia96731725t_unit,X7: a,X8: a,X9: a] :
( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X8),X9)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_comm__groupE_I3_J) ).
thf(f5627,plain,
spl54_254,
inference(avatar_split_clause,[],[f1378,f5625]) ).
thf(f1378,plain,
! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f928]) ).
thf(f928,plain,
! [X0: a,X1: nat,X2: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f556]) ).
thf(f556,plain,
! [X0: a,X1: nat,X2: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ),
inference(fool_elimination,[],[f555]) ).
thf(f555,plain,
! [X0: a,X1: nat,X2: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ),
inference(rectify,[],[f96]) ).
thf(f96,axiom,
! [X7: a,X34: nat,X35: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X35),X7)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X35),X7)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add_Onat__pow__comm) ).
thf(f5623,plain,
spl54_253,
inference(avatar_split_clause,[],[f1166,f5621]) ).
thf(f5621,plain,
( spl54_253
<=> ! [X2: a,X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK23,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,sK24,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK24,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_253])]) ).
thf(f1166,plain,
! [X2: a,X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK23,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,sK24,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK24,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1059]) ).
thf(f1059,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( ! [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK23,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( ( vAPP(partia1833973666xt_a_b,a,sK24,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK24,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f1056,f1058,f1057]) ).
thf(f1057,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ! [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ! [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK23,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1058,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X3) != X3 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,sK24,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK24,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1056,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ? [X1: a] :
( ! [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X3) != X3 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(rectify,[],[f1019]) ).
thf(f1019,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ? [X9: a] :
( ! [X10: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X10),X9) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X10),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X8: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X8) != X8 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(definition_folding,[],[f724,f1018,f1017,f1016]) ).
thf(f1016,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1017,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1018,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X6: a] :
( ? [X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X6),X7) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X7),X6) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f724,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ? [X9: a] :
( ! [X10: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X10),X9) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X10),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X8: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X8) != X8 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X6: a] :
( ? [X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X6),X7) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X7),X6) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(flattening,[],[f723]) ).
thf(f723,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ? [X9: a] :
( ! [X10: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X10),X9) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X10),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X8: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X8) != X8 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X6: a] :
( ? [X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X6),X7) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X7),X6) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(ennf_transformation,[],[f310]) ).
thf(f310,plain,
! [X0: partia1833973666xt_a_b] :
( ! [X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ! [X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ! [X3: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ! [X4: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ! [X5: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X4),X5)) ) ) ) )
=> ( ! [X6: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ! [X7: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X6),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X7),X6) ) ) )
=> ( ! [X8: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X8) = X8 ) )
=> ( ! [X9: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ? [X10: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X10),X9) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X10),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) )
=> ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f309]) ).
thf(f309,plain,
! [X0: partia1833973666xt_a_b] :
( ! [X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ! [X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( ! [X3: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ! [X4: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ! [X5: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X4),X5)) ) ) ) )
=> ( ! [X6: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X6),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X7),X6) ) ) )
=> ( ! [X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X8) = X8 ) )
=> ( ! [X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ? [X10: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X10),X9) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X10),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ) ) ) ),
inference(rectify,[],[f115]) ).
thf(f115,axiom,
! [X29: partia1833973666xt_a_b] :
( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ! [X28: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X28),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X17),X28)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ! [X28: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X28),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ! [X37: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X37),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X17),X28)),X37) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X17),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X28),X37)) ) ) ) )
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ! [X28: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X28),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X17),X28) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X28),X17) ) ) )
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)),X17) = X17 ) )
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ? [X38: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X29) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X38),X17) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X38),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ) )
=> vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X29) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_abelian__groupI) ).
thf(f5591,plain,
spl54_252,
inference(avatar_split_clause,[],[f1385,f5589]) ).
thf(f1385,plain,
! [X2: int,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f942]) ).
thf(f942,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f941]) ).
thf(f941,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f570]) ).
thf(f570,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) ) ) ),
inference(fool_elimination,[],[f569]) ).
thf(f569,plain,
! [X0: a,X1: a,X2: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) ) ) ),
inference(rectify,[],[f73]) ).
thf(f73,axiom,
! [X7: a,X8: a,X31: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X31),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X31),X7)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X31),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_add_Oint__pow__distrib) ).
thf(f5587,plain,
spl54_251,
inference(avatar_split_clause,[],[f1384,f5585]) ).
thf(f1384,plain,
! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f940]) ).
thf(f940,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f939]) ).
thf(f939,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f568]) ).
thf(f568,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) ) ) ),
inference(fool_elimination,[],[f567]) ).
thf(f567,plain,
! [X0: a,X1: a,X2: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) ) ) ),
inference(rectify,[],[f95]) ).
thf(f95,axiom,
! [X7: a,X8: a,X34: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add_Onat__pow__distrib) ).
thf(f5525,plain,
spl54_250,
inference(avatar_split_clause,[],[f1390,f5523]) ).
thf(f1390,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f952]) ).
thf(f952,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f951]) ).
thf(f951,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f580]) ).
thf(f580,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),X2) ) ) ) ),
inference(fool_elimination,[],[f579]) ).
thf(f579,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),X2) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f24,axiom,
! [X7: a,X8: a,X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X8),X9)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_m__assoc) ).
thf(f5521,plain,
spl54_249,
inference(avatar_split_clause,[],[f1389,f5519]) ).
thf(f1389,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f950]) ).
thf(f950,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f949]) ).
thf(f949,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f578]) ).
thf(f578,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) ) ) ) ),
inference(fool_elimination,[],[f577]) ).
thf(f577,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),X2) ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f27,axiom,
! [X7: a,X8: a,X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)),X9) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),X9)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_add_Om__assoc) ).
thf(f5514,plain,
spl54_248,
inference(avatar_split_clause,[],[f1388,f5512]) ).
thf(f1388,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f948]) ).
thf(f948,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f947]) ).
thf(f947,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f576]) ).
thf(f576,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) ) ) ) ),
inference(fool_elimination,[],[f575]) ).
thf(f575,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f36,axiom,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_right__inv__add) ).
thf(f5510,plain,
spl54_247,
inference(avatar_split_clause,[],[f1387,f5508]) ).
thf(f1387,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f946]) ).
thf(f946,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f945]) ).
thf(f945,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f574]) ).
thf(f574,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) ) ) ) ),
inference(fool_elimination,[],[f573]) ).
thf(f573,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X2)) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f26,axiom,
! [X7: a,X8: a,X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X8),X9)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X9)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_m__lcomm) ).
thf(f5506,plain,
spl54_246,
inference(avatar_split_clause,[],[f1386,f5504]) ).
thf(f1386,plain,
! [X2: a,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f944]) ).
thf(f944,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f943]) ).
thf(f943,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f572]) ).
thf(f572,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)) ) ) ) ),
inference(fool_elimination,[],[f571]) ).
thf(f571,plain,
! [X0: a,X1: a,X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X2)) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f29,axiom,
! [X7: a,X8: a,X9: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X9),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),X9)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X9)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add_Om__lcomm) ).
thf(f5488,plain,
spl54_245,
inference(avatar_split_clause,[],[f1177,f5486]) ).
thf(f5486,plain,
( spl54_245
<=> ! [X2: a,X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK30,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,sK31,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK31,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_245])]) ).
thf(f1177,plain,
! [X2: a,X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK30,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,sK31,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK31,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(cnf_transformation,[],[f1073]) ).
thf(f1073,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( ! [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK30,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( ( vAPP(partia1833973666xt_a_b,a,sK31,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK31,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f1070,f1072,f1071]) ).
thf(f1071,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ! [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ! [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK30,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1072,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X3) != X3 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,sK31,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK31,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1070,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ? [X1: a] :
( ! [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X3) != X3 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(rectify,[],[f1022]) ).
thf(f1022,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ? [X7: a] :
( ! [X8: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X8),X7) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X6: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X6) != X6 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(definition_folding,[],[f726,f1021,f1020]) ).
thf(f1020,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1021,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f726,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ? [X7: a] :
( ! [X8: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X8),X7) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X6: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X6) != X6 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(flattening,[],[f725]) ).
thf(f725,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ? [X7: a] :
( ! [X8: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X8),X7) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X6: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X6) != X6 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(ennf_transformation,[],[f312]) ).
thf(f312,plain,
! [X0: partia1833973666xt_a_b] :
( ! [X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ! [X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ! [X3: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ! [X4: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ! [X5: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X4),X5)) ) ) ) )
=> ( ! [X6: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X6) = X6 ) )
=> ( ! [X7: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ? [X8: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X8),X7) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) )
=> ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ) ) ) ),
inference(fool_elimination,[],[f311]) ).
thf(f311,plain,
! [X0: partia1833973666xt_a_b] :
( ! [X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ! [X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( ! [X3: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ! [X4: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ! [X5: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X4),X5)) ) ) ) )
=> ( ! [X6: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X6) = X6 ) )
=> ( ! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ? [X8: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X8),X7) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ) ) ),
inference(rectify,[],[f195]) ).
thf(f195,axiom,
! [X36: partia1833973666xt_a_b] :
( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ! [X28: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X28),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X17),X28)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36)) ) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ! [X28: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X28),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ! [X37: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X37),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X17),X28)),X37) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X17),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X28),X37)) ) ) ) )
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36)),X17) = X17 ) )
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ? [X38: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X38),X17) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X38),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36)) ) )
=> vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X36) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_groupI) ).
thf(f5484,plain,
spl54_244,
inference(avatar_split_clause,[],[f1152,f5482]) ).
thf(f1152,plain,
! [X2: a,X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),vAPP(partia96731725t_unit,a,sK14,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(partia96731725t_unit,a,sK15,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1040]) ).
thf(f1040,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( ! [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),vAPP(partia96731725t_unit,a,sK14,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( ( vAPP(partia96731725t_unit,a,sK15,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f1037,f1039,f1038]) ).
thf(f1038,plain,
! [X0: partia96731725t_unit] :
( ? [X1: a] :
( ! [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ! [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),vAPP(partia96731725t_unit,a,sK14,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1039,plain,
! [X0: partia96731725t_unit] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X3) != X3 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ( vAPP(partia96731725t_unit,a,sK15,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1037,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ? [X1: a] :
( ! [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X3) != X3 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(rectify,[],[f1015]) ).
thf(f1015,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ? [X7: a] :
( ! [X8: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X8),X7) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ? [X6: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X6) != X6 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(definition_folding,[],[f722,f1014,f1013]) ).
thf(f1013,plain,
! [X0: partia96731725t_unit] :
( ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f1014,plain,
! [X0: partia96731725t_unit] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f722,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ? [X7: a] :
( ! [X8: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X8),X7) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ? [X6: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X6) != X6 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
inference(flattening,[],[f721]) ).
thf(f721,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ? [X7: a] :
( ! [X8: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X8),X7) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ? [X6: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X6) != X6 )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
inference(ennf_transformation,[],[f308]) ).
thf(f308,plain,
! [X0: partia96731725t_unit] :
( ! [X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ! [X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ! [X3: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ! [X4: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ! [X5: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X4),X5)) ) ) ) )
=> ( ! [X6: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X6) = X6 ) )
=> ( ! [X7: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ? [X8: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X8),X7) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) )
=> ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ) ) ) ),
inference(fool_elimination,[],[f307]) ).
thf(f307,plain,
! [X0: partia96731725t_unit] :
( ! [X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ! [X2: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( ! [X3: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ! [X4: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ! [X5: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X4)),X5) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X4),X5)) ) ) ) )
=> ( ! [X6: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),X6) = X6 ) )
=> ( ! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ? [X8: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X8),X7) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ) ) ),
inference(rectify,[],[f194]) ).
thf(f194,axiom,
! [X36: partia96731725t_unit] :
( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ! [X28: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X28),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X17),X28)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36)) ) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X36)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ! [X28: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X28),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ! [X37: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X37),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X17),X28)),X37) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X17),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X28),X37)) ) ) ) )
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),vAPP(partia96731725t_unit,a,one_a_Product_unit,X36)),X17) = X17 ) )
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ? [X38: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X38),X17) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X38),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36)) ) )
=> vAPP(partia96731725t_unit,$o,group_a_Product_unit,X36) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_groupI) ).
thf(f5456,plain,
( spl54_38
| spl54_49
| ~ spl54_183 ),
inference(avatar_split_clause,[],[f5202,f3886,f2008,f1926]) ).
thf(f5455,plain,
spl54_243,
inference(avatar_split_clause,[],[f1416,f5453]) ).
thf(f1416,plain,
! [X2: a,X3: nat,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f990]) ).
thf(f990,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f989]) ).
thf(f989,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f612]) ).
thf(f612,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: nat] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X1)),X2) ) ) ) ),
inference(fool_elimination,[],[f611]) ).
thf(f611,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: nat] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X1)),X2) ) ) ) ),
inference(rectify,[],[f101]) ).
thf(f101,axiom,
! [X29: partia1833973666xt_a_b,X0: a,X1: a,X30: nat] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X29),X30),X0)),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X29),X30),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X0),X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_semiring_Oadd__pow__ldistr) ).
thf(f5451,plain,
spl54_242,
inference(avatar_split_clause,[],[f1415,f5449]) ).
thf(f1415,plain,
! [X2: a,X3: nat,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f988]) ).
thf(f988,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f987]) ).
thf(f987,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f610]) ).
thf(f610,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: nat] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X2)) ) ) ) ),
inference(fool_elimination,[],[f609]) ).
thf(f609,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a,X3: nat] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X0),X3),X2)) ) ) ) ),
inference(rectify,[],[f102]) ).
thf(f102,axiom,
! [X29: partia1833973666xt_a_b,X0: a,X1: a,X30: nat] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X29),X30),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,X29),X30),X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_semiring_Oadd__pow__rdistr) ).
thf(f5447,plain,
spl54_241,
inference(avatar_split_clause,[],[f1165,f5445]) ).
thf(f5445,plain,
( spl54_241
<=> ! [X2: a,X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK23,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_241])]) ).
thf(f1165,plain,
! [X2: a,X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK23,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1059]) ).
thf(f5425,plain,
spl54_240,
inference(avatar_split_clause,[],[f1377,f5423]) ).
thf(f1377,plain,
! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f927]) ).
thf(f927,plain,
! [X0: a,X1: int,X2: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f554]) ).
thf(f554,plain,
! [X0: a,X1: int,X2: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) ) ),
inference(fool_elimination,[],[f553]) ).
thf(f553,plain,
! [X0: a,X1: int,X2: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0))) ) ),
inference(rectify,[],[f234]) ).
thf(f234,axiom,
! [X7: a,X34: int,X35: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X34),X35)),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X34),X7)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X35),X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_add_Oint__pow__diff) ).
thf(f5035,plain,
( spl54_239
| ~ spl54_49
| ~ spl54_149 ),
inference(avatar_split_clause,[],[f3458,f3454,f2008,f5033]) ).
thf(f3458,plain,
( ! [X0: a,X1: nat] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) )
| ~ spl54_49
| ~ spl54_149 ),
inference(forward_demodulation,[],[f3457,f2010]) ).
thf(f3457,plain,
( ! [X0: a,X1: nat] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
| ~ spl54_49
| ~ spl54_149 ),
inference(forward_demodulation,[],[f3455,f2010]) ).
thf(f5007,plain,
( spl54_238
| ~ spl54_32
| ~ spl54_94 ),
inference(avatar_split_clause,[],[f4330,f2333,f1899,f5004]) ).
thf(f4330,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_32
| ~ spl54_94 ),
inference(trivial_inequality_removal,[],[f3505]) ).
thf(f3505,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_32
| ~ spl54_94 ),
inference(superposition,[],[f2334,f1901]) ).
thf(f4988,plain,
spl54_237,
inference(avatar_split_clause,[],[f1695,f4985]) ).
thf(f4985,plain,
( spl54_237
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s2))),s3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_237])]) ).
thf(f1695,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s2))),s3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)),
inference(forward_demodulation,[],[f1114,f1113]) ).
thf(f1114,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s2))),s3),
inference(cnf_transformation,[],[f6]) ).
thf(f6,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s2))),s3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_061_As_A_092_060otimes_062_A_Is_H_H_A_092_060otimes_062_As_H_J_A_092_060otimes_062_As_H_H_092_060close_062) ).
thf(f4983,plain,
spl54_236,
inference(avatar_split_clause,[],[f1113,f4980]) ).
thf(f4978,plain,
spl54_235,
inference(avatar_split_clause,[],[f1112,f4975]) ).
thf(f1112,plain,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),
inference(cnf_transformation,[],[f8]) ).
thf(f8,axiom,
vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_H_H_A_092_060otimes_062_As_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062) ).
thf(f4960,plain,
spl54_234,
inference(avatar_split_clause,[],[f1369,f4958]) ).
thf(f1369,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f916]) ).
thf(f916,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f915]) ).
thf(f915,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f540]) ).
thf(f540,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) ) ) ) ),
inference(fool_elimination,[],[f539]) ).
thf(f539,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) ) ) ) ),
inference(rectify,[],[f247]) ).
thf(f247,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X7)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X8)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_abelian__group_Ominus__add) ).
thf(f4765,plain,
spl54_233,
inference(avatar_split_clause,[],[f1383,f4763]) ).
thf(f1383,plain,
! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f938]) ).
thf(f938,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f937]) ).
thf(f937,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f566]) ).
thf(f566,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) ) ) ),
inference(fool_elimination,[],[f565]) ).
thf(f565,plain,
! [X0: a,X1: a,X2: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)),X1) ) ) ),
inference(rectify,[],[f91]) ).
