TSTP Solution File: SYO500^1.005 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO500^1.005 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:11:35 EDT 2024
% Result : Theorem 2.99s 0.79s
% Output : Refutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 127
% Syntax : Number of formulae : 3013 ( 5 unt; 14 typ; 0 def)
% Number of atoms : 35013 (2473 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 18917 (8981 ~;9825 |; 0 &; 0 @)
% ( 111 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 23 ( 22 >; 1 *; 0 +; 0 <<)
% Number of symbols : 129 ( 126 usr; 114 con; 0-6 aty)
% Number of variables : 31 ( 0 ^ 25 !; 0 ?; 31 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: $o ).
thf(func_def_1,type,
f0: $o > $o ).
thf(func_def_2,type,
f1: $o > $o ).
thf(func_def_3,type,
f2: $o > $o ).
thf(func_def_4,type,
f3: $o > $o ).
thf(func_def_5,type,
f4: $o > $o ).
thf(func_def_10,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_11,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vIMP: $o > $o > $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f20483,plain,
$false,
inference(avatar_sat_refutation,[],[f17,f26,f72,f81,f90,f99,f108,f117,f126,f135,f144,f147,f275,f294,f299,f308,f321,f333,f344,f370,f382,f531,f639,f743,f822,f915,f1123,f1172,f1220,f1423,f1426,f1442,f1584,f1663,f1709,f1718,f1758,f1777,f2124,f2230,f2231,f2232,f2233,f2317,f2417,f2490,f2503,f2600,f2643,f2824,f2854,f2931,f2969,f3047,f3055,f3060,f3187,f3199,f3208,f3394,f3498,f3508,f3513,f3528,f3533,f3537,f3708,f3796,f3841,f3850,f3873,f3875,f3909,f3932,f4160,f4163,f4164,f4472,f4507,f4517,f4668,f4702,f4718,f4834,f4838,f4846,f4850,f4858,f4875,f4913,f4917,f4935,f4941,f4969,f4974,f5064,f5068,f5166,f5185,f5232,f5252,f5258,f5276,f5323,f5371,f5376,f5396,f5537,f5860,f5865,f5877,f5879,f5880,f5893,f5894,f6002,f6016,f6030,f6054,f6135,f6173,f6186,f6200,f6257,f6258,f6269,f6350,f6438,f6440,f6539,f6550,f6587,f6611,f6767,f6801,f6831,f6859,f6869,f6879,f6886,f6934,f6952,f7037,f7047,f7057,f7064,f7079,f7106,f7118,f7166,f7227,f7229,f7282,f7320,f7334,f7337,f7538,f7542,f7580,f7597,f7602,f7643,f7709,f7714,f7727,f7761,f7769,f7794,f7817,f7852,f7877,f7921,f7933,f8022,f8039,f8041,f8071,f8074,f8076,f8077,f8091,f8114,f8117,f8129,f8152,f8166,f8184,f8248,f8262,f8278,f8290,f8294,f8295,f8296,f8298,f8299,f8300,f8311,f8312,f8313,f8317,f8345,f8363,f8393,f8469,f8473,f8481,f8484,f8505,f8507,f8615,f8628,f8629,f8631,f8679,f8687,f8762,f8763,f8764,f8774,f8779,f8801,f8803,f8829,f8836,f8858,f8943,f8944,f8958,f8972,f9274,f9281,f9287,f9293,f9328,f9447,f9453,f9459,f9475,f9486,f9506,f9528,f9559,f9586,f9590,f9602,f9627,f9629,f9633,f9649,f9694,f9715,f9741,f10012,f10020,f10022,f10061,f10115,f10155,f10166,f10173,f10321,f10353,f10390,f10422,f10423,f10459,f10484,f10497,f10516,f10577,f10590,f10592,f10620,f10639,f10656,f10668,f10678,f10710,f10824,f10837,f10932,f10954,f10959,f11008,f11064,f11065,f11066,f11067,f11068,f11110,f11111,f11136,f11138,f11258,f11269,f11290,f11292,f11294,f11316,f11331,f11382,f11389,f11391,f11392,f11403,f11493,f11494,f11495,f11498,f11512,f11610,f11633,f11642,f11661,f11663,f11708,f11741,f11744,f11800,f11873,f11936,f11970,f12153,f12200,f12212,f12218,f12221,f12240,f12288,f12292,f12297,f12729,f12756,f12784,f12785,f12813,f12894,f12923,f13033,f13060,f13085,f13106,f13174,f13178,f13268,f13282,f13290,f13303,f13309,f13313,f13331,f13341,f13346,f13348,f13349,f13357,f13453,f13475,f13483,f13484,f13500,f13523,f13525,f13527,f13539,f13540,f13551,f13592,f13741,f13742,f13753,f13808,f13856,f13859,f13862,f13875,f13896,f13900,f13916,f13917,f14254,f14255,f14259,f14261,f14278,f14407,f14412,f14560,f14562,f14563,f14564,f14565,f14568,f14617,f14752,f14771,f14815,f14818,f14856,f14866,f14917,f14918,f14928,f14935,f14936,f14960,f14975,f14983,f14989,f15008,f15029,f15092,f15093,f15095,f15096,f15141,f15163,f15166,f15227,f15248,f15268,f15293,f15312,f15328,f15329,f15452,f15481,f15496,f15525,f15526,f15527,f15528,f15529,f15530,f15532,f15563,f15576,f15629,f15722,f15742,f15747,f15759,f15763,f15789,f15805,f15811,f15950,f15964,f15966,f15967,f15968,f15971,f15975,f16027,f16118,f16131,f16138,f16141,f16146,f16154,f16159,f16253,f16506,f16515,f16516,f16519,f16529,f16685,f16721,f16740,f16780,f16872,f16934,f16959,f16961,f16962,f17001,f17030,f17173,f17177,f17191,f17203,f17256,f17377,f17384,f17385,f17389,f17396,f17442,f17464,f17470,f17651,f17679,f17686,f17875,f17896,f17971,f17972,f17973,f18045,f18065,f18089,f18122,f18194,f18256,f18269,f18320,f18582,f18643,f18700,f18786,f18788,f18789,f18790,f18850,f18906,f18947,f18967,f18980,f18986,f18998,f19013,f19017,f19021,f19027,f19054,f19086,f19091,f19096,f19101,f19108,f19185,f19201,f19213,f19401,f19435,f19491,f19509,f19516,f19525,f19560,f19632,f19658,f19755,f19757,f19850,f19864,f19987,f19989,f20027,f20050,f20056,f20061,f20077,f20104,f20115,f20121,f20134,f20317,f20318,f20324,f20337,f20386]) ).
thf(f20386,plain,
( ~ spl0_1
| ~ spl0_31
| ~ spl0_40
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_84
| ~ spl0_85
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(avatar_contradiction_clause,[],[f20385]) ).
thf(f20385,plain,
( $false
| ~ spl0_1
| ~ spl0_31
| ~ spl0_40
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_84
| ~ spl0_85
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(trivial_inequality_removal,[],[f20384]) ).
thf(f20384,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_31
| ~ spl0_40
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_84
| ~ spl0_85
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f20383,f20203]) ).
thf(f20203,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_31
| ~ spl0_40
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_84
| ~ spl0_85 ),
inference(forward_demodulation,[],[f20202,f358]) ).
thf(f358,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f356]) ).
thf(f356,plain,
( spl0_40
<=> ( $false = vAPP($o,$o,f0,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
thf(f20202,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_31
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_84
| ~ spl0_85 ),
inference(forward_demodulation,[],[f20201,f20122]) ).
thf(f20122,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_84
| ~ spl0_85 ),
inference(forward_demodulation,[],[f5869,f5873]) ).
thf(f5873,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f5871]) ).
thf(f5871,plain,
( spl0_85
<=> ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
thf(f5869,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f5867]) ).
thf(f5867,plain,
( spl0_84
<=> ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
thf(f20201,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_31
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f20200,f20135]) ).
thf(f20135,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f1118,f1713]) ).
thf(f1713,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1711]) ).
thf(f1711,plain,
( spl0_68
<=> ( $false = vAPP($o,$o,f3,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
thf(f1118,plain,
( ( $true = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1116]) ).
thf(f1116,plain,
( spl0_65
<=> ( $true = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
thf(f20200,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_31
| ~ spl0_63 ),
inference(forward_demodulation,[],[f307,f1107]) ).
thf(f1107,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1105]) ).
thf(f1105,plain,
( spl0_63
<=> ( $false = vAPP($o,$o,f2,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
thf(f307,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f305,plain,
( spl0_31
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
thf(f20383,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_84
| ~ spl0_85
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f20382,f358]) ).
thf(f20382,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_1
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_84
| ~ spl0_85
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f20381,f20122]) ).
thf(f20381,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_1
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f20380,f20135]) ).
thf(f20380,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_1
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f20379,f1107]) ).
thf(f20379,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_1
| ~ spl0_65
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f20364,f20135]) ).
thf(f20364,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(backward_demodulation,[],[f20306,f13498]) ).
thf(f13498,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f13497]) ).
thf(f13497,plain,
( spl0_116
<=> ( $false = vAPP($o,$o,f3,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
thf(f20306,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f20305,f12664]) ).
thf(f12664,plain,
( ( $true = vAPP($o,$o,f4,$true) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f12662]) ).
thf(f12662,plain,
( spl0_102
<=> ( $true = vAPP($o,$o,f4,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
thf(f20305,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f20304,f12664]) ).
thf(f20304,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f20303,f12664]) ).
thf(f20303,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| ~ spl0_1
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12,f12612]) ).
thf(f12612,plain,
( ( x = $true )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f12610]) ).
thf(f12610,plain,
( spl0_101
<=> ( x = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
thf(f12,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))) = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
thf(f10,plain,
( spl0_1
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f20337,plain,
( ~ spl0_122
| spl0_17
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f20336,f12662,f12610,f119,f16104]) ).
thf(f16104,plain,
( spl0_122
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
thf(f119,plain,
( spl0_17
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f20336,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| spl0_17
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19973,f12664]) ).
thf(f19973,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))))) )
| spl0_17
| ~ spl0_101 ),
inference(forward_demodulation,[],[f120,f12612]) ).
thf(f120,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))))) != $false )
| spl0_17 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f20324,plain,
( ~ spl0_26
| ~ spl0_102
| spl0_117 ),
inference(avatar_split_clause,[],[f20107,f14404,f12662,f272]) ).
thf(f272,plain,
( spl0_26
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f14404,plain,
( spl0_117
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
thf(f20107,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_102
| spl0_117 ),
inference(forward_demodulation,[],[f20094,f12664]) ).
thf(f20094,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_102
| spl0_117 ),
inference(backward_demodulation,[],[f14405,f12664]) ).
thf(f14405,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| spl0_117 ),
inference(avatar_component_clause,[],[f14404]) ).
thf(f20318,plain,
( ~ spl0_26
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f20283,f12662,f12610,f19,f272]) ).
thf(f19,plain,
( spl0_3
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f20283,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f20282,f12664]) ).
thf(f20282,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f20281,f12664]) ).
thf(f20281,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f20280,f12664]) ).
thf(f20280,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f20,f12612]) ).
thf(f20,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))) != $false )
| spl0_3 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f20317,plain,
( ~ spl0_8
| spl0_2
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f20294,f12662,f12610,f14,f78]) ).
thf(f78,plain,
( spl0_8
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f14,plain,
( spl0_2
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f20294,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| spl0_2
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f20293,f12664]) ).
thf(f20293,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_2
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15,f12612]) ).
thf(f15,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) != $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f20134,plain,
( spl0_63
| ~ spl0_67
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f20133,f4852,f1555,f1105]) ).
thf(f1555,plain,
( spl0_67
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
thf(f4852,plain,
( spl0_81
<=> ( $true = vAPP($o,$o,f3,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
thf(f20133,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_67
| ~ spl0_81 ),
inference(forward_demodulation,[],[f1557,f4854]) ).
thf(f4854,plain,
( ( $true = vAPP($o,$o,f3,$true) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f4852]) ).
thf(f1557,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1555]) ).
thf(f20121,plain,
( spl0_73
| ~ spl0_85
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f20120,f7918,f5871,f3150]) ).
thf(f3150,plain,
( spl0_73
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
thf(f7918,plain,
( spl0_92
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
thf(f20120,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_85
| ~ spl0_92 ),
inference(backward_demodulation,[],[f7920,f5873]) ).
thf(f7920,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f7918]) ).
thf(f20115,plain,
( spl0_63
| ~ spl0_81
| ~ spl0_102
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f20114,f15961,f12662,f4852,f1105]) ).
thf(f15961,plain,
( spl0_121
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
thf(f20114,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_81
| ~ spl0_102
| ~ spl0_121 ),
inference(forward_demodulation,[],[f20113,f4854]) ).
thf(f20113,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ~ spl0_81
| ~ spl0_102
| ~ spl0_121 ),
inference(forward_demodulation,[],[f20112,f4854]) ).
thf(f20112,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ~ spl0_81
| ~ spl0_102
| ~ spl0_121 ),
inference(forward_demodulation,[],[f20097,f4854]) ).
thf(f20097,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ~ spl0_102
| ~ spl0_121 ),
inference(backward_demodulation,[],[f15962,f12664]) ).
thf(f15962,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f15961]) ).
thf(f20104,plain,
( spl0_63
| ~ spl0_81
| ~ spl0_102
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f20103,f13470,f12662,f4852,f1105]) ).
thf(f13470,plain,
( spl0_114
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
thf(f20103,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_81
| ~ spl0_102
| ~ spl0_114 ),
inference(forward_demodulation,[],[f20102,f4854]) ).
thf(f20102,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ~ spl0_102
| ~ spl0_114 ),
inference(forward_demodulation,[],[f20101,f12664]) ).
thf(f20101,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ~ spl0_102
| ~ spl0_114 ),
inference(forward_demodulation,[],[f20092,f12664]) ).
thf(f20092,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))) )
| ~ spl0_102
| ~ spl0_114 ),
inference(backward_demodulation,[],[f13472,f12664]) ).
thf(f13472,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f13470]) ).
thf(f20077,plain,
( ~ spl0_110
| ~ spl0_101
| spl0_113 ),
inference(avatar_split_clause,[],[f20076,f13057,f12610,f12920]) ).
thf(f12920,plain,
( spl0_110
<=> ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
thf(f13057,plain,
( spl0_113
<=> ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
thf(f20076,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))) )
| ~ spl0_101
| spl0_113 ),
inference(forward_demodulation,[],[f13058,f12612]) ).
thf(f13058,plain,
( ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) != $false )
| spl0_113 ),
inference(avatar_component_clause,[],[f13057]) ).
thf(f20061,plain,
( ~ spl0_37
| ~ spl0_53
| ~ spl0_79
| spl0_93 ),
inference(avatar_split_clause,[],[f20060,f8126,f4810,f750,f341]) ).
thf(f341,plain,
( spl0_37
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
thf(f750,plain,
( spl0_53
<=> ( $true = vAPP($o,$o,f1,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
thf(f4810,plain,
( spl0_79
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
thf(f8126,plain,
( spl0_93
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
thf(f20060,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_53
| ~ spl0_79
| spl0_93 ),
inference(forward_demodulation,[],[f20057,f752]) ).
thf(f752,plain,
( ( $true = vAPP($o,$o,f1,$false) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f750]) ).
thf(f20057,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_79
| spl0_93 ),
inference(backward_demodulation,[],[f8128,f4812]) ).
thf(f4812,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f4810]) ).
thf(f8128,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_93 ),
inference(avatar_component_clause,[],[f8126]) ).
thf(f20056,plain,
( spl0_79
| ~ spl0_47
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f19170,f1711,f718,f4810]) ).
thf(f718,plain,
( spl0_47
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
thf(f19170,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_47
| ~ spl0_68 ),
inference(forward_demodulation,[],[f720,f1713]) ).
thf(f720,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f718]) ).
thf(f20050,plain,
( ~ spl0_3
| ~ spl0_22
| spl0_40
| ~ spl0_53
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(avatar_contradiction_clause,[],[f20049]) ).
thf(f20049,plain,
( $false
| ~ spl0_3
| ~ spl0_22
| spl0_40
| ~ spl0_53
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(subsumption_resolution,[],[f20048,f357]) ).
thf(f357,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_40 ),
inference(avatar_component_clause,[],[f356]) ).
thf(f20048,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_3
| ~ spl0_22
| ~ spl0_53
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f20047,f143]) ).
thf(f143,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f141,plain,
( spl0_22
<=> ( $true = vAPP($o,$o,f0,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f20047,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_3
| ~ spl0_22
| ~ spl0_53
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f20046,f143]) ).
thf(f20046,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_3
| ~ spl0_53
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f20045,f752]) ).
thf(f20045,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_3
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f20044,f4823]) ).
thf(f4823,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f4821]) ).
thf(f4821,plain,
( spl0_80
<=> ( $false = vAPP($o,$o,f2,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
thf(f20044,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_3
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f20043,f4823]) ).
thf(f20043,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_3
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f20042,f4823]) ).
thf(f20042,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_3
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f19829,f19992]) ).
thf(f19992,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_87
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13480,f6681]) ).
thf(f6681,plain,
( ( $false = vAPP($o,$o,f4,$true) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f6680]) ).
thf(f6680,plain,
( spl0_87
<=> ( $false = vAPP($o,$o,f4,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
thf(f13480,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f13478]) ).
thf(f13478,plain,
( spl0_115
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
thf(f19829,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| ~ spl0_3
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19828,f6681]) ).
thf(f19828,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f21,f12612]) ).
thf(f21,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))) = $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f20027,plain,
( ~ spl0_22
| spl0_40
| ~ spl0_53
| ~ spl0_89 ),
inference(avatar_contradiction_clause,[],[f20026]) ).
thf(f20026,plain,
( $false
| ~ spl0_22
| spl0_40
| ~ spl0_53
| ~ spl0_89 ),
inference(subsumption_resolution,[],[f20025,f357]) ).