thf(f91,axiom,
! [X0: a,X1: a,X30: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X30),X0)),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X30),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__pow__ldistr) ).
thf(f4761,plain,
spl54_232,
inference(avatar_split_clause,[],[f1382,f4759]) ).
thf(f1382,plain,
! [X2: int,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f936]) ).
thf(f936,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f935]) ).
thf(f935,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f564]) ).
thf(f564,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) ) ) ),
inference(fool_elimination,[],[f563]) ).
thf(f563,plain,
! [X0: a,X1: a,X2: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X1)) ) ) ),
inference(rectify,[],[f69]) ).
thf(f69,axiom,
! [X0: a,X1: a,X30: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X30),X1)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X30),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_add__pow__rdistr__int) ).
thf(f4757,plain,
spl54_231,
inference(avatar_split_clause,[],[f1381,f4755]) ).
thf(f1381,plain,
! [X2: int,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f934]) ).
thf(f934,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f933]) ).
thf(f933,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f562]) ).
thf(f562,plain,
! [X0: a,X1: a,X2: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),X1) ) ) ),
inference(fool_elimination,[],[f561]) ).
thf(f561,plain,
! [X0: a,X1: a,X2: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)),X1) ) ) ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
! [X0: a,X1: a,X30: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X30),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X30),X0)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_add__pow__ldistr__int) ).
thf(f4753,plain,
spl54_230,
inference(avatar_split_clause,[],[f1380,f4751]) ).
thf(f1380,plain,
! [X2: nat,X0: a,X1: a] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f932]) ).
thf(f932,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f931]) ).
thf(f931,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f560]) ).
thf(f560,plain,
! [X0: a,X1: a,X2: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) ) ) ),
inference(fool_elimination,[],[f559]) ).
thf(f559,plain,
! [X0: a,X1: a,X2: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X1)) ) ) ),
inference(rectify,[],[f92]) ).
thf(f92,axiom,
! [X0: a,X1: a,X30: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X30),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X30),X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__pow__rdistr) ).
thf(f4749,plain,
spl54_229,
inference(avatar_split_clause,[],[f1176,f4747]) ).
thf(f4747,plain,
( spl54_229
<=> ! [X2: a,X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK30,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_229])]) ).
thf(f1176,plain,
! [X2: a,X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK30,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(cnf_transformation,[],[f1073]) ).
thf(f4745,plain,
spl54_228,
inference(avatar_split_clause,[],[f1151,f4743]) ).
thf(f1151,plain,
! [X2: a,X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),vAPP(partia96731725t_unit,a,sK14,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1040]) ).
thf(f4730,plain,
spl54_227,
inference(avatar_split_clause,[],[f1173,f4728]) ).
thf(f4728,plain,
( spl54_227
<=> ! [X0: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,a,sK28,X0))),vAPP(partia1833973666xt_a_b,a,sK29,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,a,sK29,X0))) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_227])]) ).
thf(f1173,plain,
! [X0: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,a,sK28,X0))),vAPP(partia1833973666xt_a_b,a,sK29,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,a,sK29,X0))) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ),
inference(cnf_transformation,[],[f1069]) ).
thf(f1069,plain,
! [X0: partia1833973666xt_a_b] :
( ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,a,sK28,X0))),vAPP(partia1833973666xt_a_b,a,sK29,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,a,sK29,X0))) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK29,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29])],[f1065,f1068,f1067,f1066]) ).
thf(f1066,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),X2)),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1067,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),X2)),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,a,sK28,X0))),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK28,X0)),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1068,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,a,sK28,X0))),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK28,X0)),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,a,sK28,X0))),vAPP(partia1833973666xt_a_b,a,sK29,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,a,sK29,X0))) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK29,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1065,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ),
inference(rectify,[],[f1064]) ).
thf(f1064,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ),
inference(nnf_transformation,[],[f1020]) ).
thf(f4726,plain,
spl54_226,
inference(avatar_split_clause,[],[f1162,f4724]) ).
thf(f4724,plain,
( spl54_226
<=> ! [X0: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,a,sK22,X0))) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,a,sK21,X0))),vAPP(partia1833973666xt_a_b,a,sK22,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_226])]) ).
thf(f1162,plain,
! [X0: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,a,sK22,X0))) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,a,sK21,X0))),vAPP(partia1833973666xt_a_b,a,sK22,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ),
inference(cnf_transformation,[],[f1055]) ).
thf(f1055,plain,
! [X0: partia1833973666xt_a_b] :
( ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,a,sK22,X0))) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,a,sK21,X0))),vAPP(partia1833973666xt_a_b,a,sK22,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK22,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f1051,f1054,f1053,f1052]) ).
thf(f1052,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),X2)),X3) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1053,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),X2)),X3) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK21,X0)),X3)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,a,sK21,X0))),X3) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1054,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK21,X0)),X3)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,a,sK21,X0))),X3) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,a,sK22,X0))) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,a,sK21,X0))),vAPP(partia1833973666xt_a_b,a,sK22,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK22,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1051,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X3)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),X3) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ),
inference(rectify,[],[f1050]) ).
thf(f1050,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ),
inference(nnf_transformation,[],[f1016]) ).
thf(f4722,plain,
spl54_225,
inference(avatar_split_clause,[],[f1148,f4720]) ).
thf(f1148,plain,
! [X0: partia96731725t_unit] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,a,sK12,X0))),vAPP(partia96731725t_unit,a,sK13,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,a,sK13,X0))) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f1036]) ).
thf(f1036,plain,
! [X0: partia96731725t_unit] :
( ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,a,sK12,X0))),vAPP(partia96731725t_unit,a,sK13,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,a,sK13,X0))) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK13,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f1032,f1035,f1034,f1033]) ).
thf(f1033,plain,
! [X0: partia96731725t_unit] :
( ? [X1: a] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),X2)),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1034,plain,
! [X0: partia96731725t_unit] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),X2)),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,a,sK12,X0))),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,X0)),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1035,plain,
! [X0: partia96731725t_unit] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,a,sK12,X0))),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,X0)),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,a,sK12,X0))),vAPP(partia96731725t_unit,a,sK13,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,a,sK13,X0))) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK13,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1032,plain,
! [X0: partia96731725t_unit] :
( ? [X1: a] :
( ? [X2: a] :
( ? [X3: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),X3) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X3)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ),
inference(rectify,[],[f1031]) ).
thf(f1031,plain,
! [X0: partia96731725t_unit] :
( ? [X3: a] :
( ? [X4: a] :
( ? [X5: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),X4)),X5) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X4),X5)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X5),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X4),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X3),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ),
inference(nnf_transformation,[],[f1013]) ).
thf(f4710,plain,
spl54_224,
inference(avatar_split_clause,[],[f1340,f4708]) ).
thf(f4708,plain,
( spl54_224
<=> ! [X2: a,X0: a,X1: a] :
( ( X0 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_224])]) ).
thf(f1340,plain,
! [X2: a,X0: a,X1: a] :
( ( X0 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) ) ),
inference(cnf_transformation,[],[f859]) ).
thf(f859,plain,
! [X0: a,X1: a,X2: a] :
( ( X0 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) ) ),
inference(flattening,[],[f858]) ).
thf(f858,plain,
! [X0: a,X1: a,X2: a] :
( ( X0 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) ) ),
inference(ennf_transformation,[],[f482]) ).
thf(f482,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2) )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( X0 = X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f481]) ).
thf(f481,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X2) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( X0 = X2 ) ) ) ) ) ),
inference(rectify,[],[f71]) ).
thf(f71,axiom,
! [X8: a,X7: a,X16: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X8),X7) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X16) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X16),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( X8 = X16 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_inv__unique) ).
thf(f4706,plain,
spl54_223,
inference(avatar_split_clause,[],[f1339,f4704]) ).
thf(f1339,plain,
! [X2: a,X0: a,X1: a] :
( ( X0 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(cnf_transformation,[],[f857]) ).
thf(f857,plain,
! [X0: a,X1: a,X2: a] :
( ( X0 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(flattening,[],[f856]) ).
thf(f856,plain,
! [X0: a,X1: a,X2: a] :
( ( X0 = X2 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(ennf_transformation,[],[f480]) ).
thf(f480,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2) )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( X0 = X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f479]) ).
thf(f479,plain,
! [X0: a,X1: a,X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X2) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( X0 = X2 ) ) ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f31,axiom,
! [X8: a,X7: a,X16: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),X7) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X16) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X16),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( X8 = X16 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_local_Ominus__unique) ).
thf(f4677,plain,
spl54_222,
inference(avatar_split_clause,[],[f1286,f4675]) ).
thf(f1286,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f825]) ).
thf(f825,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f824]) ).
thf(f824,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f444]) ).
thf(f444,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ) ),
inference(fool_elimination,[],[f443]) ).
thf(f443,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ) ),
inference(rectify,[],[f223]) ).
thf(f223,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X8)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add_Oinv__mult__group) ).
thf(f4673,plain,
spl54_221,
inference(avatar_split_clause,[],[f1285,f4671]) ).
thf(f1285,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f823]) ).
thf(f823,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f822]) ).
thf(f822,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f442]) ).
thf(f442,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) ) ) ),
inference(fool_elimination,[],[f441]) ).
thf(f441,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) ) ) ),
inference(rectify,[],[f218]) ).
thf(f218,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_local_Ominus__add) ).
thf(f4669,plain,
spl54_220,
inference(avatar_split_clause,[],[f1164,f4667]) ).
thf(f4667,plain,
( spl54_220
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,sK24,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK24,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_220])]) ).
thf(f1164,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,sK24,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK24,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1059]) ).
thf(f4641,plain,
spl54_219,
inference(avatar_split_clause,[],[f1376,f4639]) ).
thf(f1376,plain,
! [X2: nat,X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f926]) ).
thf(f926,plain,
! [X0: a,X1: nat,X2: nat] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f552]) ).
thf(f552,plain,
! [X0: a,X1: nat,X2: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) ) ),
inference(fool_elimination,[],[f551]) ).
thf(f551,plain,
! [X0: a,X1: nat,X2: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)),X0) ) ),
inference(rectify,[],[f103]) ).
thf(f103,axiom,
! [X7: a,X34: nat,X35: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X35),X7)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X34),X35)),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_add_Onat__pow__mult) ).
thf(f4637,plain,
spl54_218,
inference(avatar_split_clause,[],[f1375,f4635]) ).
thf(f1375,plain,
! [X2: int,X0: a,X1: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f925]) ).
thf(f925,plain,
! [X0: a,X1: int,X2: int] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f550]) ).
thf(f550,plain,
! [X0: a,X1: int,X2: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) ) ),
inference(fool_elimination,[],[f549]) ).
thf(f549,plain,
! [X0: a,X1: int,X2: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X2),X0)) ) ),
inference(rectify,[],[f90]) ).
thf(f90,axiom,
! [X7: a,X31: int,X33: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X31),X33)),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X31),X7)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X33),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add_Oint__pow__mult) ).
thf(f4630,plain,
spl54_217,
inference(avatar_split_clause,[],[f1124,f4627]) ).
thf(f4627,plain,
( spl54_217
<=> ( minus_minus_int = vAPP(sTfun(int,int),sTfun(int,sTfun(int,int)),vAPP(sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,int),sTfun(int,sTfun(int,int))),cCOMB,vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),vAPP(sTfun(sTfun(int,int),sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int)))),bCOMB,bCOMB),plus_plus_int)),uminus_uminus_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_217])]) ).
thf(f1124,plain,
minus_minus_int = vAPP(sTfun(int,int),sTfun(int,sTfun(int,int)),vAPP(sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,int),sTfun(int,sTfun(int,int))),cCOMB,vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),vAPP(sTfun(sTfun(int,int),sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int)))),bCOMB,bCOMB),plus_plus_int)),uminus_uminus_int),
inference(cnf_transformation,[],[f292]) ).
thf(f292,plain,
minus_minus_int = vAPP(sTfun(int,int),sTfun(int,sTfun(int,int)),vAPP(sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,int),sTfun(int,sTfun(int,int))),cCOMB,vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),vAPP(sTfun(sTfun(int,int),sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int)))),bCOMB,bCOMB),plus_plus_int)),uminus_uminus_int),
inference(fool_elimination,[],[f291]) ).
thf(f291,plain,
( minus_minus_int
= ( ^ [X0: int,X1: int] : vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,uminus_uminus_int,X1)) ) ),
inference(rectify,[],[f265]) ).
thf(f265,axiom,
( minus_minus_int
= ( ^ [X42: int,X43: int] : vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X42),vAPP(int,int,uminus_uminus_int,X43)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_ab__group__add__class_Oab__diff__conv__add__uminus) ).
thf(f4615,plain,
spl54_216,
inference(avatar_split_clause,[],[f1368,f4613]) ).
thf(f1368,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f914]) ).
thf(f914,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f913]) ).
thf(f913,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f538]) ).
thf(f538,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2) ) ) ) ),
inference(fool_elimination,[],[f537]) ).
thf(f537,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2) ) ) ) ),
inference(rectify,[],[f254]) ).
thf(f254,axiom,
! [X36: partia1833973666xt_a_b,X0: a,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X0)),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_abelian__group_Oinv__add) ).
thf(f4601,plain,
spl54_215,
inference(avatar_split_clause,[],[f1175,f4599]) ).
thf(f4599,plain,
( spl54_215
<=> ! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,sK31,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK31,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_215])]) ).
thf(f1175,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,sK31,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,a,sK31,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(cnf_transformation,[],[f1073]) ).
thf(f4597,plain,
spl54_214,
inference(avatar_split_clause,[],[f1150,f4595]) ).
thf(f1150,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(partia96731725t_unit,a,sK15,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,a,sK15,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1040]) ).
thf(f4564,plain,
( spl54_38
| spl54_49
| ~ spl54_183 ),
inference(avatar_split_clause,[],[f4078,f3886,f2008,f1926]) ).
thf(f4078,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| spl54_49
| ~ spl54_183 ),
inference(trivial_inequality_removal,[],[f4026]) ).
thf(f4026,plain,
( ( vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) != vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| spl54_49
| ~ spl54_183 ),
inference(superposition,[],[f2009,f3887]) ).
thf(f4562,plain,
spl54_213,
inference(avatar_split_clause,[],[f1284,f4560]) ).
thf(f1284,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f821]) ).
thf(f821,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f820]) ).
thf(f820,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f440]) ).
thf(f440,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) ) ) ),
inference(fool_elimination,[],[f439]) ).
thf(f439,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) ) ) ),
inference(rectify,[],[f225]) ).
thf(f225,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X8)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X8)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_r__minus) ).
thf(f4558,plain,
spl54_212,
inference(avatar_split_clause,[],[f1283,f4556]) ).
thf(f1283,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f819]) ).
thf(f819,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f818]) ).
thf(f818,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f438]) ).
thf(f438,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) ) ) ),
inference(fool_elimination,[],[f437]) ).
thf(f437,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) ) ) ),
inference(rectify,[],[f226]) ).
thf(f226,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X8)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)),X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_l__minus) ).
thf(f4554,plain,
spl54_211,
inference(avatar_split_clause,[],[f1282,f4552]) ).
thf(f1282,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f817]) ).
thf(f817,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f816]) ).
thf(f816,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f436]) ).
thf(f436,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) ) ) ),
inference(fool_elimination,[],[f435]) ).
thf(f435,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) ) ) ),
inference(rectify,[],[f215]) ).
thf(f215,axiom,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_inv__add) ).
thf(f4550,plain,
spl54_210,
inference(avatar_split_clause,[],[f1243,f4548]) ).
thf(f4548,plain,
( spl54_210
<=> ! [X0: partia1833973666xt_a_b,X1: partia1833973666xt_a_b] :
( ( X0 = X1 )
| ( vAPP(partia1833973666xt_a_b,b,more_a_b,X0) != vAPP(partia1833973666xt_a_b,b,more_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0) != vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) != vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) != vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_210])]) ).
thf(f1243,plain,
! [X0: partia1833973666xt_a_b,X1: partia1833973666xt_a_b] :
( ( X0 = X1 )
| ( vAPP(partia1833973666xt_a_b,b,more_a_b,X0) != vAPP(partia1833973666xt_a_b,b,more_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0) != vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) != vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) != vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1) ) ),
inference(cnf_transformation,[],[f758]) ).
thf(f758,plain,
! [X0: partia1833973666xt_a_b,X1: partia1833973666xt_a_b] :
( ( X0 = X1 )
| ( vAPP(partia1833973666xt_a_b,b,more_a_b,X0) != vAPP(partia1833973666xt_a_b,b,more_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0) != vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) != vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) != vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1) ) ),
inference(flattening,[],[f757]) ).
thf(f757,plain,
! [X0: partia1833973666xt_a_b,X1: partia1833973666xt_a_b] :
( ( X0 = X1 )
| ( vAPP(partia1833973666xt_a_b,b,more_a_b,X0) != vAPP(partia1833973666xt_a_b,b,more_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0) != vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) != vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1) )
| ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) != vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1) ) ),
inference(ennf_transformation,[],[f687]) ).
thf(f687,plain,
! [X0: partia1833973666xt_a_b,X1: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X1) )
=> ( ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) = vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X1) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X1) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(partia1833973666xt_a_b,a,zero_a_b,X1) )
=> ( ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0) = vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X1) )
=> ( ( vAPP(partia1833973666xt_a_b,b,more_a_b,X0) = vAPP(partia1833973666xt_a_b,b,more_a_b,X1) )
=> ( X0 = X1 ) ) ) ) ) ) ),
inference(rectify,[],[f107]) ).
thf(f107,axiom,
! [X3: partia1833973666xt_a_b,X5: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X3) = vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X5) )
=> ( ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X3) = vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X5) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X3) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X5) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X3) = vAPP(partia1833973666xt_a_b,a,zero_a_b,X5) )
=> ( ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X3) = vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X5) )
=> ( ( vAPP(partia1833973666xt_a_b,b,more_a_b,X3) = vAPP(partia1833973666xt_a_b,b,more_a_b,X5) )
=> ( X3 = X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ring_Oequality) ).
thf(f4301,plain,
( spl54_209
| ~ spl54_49
| ~ spl54_148 ),
inference(avatar_split_clause,[],[f3452,f3449,f2008,f4299]) ).
thf(f3452,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) ) )
| ~ spl54_49
| ~ spl54_148 ),
inference(forward_demodulation,[],[f3450,f2010]) ).
thf(f4295,plain,
( ~ spl54_141
| spl54_32
| ~ spl54_49 ),
inference(avatar_split_clause,[],[f3340,f2008,f1899,f3336]) ).
thf(f3340,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| spl54_32
| ~ spl54_49 ),
inference(forward_demodulation,[],[f1900,f2010]) ).
thf(f1900,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| spl54_32 ),
inference(avatar_component_clause,[],[f1899]) ).
thf(f4267,plain,
( spl54_208
| ~ spl54_32
| ~ spl54_93 ),
inference(avatar_split_clause,[],[f2354,f2329,f1899,f4264]) ).
thf(f2354,plain,
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_32
| ~ spl54_93 ),
inference(trivial_inequality_removal,[],[f2351]) ).
thf(f2351,plain,
( ( $true != $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,sK8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ~ spl54_32
| ~ spl54_93 ),
inference(superposition,[],[f2330,f1901]) ).
thf(f4247,plain,
spl54_207,
inference(avatar_split_clause,[],[f1379,f4245]) ).
thf(f1379,plain,
! [X2: nat,X0: a,X1: nat] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)),X0) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f930]) ).
thf(f930,plain,
! [X0: a,X1: nat,X2: nat] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)),X0) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f929]) ).
thf(f929,plain,
! [X0: a,X1: nat,X2: nat] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)),X0) )
| ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f558]) ).
thf(f558,plain,
! [X0: a,X1: nat,X2: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)),X0) ) ) ),
inference(fool_elimination,[],[f557]) ).
thf(f557,plain,
! [X0: a,X1: nat,X2: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X2),X0) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)),X0) ) ) ),
inference(rectify,[],[f105]) ).
thf(f105,axiom,
! [X7: a,X35: nat,X34: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X35),X7) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X35),X34)),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_add_Opow__eq__div2) ).
thf(f4243,plain,
spl54_206,
inference(avatar_split_clause,[],[f1354,f4241]) ).
thf(f4241,plain,
( spl54_206
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_206])]) ).
thf(f1354,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f887]) ).
thf(f887,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(flattening,[],[f886]) ).
thf(f886,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(ennf_transformation,[],[f510]) ).
thf(f510,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) ) ) ) ) ),
inference(fool_elimination,[],[f509]) ).
thf(f509,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0)
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) ) ) ) ) ),
inference(rectify,[],[f197]) ).
thf(f197,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X36)
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X7),X8) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X8),X7) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_group_Oinv__comm) ).
thf(f4239,plain,
spl54_205,
inference(avatar_split_clause,[],[f1346,f4237]) ).
thf(f1346,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f871]) ).
thf(f871,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(flattening,[],[f870]) ).
thf(f870,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) != vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(ennf_transformation,[],[f494]) ).
thf(f494,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) ) ) ) ) ),
inference(fool_elimination,[],[f493]) ).
thf(f493,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0)
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) ) ) ) ) ),
inference(rectify,[],[f196]) ).
thf(f196,axiom,
! [X36: partia96731725t_unit,X7: a,X8: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X36)
=> ( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X7),X8) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X8),X7) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_group_Oinv__comm) ).
thf(f4235,plain,
spl54_204,
inference(avatar_split_clause,[],[f1163,f4233]) ).
thf(f1163,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK23,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK24,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP4,X0) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP2,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1059]) ).
thf(f4196,plain,
spl54_203,
inference(avatar_split_clause,[],[f1367,f4194]) ).
thf(f1367,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f912]) ).
thf(f912,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f911]) ).
thf(f911,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f536]) ).
thf(f536,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = X2 ) ) ) ),
inference(fool_elimination,[],[f535]) ).
thf(f535,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)) = X2 ) ) ) ),
inference(rectify,[],[f249]) ).
thf(f249,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X7)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X7),X8)) = X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_abelian__group_Or__neg1) ).
thf(f4192,plain,
spl54_202,
inference(avatar_split_clause,[],[f1366,f4190]) ).
thf(f1366,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f910]) ).
thf(f910,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f909]) ).
thf(f909,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2)) = X2 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f534]) ).
thf(f534,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2)) = X2 ) ) ) ),
inference(fool_elimination,[],[f533]) ).
thf(f533,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X2)) = X2 ) ) ) ),
inference(rectify,[],[f248]) ).
thf(f248,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X7)),X8)) = X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_abelian__group_Or__neg2) ).
thf(f4170,plain,
spl54_201,
inference(avatar_split_clause,[],[f1246,f4168]) ).
thf(f1246,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) ) ),
inference(cnf_transformation,[],[f764]) ).
thf(f764,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) ) ),
inference(flattening,[],[f763]) ).
thf(f763,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) ) ),
inference(ennf_transformation,[],[f378]) ).
thf(f378,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) ) ) ) ),
inference(fool_elimination,[],[f377]) ).
thf(f377,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) ) ) ) ),
inference(rectify,[],[f190]) ).
thf(f190,axiom,
! [X7: a,X8: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X8) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X8),X7) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Units__inv__comm) ).
thf(f4166,plain,
spl54_200,
inference(avatar_split_clause,[],[f1245,f4164]) ).
thf(f1245,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(cnf_transformation,[],[f762]) ).
thf(f762,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(flattening,[],[f761]) ).
thf(f761,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(ennf_transformation,[],[f376]) ).
thf(f376,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ) ),
inference(fool_elimination,[],[f375]) ).
thf(f375,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f35,axiom,
! [X7: a,X8: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8) = vAPP(partia1833973666xt_a_b,a,zero_a_b,r) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add_Oinv__comm) ).
thf(f4162,plain,
spl54_199,
inference(avatar_split_clause,[],[f1174,f4160]) ).
thf(f1174,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK30,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK31,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP5,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true = vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(cnf_transformation,[],[f1073]) ).
thf(f4158,plain,
spl54_198,
inference(avatar_split_clause,[],[f1149,f4156]) ).
thf(f1149,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK14,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK15,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP0,X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true = vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1040]) ).
thf(f4154,plain,
( spl54_197
| ~ spl54_7
| ~ spl54_10 ),
inference(avatar_split_clause,[],[f1803,f1789,f1776,f4151]) ).
thf(f4151,plain,
( spl54_197
<=> ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_197])]) ).
thf(f4129,plain,
spl54_196,
inference(avatar_split_clause,[],[f1281,f4127]) ).
thf(f1281,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f815]) ).
thf(f815,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f814]) ).
thf(f814,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f434]) ).
thf(f434,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = X1 ) ) ),
inference(fool_elimination,[],[f433]) ).
thf(f433,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)) = X1 ) ) ),
inference(rectify,[],[f217]) ).
thf(f217,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)) = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_r__neg1) ).
thf(f4125,plain,
spl54_195,
inference(avatar_split_clause,[],[f1280,f4123]) ).
thf(f1280,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f813]) ).
thf(f813,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f812]) ).
thf(f812,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1)) = X1 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f432]) ).
thf(f432,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1)) = X1 ) ) ),
inference(fool_elimination,[],[f431]) ).
thf(f431,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X1)) = X1 ) ) ),
inference(rectify,[],[f216]) ).
thf(f216,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)),X8)) = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_r__neg2) ).
thf(f4090,plain,
spl54_194,
inference(avatar_split_clause,[],[f1365,f4088]) ).
thf(f1365,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f908]) ).
thf(f908,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f907]) ).
thf(f907,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f532]) ).
thf(f532,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) ) ) ) ),
inference(fool_elimination,[],[f531]) ).
thf(f531,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) ) ) ) ),
inference(rectify,[],[f112]) ).
thf(f112,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X8),X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_abelian__groupE_I4_J) ).
thf(f4022,plain,
spl54_193,
inference(avatar_split_clause,[],[f1359,f4020]) ).
thf(f1359,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f897]) ).
thf(f897,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f896]) ).
thf(f896,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f520]) ).
thf(f520,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) ) ) ) ),
inference(fool_elimination,[],[f519]) ).
thf(f519,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) ) ) ) ),
inference(rectify,[],[f86]) ).
thf(f86,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X8),X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_semiring_Osemiring__simprules_I7_J) ).
thf(f4018,plain,
spl54_192,
inference(avatar_split_clause,[],[f1352,f4016]) ).
thf(f1352,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(cnf_transformation,[],[f883]) ).
thf(f883,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(flattening,[],[f882]) ).
thf(f882,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(ennf_transformation,[],[f506]) ).
thf(f506,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) ) ) ) ),
inference(fool_elimination,[],[f505]) ).
thf(f505,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) ) ) ) ),
inference(rectify,[],[f276]) ).
thf(f276,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X8),X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_comm__groupE_I4_J) ).
thf(f4014,plain,
spl54_191,
inference(avatar_split_clause,[],[f1351,f4012]) ).
thf(f1351,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) ),
inference(cnf_transformation,[],[f881]) ).
thf(f881,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) ),
inference(flattening,[],[f880]) ).
thf(f880,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) ),
inference(ennf_transformation,[],[f504]) ).
thf(f504,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X1 ) ) ) ) ) ),
inference(fool_elimination,[],[f503]) ).
thf(f503,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,field_a_b,X0)
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = X1 ) ) ) ) ) ),
inference(rectify,[],[f100]) ).
thf(f100,axiom,
! [X29: partia1833973666xt_a_b,X0: a,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,field_a_b,X29)
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X29) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X0),X1) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X29) = X1 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X29) = X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_integral) ).
thf(f4010,plain,
spl54_190,
inference(avatar_split_clause,[],[f1344,f4008]) ).
thf(f1344,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(cnf_transformation,[],[f867]) ).
thf(f867,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(flattening,[],[f866]) ).
thf(f866,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(ennf_transformation,[],[f490]) ).
thf(f490,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( $true = vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) ) ) ) ),
inference(fool_elimination,[],[f489]) ).
thf(f489,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) ) ) ) ),
inference(rectify,[],[f275]) ).
thf(f275,axiom,
! [X36: partia96731725t_unit,X7: a,X8: a] :
( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X8),X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_comm__groupE_I4_J) ).
thf(f4004,plain,
spl54_189,
inference(avatar_split_clause,[],[f1363,f4002]) ).
thf(f4002,plain,
( spl54_189
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_189])]) ).
thf(f1363,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f904]) ).
thf(f904,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f903]) ).
thf(f903,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) != vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f528]) ).
thf(f528,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2) = X1 ) ) ) ) ),
inference(fool_elimination,[],[f527]) ).
thf(f527,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2) = X1 ) ) ) ) ),
inference(rectify,[],[f253]) ).
thf(f253,axiom,
! [X36: partia1833973666xt_a_b,X8: a,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X8),X7) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X7) = X8 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_abelian__group_Ominus__equality) ).
thf(f3990,plain,
spl54_188,
inference(avatar_split_clause,[],[f1277,f3988]) ).
thf(f1277,plain,
! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f807]) ).
thf(f807,plain,
! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f426]) ).
thf(f426,plain,
! [X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ),
inference(fool_elimination,[],[f425]) ).
thf(f425,plain,
! [X0: a,X1: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ),
inference(rectify,[],[f104]) ).
thf(f104,axiom,
! [X7: a,X34: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X34)),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Onat__pow__Suc2) ).
thf(f3904,plain,
spl54_187,
inference(avatar_split_clause,[],[f1371,f3902]) ).
thf(f1371,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f920]) ).
thf(f920,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f919]) ).
thf(f919,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f544]) ).
thf(f544,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ) ),
inference(fool_elimination,[],[f543]) ).
thf(f543,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(rectify,[],[f110]) ).
thf(f110,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_abelian__groupE_I1_J) ).
thf(f3900,plain,
spl54_186,
inference(avatar_split_clause,[],[f1370,f3898]) ).
thf(f1370,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f918]) ).
thf(f918,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f917]) ).
thf(f917,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f542]) ).
thf(f542,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ) ),
inference(fool_elimination,[],[f541]) ).
thf(f541,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(rectify,[],[f114]) ).
thf(f114,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_abelian__group_Ominus__closed) ).
thf(f3896,plain,
spl54_185,
inference(avatar_split_clause,[],[f1361,f3894]) ).
thf(f1361,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f901]) ).
thf(f901,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f900]) ).
thf(f900,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f524]) ).
thf(f524,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ) ),
inference(fool_elimination,[],[f523]) ).
thf(f523,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_semiring_Osemiring__simprules_I3_J) ).
thf(f3892,plain,
spl54_184,
inference(avatar_split_clause,[],[f1360,f3890]) ).
thf(f1360,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f899]) ).
thf(f899,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f898]) ).
thf(f898,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f522]) ).
thf(f522,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ) ),
inference(fool_elimination,[],[f521]) ).
thf(f521,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(rectify,[],[f84]) ).
thf(f84,axiom,
! [X29: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_semiring_Osemiring__simprules_I1_J) ).
thf(f3888,plain,
( spl54_183
| ~ spl54_2
| ~ spl54_12 ),
inference(avatar_split_clause,[],[f1809,f1797,f1725,f3886]) ).
thf(f1797,plain,
( spl54_12
<=> ! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_12])]) ).
thf(f1809,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_12 ),
inference(trivial_inequality_removal,[],[f1808]) ).
thf(f1808,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) )
| ( $false = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) )
| ~ spl54_2
| ~ spl54_12 ),
inference(superposition,[],[f1798,f1726]) ).
thf(f1798,plain,
( ! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
| ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) ) )
| ~ spl54_12 ),
inference(avatar_component_clause,[],[f1797]) ).
thf(f3884,plain,
spl54_182,
inference(avatar_split_clause,[],[f1353,f3882]) ).
thf(f1353,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(cnf_transformation,[],[f885]) ).
thf(f885,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(flattening,[],[f884]) ).
thf(f884,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(ennf_transformation,[],[f508]) ).
thf(f508,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ) ),
inference(fool_elimination,[],[f507]) ).
thf(f507,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(rectify,[],[f280]) ).
thf(f280,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_comm__groupE_I1_J) ).
thf(f3880,plain,
spl54_181,
inference(avatar_split_clause,[],[f1345,f3878]) ).
thf(f1345,plain,
! [X2: a,X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(cnf_transformation,[],[f869]) ).
thf(f869,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(flattening,[],[f868]) ).
thf(f868,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(ennf_transformation,[],[f492]) ).
thf(f492,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( ( $true = vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ) ),
inference(fool_elimination,[],[f491]) ).
thf(f491,plain,
! [X0: partia96731725t_unit,X1: a,X2: a] :
( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
inference(rectify,[],[f279]) ).
thf(f279,axiom,
! [X36: partia96731725t_unit,X7: a,X8: a] :
( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X7),X8)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_comm__groupE_I1_J) ).
thf(f3876,plain,
spl54_180,
inference(avatar_split_clause,[],[f1276,f3874]) ).
thf(f1276,plain,
! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f806]) ).
thf(f806,plain,
! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f424]) ).
thf(f424,plain,
! [X0: a,X1: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ),
inference(fool_elimination,[],[f423]) ).
thf(f423,plain,
! [X0: a,X1: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ),
inference(rectify,[],[f228]) ).
thf(f228,axiom,
! [X7: a,X31: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X31),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X31),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add_Oint__pow__inv) ).
thf(f3872,plain,
spl54_179,
inference(avatar_split_clause,[],[f1275,f3870]) ).
thf(f1275,plain,
! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f805]) ).
thf(f805,plain,
! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f422]) ).
thf(f422,plain,
! [X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ),
inference(fool_elimination,[],[f421]) ).
thf(f421,plain,
! [X0: a,X1: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ),
inference(rectify,[],[f227]) ).
thf(f227,axiom,
! [X7: a,X31: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X31),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X31),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_add_Onat__pow__inv) ).
thf(f3858,plain,
spl54_178,
inference(avatar_split_clause,[],[f1274,f3856]) ).
thf(f1274,plain,
! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f804]) ).
thf(f804,plain,
! [X0: a,X1: nat] :
( ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f420]) ).
thf(f420,plain,
! [X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ),
inference(fool_elimination,[],[f419]) ).
thf(f419,plain,
! [X0: a,X1: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X1))),X0) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)) ) ),
inference(rectify,[],[f269]) ).
thf(f269,axiom,
! [X7: a,X34: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,vAPP(nat,int,semiri2019852685at_int,X34))),X7) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_add_Oint__pow__neg__int) ).
thf(f3838,plain,
spl54_177,
inference(avatar_split_clause,[],[f1279,f3836]) ).
thf(f1279,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f811]) ).
thf(f811,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f810]) ).