thf(f20025,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_22
| ~ spl0_53
| ~ spl0_89 ),
inference(forward_demodulation,[],[f20024,f143]) ).
thf(f20024,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_22
| ~ spl0_53
| ~ spl0_89 ),
inference(forward_demodulation,[],[f20023,f143]) ).
thf(f20023,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_53
| ~ spl0_89 ),
inference(forward_demodulation,[],[f6949,f752]) ).
thf(f6949,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f6948]) ).
thf(f6948,plain,
( spl0_89
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
thf(f19989,plain,
( spl0_23
| ~ spl0_87
| ~ spl0_101
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f19988,f13057,f12610,f6680,f259]) ).
thf(f259,plain,
( spl0_23
<=> ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f19988,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_87
| ~ spl0_101
| ~ spl0_113 ),
inference(forward_demodulation,[],[f19697,f6681]) ).
thf(f19697,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))) )
| ~ spl0_101
| ~ spl0_113 ),
inference(forward_demodulation,[],[f13059,f12612]) ).
thf(f13059,plain,
( ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f13057]) ).
thf(f19987,plain,
( spl0_23
| ~ spl0_87
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f19986,f12920,f6680,f259]) ).
thf(f19986,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_87
| ~ spl0_110 ),
inference(forward_demodulation,[],[f12922,f6681]) ).
thf(f12922,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f12920]) ).
thf(f19864,plain,
( spl0_89
| ~ spl0_24
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f19800,f6680,f4821,f1711,f263,f6948]) ).
thf(f263,plain,
( spl0_24
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f19800,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_24
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87 ),
inference(forward_demodulation,[],[f19799,f4823]) ).
thf(f19799,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_24
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87 ),
inference(forward_demodulation,[],[f19798,f4823]) ).
thf(f19798,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_24
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87 ),
inference(forward_demodulation,[],[f19797,f4823]) ).
thf(f19797,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_24
| ~ spl0_68
| ~ spl0_87 ),
inference(forward_demodulation,[],[f19796,f1713]) ).
thf(f19796,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_24
| ~ spl0_87 ),
inference(forward_demodulation,[],[f265,f6681]) ).
thf(f265,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f19850,plain,
( ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f19849]) ).
thf(f19849,plain,
( $false
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_120 ),
inference(trivial_inequality_removal,[],[f19848]) ).
thf(f19848,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19847,f15949]) ).
thf(f15949,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f15947]) ).
thf(f15947,plain,
( spl0_120
<=> ( $false = vAPP($o,$o,f0,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
thf(f19847,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19846,f2469]) ).
thf(f2469,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f2467]) ).
thf(f2467,plain,
( spl0_70
<=> ( $false = vAPP($o,$o,f1,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
thf(f19846,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19845,f2469]) ).
thf(f19845,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19844,f2469]) ).
thf(f19844,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19843,f4823]) ).
thf(f19843,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19842,f1713]) ).
thf(f19842,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19841,f1713]) ).
thf(f19841,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19840,f1713]) ).
thf(f19840,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_2
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f19839,f6681]) ).
thf(f19839,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_2
| ~ spl0_101 ),
inference(forward_demodulation,[],[f16,f12612]) ).
thf(f16,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f19757,plain,
( ~ spl0_63
| spl0_67
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f19756,f4852,f1555,f1105]) ).
thf(f19756,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_67
| ~ spl0_81 ),
inference(forward_demodulation,[],[f1556,f4854]) ).
thf(f1556,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| spl0_67 ),
inference(avatar_component_clause,[],[f1555]) ).
thf(f19755,plain,
( ~ spl0_63
| spl0_69
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f19754,f4852,f1715,f1105]) ).
thf(f1715,plain,
( spl0_69
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
thf(f19754,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_69
| ~ spl0_81 ),
inference(forward_demodulation,[],[f19753,f4854]) ).
thf(f19753,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| spl0_69
| ~ spl0_81 ),
inference(forward_demodulation,[],[f1716,f4854]) ).
thf(f1716,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| spl0_69 ),
inference(avatar_component_clause,[],[f1715]) ).
thf(f19658,plain,
( ~ spl0_29
| spl0_26
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f19552,f4852,f272,f291]) ).
thf(f291,plain,
( spl0_29
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
thf(f19552,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_26
| ~ spl0_81 ),
inference(forward_demodulation,[],[f273,f4854]) ).
thf(f273,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_26 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f19632,plain,
( spl0_3
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f19631]) ).
thf(f19631,plain,
( $false
| spl0_3
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102
| ~ spl0_120 ),
inference(subsumption_resolution,[],[f19630,f15949]) ).
thf(f19630,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_3
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19629,f15949]) ).
thf(f19629,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_3
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19628,f15949]) ).
thf(f19628,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_3
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19627,f2469]) ).
thf(f19627,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_3
| ~ spl0_63
| ~ spl0_80
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19626,f4823]) ).
thf(f19626,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_3
| ~ spl0_63
| ~ spl0_80
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19625,f4823]) ).
thf(f19625,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_3
| ~ spl0_63
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19624,f1107]) ).
thf(f19624,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_3
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19623,f4854]) ).
thf(f19623,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19622,f12664]) ).
thf(f19622,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19621,f12664]) ).
thf(f19621,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19620,f12664]) ).
thf(f19620,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f20,f12612]) ).
thf(f19560,plain,
( spl0_26
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f19559]) ).
thf(f19559,plain,
( $false
| spl0_26
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_120 ),
inference(subsumption_resolution,[],[f19558,f15949]) ).
thf(f19558,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_26
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19557,f15949]) ).
thf(f19557,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_26
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19556,f15949]) ).
thf(f19556,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_26
| ~ spl0_63
| ~ spl0_70
| ~ spl0_80
| ~ spl0_81 ),
inference(forward_demodulation,[],[f19555,f2469]) ).
thf(f19555,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_26
| ~ spl0_63
| ~ spl0_80
| ~ spl0_81 ),
inference(forward_demodulation,[],[f19554,f4823]) ).
thf(f19554,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_26
| ~ spl0_63
| ~ spl0_80
| ~ spl0_81 ),
inference(forward_demodulation,[],[f19553,f4823]) ).
thf(f19553,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_26
| ~ spl0_63
| ~ spl0_81 ),
inference(forward_demodulation,[],[f19552,f1107]) ).
thf(f19525,plain,
( spl0_88
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f19524]) ).
thf(f19524,plain,
( $false
| spl0_88
| ~ spl0_120 ),
inference(subsumption_resolution,[],[f19523,f15949]) ).
thf(f19523,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_88
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19522,f15949]) ).
thf(f19522,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_88
| ~ spl0_120 ),
inference(forward_demodulation,[],[f6933,f15949]) ).
thf(f6933,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_88 ),
inference(avatar_component_clause,[],[f6931]) ).
thf(f6931,plain,
( spl0_88
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
thf(f19516,plain,
( ~ spl0_70
| ~ spl0_80
| spl0_93
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f19515]) ).
thf(f19515,plain,
( $false
| ~ spl0_70
| ~ spl0_80
| spl0_93
| ~ spl0_120 ),
inference(subsumption_resolution,[],[f19514,f15949]) ).
thf(f19514,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_70
| ~ spl0_80
| spl0_93
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19513,f15949]) ).
thf(f19513,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_70
| ~ spl0_80
| spl0_93
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19512,f15949]) ).
thf(f19512,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f19511,f2469]) ).
thf(f19511,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f19510,f4823]) ).
thf(f19510,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f8128,f4823]) ).
thf(f19509,plain,
( ~ spl0_67
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| spl0_117
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f19508]) ).
thf(f19508,plain,
( $false
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| spl0_117
| ~ spl0_120 ),
inference(subsumption_resolution,[],[f19507,f15949]) ).
thf(f19507,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| spl0_117
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19506,f15949]) ).
thf(f19506,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| spl0_117
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19505,f15949]) ).
thf(f19505,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| spl0_117 ),
inference(forward_demodulation,[],[f19504,f2469]) ).
thf(f19504,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_67
| ~ spl0_80
| ~ spl0_102
| spl0_117 ),
inference(forward_demodulation,[],[f19503,f4823]) ).
thf(f19503,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_67
| ~ spl0_80
| ~ spl0_102
| spl0_117 ),
inference(forward_demodulation,[],[f19502,f4823]) ).
thf(f19502,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_67
| ~ spl0_102
| spl0_117 ),
inference(forward_demodulation,[],[f19501,f1557]) ).
thf(f19501,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_102
| spl0_117 ),
inference(forward_demodulation,[],[f19500,f12664]) ).
thf(f19500,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_102
| spl0_117 ),
inference(forward_demodulation,[],[f14405,f12664]) ).
thf(f19491,plain,
( spl0_116
| ~ spl0_102
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f19039,f13478,f12662,f13497]) ).
thf(f19039,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_102
| ~ spl0_115 ),
inference(forward_demodulation,[],[f19038,f12664]) ).
thf(f19038,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$true)) )
| ~ spl0_102
| ~ spl0_115 ),
inference(forward_demodulation,[],[f19033,f12664]) ).
thf(f19033,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))) )
| ~ spl0_102
| ~ spl0_115 ),
inference(backward_demodulation,[],[f13480,f12664]) ).
thf(f19435,plain,
( ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f19434]) ).
thf(f19434,plain,
( $false
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(trivial_inequality_removal,[],[f19433]) ).
thf(f19433,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19432,f15949]) ).
thf(f19432,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19431,f2469]) ).
thf(f19431,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19430,f2469]) ).
thf(f19430,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19429,f2469]) ).
thf(f19429,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19428,f4823]) ).
thf(f19428,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19427,f1713]) ).
thf(f19427,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_2
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19426,f1713]) ).
thf(f19426,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_2
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19425,f13498]) ).
thf(f19425,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_2
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f19424,f12664]) ).
thf(f19424,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_2
| ~ spl0_101 ),
inference(forward_demodulation,[],[f16,f12612]) ).
thf(f19401,plain,
( ~ spl0_6
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f19400]) ).
thf(f19400,plain,
( $false
| ~ spl0_6
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(trivial_inequality_removal,[],[f19399]) ).
thf(f19399,plain,
( ( $true = $false )
| ~ spl0_6
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f19398,f15949]) ).
thf(f19398,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_6
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19397,f2469]) ).
thf(f19397,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_6
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19396,f2469]) ).
thf(f19396,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_6
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19395,f2469]) ).
thf(f19395,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_6
| ~ spl0_68
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19394,f4823]) ).
thf(f19394,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_6
| ~ spl0_68
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19393,f1713]) ).
thf(f19393,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_6
| ~ spl0_68
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19392,f1713]) ).
thf(f19392,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_6
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19391,f13498]) ).
thf(f19391,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_6
| ~ spl0_102 ),
inference(forward_demodulation,[],[f71,f12664]) ).
thf(f71,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f69,plain,
( spl0_6
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f19213,plain,
( spl0_89
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f19212,f14404,f13497,f12662,f4821,f6948]) ).
thf(f19212,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(forward_demodulation,[],[f19211,f4823]) ).
thf(f19211,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(forward_demodulation,[],[f19210,f4823]) ).
thf(f19210,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(forward_demodulation,[],[f19209,f4823]) ).
thf(f19209,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(forward_demodulation,[],[f19208,f13498]) ).
thf(f19208,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_102
| ~ spl0_117 ),
inference(forward_demodulation,[],[f19207,f12664]) ).
thf(f19207,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_102
| ~ spl0_117 ),
inference(forward_demodulation,[],[f14406,f12664]) ).
thf(f14406,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f14404]) ).
thf(f19201,plain,
( ~ spl0_70
| ~ spl0_80
| spl0_122
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f19116,f16121,f16104,f4821,f2467]) ).
thf(f16121,plain,
( spl0_124
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
thf(f19116,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_80
| spl0_122
| ~ spl0_124 ),
inference(backward_demodulation,[],[f18995,f4823]) ).
thf(f18995,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| spl0_122
| ~ spl0_124 ),
inference(backward_demodulation,[],[f16106,f16123]) ).
thf(f16123,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f16121]) ).
thf(f16106,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| spl0_122 ),
inference(avatar_component_clause,[],[f16104]) ).
thf(f19185,plain,
( spl0_14
| ~ spl0_18
| ~ spl0_53
| ~ spl0_63 ),
inference(avatar_contradiction_clause,[],[f19184]) ).
thf(f19184,plain,
( $false
| spl0_14
| ~ spl0_18
| ~ spl0_53
| ~ spl0_63 ),
inference(subsumption_resolution,[],[f19183,f125]) ).
thf(f125,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f123,plain,
( spl0_18
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f19183,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_14
| ~ spl0_53
| ~ spl0_63 ),
inference(forward_demodulation,[],[f19182,f752]) ).
thf(f19182,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_14
| ~ spl0_63 ),
inference(forward_demodulation,[],[f106,f1107]) ).
thf(f106,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_14 ),
inference(avatar_component_clause,[],[f105]) ).
thf(f105,plain,
( spl0_14
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f19108,plain,
( spl0_80
| ~ spl0_68
| ~ spl0_91
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f19107,f8283,f7914,f1711,f4821]) ).
thf(f7914,plain,
( spl0_91
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
thf(f8283,plain,
( spl0_94
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
thf(f19107,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_68
| ~ spl0_91
| ~ spl0_94 ),
inference(forward_demodulation,[],[f19106,f1713]) ).
thf(f19106,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_68
| ~ spl0_91
| ~ spl0_94 ),
inference(forward_demodulation,[],[f19105,f1713]) ).
thf(f19105,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_91
| ~ spl0_94 ),
inference(forward_demodulation,[],[f7916,f8285]) ).
thf(f8285,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f8283]) ).
thf(f7916,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f7914]) ).
thf(f19101,plain,
( spl0_80
| ~ spl0_102
| ~ spl0_114
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f19100,f13497,f13470,f12662,f4821]) ).
thf(f19100,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_102
| ~ spl0_114
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19099,f13498]) ).
thf(f19099,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ~ spl0_102
| ~ spl0_114 ),
inference(forward_demodulation,[],[f19098,f12664]) ).
thf(f19098,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ~ spl0_102
| ~ spl0_114 ),
inference(forward_demodulation,[],[f19097,f12664]) ).
thf(f19097,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))) )
| ~ spl0_102
| ~ spl0_114 ),
inference(forward_demodulation,[],[f13472,f12664]) ).
thf(f19096,plain,
( ~ spl0_68
| ~ spl0_102
| ~ spl0_116
| spl0_119 ),
inference(avatar_contradiction_clause,[],[f19095]) ).
thf(f19095,plain,
( $false
| ~ spl0_68
| ~ spl0_102
| ~ spl0_116
| spl0_119 ),
inference(subsumption_resolution,[],[f19094,f1713]) ).
thf(f19094,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_68
| ~ spl0_102
| ~ spl0_116
| spl0_119 ),
inference(forward_demodulation,[],[f19093,f1713]) ).
thf(f19093,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_102
| ~ spl0_116
| spl0_119 ),
inference(forward_demodulation,[],[f19092,f13498]) ).
thf(f19092,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ~ spl0_102
| spl0_119 ),
inference(forward_demodulation,[],[f15945,f12664]) ).
thf(f15945,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| spl0_119 ),
inference(avatar_component_clause,[],[f15943]) ).
thf(f15943,plain,
( spl0_119
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
thf(f19091,plain,
( spl0_80
| ~ spl0_68
| ~ spl0_102
| ~ spl0_116
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f19090,f15961,f13497,f12662,f1711,f4821]) ).
thf(f19090,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_68
| ~ spl0_102
| ~ spl0_116
| ~ spl0_121 ),
inference(forward_demodulation,[],[f19089,f1713]) ).
thf(f19089,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_68
| ~ spl0_102
| ~ spl0_116
| ~ spl0_121 ),
inference(forward_demodulation,[],[f19088,f1713]) ).
thf(f19088,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_102
| ~ spl0_116
| ~ spl0_121 ),
inference(forward_demodulation,[],[f19087,f13498]) ).
thf(f19087,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ~ spl0_102
| ~ spl0_121 ),
inference(forward_demodulation,[],[f15962,f12664]) ).
thf(f19086,plain,
( spl0_2
| ~ spl0_12
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(avatar_contradiction_clause,[],[f19085]) ).
thf(f19085,plain,
( $false
| spl0_2
| ~ spl0_12
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(subsumption_resolution,[],[f19084,f19000]) ).
thf(f19000,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_12
| ~ spl0_116 ),
inference(backward_demodulation,[],[f98,f13498]) ).
thf(f98,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f96]) ).
thf(f96,plain,
( spl0_12
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f19084,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_2
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19083,f1713]) ).
thf(f19083,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| spl0_2
| ~ spl0_68
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19082,f1713]) ).
thf(f19082,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| spl0_2
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f19081,f13498]) ).
thf(f19081,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| spl0_2
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f17587,f12664]) ).
thf(f17587,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_2
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15,f12612]) ).
thf(f19054,plain,
( ~ spl0_79
| ~ spl0_23
| spl0_32
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f19050,f8283,f314,f259,f4810]) ).
thf(f314,plain,
( spl0_32
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
thf(f19050,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_23
| spl0_32
| ~ spl0_94 ),
inference(backward_demodulation,[],[f18472,f8285]) ).
thf(f18472,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_23
| spl0_32 ),
inference(backward_demodulation,[],[f315,f261]) ).
thf(f261,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f315,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| spl0_32 ),
inference(avatar_component_clause,[],[f314]) ).
thf(f19027,plain,
( ~ spl0_80
| spl0_114
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f19026,f13478,f13470,f4821]) ).
thf(f19026,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_114
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13471,f13480]) ).
thf(f13471,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))) )
| spl0_114 ),
inference(avatar_component_clause,[],[f13470]) ).
thf(f19021,plain,
( ~ spl0_4
| spl0_74
| ~ spl0_101
| ~ spl0_116
| ~ spl0_119 ),
inference(avatar_contradiction_clause,[],[f19020]) ).