thf(f810,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f430]) ).
thf(f430,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) ) ) ),
inference(fool_elimination,[],[f429]) ).
thf(f429,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) ) ) ),
inference(rectify,[],[f25]) ).
thf(f25,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X8),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_m__comm) ).
thf(f3834,plain,
spl54_176,
inference(avatar_split_clause,[],[f1278,f3832]) ).
thf(f1278,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f809]) ).
thf(f809,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f808]) ).
thf(f808,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f428]) ).
thf(f428,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ),
inference(fool_elimination,[],[f427]) ).
thf(f427,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) ) ) ),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add_Om__comm) ).
thf(f3826,plain,
spl54_175,
inference(avatar_split_clause,[],[f1244,f3824]) ).
thf(f1244,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(cnf_transformation,[],[f760]) ).
thf(f760,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(flattening,[],[f759]) ).
thf(f759,plain,
! [X0: a,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) ) ),
inference(ennf_transformation,[],[f374]) ).
thf(f374,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X0 ) ) ) ),
inference(fool_elimination,[],[f373]) ).
thf(f373,plain,
! [X0: a,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1) = X0 ) ) ) ),
inference(rectify,[],[f232]) ).
thf(f232,axiom,
! [X8: a,X7: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X8),X7) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7) = X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_minus__equality) ).
thf(f3812,plain,
spl54_174,
inference(avatar_split_clause,[],[f1273,f3810]) ).
thf(f1273,plain,
! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f803]) ).
thf(f803,plain,
! [X0: a,X1: int] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f418]) ).
thf(f418,plain,
! [X0: a,X1: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) ) ),
inference(fool_elimination,[],[f417]) ).
thf(f417,plain,
! [X0: a,X1: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X1)),X0) ) ),
inference(rectify,[],[f256]) ).
thf(f256,axiom,
! [X7: a,X31: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X31),X7)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),vAPP(int,int,uminus_uminus_int,X31)),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add_Oint__pow__neg) ).
thf(f3775,plain,
spl54_173,
inference(avatar_split_clause,[],[f1536,f3773]) ).
thf(f3773,plain,
( spl54_173
<=> ! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_173])]) ).
thf(f1536,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(duplicate_literal_removal,[],[f1364]) ).
thf(f1364,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f906]) ).
thf(f906,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f905]) ).
thf(f905,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( X1 = X2 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f530]) ).
thf(f530,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
=> ( X1 = X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f529]) ).
thf(f529,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
=> ( X1 = X2 ) ) ) ) ) ),
inference(rectify,[],[f120]) ).
thf(f120,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),X7),X8) = vAPP(partia1833973666xt_a_b,a,zero_a_b,X36) )
=> ( X7 = X8 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_abelian__group_Ominus__to__eq) ).
thf(f3761,plain,
spl54_172,
inference(avatar_split_clause,[],[f1294,f3759]) ).
thf(f1294,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f841]) ).
thf(f841,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f840]) ).
thf(f840,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f460]) ).
thf(f460,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
inference(fool_elimination,[],[f459]) ).
thf(f459,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(rectify,[],[f41]) ).
thf(f41,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_semiring__simprules_I3_J) ).
thf(f3757,plain,
spl54_171,
inference(avatar_split_clause,[],[f1293,f3755]) ).
thf(f1293,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f839]) ).
thf(f839,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f838]) ).
thf(f838,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f458]) ).
thf(f458,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
inference(fool_elimination,[],[f457]) ).
thf(f457,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(rectify,[],[f39]) ).
thf(f39,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add_Om__closed) ).
thf(f3753,plain,
spl54_170,
inference(avatar_split_clause,[],[f1292,f3751]) ).
thf(f1292,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f837]) ).
thf(f837,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f836]) ).
thf(f836,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f456]) ).
thf(f456,plain,
! [X0: a,X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
inference(fool_elimination,[],[f455]) ).
thf(f455,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_minus__closed) ).
thf(f3749,plain,
spl54_169,
inference(avatar_split_clause,[],[f1272,f3747]) ).
thf(f1272,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(cnf_transformation,[],[f802]) ).
thf(f802,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(flattening,[],[f801]) ).
thf(f801,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(ennf_transformation,[],[f416]) ).
thf(f416,plain,
! [X0: a,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ) ),
inference(fool_elimination,[],[f415]) ).
thf(f415,plain,
! [X0: a,X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(rectify,[],[f191]) ).
thf(f191,axiom,
! [X7: a,X8: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X8)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Units__m__closed) ).
thf(f3745,plain,
spl54_168,
inference(avatar_split_clause,[],[f1440,f3742]) ).
thf(f1440,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(cnf_transformation,[],[f660]) ).
thf(f660,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(fool_elimination,[],[f659]) ).
thf(f659,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_f5) ).
thf(f3740,plain,
spl54_167,
inference(avatar_split_clause,[],[f1439,f3737]) ).
thf(f1439,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(cnf_transformation,[],[f658]) ).
thf(f658,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(fool_elimination,[],[f657]) ).
thf(f657,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
inference(rectify,[],[f12]) ).
thf(f12,axiom,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f4) ).
thf(f3735,plain,
spl54_166,
inference(avatar_split_clause,[],[f1155,f3733]) ).
thf(f3733,plain,
( spl54_166
<=> ! [X0: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,a,sK17,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,a,sK16,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_166])]) ).
thf(f1155,plain,
! [X0: partia1833973666xt_a_b] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,a,sK17,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,a,sK16,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ),
inference(cnf_transformation,[],[f1045]) ).
thf(f1045,plain,
! [X0: partia1833973666xt_a_b] :
( ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,a,sK17,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,a,sK16,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f1042,f1044,f1043]) ).
thf(f1043,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK16,X0)),X2) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK16,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1044,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK16,X0)),X2) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),vAPP(partia1833973666xt_a_b,a,sK16,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,a,sK17,X0)) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,a,sK16,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1042,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ),
inference(rectify,[],[f1041]) ).
thf(f1041,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X6: a] :
( ? [X7: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X6),X7) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X7),X6) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X6),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ),
inference(nnf_transformation,[],[f1018]) ).
thf(f3731,plain,
( spl54_165
| ~ spl54_2
| spl54_141 ),
inference(avatar_split_clause,[],[f3429,f3336,f1725,f3728]) ).
thf(f3429,plain,
( ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_2
| spl54_141 ),
inference(trivial_inequality_removal,[],[f3428]) ).
thf(f3428,plain,
( ( $true != $true )
| ( $false = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ~ spl54_2
| spl54_141 ),
inference(superposition,[],[f3337,f1726]) ).
thf(f3337,plain,
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| spl54_141 ),
inference(avatar_component_clause,[],[f3336]) ).
thf(f3722,plain,
spl54_164,
inference(avatar_split_clause,[],[f1237,f3720]) ).
thf(f1237,plain,
! [X0: nat,X1: a] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),X1) ),
inference(cnf_transformation,[],[f685]) ).
thf(f685,plain,
! [X0: nat,X1: a] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),X1)),X1) ),
inference(rectify,[],[f109]) ).
thf(f109,axiom,
! [X34: nat,X7: a] : ( vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),vAPP(nat,nat,suc,X34)),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)),X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_add_Onat__pow__Suc) ).
thf(f3660,plain,
spl54_163,
inference(avatar_split_clause,[],[f1270,f3658]) ).
thf(f1270,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f1107]) ).
thf(f1107,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f798,f1106]) ).
thf(f1106,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f798,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f797]) ).
thf(f797,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f412]) ).
thf(f412,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ) ),
inference(fool_elimination,[],[f411]) ).
thf(f411,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X2),X1) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(rectify,[],[f117]) ).
thf(f117,axiom,
! [X29: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ? [X17: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X29) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X17),X7) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_abelian__groupE_I6_J) ).
thf(f3656,plain,
spl54_162,
inference(avatar_split_clause,[],[f1268,f3654]) ).
thf(f1268,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f796]) ).
thf(f796,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f795]) ).
thf(f795,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f410]) ).
thf(f410,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X1) ) ) ),
inference(fool_elimination,[],[f409]) ).
thf(f409,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),X1) ) ) ),
inference(rectify,[],[f251]) ).
thf(f251,axiom,
! [X36: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X7)),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_abelian__group_Ol__neg) ).
thf(f3652,plain,
spl54_161,
inference(avatar_split_clause,[],[f1267,f3650]) ).
thf(f1267,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f794]) ).
thf(f794,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f793]) ).
thf(f793,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f408]) ).
thf(f408,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) ) ) ),
inference(fool_elimination,[],[f407]) ).
thf(f407,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) ) ) ),
inference(rectify,[],[f252]) ).
thf(f252,axiom,
! [X36: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X7),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_abelian__group_Or__neg) ).
thf(f3648,plain,
spl54_160,
inference(avatar_split_clause,[],[f1259,f3646]) ).
thf(f1259,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f1105]) ).
thf(f1105,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f778,f1104]) ).
thf(f1104,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f778,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(flattening,[],[f777]) ).
thf(f777,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(ennf_transformation,[],[f392]) ).
thf(f392,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ) ),
inference(fool_elimination,[],[f391]) ).
thf(f391,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ? [X2: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X2),X1) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(rectify,[],[f199]) ).
thf(f199,axiom,
! [X36: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ? [X17: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X17),X7) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_group_Ol__inv__ex) ).
thf(f3644,plain,
spl54_159,
inference(avatar_split_clause,[],[f1257,f3642]) ).
thf(f1257,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f1103]) ).
thf(f1103,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f776,f1102]) ).
thf(f1102,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f776,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(flattening,[],[f775]) ).
thf(f775,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(ennf_transformation,[],[f390]) ).
thf(f390,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ) ),
inference(fool_elimination,[],[f389]) ).
thf(f389,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(rectify,[],[f213]) ).
thf(f213,axiom,
! [X36: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ? [X17: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36),X7),X17) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_group_Or__inv__ex) ).
thf(f3640,plain,
spl54_158,
inference(avatar_split_clause,[],[f1255,f3638]) ).
thf(f1255,plain,
! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f1101]) ).
thf(f1101,plain,
! [X0: partia96731725t_unit,X1: a] :
( ( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f774,f1100]) ).
thf(f1100,plain,
! [X0: partia96731725t_unit,X1: a] :
( ? [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f774,plain,
! [X0: partia96731725t_unit,X1: a] :
( ? [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(flattening,[],[f773]) ).
thf(f773,plain,
! [X0: partia96731725t_unit,X1: a] :
( ? [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(ennf_transformation,[],[f388]) ).
thf(f388,plain,
! [X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ? [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ) ),
inference(fool_elimination,[],[f387]) ).
thf(f387,plain,
! [X0: partia96731725t_unit,X1: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ? [X2: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X2),X1) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
inference(rectify,[],[f198]) ).
thf(f198,axiom,
! [X36: partia96731725t_unit,X7: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ? [X17: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X17),X7) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_group_Ol__inv__ex) ).
thf(f3636,plain,
spl54_157,
inference(avatar_split_clause,[],[f1253,f3634]) ).
thf(f1253,plain,
! [X0: partia96731725t_unit,X1: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f1099]) ).
thf(f1099,plain,
! [X0: partia96731725t_unit,X1: a] :
( ( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f772,f1098]) ).
thf(f1098,plain,
! [X0: partia96731725t_unit,X1: a] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f772,plain,
! [X0: partia96731725t_unit,X1: a] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(flattening,[],[f771]) ).
thf(f771,plain,
! [X0: partia96731725t_unit,X1: a] :
( ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(ennf_transformation,[],[f386]) ).
thf(f386,plain,
! [X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
=> ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ) ),
inference(fool_elimination,[],[f385]) ).
thf(f385,plain,
! [X0: partia96731725t_unit,X1: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0))
=> ? [X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2) = vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
inference(rectify,[],[f212]) ).
thf(f212,axiom,
! [X36: partia96731725t_unit,X7: a] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36))
=> ? [X17: a] :
( ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X36) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36),X7),X17) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_group_Or__inv__ex) ).
thf(f3628,plain,
spl54_156,
inference(avatar_split_clause,[],[f1362,f3626]) ).
thf(f1362,plain,
! [X2: a,X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f902]) ).
thf(f902,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f526]) ).
thf(f526,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) ) ),
inference(fool_elimination,[],[f525]) ).
thf(f525,plain,
! [X0: partia1833973666xt_a_b,X1: a,X2: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X0),X1),X2) ) ),
inference(rectify,[],[f250]) ).
thf(f250,axiom,
! [X36: partia1833973666xt_a_b,X7: a,X8: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,X36),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X36),X7),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_abelian__group_Ominus__eq) ).
thf(f3605,plain,
spl54_155,
inference(avatar_split_clause,[],[f1264,f3603]) ).
thf(f1264,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f788]) ).
thf(f788,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f787]) ).
thf(f787,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f402]) ).
thf(f402,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) ) ) ),
inference(fool_elimination,[],[f401]) ).
thf(f401,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) ) ) ),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
! [X29: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X29) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)),X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_semiring_Ol__null) ).
thf(f3601,plain,
spl54_154,
inference(avatar_split_clause,[],[f1263,f3599]) ).
thf(f1263,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f786]) ).
thf(f786,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f785]) ).
thf(f785,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f400]) ).
thf(f400,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) ) ) ),
inference(fool_elimination,[],[f399]) ).
thf(f399,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) ) ) ),
inference(rectify,[],[f66]) ).
thf(f66,axiom,
! [X29: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X29) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),X7),vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_semiring_Or__null) ).
thf(f3597,plain,
spl54_153,
inference(avatar_split_clause,[],[f1204,f3595]) ).
thf(f3595,plain,
( spl54_153
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( vAPP(a,a,sK35,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK35,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_153])]) ).
thf(f1204,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( vAPP(a,a,sK35,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK35,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1081]) ).
thf(f1081,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( ( vAPP(a,a,sK35,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK35,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f751,f1080]) ).
thf(f1080,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != X1 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
=> ( ( vAPP(a,a,sK35,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK35,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f751,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ? [X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != X1 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f750]) ).
thf(f750,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ? [X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) != X1 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f358]) ).
thf(f358,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ! [X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = X1 ) )
=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 ) ) ),
inference(fool_elimination,[],[f357]) ).
thf(f357,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ! [X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) = X1 ) )
=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 ) ) ),
inference(rectify,[],[f72]) ).
thf(f72,axiom,
! [X18: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X18),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X18),X17) = X17 ) )
=> ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_one__unique) ).
thf(f3593,plain,
spl54_152,
inference(avatar_split_clause,[],[f1202,f3591]) ).
thf(f3591,plain,
( spl54_152
<=> ! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( vAPP(a,a,sK34,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK34,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_152])]) ).
thf(f1202,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( vAPP(a,a,sK34,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK34,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1079]) ).
thf(f1079,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( ( vAPP(a,a,sK34,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK34,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f749,f1078]) ).
thf(f1078,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X1 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
=> ( ( vAPP(a,a,sK34,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK34,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f749,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ? [X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X1 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(flattening,[],[f748]) ).
thf(f748,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ? [X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) != X1 )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f356]) ).
thf(f356,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( ! [X1: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X1 ) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ) ),
inference(fool_elimination,[],[f355]) ).
thf(f355,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ! [X1: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) = X1 ) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f33,axiom,
! [X18: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X18),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X18),X17) = X17 ) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add_Oone__unique) ).
thf(f3468,plain,
( spl54_151
| ~ spl54_49
| ~ spl54_147 ),
inference(avatar_split_clause,[],[f3447,f3444,f2008,f3466]) ).
thf(f3447,plain,
( ! [X0: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) )
| ~ spl54_49
| ~ spl54_147 ),
inference(forward_demodulation,[],[f3445,f2010]) ).
thf(f3462,plain,
spl54_150,
inference(avatar_split_clause,[],[f1296,f3460]) ).
thf(f1296,plain,
! [X0: a,X1: int] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f843]) ).
thf(f843,plain,
! [X0: a,X1: int] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f464]) ).
thf(f464,plain,
! [X0: a,X1: int] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(fool_elimination,[],[f463]) ).
thf(f463,plain,
! [X0: a,X1: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ),
inference(rectify,[],[f76]) ).
thf(f76,axiom,
! [X7: a,X31: int] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X31),X7)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add_Oint__pow__closed) ).
thf(f3456,plain,
spl54_149,
inference(avatar_split_clause,[],[f1295,f3454]) ).
thf(f1295,plain,
! [X0: a,X1: nat] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f842]) ).
thf(f842,plain,
! [X0: a,X1: nat] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f462]) ).
thf(f462,plain,
! [X0: a,X1: nat] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(fool_elimination,[],[f461]) ).
thf(f461,plain,
! [X0: a,X1: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ),
inference(rectify,[],[f97]) ).
thf(f97,axiom,
! [X7: a,X34: nat] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),X7)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add_Onat__pow__closed) ).
thf(f3451,plain,
spl54_148,
inference(avatar_split_clause,[],[f1199,f3449]) ).
thf(f1199,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f746]) ).
thf(f746,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f352]) ).
thf(f352,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) ) ),
inference(fool_elimination,[],[f351]) ).
thf(f351,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),X0) ) ),
inference(rectify,[],[f233]) ).
thf(f233,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_l__neg) ).
thf(f3446,plain,
spl54_147,
inference(avatar_split_clause,[],[f1198,f3444]) ).
thf(f1198,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f745]) ).
thf(f745,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f350]) ).
thf(f350,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ),
inference(fool_elimination,[],[f349]) ).
thf(f349,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) ) ),
inference(rectify,[],[f231]) ).
thf(f231,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_r__neg) ).
thf(f3440,plain,
( ~ spl54_146
| spl54_145 ),
inference(avatar_split_clause,[],[f3435,f3431,f3437]) ).
thf(f3431,plain,
( spl54_145
<=> ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_145])]) ).
thf(f3435,plain,
( ( $true != vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) )
| spl54_145 ),
inference(forward_demodulation,[],[f3433,f1113]) ).
thf(f3433,plain,
( ( vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) != $true )
| spl54_145 ),
inference(avatar_component_clause,[],[f3431]) ).
thf(f3434,plain,
~ spl54_145,
inference(avatar_split_clause,[],[f1110,f3431]) ).
thf(f1110,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) != $true,
inference(cnf_transformation,[],[f663]) ).
thf(f663,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) != $true,
inference(flattening,[],[f288]) ).
thf(f288,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) != $true,
inference(fool_elimination,[],[f287]) ).
thf(f287,plain,
~ vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
inference(rectify,[],[f284]) ).
thf(f284,negated_conjecture,
~ vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
inference(negated_conjecture,[],[f283]) ).
thf(f283,conjecture,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)))),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f3352,plain,
spl54_144,
inference(avatar_split_clause,[],[f1717,f3350]) ).
thf(f1717,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)) ),
inference(forward_demodulation,[],[f1319,f1304]) ).
thf(f1304,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
inference(cnf_transformation,[],[f695]) ).
thf(f695,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
inference(rectify,[],[f121]) ).
thf(f121,axiom,
! [X31: nat,X33: nat,X30: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X31),X33)),X30) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X31),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X33),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_diff__diff__left) ).
thf(f1319,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)) ),
inference(cnf_transformation,[],[f702]) ).
thf(f702,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)) ),
inference(rectify,[],[f122]) ).
thf(f122,axiom,
! [X35: nat,X34: nat,X30: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X35)),X34)),vAPP(nat,nat,suc,X30)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X35),X34)),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Suc__diff__diff) ).
thf(f3348,plain,
spl54_143,
inference(avatar_split_clause,[],[f1271,f3346]) ).
thf(f1271,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f800]) ).
thf(f800,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f799]) ).
thf(f799,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f414]) ).
thf(f414,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
inference(fool_elimination,[],[f413]) ).
thf(f413,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ),
inference(rectify,[],[f242]) ).
thf(f242,axiom,
! [X36: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X7)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_abelian__group_Oa__inv__closed) ).
thf(f3344,plain,
spl54_142,
inference(avatar_split_clause,[],[f1269,f3342]) ).
thf(f1269,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK52,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f1107]) ).
thf(f3339,plain,
( spl54_141
| ~ spl54_32
| ~ spl54_49 ),
inference(avatar_split_clause,[],[f3277,f2008,f1899,f3336]) ).
thf(f3334,plain,
spl54_140,
inference(avatar_split_clause,[],[f1258,f3332]) ).
thf(f1258,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK51,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f1105]) ).
thf(f3330,plain,
spl54_139,
inference(avatar_split_clause,[],[f1256,f3328]) ).
thf(f1256,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,vAPP(a,sTfun(partia1833973666xt_a_b,a),sK50,X1),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f1103]) ).
thf(f3326,plain,
spl54_138,
inference(avatar_split_clause,[],[f1254,f3324]) ).
thf(f1254,plain,
! [X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK49,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f1101]) ).
thf(f3322,plain,
spl54_137,
inference(avatar_split_clause,[],[f1252,f3320]) ).
thf(f1252,plain,
! [X0: partia96731725t_unit,X1: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,vAPP(a,sTfun(partia96731725t_unit,a),sK48,X1),X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f1099]) ).
thf(f3308,plain,
spl54_136,
inference(avatar_split_clause,[],[f1169,f3306]) ).
thf(f1169,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,a,sK26,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(cnf_transformation,[],[f1063]) ).
thf(f1063,plain,
! [X0: partia1833973666xt_a_b] :
( ( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,a,sK26,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK26,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f1060,f1062,f1061]) ).
thf(f1061,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1062,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,a,sK26,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK26,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1060,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(nnf_transformation,[],[f1021]) ).
thf(f3304,plain,
spl54_135,
inference(avatar_split_clause,[],[f1158,f3302]) ).
thf(f1158,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,a,sK19,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1049]) ).
thf(f1049,plain,
! [X0: partia1833973666xt_a_b] :
( ( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,a,sK19,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK19,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f1046,f1048,f1047]) ).
thf(f1047,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1048,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
=> ( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,a,sK19,X0))),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK19,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1046,plain,
! [X0: partia1833973666xt_a_b] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),X2)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(nnf_transformation,[],[f1017]) ).
thf(f3300,plain,
spl54_134,
inference(avatar_split_clause,[],[f1144,f3298]) ).
thf(f1144,plain,
! [X0: partia96731725t_unit] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,a,sK10,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1030]) ).
thf(f1030,plain,
! [X0: partia96731725t_unit] :
( ( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,a,sK10,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK10,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f1027,f1029,f1028]) ).
thf(f1028,plain,
! [X0: partia96731725t_unit] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1029,plain,
! [X0: partia96731725t_unit] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
=> ( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,a,sK10,X0))),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK10,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1027,plain,
! [X0: partia96731725t_unit] :
( ? [X1: a] :
( ? [X2: a] :
( ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0),X1),X2)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X2),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(nnf_transformation,[],[f1014]) ).
thf(f3241,plain,
spl54_133,
inference(avatar_split_clause,[],[f1266,f3239]) ).
thf(f1266,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f792]) ).
thf(f792,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f791]) ).
thf(f791,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f406]) ).
thf(f406,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 ) ) ),
inference(fool_elimination,[],[f405]) ).
thf(f405,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 ) ) ),
inference(rectify,[],[f116]) ).
thf(f116,axiom,
! [X29: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)),X7) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_abelian__groupE_I5_J) ).
thf(f3237,plain,
spl54_132,
inference(avatar_split_clause,[],[f1262,f3235]) ).
thf(f1262,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f784]) ).
thf(f784,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f783]) ).
thf(f783,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f398]) ).
thf(f398,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X1) = X1 ) ) ),
inference(fool_elimination,[],[f397]) ).
thf(f397,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),X1) = X1 ) ) ),
inference(rectify,[],[f81]) ).
thf(f81,axiom,
! [X29: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X29),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X29)),X7) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_semiring_Osemiring__simprules_I9_J) ).
thf(f3233,plain,
spl54_131,
inference(avatar_split_clause,[],[f1261,f3231]) ).
thf(f1261,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f782]) ).
thf(f782,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f781]) ).
thf(f781,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f396]) ).
thf(f396,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 ) ) ),
inference(fool_elimination,[],[f395]) ).
thf(f395,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),X1) = X1 ) ) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X29: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)),X7) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_semiring_Osemiring__simprules_I6_J) ).
thf(f3229,plain,
spl54_130,
inference(avatar_split_clause,[],[f1260,f3227]) ).
thf(f1260,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f780]) ).
thf(f780,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(flattening,[],[f779]) ).
thf(f779,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f394]) ).
thf(f394,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) = X1 ) ) ),
inference(fool_elimination,[],[f393]) ).
thf(f393,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X0),X1),vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)) = X1 ) ) ),
inference(rectify,[],[f63]) ).
thf(f63,axiom,
! [X29: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,X29),X7),vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_semiring_Osemiring__simprules_I11_J) ).
thf(f3225,plain,
spl54_129,
inference(avatar_split_clause,[],[f1236,f3223]) ).
thf(f1236,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) ),
inference(cnf_transformation,[],[f684]) ).
thf(f684,plain,
! [X0: a,X1: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X1)) ),
inference(rectify,[],[f229]) ).
thf(f229,axiom,
! [X7: a,X8: a] : ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),X7),X8) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_minus__eq) ).
thf(f3217,plain,
( ~ spl54_33
| ~ spl54_38 ),
inference(avatar_contradiction_clause,[],[f3216]) ).
thf(f3216,plain,
( $false
| ~ spl54_33
| ~ spl54_38 ),
inference(trivial_inequality_removal,[],[f3215]) ).
thf(f3215,plain,
( ( $true = $false )
| ~ spl54_33
| ~ spl54_38 ),
inference(forward_demodulation,[],[f1905,f1928]) ).
thf(f1928,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| ~ spl54_38 ),
inference(avatar_component_clause,[],[f1926]) ).
thf(f3213,plain,
( spl54_128
| spl54_33 ),
inference(avatar_split_clause,[],[f1132,f1903,f3211]) ).
thf(f1132,plain,
! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $true )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1026]) ).
thf(f1026,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $true )
| ( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f720,f1025]) ).
thf(f1025,plain,
( ? [X0: a] :
( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
=> ( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),sK8) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f720,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $true )
| ? [X0: a] :
( ! [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ) ),
inference(ennf_transformation,[],[f302]) ).
thf(f302,plain,
( ! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ) )
=> ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $true ) ),
inference(fool_elimination,[],[f301]) ).
thf(f301,plain,
( ! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
=> vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) ),
inference(rectify,[],[f188]) ).
thf(f188,axiom,
( ! [X17: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ? [X38: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X38),X17) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X38),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
=> vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_group__l__invI) ).
thf(f3143,plain,
spl54_127,
inference(avatar_split_clause,[],[f1454,f3141]) ).
thf(f3139,plain,
spl54_126,
inference(avatar_split_clause,[],[f1265,f3137]) ).
thf(f1265,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f790]) ).
thf(f790,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(flattening,[],[f789]) ).
thf(f789,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) = X1 )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f404]) ).
thf(f404,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) = X1 ) ) ),
inference(fool_elimination,[],[f403]) ).
thf(f403,plain,
! [X0: partia1833973666xt_a_b,X1: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X0),X1)) = X1 ) ) ),
inference(rectify,[],[f243]) ).
thf(f243,axiom,
! [X36: partia1833973666xt_a_b,X7: a] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X36)
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,X36),X7)) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_abelian__group_Ominus__minus) ).
thf(f3103,plain,
( spl54_125
| ~ spl54_2
| ~ spl54_10 ),
inference(avatar_split_clause,[],[f1802,f1789,f1725,f3101]) ).
thf(f3101,plain,
( spl54_125
<=> ! [X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) )
| ( $false = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_125])]) ).
thf(f1802,plain,
( ! [X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) )
| ( $false = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) )
| ~ spl54_2
| ~ spl54_10 ),
inference(trivial_inequality_removal,[],[f1801]) ).
thf(f1801,plain,
( ! [X0: partia96731725t_unit] :
( ( $true != $true )
| ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) )
| ( $false = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) )
| ~ spl54_2
| ~ spl54_10 ),
inference(superposition,[],[f1790,f1726]) ).
thf(f3087,plain,
spl54_124,
inference(avatar_split_clause,[],[f1208,f3085]) ).
thf(f1208,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1085]) ).
thf(f1085,plain,
! [X0: a] :
( ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f753,f1084]) ).
thf(f1084,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,sK37,X0)),X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f753,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f362]) ).
thf(f362,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ) ),
inference(fool_elimination,[],[f361]) ).
thf(f361,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X1),X0) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(rectify,[],[f34]) ).
thf(f34,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ? [X17: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X17),X7) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add_Ol__inv__ex) ).
thf(f3083,plain,
spl54_123,
inference(avatar_split_clause,[],[f1206,f3081]) ).
thf(f1206,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1083]) ).
thf(f1083,plain,
! [X0: a] :
( ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f752,f1082]) ).
thf(f1082,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(a,a,sK36,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f752,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f360]) ).
thf(f360,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ) ),
inference(fool_elimination,[],[f359]) ).
thf(f359,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),X1) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ? [X17: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),X17) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add_Or__inv__ex) ).
thf(f3079,plain,
spl54_122,
inference(avatar_split_clause,[],[f1197,f3077]) ).
thf(f1197,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f744]) ).
thf(f744,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f348]) ).
thf(f348,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ),
inference(fool_elimination,[],[f347]) ).
thf(f347,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) ) ),
inference(rectify,[],[f56]) ).
thf(f56,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_l__null) ).
thf(f3075,plain,
spl54_121,
inference(avatar_split_clause,[],[f1196,f3073]) ).
thf(f1196,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f743]) ).
thf(f743,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f346]) ).
thf(f346,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
inference(fool_elimination,[],[f345]) ).
thf(f345,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
inference(rectify,[],[f55]) ).
thf(f55,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_r__null) ).
thf(f3071,plain,
spl54_120,
inference(avatar_split_clause,[],[f1189,f3069]) ).
thf(f1189,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(cnf_transformation,[],[f1077]) ).
thf(f1077,plain,
! [X0: a] :
( ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f736,f1076]) ).
thf(f1076,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,sK33,X0)),X0) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f736,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(ennf_transformation,[],[f332]) ).
thf(f332,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ) ),
inference(fool_elimination,[],[f331]) ).
thf(f331,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X1),X0) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(rectify,[],[f186]) ).
thf(f186,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ? [X17: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X17),X7) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_Units__l__inv__ex) ).
thf(f3067,plain,
spl54_119,
inference(avatar_split_clause,[],[f1187,f3065]) ).
thf(f1187,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(cnf_transformation,[],[f1075]) ).
thf(f1075,plain,
! [X0: a] :
( ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f735,f1074]) ).
thf(f1074,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
=> ( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(a,a,sK32,X0)) )
& ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f735,plain,
! [X0: a] :
( ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(ennf_transformation,[],[f330]) ).
thf(f330,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
& ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ) ),
inference(fool_elimination,[],[f329]) ).
thf(f329,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ? [X1: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),X1) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(rectify,[],[f187]) ).
thf(f187,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> ? [X17: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),X17) )
& vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X17),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_Units__r__inv__ex) ).
thf(f3048,plain,
spl54_118,
inference(avatar_split_clause,[],[f1203,f3046]) ).
thf(f1203,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = X0 )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK35,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1081]) ).
thf(f3044,plain,
spl54_117,
inference(avatar_split_clause,[],[f1201,f3042]) ).
thf(f1201,plain,
! [X0: a] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = X0 )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK34,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1079]) ).
thf(f3031,plain,
spl54_116,
inference(avatar_split_clause,[],[f1209,f3029]) ).
thf(f1209,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f754]) ).
thf(f754,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f364]) ).
thf(f364,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(fool_elimination,[],[f363]) ).
thf(f363,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ),
inference(rectify,[],[f236]) ).
thf(f236,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add_Oinv__closed) ).
thf(f2502,plain,
spl54_115,
inference(avatar_split_clause,[],[f1716,f2500]) ).
thf(f2497,plain,
spl54_114,
inference(avatar_split_clause,[],[f1714,f2495]) ).
thf(f2493,plain,
spl54_113,
inference(avatar_split_clause,[],[f1712,f2491]) ).
thf(f1712,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X2)) ),
inference(forward_demodulation,[],[f1306,f1304]) ).
thf(f1306,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) ),
inference(cnf_transformation,[],[f696]) ).
thf(f696,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2)),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1)),X2) ),
inference(rectify,[],[f129]) ).
thf(f129,axiom,
! [X31: nat,X33: nat,X30: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X31),X33)),X30) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X31),X30)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_diff__commute) ).
thf(f2489,plain,
spl54_112,
inference(avatar_split_clause,[],[f1318,f2487]) ).
thf(f1318,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ),
inference(cnf_transformation,[],[f701]) ).
thf(f701,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ),
inference(rectify,[],[f141]) ).
thf(f141,axiom,
! [X0: int,X2: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_add__diff__cancel__right) ).
thf(f2485,plain,
spl54_111,
inference(avatar_split_clause,[],[f1314,f2483]) ).
thf(f1314,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ),
inference(cnf_transformation,[],[f183]) ).
thf(f183,axiom,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_diff__diff__add) ).
thf(f2481,plain,
spl54_110,
inference(avatar_split_clause,[],[f1313,f2479]) ).
thf(f2477,plain,
spl54_109,
inference(avatar_split_clause,[],[f1311,f2475]) ).
thf(f1311,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) ),
inference(cnf_transformation,[],[f170]) ).
thf(f170,axiom,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(f2473,plain,
spl54_108,
inference(avatar_split_clause,[],[f1310,f2471]) ).
thf(f1310,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ),
inference(cnf_transformation,[],[f698]) ).
thf(f698,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ),
inference(rectify,[],[f156]) ).
thf(f156,axiom,
! [X1: int,X0: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_add_Oleft__commute) ).
thf(f2469,plain,
spl54_107,
inference(avatar_split_clause,[],[f1308,f2467]) ).
thf(f2465,plain,
spl54_106,
inference(avatar_split_clause,[],[f1304,f2463]) ).
thf(f2461,plain,
spl54_105,
inference(avatar_split_clause,[],[f1302,f2459]) ).
thf(f1302,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,[],[f171]) ).
thf(f171,axiom,
! [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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(f2456,plain,
spl54_104,
inference(avatar_split_clause,[],[f1301,f2454]) ).
thf(f1301,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,[],[f694]) ).
thf(f694,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,[],[f157]) ).
thf(f157,axiom,
! [X1: nat,X0: 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_add_Oleft__commute) ).
thf(f2452,plain,
spl54_103,
inference(avatar_split_clause,[],[f1300,f2450]) ).
thf(f1300,plain,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) ),
inference(cnf_transformation,[],[f693]) ).