thf(f19020,plain,
( $false
| ~ spl0_4
| spl0_74
| ~ spl0_101
| ~ spl0_116
| ~ spl0_119 ),
inference(subsumption_resolution,[],[f19004,f18982]) ).
thf(f18982,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_101
| ~ spl0_119 ),
inference(forward_demodulation,[],[f17565,f15944]) ).
thf(f15944,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f15943]) ).
thf(f17565,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_4
| ~ spl0_101 ),
inference(forward_demodulation,[],[f25,f12612]) ).
thf(f25,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) = $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f23,plain,
( spl0_4
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f19004,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_74
| ~ spl0_116 ),
inference(backward_demodulation,[],[f3169,f13498]) ).
thf(f3169,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_74 ),
inference(avatar_component_clause,[],[f3168]) ).
thf(f3168,plain,
( spl0_74
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
thf(f19017,plain,
( ~ spl0_80
| spl0_67
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f19002,f13497,f1555,f4821]) ).
thf(f19002,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_67
| ~ spl0_116 ),
inference(backward_demodulation,[],[f1556,f13498]) ).
thf(f19013,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_101
| ~ spl0_116
| ~ spl0_119 ),
inference(avatar_contradiction_clause,[],[f19012]) ).
thf(f19012,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_101
| ~ spl0_116
| ~ spl0_119 ),
inference(trivial_inequality_removal,[],[f19011]) ).
thf(f19011,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_12
| ~ spl0_101
| ~ spl0_116
| ~ spl0_119 ),
inference(forward_demodulation,[],[f19000,f18982]) ).
thf(f18998,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_101
| ~ spl0_119
| ~ spl0_124 ),
inference(avatar_contradiction_clause,[],[f18997]) ).
thf(f18997,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_101
| ~ spl0_119
| ~ spl0_124 ),
inference(trivial_inequality_removal,[],[f18996]) ).
thf(f18996,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_101
| ~ spl0_119
| ~ spl0_124 ),
inference(forward_demodulation,[],[f18994,f18982]) ).
thf(f18994,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_8
| ~ spl0_124 ),
inference(backward_demodulation,[],[f80,f16123]) ).
thf(f80,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f18986,plain,
( spl0_118
| ~ spl0_11
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f18171,f12610,f92,f15719]) ).
thf(f15719,plain,
( spl0_118
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
thf(f92,plain,
( spl0_11
<=> ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f18171,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ~ spl0_11
| ~ spl0_101 ),
inference(forward_demodulation,[],[f94,f12612]) ).
thf(f94,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f18980,plain,
( spl0_80
| ~ spl0_119
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f18979,f15961,f15943,f4821]) ).
thf(f18979,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_119
| ~ spl0_121 ),
inference(backward_demodulation,[],[f15962,f15944]) ).
thf(f18967,plain,
( spl0_121
| ~ spl0_15
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f18826,f12610,f110,f15961]) ).
thf(f110,plain,
( spl0_15
<=> ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f18826,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| ~ spl0_15
| ~ spl0_101 ),
inference(forward_demodulation,[],[f112,f12612]) ).
thf(f112,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f18947,plain,
( ~ spl0_4
| ~ spl0_18
| ~ spl0_53
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f18946]) ).
thf(f18946,plain,
( $false
| ~ spl0_4
| ~ spl0_18
| ~ spl0_53
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(trivial_inequality_removal,[],[f18945]) ).
thf(f18945,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_18
| ~ spl0_53
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f125,f18944]) ).
thf(f18944,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_53
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18943,f752]) ).
thf(f18943,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18252,f4823]) ).
thf(f18252,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18251,f1713]) ).
thf(f18251,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18250,f1713]) ).
thf(f18250,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18249,f1713]) ).
thf(f18249,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_4
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f17565,f6681]) ).
thf(f18906,plain,
( ~ spl0_21
| ~ spl0_53
| ~ spl0_68
| ~ spl0_80
| spl0_83
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f18905]) ).
thf(f18905,plain,
( $false
| ~ spl0_21
| ~ spl0_53
| ~ spl0_68
| ~ spl0_80
| spl0_83
| ~ spl0_87
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f18904,f5274]) ).
thf(f5274,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_83 ),
inference(avatar_component_clause,[],[f5273]) ).
thf(f5273,plain,
( spl0_83
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
thf(f18904,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_21
| ~ spl0_53
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18890,f752]) ).
thf(f18890,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_21
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f18691,f4823]) ).
thf(f18691,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_21
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18690,f1713]) ).
thf(f18690,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_21
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18689,f1713]) ).
thf(f18689,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_21
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18688,f1713]) ).
thf(f18688,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_21
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18687,f6681]) ).
thf(f18687,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))))))) )
| ~ spl0_21
| ~ spl0_101 ),
inference(forward_demodulation,[],[f139,f12612]) ).
thf(f139,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))))))) = $false )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f137,plain,
( spl0_21
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f18850,plain,
( spl0_80
| ~ spl0_15
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f18830,f12610,f6680,f1711,f110,f4821]) ).
thf(f18830,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_15
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18829,f1713]) ).
thf(f18829,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_15
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18828,f1713]) ).
thf(f18828,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_15
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18827,f1713]) ).
thf(f18827,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_15
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18826,f6681]) ).
thf(f18790,plain,
( ~ spl0_83
| ~ spl0_64
| ~ spl0_81
| spl0_123 ),
inference(avatar_split_clause,[],[f18665,f16115,f4852,f1110,f5273]) ).
thf(f1110,plain,
( spl0_64
<=> ( $true = vAPP($o,$o,f2,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
thf(f16115,plain,
( spl0_123
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
thf(f18665,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_64
| ~ spl0_81
| spl0_123 ),
inference(forward_demodulation,[],[f18664,f1112]) ).
thf(f1112,plain,
( ( $true = vAPP($o,$o,f2,$true) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1110]) ).
thf(f18664,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| ~ spl0_81
| spl0_123 ),
inference(forward_demodulation,[],[f18663,f4854]) ).
thf(f18663,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))) )
| ~ spl0_81
| spl0_123 ),
inference(forward_demodulation,[],[f18662,f4854]) ).
thf(f18662,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_81
| spl0_123 ),
inference(forward_demodulation,[],[f16117,f4854]) ).
thf(f16117,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))) )
| spl0_123 ),
inference(avatar_component_clause,[],[f16115]) ).
thf(f18789,plain,
( spl0_71
| ~ spl0_64
| ~ spl0_81
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f18670,f16104,f4852,f1110,f2471]) ).
thf(f2471,plain,
( spl0_71
<=> ( $false = vAPP($o,$o,f1,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
thf(f18670,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_64
| ~ spl0_81
| ~ spl0_122 ),
inference(forward_demodulation,[],[f18669,f1112]) ).
thf(f18669,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_81
| ~ spl0_122 ),
inference(forward_demodulation,[],[f18668,f4854]) ).
thf(f18668,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| ~ spl0_81
| ~ spl0_122 ),
inference(forward_demodulation,[],[f18667,f4854]) ).
thf(f18667,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ~ spl0_81
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16105,f4854]) ).
thf(f16105,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f16104]) ).
thf(f18788,plain,
( spl0_50
| ~ spl0_1
| ~ spl0_64
| spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f18746,f13478,f12610,f6680,f4821,f1110,f10,f733]) ).
thf(f733,plain,
( spl0_50
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
thf(f18746,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_1
| ~ spl0_64
| spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f18745,f1112]) ).
thf(f18745,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_64
| spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f18744,f1112]) ).
thf(f18744,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_1
| spl0_80
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(subsumption_resolution,[],[f18728,f4822]) ).
thf(f4822,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_80 ),
inference(avatar_component_clause,[],[f4821]) ).
thf(f18728,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_1
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(superposition,[],[f18427,f4]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f18427,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_1
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f18426,f18414]) ).
thf(f18414,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_87
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13480,f6681]) ).
thf(f18426,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| ~ spl0_1
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f17597,f6681]) ).
thf(f17597,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| ~ spl0_1
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12,f12612]) ).
thf(f18786,plain,
( spl0_50
| ~ spl0_1
| spl0_49
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f18761,f13478,f12610,f6680,f1711,f729,f10,f733]) ).
thf(f729,plain,
( spl0_49
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
thf(f18761,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_1
| spl0_49
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(subsumption_resolution,[],[f18730,f18361]) ).
thf(f18361,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| spl0_49
| ~ spl0_68 ),
inference(forward_demodulation,[],[f730,f1713]) ).
thf(f730,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| spl0_49 ),
inference(avatar_component_clause,[],[f729]) ).
thf(f18730,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_1
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(superposition,[],[f18427,f4]) ).
thf(f18700,plain,
( ~ spl0_1
| ~ spl0_57
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f18699]) ).
thf(f18699,plain,
( $false
| ~ spl0_1
| ~ spl0_57
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115
| ~ spl0_120 ),
inference(trivial_inequality_removal,[],[f18698]) ).
thf(f18698,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_57
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115
| ~ spl0_120 ),
inference(forward_demodulation,[],[f18697,f15949]) ).
thf(f18697,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_57
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115
| ~ spl0_120 ),
inference(forward_demodulation,[],[f18695,f15949]) ).
thf(f18695,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_1
| ~ spl0_57
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(backward_demodulation,[],[f18427,f18334]) ).
thf(f18334,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_57
| ~ spl0_68 ),
inference(forward_demodulation,[],[f776,f1713]) ).
thf(f776,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f774]) ).
thf(f774,plain,
( spl0_57
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
thf(f18643,plain,
( spl0_3
| ~ spl0_51
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f18642]) ).
thf(f18642,plain,
( $false
| spl0_3
| ~ spl0_51
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115
| ~ spl0_120 ),
inference(subsumption_resolution,[],[f18641,f15949]) ).
thf(f18641,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_3
| ~ spl0_51
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115
| ~ spl0_120 ),
inference(forward_demodulation,[],[f18640,f15949]) ).
thf(f18640,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_3
| ~ spl0_51
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115
| ~ spl0_120 ),
inference(forward_demodulation,[],[f18639,f15949]) ).
thf(f18639,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_3
| ~ spl0_51
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f18417,f18357]) ).
thf(f18357,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f741,f1713]) ).
thf(f741,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f739]) ).
thf(f739,plain,
( spl0_51
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
thf(f18417,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| spl0_3
| ~ spl0_87
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f18416,f18414]) ).
thf(f18416,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| spl0_3
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f17574,f6681]) ).
thf(f17574,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f20,f12612]) ).
thf(f18582,plain,
( ~ spl0_64
| ~ spl0_71
| ~ spl0_81
| spl0_122 ),
inference(avatar_contradiction_clause,[],[f18581]) ).
thf(f18581,plain,
( $false
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81
| spl0_122 ),
inference(subsumption_resolution,[],[f18574,f2472]) ).
thf(f2472,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f2471]) ).
thf(f18574,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ~ spl0_64
| ~ spl0_81
| spl0_122 ),
inference(backward_demodulation,[],[f18078,f1112]) ).
thf(f18078,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_81
| spl0_122 ),
inference(forward_demodulation,[],[f18077,f4854]) ).
thf(f18077,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| ~ spl0_81
| spl0_122 ),
inference(forward_demodulation,[],[f18070,f4854]) ).
thf(f18070,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ~ spl0_81
| spl0_122 ),
inference(backward_demodulation,[],[f16106,f4854]) ).
thf(f18320,plain,
( ~ spl0_19
| ~ spl0_65
| ~ spl0_68
| spl0_70
| ~ spl0_71
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f18319]) ).
thf(f18319,plain,
( $false
| ~ spl0_19
| ~ spl0_65
| ~ spl0_68
| spl0_70
| ~ spl0_71
| ~ spl0_87
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f18318,f2468]) ).
thf(f2468,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| spl0_70 ),
inference(avatar_component_clause,[],[f2467]) ).
thf(f18318,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_19
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18311,f2472]) ).
thf(f18311,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_19
| ~ spl0_65
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f18231,f18308]) ).
thf(f18308,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f1118,f1713]) ).
thf(f18231,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_19
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18230,f1713]) ).
thf(f18230,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_19
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18229,f1713]) ).
thf(f18229,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| ~ spl0_19
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18228,f1713]) ).
thf(f18228,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_19
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f16237,f6681]) ).
thf(f16237,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))) )
| ~ spl0_19
| ~ spl0_101 ),
inference(forward_demodulation,[],[f130,f12612]) ).
thf(f130,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))) = $false )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f128,plain,
( spl0_19
<=> ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f18269,plain,
( ~ spl0_80
| ~ spl0_68
| ~ spl0_87
| spl0_121 ),
inference(avatar_split_clause,[],[f18268,f15961,f6680,f1711,f4821]) ).
thf(f18268,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_68
| ~ spl0_87
| spl0_121 ),
inference(forward_demodulation,[],[f18267,f1713]) ).
thf(f18267,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_68
| ~ spl0_87
| spl0_121 ),
inference(forward_demodulation,[],[f18266,f1713]) ).
thf(f18266,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_68
| ~ spl0_87
| spl0_121 ),
inference(forward_demodulation,[],[f18265,f1713]) ).
thf(f18265,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_87
| spl0_121 ),
inference(forward_demodulation,[],[f15963,f6681]) ).
thf(f15963,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| spl0_121 ),
inference(avatar_component_clause,[],[f15961]) ).
thf(f18256,plain,
( ~ spl0_4
| ~ spl0_19
| spl0_40
| ~ spl0_53
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f18255]) ).
thf(f18255,plain,
( $false
| ~ spl0_4
| ~ spl0_19
| spl0_40
| ~ spl0_53
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f18254,f357]) ).
thf(f18254,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| ~ spl0_19
| ~ spl0_53
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18253,f752]) ).
thf(f18253,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_19
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f18252,f18231]) ).
thf(f18194,plain,
( ~ spl0_93
| spl0_29
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f18150,f1105,f291,f8126]) ).
thf(f18150,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_29
| ~ spl0_63 ),
inference(forward_demodulation,[],[f292,f1107]) ).
thf(f292,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_29 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f18122,plain,
( ~ spl0_40
| ~ spl0_53
| spl0_57
| ~ spl0_68
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f18121,f4821,f1711,f774,f750,f356]) ).
thf(f18121,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| ~ spl0_53
| spl0_57
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f18120,f752]) ).
thf(f18120,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_57
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f18119,f4823]) ).
thf(f18119,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| spl0_57
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f18118,f4823]) ).
thf(f18118,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| spl0_57
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f18117,f4823]) ).
thf(f18117,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_57
| ~ spl0_68 ),
inference(forward_demodulation,[],[f775,f1713]) ).
thf(f775,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| spl0_57 ),
inference(avatar_component_clause,[],[f774]) ).
thf(f18089,plain,
( ~ spl0_40
| ~ spl0_53
| ~ spl0_63
| spl0_75
| ~ spl0_81
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f18088,f5871,f4852,f3173,f1105,f750,f356]) ).
thf(f3173,plain,
( spl0_75
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
thf(f18088,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| ~ spl0_53
| ~ spl0_63
| spl0_75
| ~ spl0_81
| ~ spl0_85 ),
inference(forward_demodulation,[],[f18087,f5873]) ).
thf(f18087,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_53
| ~ spl0_63
| spl0_75
| ~ spl0_81 ),
inference(forward_demodulation,[],[f18086,f752]) ).
thf(f18086,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_63
| spl0_75
| ~ spl0_81 ),
inference(forward_demodulation,[],[f18085,f1107]) ).
thf(f18085,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_75
| ~ spl0_81 ),
inference(forward_demodulation,[],[f18084,f4854]) ).
thf(f18084,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_75
| ~ spl0_81 ),
inference(forward_demodulation,[],[f3174,f4854]) ).
thf(f3174,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| spl0_75 ),
inference(avatar_component_clause,[],[f3173]) ).
thf(f18065,plain,
( spl0_68
| ~ spl0_9
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f18064,f12610,f6680,f83,f1711]) ).
thf(f83,plain,
( spl0_9
<=> ( vAPP($o,$o,f3,vAPP($o,$o,f4,x)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f18064,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_9
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f17963,f6681]) ).
thf(f17963,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$true)) )
| ~ spl0_9
| ~ spl0_101 ),
inference(forward_demodulation,[],[f85,f12612]) ).
thf(f85,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f4,x)) = $false )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f18045,plain,
( ~ spl0_40
| ~ spl0_53
| spl0_95 ),
inference(avatar_split_clause,[],[f18044,f8287,f750,f356]) ).
thf(f8287,plain,
( spl0_95
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
thf(f18044,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| ~ spl0_53
| spl0_95 ),
inference(forward_demodulation,[],[f8288,f752]) ).
thf(f8288,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_95 ),
inference(avatar_component_clause,[],[f8287]) ).
thf(f17973,plain,
( spl0_40
| ~ spl0_4
| ~ spl0_53
| ~ spl0_85
| ~ spl0_101
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f17865,f15961,f12610,f5871,f750,f23,f356]) ).
thf(f17865,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| ~ spl0_53
| ~ spl0_85
| ~ spl0_101
| ~ spl0_121 ),
inference(forward_demodulation,[],[f17864,f5873]) ).
thf(f17864,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_53
| ~ spl0_101
| ~ spl0_121 ),
inference(forward_demodulation,[],[f17863,f752]) ).
thf(f17863,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_101
| ~ spl0_121 ),
inference(forward_demodulation,[],[f17565,f15962]) ).
thf(f17972,plain,
( ~ spl0_22
| spl0_6
| ~ spl0_53
| ~ spl0_85
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f17868,f15961,f5871,f750,f69,f141]) ).
thf(f17868,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_6
| ~ spl0_53
| ~ spl0_85
| ~ spl0_121 ),
inference(forward_demodulation,[],[f17867,f5873]) ).
thf(f17867,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_6
| ~ spl0_53
| ~ spl0_121 ),
inference(forward_demodulation,[],[f17866,f752]) ).