thf(f693,plain,
! [X0: int,X1: int,X2: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X2)) ),
inference(rectify,[],[f145]) ).
thf(f145,axiom,
! [X2: int,X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_add__diff__cancel__left) ).
thf(f2448,plain,
spl54_102,
inference(avatar_split_clause,[],[f1299,f2446]) ).
thf(f1299,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,[],[f692]) ).
thf(f692,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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(rectify,[],[f136]) ).
thf(f136,axiom,
! [X35: nat,X30: nat,X34: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X35),X34) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X30)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X34),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_diff__cancel2) ).
thf(f2444,plain,
spl54_101,
inference(avatar_split_clause,[],[f1297,f2442]) ).
thf(f1297,plain,
! [X2: nat,X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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,[],[f690]) ).
thf(f690,plain,
! [X0: nat,X1: nat,X2: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_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(rectify,[],[f137]) ).
thf(f137,axiom,
! [X30: nat,X35: nat,X34: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X35),X34) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X30),X35)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X30),X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_Nat_Odiff__cancel) ).
thf(f2408,plain,
spl54_100,
inference(avatar_split_clause,[],[f1195,f2406]) ).
thf(f1195,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f742]) ).
thf(f742,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f344]) ).
thf(f344,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 ) ),
inference(fool_elimination,[],[f343]) ).
thf(f343,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X0) = X0 ) ),
inference(rectify,[],[f78]) ).
thf(f78,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),X7) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_l__one) ).
thf(f2404,plain,
spl54_99,
inference(avatar_split_clause,[],[f1194,f2402]) ).
thf(f1194,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f741]) ).
thf(f741,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f342]) ).
thf(f342,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 ) ),
inference(fool_elimination,[],[f341]) ).
thf(f341,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X0) = X0 ) ),
inference(rectify,[],[f44]) ).
thf(f44,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),X7) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_l__zero) ).
thf(f2399,plain,
spl54_98,
inference(avatar_split_clause,[],[f1193,f2397]) ).
thf(f1193,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f740]) ).
thf(f740,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f340]) ).
thf(f340,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 ) ),
inference(fool_elimination,[],[f339]) ).
thf(f339,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X0 ) ),
inference(rectify,[],[f79]) ).
thf(f79,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),X7),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_r__one) ).
thf(f2395,plain,
spl54_97,
inference(avatar_split_clause,[],[f1192,f2393]) ).
thf(f1192,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f739]) ).
thf(f739,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f338]) ).
thf(f338,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 ) ),
inference(fool_elimination,[],[f337]) ).
thf(f337,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X0 ) ),
inference(rectify,[],[f43]) ).
thf(f43,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),X7),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_r__zero) ).
thf(f2381,plain,
spl54_96,
inference(avatar_split_clause,[],[f1372,f2379]) ).
thf(f1372,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1109]) ).
thf(f1109,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK53,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,X0))) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f922,f1108]) ).
thf(f1108,plain,
! [X0: nat > $o] :
( ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3)) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK53,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK53,X0))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f922,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(flattening,[],[f921]) ).
thf(f921,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ? [X3: nat] :
( ( $true != vAPP(nat,$o,X0,X3) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f546]) ).
thf(f546,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ! [X3: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3)) )
=> ( $true = vAPP(nat,$o,X0,X3) ) )
=> ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ) ),
inference(fool_elimination,[],[f545]) ).
thf(f545,plain,
! [X0: nat > $o,X1: nat,X2: nat] :
( vAPP(nat,$o,X0,X1)
=> ( ! [X3: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3))
=> vAPP(nat,$o,X0,X3) )
=> vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) ) ),
inference(rectify,[],[f133]) ).
thf(f133,axiom,
! [X20: nat > $o,X30: nat,X31: nat] :
( vAPP(nat,$o,X20,X30)
=> ( ! [X41: nat] :
( vAPP(nat,$o,X20,vAPP(nat,nat,suc,X41))
=> vAPP(nat,$o,X20,X41) )
=> vAPP(nat,$o,X20,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X30),X31)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_zero__induct__lemma) ).
thf(f2368,plain,
spl54_95,
inference(avatar_split_clause,[],[f1191,f2366]) ).
thf(f1191,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f738]) ).
thf(f738,plain,
! [X0: a] :
( ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(ennf_transformation,[],[f336]) ).
thf(f336,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 ) ),
inference(fool_elimination,[],[f335]) ).
thf(f335,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X0)) = X0 ) ),
inference(rectify,[],[f235]) ).
thf(f235,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r))
=> ( vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),X7)) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_local_Ominus__minus) ).
thf(f2335,plain,
spl54_94,
inference(avatar_split_clause,[],[f1207,f2333]) ).
thf(f1207,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK37,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1085]) ).
thf(f2331,plain,
spl54_93,
inference(avatar_split_clause,[],[f1205,f2329]) ).
thf(f1205,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK36,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) != $true ) ),
inference(cnf_transformation,[],[f1083]) ).
thf(f2327,plain,
spl54_92,
inference(avatar_split_clause,[],[f1188,f2325]) ).
thf(f1188,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK33,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(cnf_transformation,[],[f1077]) ).
thf(f2323,plain,
spl54_91,
inference(avatar_split_clause,[],[f1186,f2321]) ).
thf(f1186,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,sK32,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(cnf_transformation,[],[f1075]) ).
thf(f2310,plain,
spl54_90,
inference(avatar_split_clause,[],[f1373,f2308]) ).
thf(f1373,plain,
! [X2: nat,X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X1),X2)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK53,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f1109]) ).
thf(f2290,plain,
spl54_89,
inference(avatar_split_clause,[],[f1250,f2288]) ).
thf(f1250,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK47,X0))) ) ),
inference(cnf_transformation,[],[f1097]) ).
thf(f1097,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK47,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47])],[f768,f1096]) ).
thf(f1096,plain,
! [X0: product_prod_a_a > $o] :
( ? [X2: a,X3: a] : ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) )
=> ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK46,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK47,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f768,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ? [X2: a,X3: a] : ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) ) ),
inference(ennf_transformation,[],[f382]) ).
thf(f382,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ! [X2: a,X3: a] : ( $true = vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) )
=> ( $true = vAPP(product_prod_a_a,$o,X0,X1) ) ),
inference(fool_elimination,[],[f381]) ).
thf(f381,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ! [X2: a,X3: a] : vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3))
=> vAPP(product_prod_a_a,$o,X0,X1) ),
inference(rectify,[],[f57]) ).
thf(f57,axiom,
! [X20: product_prod_a_a > $o,X24: product_prod_a_a] :
( ! [X25: a,X26: a] : vAPP(product_prod_a_a,$o,X20,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X25),X26))
=> vAPP(product_prod_a_a,$o,X20,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_old_Oprod_Oinducts) ).
thf(f2286,plain,
spl54_88,
inference(avatar_split_clause,[],[f1249,f2284]) ).
thf(f1249,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK45,X0))) ) ),
inference(cnf_transformation,[],[f1095]) ).
thf(f1095,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK45,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45])],[f767,f1094]) ).
thf(f1094,plain,
! [X0: product_prod_a_a > $o] :
( ? [X2: a,X3: a] : ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) )
=> ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(sTfun(product_prod_a_a,$o),a,sK44,X0)),vAPP(sTfun(product_prod_a_a,$o),a,sK45,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f767,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ( $true = vAPP(product_prod_a_a,$o,X0,X1) )
| ? [X2: a,X3: a] : ( $true != vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) ) ),
inference(ennf_transformation,[],[f380]) ).
thf(f380,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ! [X2: a,X3: a] : ( $true = vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3)) )
=> ( $true = vAPP(product_prod_a_a,$o,X0,X1) ) ),
inference(fool_elimination,[],[f379]) ).
thf(f379,plain,
! [X0: product_prod_a_a > $o,X1: product_prod_a_a] :
( ! [X2: a,X3: a] : vAPP(product_prod_a_a,$o,X0,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X2),X3))
=> vAPP(product_prod_a_a,$o,X0,X1) ),
inference(rectify,[],[f60]) ).
thf(f60,axiom,
! [X20: product_prod_a_a > $o,X27: product_prod_a_a] :
( ! [X25: a,X26: a] : vAPP(product_prod_a_a,$o,X20,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X25),X26))
=> vAPP(product_prod_a_a,$o,X20,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_prod__cases) ).
thf(f2282,plain,
spl54_87,
inference(avatar_split_clause,[],[f1684,f2280]) ).
thf(f2280,plain,
( spl54_87
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,semiri1382578993at_nat,X0) = vAPP(nat,nat,semiri1382578993at_nat,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_87])]) ).
thf(f1684,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,semiri1382578993at_nat,X0) = vAPP(nat,nat,semiri1382578993at_nat,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f1683]) ).
thf(f1683,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,semiri1382578993at_nat,X0) = vAPP(nat,nat,semiri1382578993at_nat,X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f1679]) ).
thf(f1679,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,semiri1382578993at_nat,X0)),vAPP(nat,nat,semiri1382578993at_nat,X1)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1238]) ).
thf(f1238,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,semiri1382578993at_nat,X0)),vAPP(nat,nat,semiri1382578993at_nat,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ),
inference(cnf_transformation,[],[f366]) ).
thf(f366,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,semiri1382578993at_nat,X0)),vAPP(nat,nat,semiri1382578993at_nat,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ),
inference(fool_elimination,[],[f365]) ).
thf(f365,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,semiri1382578993at_nat,X0) = vAPP(nat,nat,semiri1382578993at_nat,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f271]) ).
thf(f271,axiom,
! [X35: nat,X34: nat] :
( ( vAPP(nat,nat,semiri1382578993at_nat,X35) = vAPP(nat,nat,semiri1382578993at_nat,X34) )
= ( X34 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_of__nat__eq__iff) ).
thf(f2248,plain,
spl54_86,
inference(avatar_split_clause,[],[f1235,f2246]) ).
thf(f1235,plain,
! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,uminus_uminus_int,X1)) ),
inference(cnf_transformation,[],[f259]) ).
thf(f259,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,uminus_uminus_int,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_minus__add__distrib) ).
thf(f2244,plain,
spl54_85,
inference(avatar_split_clause,[],[f1234,f2242]) ).
thf(f1234,plain,
! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,uminus_uminus_int,X0)) ),
inference(cnf_transformation,[],[f267]) ).
thf(f267,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X1)),vAPP(int,int,uminus_uminus_int,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_add_Oinverse__distrib__swap) ).
thf(f2240,plain,
spl54_84,
inference(avatar_split_clause,[],[f1233,f2238]) ).
thf(f1233,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(nat,int,semiri2019852685at_int,X1)) ),
inference(cnf_transformation,[],[f683]) ).
thf(f683,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X0)),vAPP(nat,int,semiri2019852685at_int,X1)) ),
inference(rectify,[],[f274]) ).
thf(f274,axiom,
! [X35: nat,X34: nat] : ( vAPP(nat,int,semiri2019852685at_int,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X34)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(nat,int,semiri2019852685at_int,X35)),vAPP(nat,int,semiri2019852685at_int,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_of__nat__add) ).
thf(f2236,plain,
spl54_83,
inference(avatar_split_clause,[],[f1232,f2234]) ).
thf(f1232,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,semiri1382578993at_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,semiri1382578993at_nat,X0)),vAPP(nat,nat,semiri1382578993at_nat,X1)) ),
inference(cnf_transformation,[],[f682]) ).
thf(f682,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,semiri1382578993at_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,semiri1382578993at_nat,X0)),vAPP(nat,nat,semiri1382578993at_nat,X1)) ),
inference(rectify,[],[f273]) ).
thf(f273,axiom,
! [X35: nat,X34: nat] : ( vAPP(nat,nat,semiri1382578993at_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X34)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,semiri1382578993at_nat,X35)),vAPP(nat,nat,semiri1382578993at_nat,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_of__nat__add) ).
thf(f2226,plain,
spl54_82,
inference(avatar_split_clause,[],[f1190,f2224]) ).
thf(f1190,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(cnf_transformation,[],[f737]) ).
thf(f737,plain,
! [X0: a] :
( ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true )
| ( $true != vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) ) ),
inference(ennf_transformation,[],[f334]) ).
thf(f334,plain,
! [X0: a] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) )
=> ( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true ) ),
inference(fool_elimination,[],[f333]) ).
thf(f333,plain,
! [X0: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X0),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ),
inference(rectify,[],[f189]) ).
thf(f189,axiom,
! [X7: a] :
( vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r))
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X7),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Units__closed) ).
thf(f2222,plain,
spl54_81,
inference(avatar_split_clause,[],[f1682,f2220]) ).
thf(f2220,plain,
( spl54_81
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,semiri1382578993at_nat,X0) != vAPP(nat,nat,semiri1382578993at_nat,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_81])]) ).
thf(f1682,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,semiri1382578993at_nat,X0) != vAPP(nat,nat,semiri1382578993at_nat,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f1681]) ).
thf(f1681,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,semiri1382578993at_nat,X0) != vAPP(nat,nat,semiri1382578993at_nat,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f1680]) ).
thf(f1680,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,semiri1382578993at_nat,X0)),vAPP(nat,nat,semiri1382578993at_nat,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1238]) ).
thf(f2218,plain,
spl54_80,
inference(avatar_split_clause,[],[f1704,f2215]) ).
thf(f1704,plain,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),
inference(forward_demodulation,[],[f1703,f1701]) ).
thf(f1703,plain,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)))),
inference(forward_demodulation,[],[f1702,f1113]) ).
thf(f1702,plain,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4)))),
inference(forward_demodulation,[],[f1120,f1699]) ).
thf(f1120,plain,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))))),
inference(cnf_transformation,[],[f62]) ).
thf(f62,axiom,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),a_minus_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),add_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,r),r3),r4)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_f11) ).
thf(f2202,plain,
( spl54_79
| ~ spl54_36
| ~ spl54_37
| ~ spl54_77 ),
inference(avatar_split_clause,[],[f2185,f2182,f1922,f1918,f2200]) ).
thf(f2182,plain,
( spl54_77
<=> ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_77])]) ).
thf(f2185,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) = vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0)) )
| ~ spl54_36
| ~ spl54_37
| ~ spl54_77 ),
inference(forward_demodulation,[],[f2183,f1965]) ).
thf(f2183,plain,
( ! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) )
| ~ spl54_77 ),
inference(avatar_component_clause,[],[f2182]) ).
thf(f2190,plain,
spl54_78,
inference(avatar_split_clause,[],[f1438,f2187]) ).
thf(f1438,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $true,
inference(cnf_transformation,[],[f656]) ).
thf(f656,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $true,
inference(fool_elimination,[],[f655]) ).
thf(f655,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)),
inference(rectify,[],[f239]) ).
thf(f239,axiom,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r))),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_Units__minus__one__closed) ).
thf(f2184,plain,
spl54_77,
inference(avatar_split_clause,[],[f1231,f2182]) ).
thf(f1231,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) ),
inference(cnf_transformation,[],[f681]) ).
thf(f681,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) ),
inference(rectify,[],[f268]) ).
thf(f268,axiom,
! [X1: int,X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X1)),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_minus__diff__commute) ).
thf(f2180,plain,
spl54_76,
inference(avatar_split_clause,[],[f1678,f2178]) ).
thf(f2178,plain,
( spl54_76
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_76])]) ).
thf(f1678,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) ) ),
inference(equality_proxy_clausification,[],[f1677]) ).
thf(f1677,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(equality_proxy_clausification,[],[f1673]) ).
thf(f1673,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(binary_proxy_clausification,[],[f1239]) ).
thf(f1239,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(cnf_transformation,[],[f368]) ).
thf(f368,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(fool_elimination,[],[f367]) ).
thf(f367,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f125]) ).
thf(f125,axiom,
! [X11: nat,X13: nat] :
( ( vAPP(nat,nat,suc,X11) = vAPP(nat,nat,suc,X13) )
= ( X11 = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_nat_Oinject) ).
thf(f2176,plain,
spl54_75,
inference(avatar_split_clause,[],[f1229,f2174]) ).
thf(f1229,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,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,suc,X1)) ),
inference(cnf_transformation,[],[f679]) ).
thf(f679,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,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,suc,X1)) ),
inference(rectify,[],[f124]) ).
thf(f124,axiom,
! [X35: nat,X34: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),vAPP(nat,nat,suc,X34)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_add__Suc__right) ).
thf(f2172,plain,
spl54_74,
inference(avatar_split_clause,[],[f1228,f2170]) ).
thf(f1228,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,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,suc,X0)),X1) ),
inference(cnf_transformation,[],[f678]) ).
thf(f678,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,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,suc,X0)),X1) ),
inference(rectify,[],[f130]) ).
thf(f130,axiom,
! [X35: nat,X34: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X34)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,vAPP(nat,nat,suc,X35)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_add__Suc) ).
thf(f2168,plain,
spl54_73,
inference(avatar_split_clause,[],[f1227,f2166]) ).
thf(f2166,plain,
( spl54_73
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_73])]) ).
thf(f1227,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(cnf_transformation,[],[f677]) ).
thf(f677,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f123]) ).
thf(f123,axiom,
! [X35: nat,X34: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,X35),X34) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,suc,X35)),vAPP(nat,nat,suc,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_diff__Suc__Suc) ).
thf(f2162,plain,
spl54_72,
inference(avatar_split_clause,[],[f1141,f2160]) ).
thf(f1141,plain,
! [X0: set_a] : ( vAPP(sTfun(a,$o),set_a,collect_a,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0)) = X0 ),
inference(cnf_transformation,[],[f306]) ).
thf(f306,plain,
! [X0: set_a] : ( vAPP(sTfun(a,$o),set_a,collect_a,vAPP(set_a,sTfun(a,$o),vAPP(sTfun(a,sTfun(set_a,$o)),sTfun(set_a,sTfun(a,$o)),cCOMB,member_a),X0)) = X0 ),
inference(fool_elimination,[],[f305]) ).
thf(f305,plain,
! [X0: set_a] :
( vAPP(sTfun(a,$o),set_a,collect_a,
^ [X1: a] : vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X1),X0)) = X0 ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
! [X21: set_a] :
( vAPP(sTfun(a,$o),set_a,collect_a,
^ [X22: a] : vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,X22),X21)) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Collect__mem__eq) ).
thf(f2158,plain,
spl54_71,
inference(avatar_split_clause,[],[f1140,f2156]) ).
thf(f1140,plain,
! [X0: set_Product_prod_a_a] : ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,vAPP(set_Product_prod_a_a,sTfun(product_prod_a_a,$o),vAPP(sTfun(product_prod_a_a,sTfun(set_Product_prod_a_a,$o)),sTfun(set_Product_prod_a_a,sTfun(product_prod_a_a,$o)),cCOMB,member449909584od_a_a),X0)) = X0 ),
inference(cnf_transformation,[],[f304]) ).
thf(f304,plain,
! [X0: set_Product_prod_a_a] : ( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,vAPP(set_Product_prod_a_a,sTfun(product_prod_a_a,$o),vAPP(sTfun(product_prod_a_a,sTfun(set_Product_prod_a_a,$o)),sTfun(set_Product_prod_a_a,sTfun(product_prod_a_a,$o)),cCOMB,member449909584od_a_a),X0)) = X0 ),
inference(fool_elimination,[],[f303]) ).
thf(f303,plain,
! [X0: set_Product_prod_a_a] :
( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,
^ [X1: product_prod_a_a] : vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X1),X0)) = X0 ),
inference(rectify,[],[f48]) ).
thf(f48,axiom,
! [X21: set_Product_prod_a_a] :
( vAPP(sTfun(product_prod_a_a,$o),set_Product_prod_a_a,collec645855634od_a_a,
^ [X22: product_prod_a_a] : vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,X22),X21)) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__mem__eq) ).
thf(f2154,plain,
spl54_70,
inference(avatar_split_clause,[],[f1139,f2152]) ).
thf(f1139,plain,
! [X0: int] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ),
inference(cnf_transformation,[],[f670]) ).
thf(f670,plain,
! [X0: int] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ),
inference(rectify,[],[f77]) ).
thf(f77,axiom,
! [X9: int] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(int,sTfun(a,a)),add_pow_a_b_int,r),X9),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add_Oint__pow__one) ).
thf(f2150,plain,
spl54_69,
inference(avatar_split_clause,[],[f1676,f2148]) ).
thf(f2148,plain,
( spl54_69
<=> ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_69])]) ).
thf(f1676,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) ) ),
inference(equality_proxy_clausification,[],[f1675]) ).
thf(f1675,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(equality_proxy_clausification,[],[f1674]) ).
thf(f1674,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) ) ),
inference(binary_proxy_clausification,[],[f1239]) ).
thf(f2146,plain,
spl54_68,
inference(avatar_split_clause,[],[f1138,f2144]) ).
thf(f1138,plain,
! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ),
inference(cnf_transformation,[],[f669]) ).
thf(f669,plain,
! [X0: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X0),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ),
inference(rectify,[],[f98]) ).
thf(f98,axiom,
! [X34: nat] : ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1833973666xt_a_b,sTfun(nat,sTfun(a,a)),add_pow_a_b_nat,r),X34),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add_Onat__pow__one) ).
thf(f2114,plain,
spl54_67,
inference(avatar_split_clause,[],[f1666,f2112]) ).
thf(f2112,plain,
( spl54_67
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,int,semiri2019852685at_int,X1) != vAPP(nat,int,semiri2019852685at_int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_67])]) ).
thf(f1666,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( vAPP(nat,int,semiri2019852685at_int,X1) != vAPP(nat,int,semiri2019852685at_int,X0) ) ),
inference(equality_proxy_clausification,[],[f1665]) ).
thf(f1665,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,semiri2019852685at_int,X1)),vAPP(nat,int,semiri2019852685at_int,X0)) ) ),
inference(equality_proxy_clausification,[],[f1661]) ).
thf(f1661,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $false = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,semiri2019852685at_int,X1)),vAPP(nat,int,semiri2019852685at_int,X0)) ) ),
inference(binary_proxy_clausification,[],[f1241]) ).
thf(f1241,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,semiri2019852685at_int,X1)),vAPP(nat,int,semiri2019852685at_int,X0)) ),
inference(cnf_transformation,[],[f372]) ).
thf(f372,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,semiri2019852685at_int,X1)),vAPP(nat,int,semiri2019852685at_int,X0)) ),
inference(fool_elimination,[],[f371]) ).
thf(f371,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,int,semiri2019852685at_int,X1) = vAPP(nat,int,semiri2019852685at_int,X0) )
= ( X0 = X1 ) ),
inference(rectify,[],[f272]) ).
thf(f272,axiom,
! [X35: nat,X34: nat] :
( ( vAPP(nat,int,semiri2019852685at_int,X34) = vAPP(nat,int,semiri2019852685at_int,X35) )
= ( X34 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_of__nat__eq__iff) ).
thf(f2084,plain,
spl54_66,
inference(avatar_split_clause,[],[f1185,f2082]) ).
thf(f1185,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(cnf_transformation,[],[f734]) ).
thf(f734,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) ) ),
inference(ennf_transformation,[],[f328]) ).
thf(f328,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ),
inference(fool_elimination,[],[f327]) ).
thf(f327,plain,
! [X0: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ),
inference(rectify,[],[f113]) ).
thf(f113,axiom,
! [X29: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,X29)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_abelian__groupE_I2_J) ).
thf(f2080,plain,
spl54_65,
inference(avatar_split_clause,[],[f1184,f2078]) ).
thf(f1184,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f733]) ).
thf(f733,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f326]) ).
thf(f326,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ),
inference(fool_elimination,[],[f325]) ).
thf(f325,plain,
! [X0: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ),
inference(rectify,[],[f88]) ).
thf(f88,axiom,
! [X29: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,X29)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_semiring_Osemiring__simprules_I2_J) ).
thf(f2076,plain,
spl54_64,
inference(avatar_split_clause,[],[f1183,f2074]) ).
thf(f1183,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(cnf_transformation,[],[f732]) ).
thf(f732,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) ) ),
inference(ennf_transformation,[],[f324]) ).
thf(f324,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ),
inference(fool_elimination,[],[f323]) ).
thf(f323,plain,
! [X0: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ),
inference(rectify,[],[f80]) ).
thf(f80,axiom,
! [X29: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,semiring_a_b,X29)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X29)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_semiring_Osemiring__simprules_I4_J) ).
thf(f2072,plain,
spl54_63,
inference(avatar_split_clause,[],[f1181,f2070]) ).
thf(f1181,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(cnf_transformation,[],[f730]) ).
thf(f730,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) ) ),
inference(ennf_transformation,[],[f320]) ).
thf(f320,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ) ),
inference(fool_elimination,[],[f319]) ).
thf(f319,plain,
! [X0: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) ),
inference(rectify,[],[f282]) ).
thf(f282,axiom,
! [X36: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,comm_g791708116xt_a_b,X36)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_comm__groupE_I2_J) ).
thf(f2068,plain,
spl54_62,
inference(avatar_split_clause,[],[f1178,f2066]) ).
thf(f1178,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(cnf_transformation,[],[f727]) ).
thf(f727,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) ) ),
inference(ennf_transformation,[],[f314]) ).
thf(f314,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0) )
=> ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ) ),
inference(fool_elimination,[],[f313]) ).
thf(f313,plain,
! [X0: partia96731725t_unit] :
( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X0)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) ),
inference(rectify,[],[f281]) ).
thf(f281,axiom,
! [X36: partia96731725t_unit] :
( vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,X36)
=> vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,one_a_Product_unit,X36)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_comm__groupE_I2_J) ).
thf(f2064,plain,
spl54_61,
inference(avatar_split_clause,[],[f1172,f2062]) ).
thf(f1172,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK29,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ),
inference(cnf_transformation,[],[f1069]) ).
thf(f2060,plain,
spl54_60,
inference(avatar_split_clause,[],[f1171,f2058]) ).
thf(f1171,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK28,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ),
inference(cnf_transformation,[],[f1069]) ).
thf(f2053,plain,
spl54_59,
inference(avatar_split_clause,[],[f1170,f2051]) ).
thf(f1170,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK27,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP5,X0) ) ),
inference(cnf_transformation,[],[f1069]) ).
thf(f2049,plain,
spl54_58,
inference(avatar_split_clause,[],[f1168,f2047]) ).
thf(f1168,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK26,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(cnf_transformation,[],[f1063]) ).
thf(f2045,plain,
spl54_57,
inference(avatar_split_clause,[],[f1167,f2043]) ).
thf(f1167,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK25,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP6,X0) ) ),
inference(cnf_transformation,[],[f1063]) ).
thf(f2041,plain,
spl54_56,
inference(avatar_split_clause,[],[f1161,f2039]) ).
thf(f1161,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK22,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ),
inference(cnf_transformation,[],[f1055]) ).
thf(f2037,plain,
spl54_55,
inference(avatar_split_clause,[],[f1160,f2035]) ).
thf(f1160,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK21,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ),
inference(cnf_transformation,[],[f1055]) ).
thf(f2033,plain,
spl54_54,
inference(avatar_split_clause,[],[f1159,f2031]) ).
thf(f1159,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK20,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP2,X0) ) ),
inference(cnf_transformation,[],[f1055]) ).
thf(f2029,plain,
spl54_53,
inference(avatar_split_clause,[],[f1157,f2027]) ).
thf(f1157,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK19,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1049]) ).
thf(f2025,plain,
spl54_52,
inference(avatar_split_clause,[],[f1156,f2023]) ).
thf(f1156,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK18,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP3,X0) ) ),
inference(cnf_transformation,[],[f1049]) ).
thf(f2021,plain,
spl54_51,
inference(avatar_split_clause,[],[f1154,f2019]) ).
thf(f1154,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK17,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ),
inference(cnf_transformation,[],[f1045]) ).
thf(f2017,plain,
spl54_50,
inference(avatar_split_clause,[],[f1153,f2015]) ).
thf(f1153,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,sK16,X0)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0)) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,sP4,X0) ) ),
inference(cnf_transformation,[],[f1045]) ).
thf(f2011,plain,
( spl54_49
| ~ spl54_12
| ~ spl54_33 ),
inference(avatar_split_clause,[],[f1931,f1903,f1797,f2008]) ).
thf(f1931,plain,
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) )
| ~ spl54_12
| ~ spl54_33 ),
inference(trivial_inequality_removal,[],[f1930]) ).
thf(f1930,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r) )
| ~ spl54_12
| ~ spl54_33 ),
inference(superposition,[],[f1798,f1905]) ).
thf(f2006,plain,
spl54_48,
inference(avatar_split_clause,[],[f1147,f2004]) ).
thf(f1147,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK13,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f1036]) ).
thf(f2002,plain,
spl54_47,
inference(avatar_split_clause,[],[f1146,f2000]) ).
thf(f1146,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK12,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f1036]) ).
thf(f1998,plain,
spl54_46,
inference(avatar_split_clause,[],[f1145,f1996]) ).
thf(f1145,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK11,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f1036]) ).
thf(f1994,plain,
spl54_45,
inference(avatar_split_clause,[],[f1143,f1992]) ).
thf(f1143,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK10,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1030]) ).
thf(f1990,plain,
spl54_44,
inference(avatar_split_clause,[],[f1142,f1988]) ).
thf(f1142,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia96731725t_unit,a,sK9,X0)),vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0)) )
| ( $true != vAPP(partia96731725t_unit,$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f1030]) ).
thf(f1954,plain,
spl54_43,
inference(avatar_split_clause,[],[f1437,f1951]) ).
thf(f1437,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r4),s3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(cnf_transformation,[],[f654]) ).
thf(f654,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r4),s3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(fool_elimination,[],[f653]) ).
thf(f653,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r4),s3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r4),s3)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I3_J) ).
thf(f1949,plain,
spl54_42,
inference(avatar_split_clause,[],[f1436,f1946]) ).
thf(f1436,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r3),s2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(cnf_transformation,[],[f652]) ).
thf(f652,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r3),s2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(fool_elimination,[],[f651]) ).
thf(f651,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r3),s2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r3),s2)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I2_J) ).
thf(f1944,plain,
spl54_41,
inference(avatar_split_clause,[],[f1435,f1941]) ).
thf(f1435,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r2),s)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(cnf_transformation,[],[f650]) ).
thf(f650,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r2),s)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)) = $true,
inference(fool_elimination,[],[f649]) ).
thf(f649,plain,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r2),s)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
vAPP(set_Product_prod_a_a,$o,vAPP(product_prod_a_a,sTfun(set_Product_prod_a_a,$o),member449909584od_a_a,vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,r2),s)),vAPP(partia1993116613t_unit,set_Product_prod_a_a,partia206007992t_unit,rel)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(f1939,plain,
spl54_40,
inference(avatar_split_clause,[],[f1226,f1937]) ).
thf(f1226,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = X1 ),
inference(cnf_transformation,[],[f258]) ).
thf(f258,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_minus__add__cancel) ).
thf(f1935,plain,
spl54_39,
inference(avatar_split_clause,[],[f1224,f1933]) ).
thf(f1224,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) ),
inference(cnf_transformation,[],[f262]) ).
thf(f262,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_uminus__add__conv__diff) ).
thf(f1929,plain,
( spl54_38
| ~ spl54_2
| spl54_33 ),
inference(avatar_split_clause,[],[f1908,f1903,f1725,f1926]) ).
thf(f1908,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| ~ spl54_2
| spl54_33 ),
inference(trivial_inequality_removal,[],[f1907]) ).
thf(f1907,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $false )
| ~ spl54_2
| spl54_33 ),
inference(superposition,[],[f1904,f1726]) ).
thf(f1904,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) != $true )
| spl54_33 ),
inference(avatar_component_clause,[],[f1903]) ).
thf(f1924,plain,
spl54_37,
inference(avatar_split_clause,[],[f1223,f1922]) ).
thf(f1223,plain,
! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) ),
inference(cnf_transformation,[],[f260]) ).
thf(f260,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,uminus_uminus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_minus__diff__eq) ).
thf(f1920,plain,
spl54_36,
inference(avatar_split_clause,[],[f1222,f1918]) ).
thf(f1222,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,uminus_uminus_int,X1)) ),
inference(cnf_transformation,[],[f261]) ).
thf(f261,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),vAPP(int,int,uminus_uminus_int,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_diff__minus__eq__add) ).
thf(f1916,plain,
spl54_35,
inference(avatar_split_clause,[],[f1137,f1914]) ).
thf(f1137,plain,
! [X0: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ),
inference(cnf_transformation,[],[f668]) ).
thf(f668,plain,
! [X0: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X0) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ),
inference(rectify,[],[f241]) ).
thf(f241,axiom,
! [X36: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,sTfun(a,sTfun(a,a)),mult_a_ring_ext_a_b,X36) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_units__of__mult) ).
thf(f1912,plain,
spl54_34,
inference(avatar_split_clause,[],[f1136,f1910]) ).
thf(f1136,plain,
! [X0: partia96731725t_unit] : ( vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ),
inference(cnf_transformation,[],[f667]) ).
thf(f667,plain,
! [X0: partia96731725t_unit] : ( vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X0) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ),
inference(rectify,[],[f240]) ).
thf(f240,axiom,
! [X36: partia96731725t_unit] : ( vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,X36) = vAPP(partia96731725t_unit,sTfun(a,sTfun(a,a)),mult_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_units__of__mult) ).
thf(f1906,plain,
( spl54_32
| spl54_33 ),
inference(avatar_split_clause,[],[f1131,f1903,f1899]) ).
thf(f1131,plain,
( ( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,r) = $true )
| ( $true = vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,sK8),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) ) ),
inference(cnf_transformation,[],[f1026]) ).
thf(f1891,plain,
spl54_31,
inference(avatar_split_clause,[],[f1710,f1889]) ).
thf(f1710,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X1),X0)) = X1 ),
inference(forward_demodulation,[],[f1225,f1224]) ).
thf(f1225,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X1)) = X1 ),
inference(cnf_transformation,[],[f257]) ).
thf(f257,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,uminus_uminus_int,X0)),X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_add__minus__cancel) ).
thf(f1887,plain,
spl54_30,
inference(avatar_split_clause,[],[f1221,f1885]) ).
thf(f1221,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X1) = X0 ),
inference(cnf_transformation,[],[f151]) ).
thf(f151,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,X0),X1)),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_diff__add__cancel) ).
thf(f1883,plain,
spl54_29,
inference(avatar_split_clause,[],[f1219,f1881]) ).
thf(f1219,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X1) = X0 ),
inference(cnf_transformation,[],[f139]) ).
thf(f139,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_add__diff__cancel__right_H) ).
thf(f1879,plain,
spl54_28,
inference(avatar_split_clause,[],[f1218,f1877]) ).