thf(f17866,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_6
| ~ spl0_121 ),
inference(forward_demodulation,[],[f70,f15962]) ).
thf(f70,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_6 ),
inference(avatar_component_clause,[],[f69]) ).
thf(f17971,plain,
( ~ spl0_37
| ~ spl0_53
| ~ spl0_67
| ~ spl0_80
| ~ spl0_100
| ~ spl0_101
| spl0_117 ),
inference(avatar_split_clause,[],[f17908,f14404,f12610,f12606,f4821,f1555,f750,f341]) ).
thf(f12606,plain,
( spl0_100
<=> ( vAPP($o,$o,f4,vAPP($o,$o,f4,x)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
thf(f17908,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_53
| ~ spl0_67
| ~ spl0_80
| ~ spl0_100
| ~ spl0_101
| spl0_117 ),
inference(forward_demodulation,[],[f17907,f752]) ).
thf(f17907,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_67
| ~ spl0_80
| ~ spl0_100
| ~ spl0_101
| spl0_117 ),
inference(forward_demodulation,[],[f17906,f4823]) ).
thf(f17906,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_67
| ~ spl0_80
| ~ spl0_100
| ~ spl0_101
| spl0_117 ),
inference(forward_demodulation,[],[f17905,f4823]) ).
thf(f17905,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_67
| ~ spl0_100
| ~ spl0_101
| spl0_117 ),
inference(forward_demodulation,[],[f17904,f1557]) ).
thf(f17904,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_100
| ~ spl0_101
| spl0_117 ),
inference(forward_demodulation,[],[f14405,f17740]) ).
thf(f17740,plain,
( ( $true = vAPP($o,$o,f4,vAPP($o,$o,f4,$true)) )
| ~ spl0_100
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12608,f12612]) ).
thf(f12608,plain,
( ( vAPP($o,$o,f4,vAPP($o,$o,f4,x)) = $true )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f12606]) ).
thf(f17896,plain,
( spl0_116
| ~ spl0_61
| ~ spl0_78
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f17895,f16121,f4806,f1097,f13497]) ).
thf(f1097,plain,
( spl0_61
<=> ( $true = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
thf(f4806,plain,
( spl0_78
<=> ( $true = vAPP($o,$o,f3,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
thf(f17895,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_61
| ~ spl0_78
| ~ spl0_124 ),
inference(forward_demodulation,[],[f16123,f15373]) ).
thf(f15373,plain,
( ( $true = vAPP($o,$o,f3,vAPP($o,$o,f3,$true)) )
| ~ spl0_61
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1099,f4808]) ).
thf(f4808,plain,
( ( $true = vAPP($o,$o,f3,$false) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f4806]) ).
thf(f1099,plain,
( ( $true = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1097]) ).
thf(f17875,plain,
( spl0_71
| ~ spl0_19
| ~ spl0_53
| ~ spl0_101
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f17874,f15961,f12610,f750,f128,f2471]) ).
thf(f17874,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_19
| ~ spl0_53
| ~ spl0_101
| ~ spl0_121 ),
inference(forward_demodulation,[],[f17873,f752]) ).
thf(f17873,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_19
| ~ spl0_101
| ~ spl0_121 ),
inference(forward_demodulation,[],[f16237,f15962]) ).
thf(f17686,plain,
( spl0_79
| ~ spl0_49
| ~ spl0_63
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f17487,f4806,f1105,f729,f4810]) ).
thf(f17487,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_49
| ~ spl0_63
| ~ spl0_78 ),
inference(forward_demodulation,[],[f17486,f1107]) ).
thf(f17486,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_49
| ~ spl0_78 ),
inference(forward_demodulation,[],[f731,f4808]) ).
thf(f731,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f729]) ).
thf(f17679,plain,
( ~ spl0_93
| spl0_3
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f17644,f13470,f12610,f6680,f19,f8126]) ).
thf(f17644,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_3
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f17575,f17620]) ).
thf(f17620,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| ~ spl0_87
| ~ spl0_114 ),
inference(forward_demodulation,[],[f13472,f6681]) ).
thf(f17575,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| spl0_3
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f17574,f6681]) ).
thf(f17651,plain,
( spl0_3
| ~ spl0_40
| ~ spl0_53
| ~ spl0_55
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(avatar_contradiction_clause,[],[f17650]) ).
thf(f17650,plain,
( $false
| spl0_3
| ~ spl0_40
| ~ spl0_53
| ~ spl0_55
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(subsumption_resolution,[],[f17649,f358]) ).
thf(f17649,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_3
| ~ spl0_40
| ~ spl0_53
| ~ spl0_55
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f17648,f764]) ).
thf(f764,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f762]) ).
thf(f762,plain,
( spl0_55
<=> ( $true = vAPP($o,$o,f0,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
thf(f17648,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_3
| ~ spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f17647,f358]) ).
thf(f17647,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| spl0_3
| ~ spl0_53
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f17646,f752]) ).
thf(f17646,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_3
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f17645,f1107]) ).
thf(f17645,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_3
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f17644,f17474]) ).
thf(f17474,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(backward_demodulation,[],[f16988,f1107]) ).
thf(f16988,plain,
( ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f4804,f4808]) ).
thf(f4804,plain,
( ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f4802]) ).
thf(f4802,plain,
( spl0_77
<=> ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
thf(f17470,plain,
( ~ spl0_64
| spl0_65
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f17469,f4806,f1116,f1110]) ).
thf(f17469,plain,
( ( $true != vAPP($o,$o,f2,$true) )
| spl0_65
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1117,f4808]) ).
thf(f1117,plain,
( ( $true != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| spl0_65 ),
inference(avatar_component_clause,[],[f1116]) ).
thf(f17464,plain,
( ~ spl0_70
| ~ spl0_71
| spl0_83 ),
inference(avatar_split_clause,[],[f17462,f5273,f2471,f2467]) ).
thf(f17462,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_71
| spl0_83 ),
inference(backward_demodulation,[],[f5274,f2472]) ).
thf(f17442,plain,
( spl0_71
| ~ spl0_19
| ~ spl0_52
| ~ spl0_61
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f17441,f12610,f6680,f4806,f4802,f1097,f745,f128,f2471]) ).
thf(f745,plain,
( spl0_52
<=> ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
thf(f17441,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_19
| ~ spl0_52
| ~ spl0_61
| ~ spl0_77
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f17440,f17363]) ).
thf(f17363,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_52
| ~ spl0_77
| ~ spl0_78 ),
inference(backward_demodulation,[],[f17037,f16988]) ).
thf(f17037,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_52
| ~ spl0_78 ),
inference(forward_demodulation,[],[f746,f4808]) ).
thf(f746,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f745]) ).
thf(f17440,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| ~ spl0_19
| ~ spl0_61
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f17439,f15373]) ).
thf(f17439,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_19
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f17436,f4808]) ).
thf(f17436,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_19
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f16237,f6681]) ).
thf(f17396,plain,
( ~ spl0_116
| ~ spl0_61
| ~ spl0_78
| spl0_124 ),
inference(avatar_split_clause,[],[f17395,f16121,f4806,f1097,f13497]) ).
thf(f17395,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ~ spl0_61
| ~ spl0_78
| spl0_124 ),
inference(forward_demodulation,[],[f16122,f15373]) ).
thf(f16122,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| spl0_124 ),
inference(avatar_component_clause,[],[f16121]) ).
thf(f17389,plain,
( spl0_26
| ~ spl0_100
| ~ spl0_101
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f17386,f14404,f12610,f12606,f272]) ).
thf(f17386,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_100
| ~ spl0_101
| ~ spl0_117 ),
inference(backward_demodulation,[],[f14406,f16068]) ).
thf(f16068,plain,
( ( $true = vAPP($o,$o,f4,vAPP($o,$o,f4,$true)) )
| ~ spl0_100
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12608,f12612]) ).
thf(f17385,plain,
( spl0_119
| ~ spl0_13
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f16091,f12610,f101,f15943]) ).
thf(f101,plain,
( spl0_13
<=> ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f16091,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| ~ spl0_13
| ~ spl0_101 ),
inference(forward_demodulation,[],[f103,f12612]) ).
thf(f103,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))) = $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f17384,plain,
( ~ spl0_118
| spl0_11
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f16317,f12610,f92,f15719]) ).
thf(f16317,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_11
| ~ spl0_101 ),
inference(forward_demodulation,[],[f93,f12612]) ).
thf(f93,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))) != $false )
| spl0_11 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f17377,plain,
( spl0_63
| ~ spl0_78
| ~ spl0_86
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f17376,f7914,f6547,f4806,f1105]) ).
thf(f6547,plain,
( spl0_86
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
thf(f17376,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_78
| ~ spl0_86
| ~ spl0_91 ),
inference(forward_demodulation,[],[f17375,f4808]) ).
thf(f17375,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_86
| ~ spl0_91 ),
inference(forward_demodulation,[],[f7916,f6549]) ).
thf(f6549,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f6547]) ).
thf(f17256,plain,
( spl0_40
| ~ spl0_64
| ~ spl0_76
| ~ spl0_84
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f17255,f5871,f5867,f4513,f1110,f356]) ).
thf(f4513,plain,
( spl0_76
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
thf(f17255,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_64
| ~ spl0_76
| ~ spl0_84
| ~ spl0_85 ),
inference(forward_demodulation,[],[f17254,f16983]) ).
thf(f16983,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_84
| ~ spl0_85 ),
inference(forward_demodulation,[],[f5869,f5873]) ).
thf(f17254,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_64
| ~ spl0_76
| ~ spl0_84
| ~ spl0_85 ),
inference(forward_demodulation,[],[f17253,f16983]) ).
thf(f17253,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_64
| ~ spl0_76
| ~ spl0_84
| ~ spl0_85 ),
inference(forward_demodulation,[],[f17252,f16983]) ).
thf(f17252,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_64
| ~ spl0_76 ),
inference(forward_demodulation,[],[f4515,f1112]) ).
thf(f4515,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f4513]) ).
thf(f17203,plain,
( spl0_40
| ~ spl0_3
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f17202,f13497,f13036,f12662,f12610,f19,f356]) ).
thf(f13036,plain,
( spl0_111
<=> ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))))))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
thf(f17202,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111
| ~ spl0_116 ),
inference(backward_demodulation,[],[f17143,f17201]) ).
thf(f17201,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17200,f13498]) ).
thf(f17200,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111 ),
inference(forward_demodulation,[],[f17199,f12664]) ).
thf(f17199,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))))))) )
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111 ),
inference(forward_demodulation,[],[f17198,f12664]) ).
thf(f17198,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_101
| ~ spl0_102
| ~ spl0_111 ),
inference(forward_demodulation,[],[f17197,f12664]) ).
thf(f17197,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_101
| ~ spl0_111 ),
inference(forward_demodulation,[],[f13038,f12612]) ).
thf(f13038,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))))))) = $true )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f13036]) ).
thf(f17143,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17142,f13498]) ).
thf(f17142,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f17141,f12664]) ).
thf(f17141,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f17140,f12664]) ).
thf(f17140,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f17139,f12664]) ).
thf(f17139,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f21,f12612]) ).
thf(f17191,plain,
( ~ spl0_80
| ~ spl0_102
| spl0_114
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f17190,f13497,f13470,f12662,f4821]) ).
thf(f17190,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_102
| spl0_114
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17189,f13498]) ).
thf(f17189,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ~ spl0_102
| spl0_114 ),
inference(forward_demodulation,[],[f17188,f12664]) ).
thf(f17188,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ~ spl0_102
| spl0_114 ),
inference(forward_demodulation,[],[f17187,f12664]) ).
thf(f17187,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))) )
| ~ spl0_102
| spl0_114 ),
inference(forward_demodulation,[],[f13471,f12664]) ).
thf(f17177,plain,
( spl0_80
| ~ spl0_67
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f16781,f13497,f1555,f4821]) ).
thf(f16781,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_67
| ~ spl0_116 ),
inference(forward_demodulation,[],[f1557,f13498]) ).
thf(f17173,plain,
( spl0_1
| ~ spl0_22
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(avatar_contradiction_clause,[],[f17172]) ).
thf(f17172,plain,
( $false
| spl0_1
| ~ spl0_22
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(subsumption_resolution,[],[f17171,f143]) ).
thf(f17171,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_1
| ~ spl0_22
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17170,f143]) ).
thf(f17170,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_1
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17169,f764]) ).
thf(f17169,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_1
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17168,f2469]) ).
thf(f17168,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_1
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17167,f4823]) ).
thf(f17167,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_1
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17166,f4823]) ).
thf(f17166,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_1
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17165,f4823]) ).
thf(f17165,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| spl0_1
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f17164,f13498]) ).
thf(f17164,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f17163,f12664]) ).
thf(f17163,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f17162,f12664]) ).
thf(f17162,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f17161,f12664]) ).
thf(f17161,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| spl0_1
| ~ spl0_101 ),
inference(forward_demodulation,[],[f11,f12612]) ).
thf(f11,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))) != $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
thf(f17030,plain,
( ~ spl0_22
| spl0_40
| ~ spl0_55
| ~ spl0_88 ),
inference(avatar_contradiction_clause,[],[f17029]) ).
thf(f17029,plain,
( $false
| ~ spl0_22
| spl0_40
| ~ spl0_55
| ~ spl0_88 ),
inference(subsumption_resolution,[],[f17028,f357]) ).
thf(f17028,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_22
| ~ spl0_55
| ~ spl0_88 ),
inference(forward_demodulation,[],[f17027,f143]) ).
thf(f17027,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_55
| ~ spl0_88 ),
inference(backward_demodulation,[],[f6932,f764]) ).
thf(f6932,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f6931]) ).
thf(f17001,plain,
( ~ spl0_63
| spl0_69
| ~ spl0_78
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f17000,f13497,f4806,f1715,f1105]) ).
thf(f17000,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_69
| ~ spl0_78
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16999,f4808]) ).
thf(f16999,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| spl0_69
| ~ spl0_116 ),
inference(forward_demodulation,[],[f1716,f13498]) ).
thf(f16962,plain,
( spl0_88
| ~ spl0_70
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f15783,f6948,f2467,f6931]) ).
thf(f15783,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| ~ spl0_89 ),
inference(forward_demodulation,[],[f6949,f2469]) ).
thf(f16961,plain,
( spl0_88
| ~ spl0_70
| ~ spl0_80
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f16747,f8126,f4821,f2467,f6931]) ).
thf(f16747,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| ~ spl0_80
| ~ spl0_93 ),
inference(forward_demodulation,[],[f16746,f2469]) ).
thf(f16746,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_80
| ~ spl0_93 ),
inference(forward_demodulation,[],[f16741,f4823]) ).
thf(f16741,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_80
| ~ spl0_93 ),
inference(backward_demodulation,[],[f8127,f4823]) ).
thf(f8127,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f8126]) ).
thf(f16959,plain,
( spl0_88
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f16761,f14404,f13497,f12662,f4821,f2467,f6931]) ).
thf(f16761,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(forward_demodulation,[],[f16760,f2469]) ).
thf(f16760,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(forward_demodulation,[],[f16759,f4823]) ).
thf(f16759,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(forward_demodulation,[],[f16745,f4823]) ).
thf(f16745,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(backward_demodulation,[],[f16558,f4823]) ).
thf(f16558,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_102
| ~ spl0_116
| ~ spl0_117 ),
inference(forward_demodulation,[],[f16557,f13498]) ).
thf(f16557,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_102
| ~ spl0_117 ),
inference(forward_demodulation,[],[f16556,f12664]) ).
thf(f16556,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_102
| ~ spl0_117 ),
inference(forward_demodulation,[],[f14406,f12664]) ).
thf(f16934,plain,
( spl0_3
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f16933]) ).
thf(f16933,plain,
( $false
| spl0_3
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(subsumption_resolution,[],[f16932,f15949]) ).
thf(f16932,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_3
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16931,f15949]) ).
thf(f16931,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_3
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16930,f15949]) ).
thf(f16930,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_3
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16929,f2469]) ).
thf(f16929,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_3
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16928,f4823]) ).
thf(f16928,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_3
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16927,f4823]) ).
thf(f16927,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_3
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16926,f4823]) ).
thf(f16926,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16925,f13498]) ).
thf(f16925,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16924,f12664]) ).
thf(f16924,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16923,f12664]) ).
thf(f16923,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16922,f12664]) ).
thf(f16922,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f20,f12612]) ).
thf(f16872,plain,
( spl0_24
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f16871]) ).
thf(f16871,plain,
( $false
| spl0_24
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(subsumption_resolution,[],[f16870,f15949]) ).
thf(f16870,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_24
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16869,f15949]) ).
thf(f16869,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_24
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16868,f15949]) ).
thf(f16868,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_24
| ~ spl0_70
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16867,f2469]) ).
thf(f16867,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_24
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16866,f4823]) ).
thf(f16866,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_24
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16865,f4823]) ).
thf(f16865,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_24
| ~ spl0_80
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16864,f4823]) ).
thf(f16864,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| spl0_24
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16863,f13498]) ).
thf(f16863,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_24
| ~ spl0_102 ),
inference(forward_demodulation,[],[f264,f12664]) ).
thf(f264,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_24 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f16780,plain,
( spl0_63
| ~ spl0_69
| ~ spl0_78
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f16779,f13497,f4806,f1715,f1105]) ).
thf(f16779,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_69
| ~ spl0_78
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16778,f4808]) ).
thf(f16778,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_69
| ~ spl0_116 ),
inference(forward_demodulation,[],[f1717,f13498]) ).
thf(f1717,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1715]) ).
thf(f16740,plain,
( spl0_80
| ~ spl0_78
| ~ spl0_91
| ~ spl0_94
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f16739,f13497,f8283,f7914,f4806,f4821]) ).
thf(f16739,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_78
| ~ spl0_91
| ~ spl0_94
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16738,f13498]) ).