thf(f1218,plain,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X0) = X1 ),
inference(cnf_transformation,[],[f143]) ).
thf(f143,axiom,
! [X0: int,X1: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus_int,vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X0),X1)),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_add__diff__cancel__left_H) ).
thf(f1875,plain,
spl54_27,
inference(avatar_split_clause,[],[f1215,f1873]) ).
thf(f1215,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) = X1 ),
inference(cnf_transformation,[],[f676]) ).
thf(f676,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X0) = X1 ),
inference(rectify,[],[f135]) ).
thf(f135,axiom,
! [X34: nat,X35: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X34),X35)),X34) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_diff__add__inverse) ).
thf(f1871,plain,
spl54_26,
inference(avatar_split_clause,[],[f1214,f1869]) ).
thf(f1214,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) = X0 ),
inference(cnf_transformation,[],[f675]) ).
thf(f675,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X0),X1)),X1) = X0 ),
inference(rectify,[],[f134]) ).
thf(f134,axiom,
! [X35: nat,X34: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus_nat,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X35),X34)),X34) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_diff__add__inverse2) ).
thf(f1867,plain,
( spl54_25
| ~ spl54_2
| spl54_22 ),
inference(avatar_split_clause,[],[f1852,f1847,f1725,f1864]) ).
thf(f1852,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $false )
| ~ spl54_2
| spl54_22 ),
inference(trivial_inequality_removal,[],[f1851]) ).
thf(f1851,plain,
( ( $true != $true )
| ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $false )
| ~ spl54_2
| spl54_22 ),
inference(superposition,[],[f1848,f1726]) ).
thf(f1848,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) != $true )
| spl54_22 ),
inference(avatar_component_clause,[],[f1847]) ).
thf(f1862,plain,
spl54_24,
inference(avatar_split_clause,[],[f1127,f1859]) ).
thf(f1859,plain,
( spl54_24
<=> ( plus_plus_int = vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(int,int)),cCOMB,plus_plus_int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_24])]) ).
thf(f1127,plain,
plus_plus_int = vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(int,int)),cCOMB,plus_plus_int),
inference(cnf_transformation,[],[f298]) ).
thf(f298,plain,
plus_plus_int = vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(int,int)),cCOMB,plus_plus_int),
inference(fool_elimination,[],[f297]) ).
thf(f297,plain,
( plus_plus_int
= ( ^ [X0: int,X1: int] : vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X1),X0) ) ),
inference(rectify,[],[f158]) ).
thf(f158,axiom,
( plus_plus_int
= ( ^ [X42: int,X43: int] : vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus_int,X43),X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add_Ocommute) ).
thf(f1857,plain,
spl54_23,
inference(avatar_split_clause,[],[f1126,f1854]) ).
thf(f1854,plain,
( spl54_23
<=> ( plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_23])]) ).
thf(f1126,plain,
plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat),
inference(cnf_transformation,[],[f296]) ).
thf(f296,plain,
plus_plus_nat = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus_nat),
inference(fool_elimination,[],[f295]) ).
thf(f295,plain,
( plus_plus_nat
= ( ^ [X0: nat,X1: nat] : vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X1),X0) ) ),
inference(rectify,[],[f159]) ).
thf(f159,axiom,
( plus_plus_nat
= ( ^ [X42: nat,X43: nat] : vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus_nat,X43),X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_add_Ocommute) ).
thf(f1850,plain,
( spl54_20
| ~ spl54_21
| spl54_22 ),
inference(avatar_split_clause,[],[f1709,f1847,f1843,f1839]) ).
thf(f1843,plain,
( spl54_21
<=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = sK7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_21])]) ).
thf(f1709,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != sK7 )
| ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) = sK7 ) ),
inference(inner_rewriting,[],[f1129]) ).
thf(f1129,plain,
( ( vAPP(partia1833973666xt_a_b,$o,field_a_b,r) = $true )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) != sK7 )
| ( vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r) ) ),
inference(cnf_transformation,[],[f1024]) ).
thf(f1837,plain,
spl54_19,
inference(avatar_split_clause,[],[f1434,f1834]) ).
thf(f1434,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true,
inference(cnf_transformation,[],[f648]) ).
thf(f648,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true,
inference(fool_elimination,[],[f647]) ).
thf(f647,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)),
inference(rectify,[],[f40]) ).
thf(f40,axiom,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__closed) ).
thf(f1832,plain,
spl54_18,
inference(avatar_split_clause,[],[f1433,f1829]) ).
thf(f1433,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true,
inference(cnf_transformation,[],[f646]) ).
thf(f646,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)) = $true,
inference(fool_elimination,[],[f645]) ).
thf(f645,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)),
inference(rectify,[],[f75]) ).
thf(f75,axiom,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_semiring__simprules_I4_J) ).
thf(f1827,plain,
spl54_17,
inference(avatar_split_clause,[],[f1432,f1824]) ).
thf(f1432,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $true,
inference(cnf_transformation,[],[f644]) ).
thf(f644,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)) = $true,
inference(fool_elimination,[],[f643]) ).
thf(f643,plain,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)),
inference(rectify,[],[f192]) ).
thf(f192,axiom,
vAPP(set_a,$o,vAPP(a,sTfun(set_a,$o),member_a,vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,r)),vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Units__one__closed) ).
thf(f1822,plain,
spl54_16,
inference(avatar_split_clause,[],[f1211,f1820]) ).
thf(f1211,plain,
! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK40,X0)),vAPP(product_prod_a_a,a,sK41,X0)) = X0 ),
inference(cnf_transformation,[],[f1089]) ).
thf(f1089,plain,
! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK40,X0)),vAPP(product_prod_a_a,a,sK41,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f672,f1088]) ).
thf(f1088,plain,
! [X0: product_prod_a_a] :
( ? [X1: a,X2: a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2) = X0 )
=> ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK40,X0)),vAPP(product_prod_a_a,a,sK41,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f672,plain,
! [X0: product_prod_a_a] :
? [X1: a,X2: a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2) = X0 ),
inference(rectify,[],[f61]) ).
thf(f61,axiom,
! [X27: product_prod_a_a] :
? [X17: a,X28: a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X17),X28) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_surj__pair) ).
thf(f1818,plain,
spl54_15,
inference(avatar_split_clause,[],[f1210,f1816]) ).
thf(f1210,plain,
! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK38,X0)),vAPP(product_prod_a_a,a,sK39,X0)) = X0 ),
inference(cnf_transformation,[],[f1087]) ).
thf(f1087,plain,
! [X0: product_prod_a_a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK38,X0)),vAPP(product_prod_a_a,a,sK39,X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f755,f1086]) ).
thf(f1086,plain,
! [X0: product_prod_a_a] :
( ? [X1: a,X2: a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2) = X0 )
=> ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,vAPP(product_prod_a_a,a,sK38,X0)),vAPP(product_prod_a_a,a,sK39,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f755,plain,
! [X0: product_prod_a_a] :
? [X1: a,X2: a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2) = X0 ),
inference(ennf_transformation,[],[f671]) ).
thf(f671,plain,
! [X0: product_prod_a_a] :
~ ! [X1: a,X2: a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X1),X2) != X0 ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X8: product_prod_a_a] :
~ ! [X25: a,X26: a] : ( vAPP(a,product_prod_a_a,vAPP(a,sTfun(a,product_prod_a_a),product_Pair_a_a,X25),X26) != X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_old_Oprod_Oexhaust) ).
thf(f1814,plain,
spl54_14,
inference(avatar_split_clause,[],[f1111,f1811]) ).
thf(f1111,plain,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),
inference(cnf_transformation,[],[f237]) ).
thf(f237,axiom,
vAPP(partia1833973666xt_a_b,a,zero_a_b,r) = vAPP(a,a,vAPP(partia1833973666xt_a_b,sTfun(a,a),a_inv_a_b,r),vAPP(partia1833973666xt_a_b,a,zero_a_b,r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_local_Ominus__zero) ).
thf(f1807,plain,
spl54_13,
inference(avatar_split_clause,[],[f1664,f1805]) ).
thf(f1805,plain,
( spl54_13
<=> ! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,int,semiri2019852685at_int,X1) = vAPP(nat,int,semiri2019852685at_int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_13])]) ).
thf(f1664,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( vAPP(nat,int,semiri2019852685at_int,X1) = vAPP(nat,int,semiri2019852685at_int,X0) ) ),
inference(equality_proxy_clausification,[],[f1663]) ).
thf(f1663,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,semiri2019852685at_int,X1)),vAPP(nat,int,semiri2019852685at_int,X0)) ) ),
inference(equality_proxy_clausification,[],[f1662]) ).
thf(f1662,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) )
| ( $true = vAPP(int,$o,vAPP(int,sTfun(int,$o),vEQ(int),vAPP(nat,int,semiri2019852685at_int,X1)),vAPP(nat,int,semiri2019852685at_int,X0)) ) ),
inference(binary_proxy_clausification,[],[f1241]) ).
thf(f1799,plain,
spl54_12,
inference(avatar_split_clause,[],[f1182,f1797]) ).
thf(f1182,plain,
! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(cnf_transformation,[],[f731]) ).
thf(f731,plain,
! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) ) ),
inference(ennf_transformation,[],[f322]) ).
thf(f322,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0) )
=> ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) ) ),
inference(fool_elimination,[],[f321]) ).
thf(f321,plain,
! [X0: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X0)
=> ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X0) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X0) ) ),
inference(rectify,[],[f203]) ).
thf(f203,axiom,
! [X36: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,group_a_ring_ext_a_b,X36)
=> ( vAPP(partia1833973666xt_a_b,set_a,partia1066395285xt_a_b,X36) = vAPP(partia1833973666xt_a_b,set_a,units_a_ring_ext_a_b,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_group_OUnits__eq) ).
thf(f1795,plain,
spl54_11,
inference(avatar_split_clause,[],[f1180,f1793]) ).
thf(f1180,plain,
! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) ),
inference(cnf_transformation,[],[f729]) ).
thf(f729,plain,
! [X0: partia1833973666xt_a_b] :
( ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) )
| ( $true != vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) ) ),
inference(ennf_transformation,[],[f318]) ).
thf(f318,plain,
! [X0: partia1833973666xt_a_b] :
( ( $true = vAPP(partia1833973666xt_a_b,$o,field_a_b,X0) )
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) ) ),
inference(fool_elimination,[],[f317]) ).
thf(f317,plain,
! [X0: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,field_a_b,X0)
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X0) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) ) ),
inference(rectify,[],[f99]) ).
thf(f99,axiom,
! [X29: partia1833973666xt_a_b] :
( vAPP(partia1833973666xt_a_b,$o,field_a_b,X29)
=> ( vAPP(partia1833973666xt_a_b,a,zero_a_b,X29) != vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_one__not__zero) ).
thf(f1791,plain,
spl54_10,
inference(avatar_split_clause,[],[f1179,f1789]) ).
thf(f1179,plain,
! [X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(cnf_transformation,[],[f728]) ).
thf(f728,plain,
! [X0: partia96731725t_unit] :
( ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) )
| ( $true != vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) ) ),
inference(ennf_transformation,[],[f316]) ).
thf(f316,plain,
! [X0: partia96731725t_unit] :
( ( $true = vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0) )
=> ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) ) ),
inference(fool_elimination,[],[f315]) ).
thf(f315,plain,
! [X0: partia96731725t_unit] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X0)
=> ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X0) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X0) ) ),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
! [X36: partia96731725t_unit] :
( vAPP(partia96731725t_unit,$o,group_a_Product_unit,X36)
=> ( vAPP(partia96731725t_unit,set_a,partia1955795460t_unit,X36) = vAPP(partia96731725t_unit,set_a,units_a_Product_unit,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_group_OUnits__eq) ).
thf(f1787,plain,
spl54_9,
inference(avatar_split_clause,[],[f1135,f1785]) ).
thf(f1135,plain,
! [X0: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ),
inference(cnf_transformation,[],[f666]) ).
thf(f666,plain,
! [X0: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X0) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X0)) ),
inference(rectify,[],[f246]) ).
thf(f246,axiom,
! [X36: partia1833973666xt_a_b] : ( vAPP(partia1833973666xt_a_b,a,one_a_ring_ext_a_b,X36) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_units__of__one) ).
thf(f1783,plain,
spl54_8,
inference(avatar_split_clause,[],[f1134,f1781]) ).
thf(f1134,plain,
! [X0: partia96731725t_unit] : ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ),
inference(cnf_transformation,[],[f665]) ).
thf(f665,plain,
! [X0: partia96731725t_unit] : ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X0) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X0)) ),
inference(rectify,[],[f245]) ).
thf(f245,axiom,
! [X36: partia96731725t_unit] : ( vAPP(partia96731725t_unit,a,one_a_Product_unit,X36) = vAPP(partia96731725t_unit,a,one_a_Product_unit,vAPP(partia96731725t_unit,partia96731725t_unit,units_873712258t_unit,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_units__of__one) ).
thf(f1779,plain,
spl54_7,
inference(avatar_split_clause,[],[f1431,f1776]) ).
thf(f1431,plain,
vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = $true,
inference(cnf_transformation,[],[f642]) ).
thf(f642,plain,
vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = $true,
inference(fool_elimination,[],[f641]) ).
thf(f641,plain,
vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)),
inference(rectify,[],[f214]) ).
thf(f214,axiom,
vAPP(partia96731725t_unit,$o,group_a_Product_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_units__group) ).
thf(f1774,plain,
spl54_6,
inference(avatar_split_clause,[],[f1430,f1771]) ).
thf(f1430,plain,
vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = $true,
inference(cnf_transformation,[],[f640]) ).
thf(f640,plain,
vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)) = $true,
inference(fool_elimination,[],[f639]) ).
thf(f639,plain,
vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)),
inference(rectify,[],[f270]) ).
thf(f270,axiom,
vAPP(partia96731725t_unit,$o,comm_g1684316527t_unit,vAPP(partia1833973666xt_a_b,partia96731725t_unit,units_1411277569xt_a_b,r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_units__comm__group) ).
thf(f1769,plain,
spl54_5,
inference(avatar_split_clause,[],[f1429,f1766]) ).
thf(f1429,plain,
vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) = $true,
inference(cnf_transformation,[],[f638]) ).
thf(f638,plain,
vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r) = $true,
inference(fool_elimination,[],[f637]) ).
thf(f637,plain,
vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r),
inference(rectify,[],[f108]) ).
thf(f108,axiom,
vAPP(partia1833973666xt_a_b,$o,abelian_group_a_b,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_is__abelian__group) ).
thf(f1764,plain,
spl54_4,
inference(avatar_split_clause,[],[f1428,f1761]) ).
thf(f1428,plain,
vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) = $true,
inference(cnf_transformation,[],[f636]) ).
thf(f636,plain,
vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r) = $true,
inference(fool_elimination,[],[f635]) ).
thf(f635,plain,
vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r),
inference(rectify,[],[f23]) ).
thf(f23,axiom,
vAPP(partia1833973666xt_a_b,$o,semiring_a_b,r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Osemiring__axioms) ).
thf(f1759,plain,
spl54_3,
inference(avatar_split_clause,[],[f1133,f1757]) ).
thf(f1757,plain,
( spl54_3
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_3])]) ).
thf(f1133,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(cnf_transformation,[],[f664]) ).
thf(f664,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(rectify,[],[f128]) ).
thf(f128,axiom,
! [X34: nat] : ( vAPP(nat,nat,suc,X34) != X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_n__not__Suc__n) ).
thf(f1727,plain,
spl54_2,
inference(avatar_split_clause,[],[f286,f1725]) ).
thf(f286,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1723,plain,
~ spl54_1,
inference(avatar_split_clause,[],[f285,f1720]) ).
thf(f1720,plain,
( spl54_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl54_1])]) ).
thf(f285,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ITP106^1 : TPTP v8.2.0. Released v7.5.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 18:28:38 EDT 2024
% 0.21/0.36 % CPUTime :
% 0.21/0.36 % (11493)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (11513)WARNING: value z3 for option sas not known
% 0.21/0.40 % (11510)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 % (11511)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (11514)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (11516)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)
% 0.21/0.40 % (11513)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)
% 0.21/0.40 % (11515)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)
% 0.21/0.40 % (11517)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.44 % (11517)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.45 % Exception at run slice level
% 0.22/0.45 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.46 % (11523)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.47 % Exception at run slice level
% 0.22/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.47 % Exception at run slice level
% 0.22/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.49 % (11524)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.49 % (11525)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.50 % (11523)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.50 % Exception at run slice level
% 0.22/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.52 % (11524)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.52 % (11526)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)
% 93.44/13.66 % (11515)First to succeed.
% 94.01/13.78 % (11515)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11493"
% 94.30/13.80 % (11515)Refutation found. Thanks to Tanya!
% 94.30/13.80 % SZS status Theorem for theBenchmark
% 94.30/13.80 % SZS output start Proof for theBenchmark
% See solution above
% 94.53/13.84 % (11515)------------------------------
% 94.53/13.84 % (11515)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 94.53/13.84 % (11515)Termination reason: Refutation
% 94.53/13.84
% 94.53/13.84 % (11515)Memory used [KB]: 184649
% 94.53/13.84 % (11515)Time elapsed: 13.375 s
% 94.53/13.84 % (11515)Instructions burned: 53040 (million)
% 94.53/13.84 % (11493)Success in time 13.178 s
%------------------------------------------------------------------------------