thf(f16738,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ~ spl0_78
| ~ spl0_91
| ~ spl0_94 ),
inference(forward_demodulation,[],[f16737,f4808]) ).
thf(f16737,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_91
| ~ spl0_94 ),
inference(forward_demodulation,[],[f7916,f8285]) ).
thf(f16721,plain,
( ~ spl0_2
| ~ spl0_70
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120
| ~ spl0_122 ),
inference(avatar_contradiction_clause,[],[f16720]) ).
thf(f16720,plain,
( $false
| ~ spl0_2
| ~ spl0_70
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120
| ~ spl0_122 ),
inference(trivial_inequality_removal,[],[f16719]) ).
thf(f16719,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_70
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16718,f15949]) ).
thf(f16718,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_70
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16717,f2469]) ).
thf(f16717,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_70
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16716,f2469]) ).
thf(f16716,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16715,f16332]) ).
thf(f16332,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_78
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16331,f13498]) ).
thf(f16331,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))) )
| ~ spl0_78
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16330,f4808]) ).
thf(f16330,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16105,f13498]) ).
thf(f16715,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_2
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16714,f13498]) ).
thf(f16714,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_2
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16713,f4808]) ).
thf(f16713,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_2
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16712,f13498]) ).
thf(f16712,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_2
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16711,f12664]) ).
thf(f16711,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_2
| ~ spl0_101 ),
inference(forward_demodulation,[],[f16,f12612]) ).
thf(f16685,plain,
( ~ spl0_8
| ~ spl0_70
| ~ spl0_78
| ~ spl0_116
| ~ spl0_120
| ~ spl0_122 ),
inference(avatar_contradiction_clause,[],[f16684]) ).
thf(f16684,plain,
( $false
| ~ spl0_8
| ~ spl0_70
| ~ spl0_78
| ~ spl0_116
| ~ spl0_120
| ~ spl0_122 ),
inference(trivial_inequality_removal,[],[f16683]) ).
thf(f16683,plain,
( ( $true = $false )
| ~ spl0_8
| ~ spl0_70
| ~ spl0_78
| ~ spl0_116
| ~ spl0_120
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16682,f15949]) ).
thf(f16682,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_8
| ~ spl0_70
| ~ spl0_78
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16681,f2469]) ).
thf(f16681,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_8
| ~ spl0_70
| ~ spl0_78
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16680,f2469]) ).
thf(f16680,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_8
| ~ spl0_78
| ~ spl0_116
| ~ spl0_122 ),
inference(forward_demodulation,[],[f16679,f16332]) ).
thf(f16679,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_8
| ~ spl0_78
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16678,f13498]) ).
thf(f16678,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_8
| ~ spl0_78
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16677,f4808]) ).
thf(f16677,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_8
| ~ spl0_116 ),
inference(forward_demodulation,[],[f80,f13498]) ).
thf(f16529,plain,
( spl0_92
| ~ spl0_4
| ~ spl0_78
| spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f16528,f13497,f12662,f12610,f4821,f4806,f23,f7918]) ).
thf(f16528,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_78
| spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(subsumption_resolution,[],[f16527,f4822]) ).
thf(f16527,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16526,f13498]) ).
thf(f16526,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16525,f4808]) ).
thf(f16525,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16524,f13498]) ).
thf(f16524,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15051,f12664]) ).
thf(f15051,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| ~ spl0_4
| ~ spl0_101 ),
inference(superposition,[],[f14791,f4]) ).
thf(f14791,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_4
| ~ spl0_101 ),
inference(forward_demodulation,[],[f25,f12612]) ).
thf(f16519,plain,
( spl0_35
| ~ spl0_31
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f16277,f4806,f4802,f305,f330]) ).
thf(f330,plain,
( spl0_35
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
thf(f16277,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_31
| ~ spl0_77
| ~ spl0_78 ),
inference(backward_demodulation,[],[f307,f16275]) ).
thf(f16275,plain,
( ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f4804,f4808]) ).
thf(f16516,plain,
( spl0_92
| ~ spl0_64
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f16296,f4513,f1110,f7918]) ).
thf(f16296,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_64
| ~ spl0_76 ),
inference(backward_demodulation,[],[f4515,f1112]) ).
thf(f16515,plain,
( spl0_50
| ~ spl0_1
| ~ spl0_64
| spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f16366,f13497,f12662,f12610,f4821,f1110,f10,f733]) ).
thf(f16366,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_1
| ~ spl0_64
| spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16365,f1112]) ).
thf(f16365,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_64
| spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16364,f1112]) ).
thf(f16364,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_1
| spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(subsumption_resolution,[],[f16345,f4822]) ).
thf(f16345,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(superposition,[],[f16266,f4]) ).
thf(f16266,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(backward_demodulation,[],[f16038,f13498]) ).
thf(f16038,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16037,f12664]) ).
thf(f16037,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15989,f12664]) ).
thf(f15989,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(backward_demodulation,[],[f14976,f12664]) ).
thf(f14976,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| ~ spl0_1
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12,f12612]) ).
thf(f16506,plain,
( ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(avatar_contradiction_clause,[],[f16505]) ).
thf(f16505,plain,
( $false
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(trivial_inequality_removal,[],[f16504]) ).
thf(f16504,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16503,f15949]) ).
thf(f16503,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16502,f15949]) ).
thf(f16502,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16501,f15949]) ).
thf(f16501,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16266,f16415]) ).
thf(f16415,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(trivial_inequality_removal,[],[f16414]) ).
thf(f16414,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16413,f15949]) ).
thf(f16413,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116
| ~ spl0_120 ),
inference(forward_demodulation,[],[f16412,f15949]) ).
thf(f16412,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16349,f358]) ).
thf(f16349,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(superposition,[],[f16266,f4]) ).
thf(f16253,plain,
( spl0_67
| ~ spl0_15
| ~ spl0_61
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f16168,f12662,f12610,f4806,f1097,f110,f1555]) ).
thf(f16168,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ~ spl0_15
| ~ spl0_61
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102 ),
inference(backward_demodulation,[],[f16087,f15373]) ).
thf(f16087,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| ~ spl0_15
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16086,f12664]) ).
thf(f16086,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| ~ spl0_15
| ~ spl0_101 ),
inference(forward_demodulation,[],[f112,f12612]) ).
thf(f16159,plain,
( spl0_120
| ~ spl0_26
| ~ spl0_35
| ~ spl0_67
| ~ spl0_70
| ~ spl0_73
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f16158,f4821,f3150,f2467,f1555,f330,f272,f15947]) ).
thf(f16158,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_26
| ~ spl0_35
| ~ spl0_67
| ~ spl0_70
| ~ spl0_73
| ~ spl0_80 ),
inference(forward_demodulation,[],[f16157,f14569]) ).
thf(f14569,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_35
| ~ spl0_73 ),
inference(backward_demodulation,[],[f332,f3152]) ).
thf(f3152,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f3150]) ).
thf(f332,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f16157,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_26
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f16156,f2469]) ).
thf(f16156,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_26
| ~ spl0_67
| ~ spl0_80 ),
inference(forward_demodulation,[],[f16155,f4823]) ).
thf(f16155,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_26
| ~ spl0_67
| ~ spl0_80 ),
inference(forward_demodulation,[],[f16148,f4823]) ).
thf(f16148,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_26
| ~ spl0_67 ),
inference(backward_demodulation,[],[f274,f1557]) ).
thf(f274,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f16154,plain,
( spl0_120
| ~ spl0_67
| ~ spl0_70
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f16153,f3168,f2467,f1555,f15947]) ).
thf(f16153,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_67
| ~ spl0_70
| ~ spl0_74 ),
inference(forward_demodulation,[],[f16152,f2469]) ).
thf(f16152,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_67
| ~ spl0_70
| ~ spl0_74 ),
inference(forward_demodulation,[],[f16151,f2469]) ).
thf(f16151,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_67
| ~ spl0_70
| ~ spl0_74 ),
inference(forward_demodulation,[],[f16147,f2469]) ).
thf(f16147,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_67
| ~ spl0_74 ),
inference(backward_demodulation,[],[f3170,f1557]) ).
thf(f3170,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f3168]) ).
thf(f16146,plain,
( spl0_116
| ~ spl0_78
| ~ spl0_94
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f15768,f10956,f8283,f4806,f13497]) ).
thf(f10956,plain,
( spl0_96
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
thf(f15768,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_78
| ~ spl0_94
| ~ spl0_96 ),
inference(forward_demodulation,[],[f15767,f4808]) ).
thf(f15767,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_94
| ~ spl0_96 ),
inference(forward_demodulation,[],[f10958,f8285]) ).
thf(f10958,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f10956]) ).
thf(f16141,plain,
( spl0_75
| spl0_116
| ~ spl0_4
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f16140,f12662,f12610,f23,f13497,f3173]) ).
thf(f16140,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_4
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15045,f12664]) ).
thf(f15045,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$true)) )
| ~ spl0_4
| ~ spl0_101 ),
inference(superposition,[],[f14791,f4]) ).
thf(f16138,plain,
( spl0_120
| ~ spl0_4
| ~ spl0_15
| ~ spl0_70
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f16137,f12662,f12610,f2467,f110,f23,f15947]) ).
thf(f16137,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_70
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16136,f2469]) ).
thf(f16136,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_70
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16135,f2469]) ).
thf(f16135,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_70
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16134,f2469]) ).
thf(f16134,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15987,f16087]) ).
thf(f15987,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_4
| ~ spl0_101
| ~ spl0_102 ),
inference(backward_demodulation,[],[f14791,f12664]) ).
thf(f16131,plain,
( spl0_124
| ~ spl0_13
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f16092,f12662,f12610,f101,f16121]) ).
thf(f16092,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ~ spl0_13
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f16091,f12664]) ).
thf(f16118,plain,
( spl0_120
| ~ spl0_123
| ~ spl0_4
| ~ spl0_70
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f16113,f12662,f12610,f2467,f23,f16115,f15947]) ).
thf(f16113,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))) )
| ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15056,f12664]) ).
thf(f15056,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_101 ),
inference(constrained_superposition,[],[f14791,f2469]) ).
thf(f16027,plain,
( spl0_120
| ~ spl0_4
| ~ spl0_70
| ~ spl0_78
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f16026,f13497,f12662,f12610,f4821,f4806,f2467,f23,f15947]) ).
thf(f16026,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_78
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16025,f2469]) ).
thf(f16025,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_78
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16024,f2469]) ).
thf(f16024,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_78
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16023,f2469]) ).
thf(f16023,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_78
| ~ spl0_80
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16022,f4823]) ).
thf(f16022,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16021,f13498]) ).
thf(f16021,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_4
| ~ spl0_78
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f16020,f4808]) ).
thf(f16020,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_4
| ~ spl0_101
| ~ spl0_102
| ~ spl0_116 ),
inference(forward_demodulation,[],[f15987,f13498]) ).
thf(f15975,plain,
( spl0_120
| ~ spl0_70
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f15769,f8287,f2467,f15947]) ).
thf(f15769,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_70
| ~ spl0_95 ),
inference(forward_demodulation,[],[f8289,f2469]) ).
thf(f8289,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f8287]) ).
thf(f15971,plain,
( spl0_120
| ~ spl0_35
| ~ spl0_73
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f15787,f6931,f3150,f330,f15947]) ).
thf(f15787,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_35
| ~ spl0_73
| ~ spl0_88 ),
inference(forward_demodulation,[],[f6932,f14569]) ).
thf(f15968,plain,
( spl0_120
| ~ spl0_41
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f15896,f367,f362,f15947]) ).
thf(f362,plain,
( spl0_41
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
thf(f367,plain,
( spl0_42
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
thf(f15896,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_41
| ~ spl0_42 ),
inference(forward_demodulation,[],[f364,f369]) ).
thf(f369,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f364,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f15967,plain,
( spl0_120
| ~ spl0_36
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f15899,f367,f337,f15947]) ).
thf(f337,plain,
( spl0_36
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
thf(f15899,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_36
| ~ spl0_42 ),
inference(backward_demodulation,[],[f369,f339]) ).
thf(f339,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f337]) ).
thf(f15966,plain,
( spl0_120
| ~ spl0_27
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f15906,f356,f282,f15947]) ).
thf(f282,plain,
( spl0_27
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f15906,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f284,f358]) ).
thf(f284,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f15964,plain,
( ~ spl0_121
| spl0_120
| ~ spl0_4
| ~ spl0_70
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15959,f12610,f2467,f23,f15947,f15961]) ).
thf(f15959,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15958,f2469]) ).
thf(f15958,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15052,f2469]) ).
thf(f15052,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_101 ),
inference(constrained_superposition,[],[f14791,f2469]) ).
thf(f15950,plain,
( ~ spl0_119
| spl0_120
| ~ spl0_4
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15941,f12610,f4821,f2467,f23,f15947,f15943]) ).
thf(f15941,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15940,f2469]) ).
thf(f15940,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15939,f2469]) ).
thf(f15939,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| ~ spl0_4
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15050,f2469]) ).
thf(f15050,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| ~ spl0_4
| ~ spl0_80
| ~ spl0_101 ),
inference(constrained_superposition,[],[f14791,f4823]) ).
thf(f15811,plain,
( ~ spl0_63
| spl0_15
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f15810,f13497,f12610,f6680,f4806,f110,f1105]) ).
thf(f15810,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_15
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_116 ),
inference(forward_demodulation,[],[f15809,f4808]) ).
thf(f15809,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| spl0_15
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_116 ),
inference(forward_demodulation,[],[f15808,f13498]) ).
thf(f15808,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| spl0_15
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15796,f4808]) ).
thf(f15796,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| spl0_15
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f15010,f6681]) ).
thf(f15010,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| spl0_15
| ~ spl0_101 ),
inference(forward_demodulation,[],[f111,f12612]) ).
thf(f111,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))) != $false )
| spl0_15 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f15805,plain,
( spl0_76
| ~ spl0_4
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f15804,f13497,f12610,f6680,f4806,f23,f4513]) ).
thf(f15804,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_116 ),
inference(forward_demodulation,[],[f15803,f4808]) ).
thf(f15803,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_4
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101
| ~ spl0_116 ),
inference(forward_demodulation,[],[f15802,f13498]) ).
thf(f15802,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_4
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15793,f4808]) ).
thf(f15793,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_4
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f14791,f6681]) ).
thf(f15789,plain,
( spl0_29
| ~ spl0_35
| ~ spl0_56
| ~ spl0_73
| ~ spl0_78
| ~ spl0_88 ),
inference(avatar_contradiction_clause,[],[f15788]) ).
thf(f15788,plain,
( $false
| spl0_29
| ~ spl0_35
| ~ spl0_56
| ~ spl0_73
| ~ spl0_78
| ~ spl0_88 ),
inference(subsumption_resolution,[],[f15787,f15725]) ).
thf(f15725,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_29
| ~ spl0_56
| ~ spl0_78 ),
inference(backward_demodulation,[],[f292,f15641]) ).
thf(f15641,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_56
| ~ spl0_78 ),
inference(forward_demodulation,[],[f770,f4808]) ).
thf(f770,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f768]) ).
thf(f768,plain,
( spl0_56
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
thf(f15763,plain,
( ~ spl0_63
| ~ spl0_78
| ~ spl0_110
| spl0_114 ),
inference(avatar_split_clause,[],[f15762,f13470,f12920,f4806,f1105]) ).
thf(f15762,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ~ spl0_78
| ~ spl0_110
| spl0_114 ),
inference(forward_demodulation,[],[f15753,f4808]) ).
thf(f15753,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_110
| spl0_114 ),
inference(backward_demodulation,[],[f13471,f12922]) ).
thf(f15759,plain,
( spl0_55
| ~ spl0_1
| ~ spl0_56
| ~ spl0_78
| ~ spl0_101
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f15758,f12920,f12610,f4806,f768,f10,f762]) ).
thf(f15758,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_56
| ~ spl0_78
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f15757,f15641]) ).
thf(f15757,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_1
| ~ spl0_78
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f15751,f4808]) ).
thf(f15751,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_110 ),
inference(backward_demodulation,[],[f14976,f12922]) ).
thf(f15747,plain,
( spl0_110
| ~ spl0_101
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f15746,f13057,f12610,f12920]) ).
thf(f15746,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))) )
| ~ spl0_101
| ~ spl0_113 ),
inference(forward_demodulation,[],[f13059,f12612]) ).
thf(f15742,plain,
( ~ spl0_14
| spl0_10
| ~ spl0_61
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f15741,f4806,f1097,f87,f105]) ).
thf(f87,plain,
( spl0_10
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f15741,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_10
| ~ spl0_61
| ~ spl0_78 ),
inference(forward_demodulation,[],[f88,f15373]) ).
thf(f88,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| spl0_10 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f15722,plain,
( spl0_118
| spl0_74
| ~ spl0_4
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15047,f12610,f23,f3168,f15719]) ).
thf(f15047,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ~ spl0_4
| ~ spl0_101 ),
inference(superposition,[],[f14791,f4]) ).
thf(f15629,plain,
( spl0_21
| ~ spl0_63
| ~ spl0_70
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_contradiction_clause,[],[f15628]) ).
thf(f15628,plain,
( $false
| spl0_21
| ~ spl0_63
| ~ spl0_70
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(subsumption_resolution,[],[f15627,f2469]) ).
thf(f15627,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| spl0_21
| ~ spl0_63
| ~ spl0_70
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15626,f2469]) ).
thf(f15626,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| spl0_21
| ~ spl0_63
| ~ spl0_70
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15613,f2469]) ).
thf(f15613,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_21
| ~ spl0_63
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(backward_demodulation,[],[f15585,f1107]) ).
thf(f15585,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true)))) )
| spl0_21
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15584,f4854]) ).
thf(f15584,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true))))) )
| spl0_21
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15583,f4854]) ).
thf(f15583,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))) )
| spl0_21
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15553,f4854]) ).
thf(f15553,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| spl0_21
| ~ spl0_101
| ~ spl0_102 ),
inference(backward_demodulation,[],[f15035,f12664]) ).
thf(f15035,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))))))) )
| spl0_21
| ~ spl0_101 ),
inference(forward_demodulation,[],[f138,f12612]) ).
thf(f138,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))))))) != $false )
| spl0_21 ),
inference(avatar_component_clause,[],[f137]) ).
thf(f15576,plain,
( ~ spl0_63
| spl0_15
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f15575,f12662,f12610,f4852,f110,f1105]) ).
thf(f15575,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_15
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15574,f4854]) ).
thf(f15574,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| spl0_15
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15573,f4854]) ).
thf(f15573,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| spl0_15
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15550,f4854]) ).
thf(f15550,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))) )
| spl0_15
| ~ spl0_101
| ~ spl0_102 ),
inference(backward_demodulation,[],[f15010,f12664]) ).
thf(f15563,plain,
( ~ spl0_63
| ~ spl0_81
| ~ spl0_102
| spl0_114 ),
inference(avatar_split_clause,[],[f15562,f13470,f12662,f4852,f1105]) ).
thf(f15562,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ~ spl0_81
| ~ spl0_102
| spl0_114 ),
inference(forward_demodulation,[],[f15561,f4854]) ).
thf(f15561,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ~ spl0_102
| spl0_114 ),
inference(forward_demodulation,[],[f15560,f12664]) ).
thf(f15560,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ~ spl0_102
| spl0_114 ),
inference(forward_demodulation,[],[f15544,f12664]) ).
thf(f15544,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))) )
| ~ spl0_102
| spl0_114 ),
inference(backward_demodulation,[],[f13471,f12664]) ).
thf(f15532,plain,
( ~ spl0_87
| spl0_23
| spl0_98 ),
inference(avatar_split_clause,[],[f15531,f12299,f259,f6680]) ).
thf(f12299,plain,
( spl0_98
<=> ( $false = vAPP($o,$o,f4,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
thf(f15531,plain,
( ( $false != vAPP($o,$o,f4,$true) )
| spl0_23
| spl0_98 ),
inference(subsumption_resolution,[],[f15520,f12300]) ).
thf(f12300,plain,
( ( $false != vAPP($o,$o,f4,$false) )
| spl0_98 ),
inference(avatar_component_clause,[],[f12299]) ).
thf(f15520,plain,
( ( $false != vAPP($o,$o,f4,$true) )
| ( $false = vAPP($o,$o,f4,$false) )
| spl0_23 ),
inference(superposition,[],[f260,f4]) ).
thf(f260,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| spl0_23 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f15530,plain,
( ~ spl0_14
| spl0_10
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f14646,f4852,f87,f105]) ).
thf(f14646,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_10
| ~ spl0_81 ),
inference(forward_demodulation,[],[f14643,f4854]) ).
thf(f14643,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_10
| ~ spl0_81 ),
inference(backward_demodulation,[],[f88,f4854]) ).
thf(f15529,plain,
( ~ spl0_14
| spl0_8
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f14767,f4852,f78,f105]) ).
thf(f14767,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_8
| ~ spl0_81 ),
inference(forward_demodulation,[],[f14766,f4854]) ).
thf(f14766,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_8
| ~ spl0_81 ),
inference(forward_demodulation,[],[f14765,f4854]) ).
thf(f14765,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| spl0_8
| ~ spl0_81 ),
inference(forward_demodulation,[],[f79,f4854]) ).
thf(f79,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| spl0_8 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f15528,plain,
( spl0_76
| ~ spl0_4
| spl0_9
| ~ spl0_81
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15073,f12610,f4852,f83,f23,f4513]) ).
thf(f15073,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| spl0_9
| ~ spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15072,f4854]) ).
thf(f15072,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_4
| spl0_9
| ~ spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15071,f4854]) ).
thf(f15071,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_4
| spl0_9
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15045,f14966]) ).
thf(f14966,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$true)) )
| spl0_9
| ~ spl0_101 ),
inference(forward_demodulation,[],[f84,f12612]) ).
thf(f84,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f4,x)) != $false )
| spl0_9 ),
inference(avatar_component_clause,[],[f83]) ).
thf(f15527,plain,
( spl0_76
| ~ spl0_4
| spl0_11
| ~ spl0_81
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15078,f12610,f4852,f92,f23,f4513]) ).
thf(f15078,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| spl0_11
| ~ spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15077,f4854]) ).
thf(f15077,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_4
| spl0_11
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15047,f14965]) ).
thf(f14965,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_11
| ~ spl0_101 ),
inference(forward_demodulation,[],[f93,f12612]) ).
thf(f15526,plain,
( spl0_76
| ~ spl0_4
| spl0_13
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15082,f12610,f101,f23,f4513]) ).
thf(f15082,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| spl0_13
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15049,f15003]) ).
thf(f15003,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| spl0_13
| ~ spl0_101 ),
inference(forward_demodulation,[],[f102,f12612]) ).
thf(f102,plain,
( ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))) != $false )
| spl0_13 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f15049,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| ~ spl0_4
| ~ spl0_101 ),
inference(superposition,[],[f14791,f4]) ).
thf(f15525,plain,
( spl0_87
| spl0_76
| ~ spl0_4
| ~ spl0_81
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15264,f12610,f4852,f23,f4513,f6680]) ).
thf(f15264,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f4,$true) )
| ~ spl0_4
| ~ spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15263,f4854]) ).
thf(f15263,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ( $false = vAPP($o,$o,f4,$true) )
| ~ spl0_4
| ~ spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15262,f4854]) ).
thf(f15262,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ( $false = vAPP($o,$o,f4,$true) )
| ~ spl0_4
| ~ spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15043,f4854]) ).
thf(f15043,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ( $false = vAPP($o,$o,f4,$true) )
| ~ spl0_4
| ~ spl0_101 ),
inference(superposition,[],[f14791,f4]) ).
thf(f15496,plain,
( ~ spl0_23
| ~ spl0_87
| spl0_110 ),
inference(avatar_split_clause,[],[f15416,f12920,f6680,f259]) ).
thf(f15416,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_87
| spl0_110 ),
inference(forward_demodulation,[],[f12921,f6681]) ).
thf(f12921,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))) )
| spl0_110 ),
inference(avatar_component_clause,[],[f12920]) ).
thf(f15481,plain,
( spl0_3
| ~ spl0_23
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f15480]) ).
thf(f15480,plain,
( $false
| spl0_3
| ~ spl0_23
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15479,f358]) ).
thf(f15479,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_3
| ~ spl0_23
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15478,f764]) ).
thf(f15478,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_3
| ~ spl0_23
| ~ spl0_40
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15477,f358]) ).
thf(f15477,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| spl0_3
| ~ spl0_23
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15476,f15338]) ).
thf(f15338,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_84
| ~ spl0_85 ),
inference(forward_demodulation,[],[f5869,f5873]) ).
thf(f15476,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_3
| ~ spl0_23
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15475,f1112]) ).
thf(f15475,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_3
| ~ spl0_23
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15474,f1112]) ).
thf(f15474,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_3
| ~ spl0_23
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15473,f1112]) ).
thf(f15473,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_3
| ~ spl0_23
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15472,f4808]) ).
thf(f15472,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| spl0_3
| ~ spl0_23
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15471,f261]) ).
thf(f15471,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| spl0_3
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14895,f6681]) ).
thf(f14895,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f20,f12612]) ).
thf(f15452,plain,
( ~ spl0_1
| ~ spl0_23
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f15451]) ).
thf(f15451,plain,
( $false
| ~ spl0_1
| ~ spl0_23
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(trivial_inequality_removal,[],[f15450]) ).
thf(f15450,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15449,f358]) ).
thf(f15449,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15448,f764]) ).
thf(f15448,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_40
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15447,f358]) ).
thf(f15447,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_64
| ~ spl0_78
| ~ spl0_84
| ~ spl0_85
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15446,f15338]) ).
thf(f15446,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15445,f1112]) ).
thf(f15445,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15444,f1112]) ).
thf(f15444,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15443,f1112]) ).
thf(f15443,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_78
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15442,f4808]) ).
thf(f15442,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_1
| ~ spl0_23
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15441,f261]) ).
thf(f15441,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| ~ spl0_1
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14976,f6681]) ).
thf(f15329,plain,
( ~ spl0_59
| spl0_13
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15319,f12610,f6680,f101,f1089]) ).
thf(f1089,plain,
( spl0_59
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
thf(f15319,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| spl0_13
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f15003,f6681]) ).
thf(f15328,plain,
( ~ spl0_68
| spl0_9
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15318,f12610,f6680,f83,f1711]) ).
thf(f15318,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| spl0_9
| ~ spl0_87
| ~ spl0_101 ),
inference(backward_demodulation,[],[f14966,f6681]) ).
thf(f15312,plain,
( ~ spl0_66
| ~ spl0_94
| spl0_96 ),
inference(avatar_split_clause,[],[f15311,f10956,f8283,f1551]) ).
thf(f1551,plain,
( spl0_66
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
thf(f15311,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_94
| spl0_96 ),
inference(forward_demodulation,[],[f10957,f8285]) ).
thf(f10957,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| spl0_96 ),
inference(avatar_component_clause,[],[f10956]) ).
thf(f15293,plain,
( spl0_3
| ~ spl0_24
| ~ spl0_100
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f15292]) ).
thf(f15292,plain,
( $false
| spl0_3
| ~ spl0_24
| ~ spl0_100
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15291,f265]) ).
thf(f15291,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_3
| ~ spl0_100
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14895,f15253]) ).
thf(f15253,plain,
( ( $true = vAPP($o,$o,f4,vAPP($o,$o,f4,$true)) )
| ~ spl0_100
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12608,f12612]) ).
thf(f15268,plain,
( spl0_94
| ~ spl0_23
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f15267,f287,f259,f8283]) ).
thf(f287,plain,
( spl0_28
<=> ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
thf(f15267,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_23
| ~ spl0_28 ),
inference(forward_demodulation,[],[f289,f261]) ).
thf(f289,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f15248,plain,
( spl0_3
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_contradiction_clause,[],[f15247]) ).
thf(f15247,plain,
( $false
| spl0_3
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(subsumption_resolution,[],[f15246,f358]) ).
thf(f15246,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_3
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15245,f764]) ).
thf(f15245,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_3
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15244,f3152]) ).
thf(f15244,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_3
| ~ spl0_64
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15243,f1112]) ).
thf(f15243,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_3
| ~ spl0_64
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15242,f1112]) ).
thf(f15242,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_3
| ~ spl0_64
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15241,f1112]) ).
thf(f15241,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_3
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15240,f4854]) ).
thf(f15240,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15239,f12664]) ).
thf(f15239,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15238,f12664]) ).
thf(f15238,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| spl0_3
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f14895,f12664]) ).
thf(f15227,plain,
( ~ spl0_1
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_contradiction_clause,[],[f15226]) ).
thf(f15226,plain,
( $false
| ~ spl0_1
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(trivial_inequality_removal,[],[f15225]) ).
thf(f15225,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15224,f358]) ).
thf(f15224,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_1
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15223,f764]) ).
thf(f15223,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_1
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15222,f3152]) ).
thf(f15222,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_1
| ~ spl0_64
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15221,f1112]) ).
thf(f15221,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_1
| ~ spl0_64
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15220,f1112]) ).
thf(f15220,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_1
| ~ spl0_64
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15219,f1112]) ).
thf(f15219,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_1
| ~ spl0_81
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15218,f4854]) ).
thf(f15218,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15217,f12664]) ).
thf(f15217,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15216,f12664]) ).
thf(f15216,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_1
| ~ spl0_101
| ~ spl0_102 ),
inference(forward_demodulation,[],[f14976,f12664]) ).
thf(f15166,plain,
( spl0_100
| ~ spl0_101
| ~ spl0_102 ),
inference(avatar_contradiction_clause,[],[f15165]) ).
thf(f15165,plain,
( $false
| spl0_100
| ~ spl0_101
| ~ spl0_102 ),
inference(subsumption_resolution,[],[f15145,f12664]) ).
thf(f15145,plain,
( ( $true != vAPP($o,$o,f4,$true) )
| spl0_100
| ~ spl0_101
| ~ spl0_102 ),
inference(backward_demodulation,[],[f13186,f12664]) ).
thf(f13186,plain,
( ( $true != vAPP($o,$o,f4,vAPP($o,$o,f4,$true)) )
| spl0_100
| ~ spl0_101 ),
inference(backward_demodulation,[],[f12607,f12612]) ).
thf(f12607,plain,
( ( vAPP($o,$o,f4,vAPP($o,$o,f4,x)) != $true )
| spl0_100 ),
inference(avatar_component_clause,[],[f12606]) ).
thf(f15163,plain,
( spl0_24
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_102 ),
inference(avatar_contradiction_clause,[],[f15162]) ).
thf(f15162,plain,
( $false
| spl0_24
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_102 ),
inference(subsumption_resolution,[],[f15161,f358]) ).
thf(f15161,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_24
| ~ spl0_55
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15160,f764]) ).
thf(f15160,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_24
| ~ spl0_64
| ~ spl0_73
| ~ spl0_81
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15159,f3152]) ).
thf(f15159,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_24
| ~ spl0_64
| ~ spl0_81
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15158,f1112]) ).
thf(f15158,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_24
| ~ spl0_64
| ~ spl0_81
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15157,f1112]) ).
thf(f15157,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_24
| ~ spl0_64
| ~ spl0_81
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15156,f1112]) ).
thf(f15156,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_24
| ~ spl0_81
| ~ spl0_102 ),
inference(forward_demodulation,[],[f15142,f4854]) ).
thf(f15142,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_24
| ~ spl0_102 ),
inference(backward_demodulation,[],[f264,f12664]) ).
thf(f15141,plain,
( spl0_87
| spl0_102 ),
inference(avatar_contradiction_clause,[],[f15140]) ).
thf(f15140,plain,
( $false
| spl0_87
| spl0_102 ),
inference(subsumption_resolution,[],[f15133,f6682]) ).
thf(f6682,plain,
( ( $false != vAPP($o,$o,f4,$true) )
| spl0_87 ),
inference(avatar_component_clause,[],[f6680]) ).
thf(f15133,plain,
( ( $false = vAPP($o,$o,f4,$true) )
| spl0_102 ),
inference(trivial_inequality_removal,[],[f15132]) ).
thf(f15132,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f4,$true) )
| spl0_102 ),
inference(superposition,[],[f12663,f4]) ).
thf(f12663,plain,
( ( $true != vAPP($o,$o,f4,$true) )
| spl0_102 ),
inference(avatar_component_clause,[],[f12662]) ).
thf(f15096,plain,
( spl0_92
| ~ spl0_4
| ~ spl0_64
| ~ spl0_81
| spl0_87
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15068,f12610,f6680,f4852,f1110,f23,f7918]) ).
thf(f15068,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_64
| ~ spl0_81
| spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15067,f1112]) ).
thf(f15067,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| ~ spl0_81
| spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15066,f4854]) ).
thf(f15066,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_4
| ~ spl0_81
| spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15065,f4854]) ).
thf(f15065,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_4
| ~ spl0_81
| spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15064,f4854]) ).
thf(f15064,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_4
| spl0_87
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15043,f6682]) ).
thf(f15095,plain,
( spl0_92
| ~ spl0_4
| spl0_9
| ~ spl0_64
| ~ spl0_81
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15074,f12610,f4852,f1110,f83,f23,f7918]) ).
thf(f15074,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| spl0_9
| ~ spl0_64
| ~ spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15073,f1112]) ).
thf(f15093,plain,
( spl0_92
| ~ spl0_4
| spl0_13
| ~ spl0_64
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15083,f12610,f1110,f101,f23,f7918]) ).
thf(f15083,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| spl0_13
| ~ spl0_64
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15082,f1112]) ).
thf(f15092,plain,
( spl0_92
| ~ spl0_4
| spl0_15
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f15091,f12610,f110,f23,f7918]) ).
thf(f15091,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| spl0_15
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15051,f15010]) ).
thf(f15029,plain,
( ~ spl0_4
| ~ spl0_21
| spl0_27
| ~ spl0_40
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f15028]) ).
thf(f15028,plain,
( $false
| ~ spl0_4
| ~ spl0_21
| spl0_27
| ~ spl0_40
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15027,f14882]) ).
thf(f14882,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f283,f358]) ).
thf(f283,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_27 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f15027,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_21
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14791,f15024]) ).
thf(f15024,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))))))) )
| ~ spl0_21
| ~ spl0_101 ),
inference(forward_demodulation,[],[f139,f12612]) ).
thf(f15008,plain,
( ~ spl0_4
| ~ spl0_17
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f15007]) ).
thf(f15007,plain,
( $false
| ~ spl0_4
| ~ spl0_17
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f15006,f14882]) ).
thf(f15006,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_70
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15005,f2469]) ).
thf(f15005,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_70
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15004,f2469]) ).
thf(f15004,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_101 ),
inference(backward_demodulation,[],[f14791,f13184]) ).
thf(f13184,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))))) )
| ~ spl0_17
| ~ spl0_101 ),
inference(backward_demodulation,[],[f121,f12612]) ).
thf(f121,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f119]) ).
thf(f14989,plain,
( ~ spl0_4
| ~ spl0_15
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f14988]) ).
thf(f14988,plain,
( $false
| ~ spl0_4
| ~ spl0_15
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f14987,f14882]) ).
thf(f14987,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_70
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14986,f2469]) ).
thf(f14986,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_70
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14985,f2469]) ).
thf(f14985,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_70
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14984,f2469]) ).
thf(f14984,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_15
| ~ spl0_101 ),
inference(backward_demodulation,[],[f14791,f13635]) ).
thf(f13635,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| ~ spl0_15
| ~ spl0_101 ),
inference(forward_demodulation,[],[f112,f12612]) ).
thf(f14983,plain,
( ~ spl0_6
| spl0_2
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f14968,f12610,f14,f69]) ).
thf(f14968,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| spl0_2
| ~ spl0_101 ),
inference(forward_demodulation,[],[f15,f12612]) ).
thf(f14975,plain,
( spl0_2
| ~ spl0_13
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f14974]) ).
thf(f14974,plain,
( $false
| spl0_2
| ~ spl0_13
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f14973,f764]) ).
thf(f14973,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_2
| ~ spl0_13
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14972,f2469]) ).
thf(f14972,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_2
| ~ spl0_13
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14971,f2469]) ).
thf(f14971,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_2
| ~ spl0_13
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14970,f2469]) ).
thf(f14970,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_2
| ~ spl0_13
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14969,f4823]) ).
thf(f14969,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_2
| ~ spl0_13
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14968,f14016]) ).
thf(f14016,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| ~ spl0_13
| ~ spl0_101 ),
inference(forward_demodulation,[],[f103,f12612]) ).
thf(f14960,plain,
( ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_111
| ~ spl0_114 ),
inference(avatar_contradiction_clause,[],[f14959]) ).
thf(f14959,plain,
( $false
| ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_111
| ~ spl0_114 ),
inference(trivial_inequality_removal,[],[f14958]) ).
thf(f14958,plain,
( ( $true = $false )
| ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_111
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14957,f358]) ).
thf(f14957,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_111
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14956,f764]) ).
thf(f14956,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_111
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14955,f2469]) ).
thf(f14955,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_80
| ~ spl0_101
| ~ spl0_111
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14954,f4823]) ).
thf(f14954,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_80
| ~ spl0_101
| ~ spl0_111
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14953,f4823]) ).
thf(f14953,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_101
| ~ spl0_111
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14952,f13472]) ).
thf(f14952,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_101
| ~ spl0_111 ),
inference(forward_demodulation,[],[f13038,f12612]) ).
thf(f14936,plain,
( spl0_87
| ~ spl0_7
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f14546,f12610,f74,f6680]) ).
thf(f74,plain,
( spl0_7
<=> ( vAPP($o,$o,f4,x) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f14546,plain,
( ( $false = vAPP($o,$o,f4,$true) )
| ~ spl0_7
| ~ spl0_101 ),
inference(forward_demodulation,[],[f76,f12612]) ).
thf(f76,plain,
( ( vAPP($o,$o,f4,x) = $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f14935,plain,
( spl0_87
| ~ spl0_9
| ~ spl0_101
| spl0_116 ),
inference(avatar_split_clause,[],[f14934,f13497,f12610,f83,f6680]) ).
thf(f14934,plain,
( ( $false = vAPP($o,$o,f4,$true) )
| ~ spl0_9
| ~ spl0_101
| spl0_116 ),
inference(subsumption_resolution,[],[f14193,f13499]) ).
thf(f13499,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| spl0_116 ),
inference(avatar_component_clause,[],[f13497]) ).
thf(f14193,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f4,$true) )
| ~ spl0_9
| ~ spl0_101 ),
inference(superposition,[],[f14018,f4]) ).
thf(f14018,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$true)) )
| ~ spl0_9
| ~ spl0_101 ),
inference(forward_demodulation,[],[f85,f12612]) ).
thf(f14928,plain,
( spl0_1
| ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_114 ),
inference(avatar_contradiction_clause,[],[f14927]) ).
thf(f14927,plain,
( $false
| spl0_1
| ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_114 ),
inference(subsumption_resolution,[],[f14926,f764]) ).
thf(f14926,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_1
| ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14925,f358]) ).
thf(f14925,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_1
| ~ spl0_55
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14924,f764]) ).
thf(f14924,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_1
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14923,f2469]) ).
thf(f14923,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_1
| ~ spl0_80
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14922,f4823]) ).
thf(f14922,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_1
| ~ spl0_80
| ~ spl0_101
| ~ spl0_114 ),
inference(forward_demodulation,[],[f14920,f4823]) ).
thf(f14920,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_1
| ~ spl0_101
| ~ spl0_114 ),
inference(backward_demodulation,[],[f14800,f13472]) ).
thf(f14800,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| spl0_1
| ~ spl0_101 ),
inference(forward_demodulation,[],[f11,f12612]) ).
thf(f14918,plain,
( ~ spl0_109
| ~ spl0_101
| spl0_111 ),
inference(avatar_split_clause,[],[f14590,f13036,f12610,f12891]) ).
thf(f12891,plain,
( spl0_109
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
thf(f14590,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_101
| spl0_111 ),
inference(forward_demodulation,[],[f13037,f12612]) ).
thf(f13037,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))))))) != $true )
| spl0_111 ),
inference(avatar_component_clause,[],[f13036]) ).
thf(f14917,plain,
( ~ spl0_4
| ~ spl0_11
| spl0_27
| ~ spl0_40
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f14916]) ).
thf(f14916,plain,
( $false
| ~ spl0_4
| ~ spl0_11
| spl0_27
| ~ spl0_40
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f14915,f14882]) ).
thf(f14915,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14914,f2469]) ).
thf(f14914,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14913,f2469]) ).
thf(f14913,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14912,f2469]) ).
thf(f14912,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_68
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14911,f4823]) ).
thf(f14911,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_68
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14910,f1713]) ).
thf(f14910,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_101 ),
inference(backward_demodulation,[],[f14791,f14762]) ).
thf(f14762,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ~ spl0_11
| ~ spl0_101 ),
inference(forward_demodulation,[],[f94,f12612]) ).
thf(f14866,plain,
( ~ spl0_4
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| spl0_93
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f14865]) ).
thf(f14865,plain,
( $false
| ~ spl0_4
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| spl0_93
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f14864,f14799]) ).
thf(f14799,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14798,f2469]) ).
thf(f14798,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14797,f2469]) ).
thf(f14797,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14796,f2469]) ).
thf(f14796,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14795,f4823]) ).
thf(f14795,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14794,f1713]) ).
thf(f14794,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14793,f1713]) ).
thf(f14793,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14792,f1713]) ).
thf(f14792,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_4
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14791,f6681]) ).
thf(f14864,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| spl0_93
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14863,f14799]) ).
thf(f14863,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_4
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| spl0_93
| ~ spl0_101 ),
inference(forward_demodulation,[],[f14862,f14799]) ).
thf(f14862,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f14861,f2469]) ).
thf(f14861,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f14860,f4823]) ).
thf(f14860,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f8128,f4823]) ).
thf(f14856,plain,
( ~ spl0_87
| ~ spl0_98
| spl0_110 ),
inference(avatar_contradiction_clause,[],[f14855]) ).
thf(f14855,plain,
( $false
| ~ spl0_87
| ~ spl0_98
| spl0_110 ),
inference(subsumption_resolution,[],[f14854,f12301]) ).
thf(f12301,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f12299]) ).
thf(f14854,plain,
( ( $false != vAPP($o,$o,f4,$false) )
| ~ spl0_87
| ~ spl0_98
| spl0_110 ),
inference(forward_demodulation,[],[f14853,f12301]) ).
thf(f14853,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_87
| spl0_110 ),
inference(forward_demodulation,[],[f12921,f6681]) ).
thf(f14818,plain,
( ~ spl0_4
| ~ spl0_55
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f14817]) ).
thf(f14817,plain,
( $false
| ~ spl0_4
| ~ spl0_55
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(trivial_inequality_removal,[],[f14816]) ).
thf(f14816,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_55
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(forward_demodulation,[],[f764,f14799]) ).
thf(f14815,plain,
( ~ spl0_4
| spl0_57
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f14814]) ).
thf(f14814,plain,
( $false
| ~ spl0_4
| spl0_57
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_87
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f14687,f14799]) ).
thf(f14687,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_57
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f14686,f2469]) ).
thf(f14686,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_57
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f14685,f4823]) ).
thf(f14685,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| spl0_57
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f14684,f4823]) ).
thf(f14684,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| spl0_57
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f14683,f4823]) ).
thf(f14683,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_57
| ~ spl0_68 ),
inference(forward_demodulation,[],[f775,f1713]) ).
thf(f14771,plain,
( ~ spl0_27
| ~ spl0_40
| ~ spl0_55 ),
inference(avatar_contradiction_clause,[],[f14770]) ).
thf(f14770,plain,
( $false
| ~ spl0_27
| ~ spl0_40
| ~ spl0_55 ),
inference(trivial_inequality_removal,[],[f14769]) ).
thf(f14769,plain,
( ( $true = $false )
| ~ spl0_27
| ~ spl0_40
| ~ spl0_55 ),
inference(backward_demodulation,[],[f764,f14750]) ).
thf(f14750,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f284,f358]) ).
thf(f14752,plain,
( spl0_4
| ~ spl0_17
| ~ spl0_21
| ~ spl0_27
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f14751]) ).
thf(f14751,plain,
( $false
| spl0_4
| ~ spl0_17
| ~ spl0_21
| ~ spl0_27
| ~ spl0_40 ),
inference(subsumption_resolution,[],[f14750,f13454]) ).
thf(f13454,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_4
| ~ spl0_17
| ~ spl0_21 ),
inference(backward_demodulation,[],[f12324,f12322]) ).
thf(f12322,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_17
| ~ spl0_21 ),
inference(backward_demodulation,[],[f139,f121]) ).
thf(f12324,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f24,f121]) ).
thf(f24,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) != $false )
| spl0_4 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f14617,plain,
( spl0_68
| ~ spl0_94
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f14614,f12299,f8283,f1711]) ).
thf(f14614,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_94
| ~ spl0_98 ),
inference(backward_demodulation,[],[f8285,f12301]) ).
thf(f14568,plain,
( ~ spl0_16
| spl0_14
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f14011,f1110,f105,f114]) ).
thf(f114,plain,
( spl0_16
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f14011,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| spl0_14
| ~ spl0_64 ),
inference(forward_demodulation,[],[f106,f1112]) ).
thf(f14565,plain,
( spl0_35
| ~ spl0_29
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f14154,f1110,f291,f330]) ).
thf(f14154,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_29
| ~ spl0_64 ),
inference(forward_demodulation,[],[f14153,f1112]) ).
thf(f14153,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_29
| ~ spl0_64 ),
inference(forward_demodulation,[],[f14152,f1112]) ).
thf(f14152,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_29
| ~ spl0_64 ),
inference(forward_demodulation,[],[f293,f1112]) ).
thf(f293,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f14564,plain,
( spl0_35
| spl0_49
| ~ spl0_3
| ~ spl0_101
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f14262,f12920,f12610,f19,f729,f330]) ).
thf(f14262,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f13702,f12922]) ).
thf(f13702,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12343,f12612]) ).
thf(f12343,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f14563,plain,
( spl0_47
| spl0_35
| ~ spl0_3
| ~ spl0_64
| ~ spl0_101
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f14267,f12920,f12610,f1110,f19,f330,f718]) ).
thf(f14267,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_3
| ~ spl0_64
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f14266,f1112]) ).
thf(f14266,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f13467,f12922]) ).
thf(f13467,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12341,f12612]) ).
thf(f12341,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f14562,plain,
( ~ spl0_3
| spl0_24
| ~ spl0_87
| ~ spl0_101
| ~ spl0_110 ),
inference(avatar_contradiction_clause,[],[f14561]) ).
thf(f14561,plain,
( $false
| ~ spl0_3
| spl0_24
| ~ spl0_87
| ~ spl0_101
| ~ spl0_110 ),
inference(subsumption_resolution,[],[f14273,f14536]) ).
thf(f14536,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| spl0_24
| ~ spl0_87 ),
inference(forward_demodulation,[],[f264,f6681]) ).
thf(f14273,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f13460,f12922]) ).
thf(f13460,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f21,f12612]) ).
thf(f14560,plain,
( ~ spl0_57
| ~ spl0_25
| spl0_42 ),
inference(avatar_split_clause,[],[f14518,f367,f268,f774]) ).
thf(f268,plain,
( spl0_25
<=> ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f14518,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_25
| spl0_42 ),
inference(backward_demodulation,[],[f368,f270]) ).
thf(f270,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f368,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))) )
| spl0_42 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f14412,plain,
( ~ spl0_58
| spl0_108
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f14411,f12920,f12887,f780]) ).
thf(f780,plain,
( spl0_58
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
thf(f12887,plain,
( spl0_108
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
thf(f14411,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| spl0_108
| ~ spl0_110 ),
inference(forward_demodulation,[],[f12888,f12922]) ).
thf(f12888,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))) )
| spl0_108 ),
inference(avatar_component_clause,[],[f12887]) ).
thf(f14407,plain,
( spl0_117
| spl0_87
| ~ spl0_3
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f14402,f12610,f19,f6680,f14404]) ).
thf(f14402,plain,
( ( $false = vAPP($o,$o,f4,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12334,f12612]) ).
thf(f12334,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ( vAPP($o,$o,f4,x) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f14278,plain,
( ~ spl0_54
| spl0_109
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f14277,f12920,f12891,f758]) ).
thf(f758,plain,
( spl0_54
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
thf(f14277,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))))) )
| spl0_109
| ~ spl0_110 ),
inference(forward_demodulation,[],[f12892,f12922]) ).
thf(f12892,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| spl0_109 ),
inference(avatar_component_clause,[],[f12891]) ).
thf(f14261,plain,
( ~ spl0_68
| ~ spl0_110
| spl0_115 ),
inference(avatar_split_clause,[],[f14260,f13478,f12920,f1711]) ).
thf(f14260,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_110
| spl0_115 ),
inference(forward_demodulation,[],[f13479,f12922]) ).
thf(f13479,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))) )
| spl0_115 ),
inference(avatar_component_clause,[],[f13478]) ).
thf(f14259,plain,
( ~ spl0_44
| ~ spl0_110
| spl0_114 ),
inference(avatar_split_clause,[],[f14258,f13470,f12920,f702]) ).
thf(f702,plain,
( spl0_44
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
thf(f14258,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_110
| spl0_114 ),
inference(forward_demodulation,[],[f13471,f12922]) ).
thf(f14255,plain,
( spl0_66
| ~ spl0_9
| ~ spl0_13
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f14019,f12610,f101,f83,f1551]) ).
thf(f14019,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_9
| ~ spl0_13
| ~ spl0_101 ),
inference(backward_demodulation,[],[f14016,f14018]) ).
thf(f14254,plain,
( ~ spl0_68
| ~ spl0_9
| spl0_11
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f14021,f12610,f92,f83,f1711]) ).
thf(f14021,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_9
| spl0_11
| ~ spl0_101 ),
inference(backward_demodulation,[],[f13732,f14018]) ).
thf(f13732,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_11
| ~ spl0_101 ),
inference(forward_demodulation,[],[f93,f12612]) ).
thf(f13917,plain,
( ~ spl0_76
| spl0_75
| ~ spl0_78
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f13912,f13497,f4806,f3173,f4513]) ).
thf(f13912,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_75
| ~ spl0_78
| ~ spl0_116 ),
inference(backward_demodulation,[],[f13829,f4808]) ).
thf(f13829,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| spl0_75
| ~ spl0_116 ),
inference(backward_demodulation,[],[f3174,f13498]) ).
thf(f13916,plain,
( spl0_14
| ~ spl0_10
| ~ spl0_78
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f13911,f13497,f4806,f87,f105]) ).
thf(f13911,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_10
| ~ spl0_78
| ~ spl0_116 ),
inference(backward_demodulation,[],[f13830,f4808]) ).
thf(f13830,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_10
| ~ spl0_116 ),
inference(backward_demodulation,[],[f89,f13498]) ).
thf(f89,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f87]) ).
thf(f13900,plain,
( spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_88 ),
inference(avatar_contradiction_clause,[],[f13899]) ).
thf(f13899,plain,
( $false
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_88 ),
inference(subsumption_resolution,[],[f13898,f11947]) ).
thf(f11947,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f283,f358]) ).
thf(f13898,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_40
| ~ spl0_55
| ~ spl0_88 ),
inference(forward_demodulation,[],[f13897,f358]) ).
thf(f13897,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_55
| ~ spl0_88 ),
inference(forward_demodulation,[],[f6932,f764]) ).
thf(f13896,plain,
( spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_89 ),
inference(avatar_contradiction_clause,[],[f13895]) ).
thf(f13895,plain,
( $false
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_89 ),
inference(subsumption_resolution,[],[f13894,f11947]) ).
thf(f13894,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_40
| ~ spl0_55
| ~ spl0_70
| ~ spl0_89 ),
inference(forward_demodulation,[],[f13893,f358]) ).
thf(f13893,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_55
| ~ spl0_70
| ~ spl0_89 ),
inference(forward_demodulation,[],[f13892,f764]) ).
thf(f13892,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| ~ spl0_89 ),
inference(forward_demodulation,[],[f6949,f2469]) ).
thf(f13875,plain,
( ~ spl0_68
| spl0_94
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f13853,f12299,f8283,f1711]) ).
thf(f13853,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| spl0_94
| ~ spl0_98 ),
inference(backward_demodulation,[],[f8284,f12301]) ).
thf(f8284,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| spl0_94 ),
inference(avatar_component_clause,[],[f8283]) ).
thf(f13862,plain,
( ~ spl0_68
| spl0_28
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f13861,f12299,f287,f1711]) ).
thf(f13861,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| spl0_28
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13860,f12301]) ).
thf(f13860,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| spl0_28
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13848,f12301]) ).
thf(f13848,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| spl0_28
| ~ spl0_98 ),
inference(backward_demodulation,[],[f288,f12301]) ).
thf(f288,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| spl0_28 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f13859,plain,
( spl0_25
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f13858]) ).
thf(f13858,plain,
( $false
| spl0_25
| ~ spl0_98 ),
inference(subsumption_resolution,[],[f13857,f12301]) ).
thf(f13857,plain,
( ( $false != vAPP($o,$o,f4,$false) )
| spl0_25
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13847,f12301]) ).
thf(f13847,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| spl0_25
| ~ spl0_98 ),
inference(backward_demodulation,[],[f269,f12301]) ).
thf(f269,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| spl0_25 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f13856,plain,
( spl0_23
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f13855]) ).
thf(f13855,plain,
( $false
| spl0_23
| ~ spl0_98 ),
inference(subsumption_resolution,[],[f13846,f12301]) ).
thf(f13846,plain,
( ( $false != vAPP($o,$o,f4,$false) )
| spl0_23
| ~ spl0_98 ),
inference(backward_demodulation,[],[f260,f12301]) ).
thf(f13808,plain,
( ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_115 ),
inference(avatar_contradiction_clause,[],[f13807]) ).
thf(f13807,plain,
( $false
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_115 ),
inference(subsumption_resolution,[],[f13806,f11947]) ).
thf(f13806,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_80
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13805,f2469]) ).
thf(f13805,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_80
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13804,f4823]) ).
thf(f13804,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_80
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13803,f4823]) ).
thf(f13803,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_80
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13802,f4823]) ).
thf(f13802,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_101
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13693,f13480]) ).
thf(f13693,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12431,f12612]) ).
thf(f12431,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))) = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40 ),
inference(subsumption_resolution,[],[f12430,f11947]) ).
thf(f12430,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))) = $false )
| ~ spl0_3
| ~ spl0_40 ),
inference(forward_demodulation,[],[f12346,f358]) ).
thf(f12346,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f13753,plain,
( spl0_47
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_63
| ~ spl0_70
| ~ spl0_101
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f13752,f12920,f12610,f2467,f1105,f762,f356,f282,f19,f718]) ).
thf(f13752,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_63
| ~ spl0_70
| ~ spl0_101
| ~ spl0_110 ),
inference(subsumption_resolution,[],[f13751,f11947]) ).
thf(f13751,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_3
| ~ spl0_40
| ~ spl0_55
| ~ spl0_63
| ~ spl0_70
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f13750,f358]) ).
thf(f13750,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_3
| ~ spl0_55
| ~ spl0_63
| ~ spl0_70
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f13749,f764]) ).
thf(f13749,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_3
| ~ spl0_63
| ~ spl0_70
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f13748,f2469]) ).
thf(f13748,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_3
| ~ spl0_63
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f13664,f1107]) ).
thf(f13664,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_3
| ~ spl0_101
| ~ spl0_110 ),
inference(forward_demodulation,[],[f13467,f12922]) ).
thf(f13742,plain,
( spl0_44
| ~ spl0_110
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f13710,f13470,f12920,f702]) ).
thf(f13710,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_110
| ~ spl0_114 ),
inference(forward_demodulation,[],[f13472,f12922]) ).
thf(f13741,plain,
( spl0_68
| ~ spl0_110
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f13707,f13478,f12920,f1711]) ).
thf(f13707,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_110
| ~ spl0_115 ),
inference(forward_demodulation,[],[f13480,f12922]) ).
thf(f13592,plain,
( ~ spl0_116
| spl0_59
| ~ spl0_78
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f13591,f4852,f4806,f1089,f13497]) ).
thf(f13591,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| spl0_59
| ~ spl0_78
| ~ spl0_81 ),
inference(forward_demodulation,[],[f13590,f4854]) ).
thf(f13590,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$true)) )
| spl0_59
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1090,f4808]) ).
thf(f1090,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| spl0_59 ),
inference(avatar_component_clause,[],[f1089]) ).
thf(f13551,plain,
( ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_70
| ~ spl0_71
| ~ spl0_80
| ~ spl0_101
| ~ spl0_109 ),
inference(avatar_contradiction_clause,[],[f13550]) ).
thf(f13550,plain,
( $false
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_70
| ~ spl0_71
| ~ spl0_80
| ~ spl0_101
| ~ spl0_109 ),
inference(trivial_inequality_removal,[],[f13549]) ).
thf(f13549,plain,
( ( $true = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_70
| ~ spl0_71
| ~ spl0_80
| ~ spl0_101
| ~ spl0_109 ),
inference(forward_demodulation,[],[f13548,f358]) ).
thf(f13548,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_70
| ~ spl0_71
| ~ spl0_80
| ~ spl0_101
| ~ spl0_109 ),
inference(forward_demodulation,[],[f13544,f764]) ).
thf(f13544,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_70
| ~ spl0_71
| ~ spl0_80
| ~ spl0_101
| ~ spl0_109 ),
inference(backward_demodulation,[],[f13465,f2469]) ).
thf(f13465,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_71
| ~ spl0_80
| ~ spl0_101
| ~ spl0_109 ),
inference(forward_demodulation,[],[f13463,f4823]) ).
thf(f13463,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_71
| ~ spl0_101
| ~ spl0_109 ),
inference(backward_demodulation,[],[f12893,f13462]) ).
thf(f13462,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_71
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12414,f12612]) ).
thf(f12414,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f12413,f11947]) ).
thf(f12413,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12412,f358]) ).
thf(f12412,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| ~ spl0_55
| ~ spl0_62
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12411,f764]) ).
thf(f12411,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| ~ spl0_62
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12342,f2472]) ).
thf(f12342,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| ~ spl0_62 ),
inference(superposition,[],[f21,f1102]) ).
thf(f1102,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f2,X0) )
| ( $false = X0 ) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1101]) ).
thf(f1101,plain,
( spl0_62
<=> ! [X0: $o] :
( ( $false = X0 )
| ( $true = vAPP($o,$o,f2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
thf(f12893,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f12891]) ).
thf(f13540,plain,
( spl0_63
| ~ spl0_44
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f13538,f4806,f702,f1105]) ).
thf(f13538,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_44
| ~ spl0_78 ),
inference(backward_demodulation,[],[f704,f4808]) ).
thf(f704,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f702]) ).
thf(f13539,plain,
( spl0_116
| ~ spl0_66
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f13537,f4806,f1551,f13497]) ).
thf(f13537,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_66
| ~ spl0_78 ),
inference(backward_demodulation,[],[f1553,f4808]) ).
thf(f1553,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1551]) ).
thf(f13527,plain,
( spl0_70
| ~ spl0_71
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f13526,f5273,f2471,f2467]) ).
thf(f13526,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_71
| ~ spl0_83 ),
inference(forward_demodulation,[],[f5275,f2472]) ).
thf(f5275,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f5273]) ).
thf(f13525,plain,
( ~ spl0_53
| ~ spl0_71
| spl0_85 ),
inference(avatar_split_clause,[],[f13524,f5871,f2471,f750]) ).
thf(f13524,plain,
( ( $true != vAPP($o,$o,f1,$false) )
| ~ spl0_71
| spl0_85 ),
inference(forward_demodulation,[],[f5872,f2472]) ).
thf(f5872,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_85 ),
inference(avatar_component_clause,[],[f5871]) ).
thf(f13523,plain,
( ~ spl0_68
| ~ spl0_86
| spl0_96 ),
inference(avatar_split_clause,[],[f13522,f10956,f6547,f1711]) ).
thf(f13522,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_86
| spl0_96 ),
inference(backward_demodulation,[],[f10957,f6549]) ).
thf(f13500,plain,
( spl0_98
| ~ spl0_116
| spl0_94 ),
inference(avatar_split_clause,[],[f12485,f8283,f13497,f12299]) ).
thf(f12485,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f4,$false) )
| spl0_94 ),
inference(superposition,[],[f8284,f4]) ).
thf(f13484,plain,
( spl0_68
| ~ spl0_9
| ~ spl0_11
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f13451,f12610,f92,f83,f1711]) ).
thf(f13451,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_9
| ~ spl0_11
| ~ spl0_101 ),
inference(forward_demodulation,[],[f13450,f13318]) ).
thf(f13318,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$true)) )
| ~ spl0_9
| ~ spl0_101 ),
inference(forward_demodulation,[],[f85,f12612]) ).
thf(f13450,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ~ spl0_11
| ~ spl0_101 ),
inference(forward_demodulation,[],[f94,f12612]) ).
thf(f13483,plain,
( spl0_29
| spl0_115
| ~ spl0_3
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f13482,f12610,f19,f13478,f291]) ).
thf(f13482,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12337,f12612]) ).
thf(f12337,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ( vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f13475,plain,
( spl0_31
| spl0_114
| ~ spl0_3
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f13474,f12610,f19,f13470,f305]) ).
thf(f13474,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12339,f12612]) ).
thf(f12339,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f13453,plain,
( spl0_95
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f13044,f2471,f762,f356,f282,f19,f8287]) ).
thf(f13044,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_71 ),
inference(backward_demodulation,[],[f12431,f12421]) ).
thf(f12421,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))) = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f12420,f11947]) ).
thf(f12420,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))) = $false )
| ~ spl0_3
| ~ spl0_40
| ~ spl0_55
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12419,f358]) ).
thf(f12419,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))) = $false )
| ~ spl0_3
| ~ spl0_55
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12418,f764]) ).
thf(f12418,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))) = $false )
| ~ spl0_3
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12343,f2472]) ).
thf(f13357,plain,
( ~ spl0_94
| ~ spl0_23
| spl0_28 ),
inference(avatar_split_clause,[],[f13356,f287,f259,f8283]) ).
thf(f13356,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_23
| spl0_28 ),
inference(backward_demodulation,[],[f288,f261]) ).
thf(f13349,plain,
( spl0_94
| spl0_81
| spl0_86 ),
inference(avatar_split_clause,[],[f13310,f6547,f4852,f8283]) ).
thf(f13310,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| spl0_81
| spl0_86 ),
inference(subsumption_resolution,[],[f12522,f13260]) ).
thf(f13260,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| spl0_81 ),
inference(trivial_inequality_removal,[],[f13259]) ).
thf(f13259,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f3,$true) )
| spl0_81 ),
inference(superposition,[],[f4853,f4]) ).
thf(f4853,plain,
( ( $true != vAPP($o,$o,f3,$true) )
| spl0_81 ),
inference(avatar_component_clause,[],[f4852]) ).
thf(f12522,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| spl0_86 ),
inference(superposition,[],[f6548,f4]) ).
thf(f6548,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))) )
| spl0_86 ),
inference(avatar_component_clause,[],[f6547]) ).
thf(f13348,plain,
( spl0_98
| spl0_81
| spl0_94 ),
inference(avatar_split_clause,[],[f13347,f8283,f4852,f12299]) ).
thf(f13347,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| spl0_81
| spl0_94 ),
inference(subsumption_resolution,[],[f12485,f13260]) ).
thf(f13346,plain,
( spl0_68
| ~ spl0_9
| spl0_15
| ~ spl0_80
| spl0_81
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f13345,f12610,f4852,f4821,f110,f83,f1711]) ).
thf(f13345,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_9
| spl0_15
| ~ spl0_80
| spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f13344,f13318]) ).
thf(f13344,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_15
| ~ spl0_80
| spl0_81
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f13343,f4823]) ).
thf(f13343,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_15
| spl0_81
| ~ spl0_101 ),
inference(forward_demodulation,[],[f13237,f13260]) ).
thf(f13237,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$true)) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_15
| ~ spl0_101 ),
inference(superposition,[],[f13183,f4]) ).
thf(f13183,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))) )
| spl0_15
| ~ spl0_101 ),
inference(backward_demodulation,[],[f111,f12612]) ).
thf(f13341,plain,
( ~ spl0_44
| spl0_69
| spl0_81 ),
inference(avatar_split_clause,[],[f13340,f4852,f1715,f702]) ).
thf(f13340,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| spl0_69
| spl0_81 ),
inference(forward_demodulation,[],[f1716,f13260]) ).
thf(f13331,plain,
( ~ spl0_66
| ~ spl0_9
| spl0_15
| ~ spl0_80
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f13330,f12610,f4821,f110,f83,f1551]) ).
thf(f13330,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_9
| spl0_15
| ~ spl0_80
| ~ spl0_101 ),
inference(forward_demodulation,[],[f13243,f13318]) ).
thf(f13243,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| spl0_15
| ~ spl0_80
| ~ spl0_101 ),
inference(trivial_inequality_removal,[],[f13240]) ).
thf(f13240,plain,
( ( $false != $false )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| spl0_15
| ~ spl0_80
| ~ spl0_101 ),
inference(constrained_superposition,[],[f13183,f4823]) ).
thf(f13313,plain,
( spl0_68
| spl0_81
| spl0_86
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f13312]) ).
thf(f13312,plain,
( $false
| spl0_68
| spl0_81
| spl0_86
| ~ spl0_98 ),
inference(subsumption_resolution,[],[f13311,f1712]) ).
thf(f1712,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| spl0_68 ),
inference(avatar_component_clause,[],[f1711]) ).
thf(f13311,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| spl0_81
| spl0_86
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13310,f12301]) ).
thf(f13309,plain,
( spl0_66
| ~ spl0_78
| spl0_81 ),
inference(avatar_contradiction_clause,[],[f13308]) ).
thf(f13308,plain,
( $false
| spl0_66
| ~ spl0_78
| spl0_81 ),
inference(subsumption_resolution,[],[f12830,f13260]) ).
thf(f12830,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| spl0_66
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1552,f4808]) ).
thf(f1552,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| spl0_66 ),
inference(avatar_component_clause,[],[f1551]) ).
thf(f13303,plain,
( spl0_5
| spl0_11
| spl0_13
| spl0_81
| ~ spl0_101 ),
inference(avatar_contradiction_clause,[],[f13302]) ).
thf(f13302,plain,
( $false
| spl0_5
| spl0_11
| spl0_13
| spl0_81
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f13301,f12509]) ).
thf(f12509,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_5
| spl0_11 ),
inference(subsumption_resolution,[],[f12502,f66]) ).
thf(f66,plain,
( ( x != $false )
| spl0_5 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f65,plain,
( spl0_5
<=> ( x = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f12502,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| ( x = $false )
| spl0_11 ),
inference(superposition,[],[f93,f4]) ).
thf(f13301,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_13
| spl0_81
| ~ spl0_101 ),
inference(subsumption_resolution,[],[f13221,f13260]) ).
thf(f13221,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))) )
| spl0_13
| ~ spl0_101 ),
inference(superposition,[],[f13182,f4]) ).
thf(f13182,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true)))) )
| spl0_13
| ~ spl0_101 ),
inference(backward_demodulation,[],[f102,f12612]) ).
thf(f13290,plain,
( spl0_67
| ~ spl0_80
| spl0_81 ),
inference(avatar_contradiction_clause,[],[f13289]) ).
thf(f13289,plain,
( $false
| spl0_67
| ~ spl0_80
| spl0_81 ),
inference(subsumption_resolution,[],[f13271,f4823]) ).
thf(f13271,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_67
| spl0_81 ),
inference(backward_demodulation,[],[f1556,f13260]) ).
thf(f13282,plain,
( ~ spl0_12
| ~ spl0_40
| ~ spl0_53
| ~ spl0_71
| ~ spl0_80
| spl0_81 ),
inference(avatar_contradiction_clause,[],[f13281]) ).
thf(f13281,plain,
( $false
| ~ spl0_12
| ~ spl0_40
| ~ spl0_53
| ~ spl0_71
| ~ spl0_80
| spl0_81 ),
inference(trivial_inequality_removal,[],[f13280]) ).
thf(f13280,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_40
| ~ spl0_53
| ~ spl0_71
| ~ spl0_80
| spl0_81 ),
inference(forward_demodulation,[],[f13279,f358]) ).
thf(f13279,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_12
| ~ spl0_53
| ~ spl0_71
| ~ spl0_80
| spl0_81 ),
inference(forward_demodulation,[],[f13278,f752]) ).
thf(f13278,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_12
| ~ spl0_53
| ~ spl0_71
| ~ spl0_80
| spl0_81 ),
inference(forward_demodulation,[],[f13277,f2472]) ).
thf(f13277,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_12
| ~ spl0_53
| ~ spl0_80
| spl0_81 ),
inference(forward_demodulation,[],[f13276,f752]) ).
thf(f13276,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_12
| ~ spl0_80
| spl0_81 ),
inference(forward_demodulation,[],[f13269,f4823]) ).
thf(f13269,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_12
| spl0_81 ),
inference(backward_demodulation,[],[f98,f13260]) ).
thf(f13268,plain,
( spl0_7
| spl0_9
| spl0_81 ),
inference(avatar_contradiction_clause,[],[f13267]) ).
thf(f13267,plain,
( $false
| spl0_7
| spl0_9
| spl0_81 ),
inference(subsumption_resolution,[],[f13260,f12478]) ).
thf(f12478,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| spl0_7
| spl0_9 ),
inference(subsumption_resolution,[],[f12475,f75]) ).
thf(f75,plain,
( ( vAPP($o,$o,f4,x) != $false )
| spl0_7 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f12475,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( vAPP($o,$o,f4,x) = $false )
| spl0_9 ),
inference(superposition,[],[f84,f4]) ).
thf(f13178,plain,
( ~ spl0_3
| spl0_5
| spl0_27
| ~ spl0_40
| ~ spl0_108 ),
inference(avatar_contradiction_clause,[],[f13177]) ).
thf(f13177,plain,
( $false
| ~ spl0_3
| spl0_5
| spl0_27
| ~ spl0_40
| ~ spl0_108 ),
inference(subsumption_resolution,[],[f13176,f11947]) ).
thf(f13176,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_3
| spl0_5
| ~ spl0_40
| ~ spl0_108 ),
inference(forward_demodulation,[],[f13175,f358]) ).
thf(f13175,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_3
| spl0_5
| ~ spl0_108 ),
inference(backward_demodulation,[],[f12355,f12889]) ).
thf(f12889,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f12887]) ).
thf(f12355,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| ~ spl0_3
| spl0_5 ),
inference(subsumption_resolution,[],[f12333,f66]) ).
thf(f12333,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))))) )
| ( x = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f13174,plain,
( spl0_5
| spl0_101 ),
inference(avatar_contradiction_clause,[],[f13173]) ).
thf(f13173,plain,
( $false
| spl0_5
| spl0_101 ),
inference(subsumption_resolution,[],[f13172,f66]) ).
thf(f13172,plain,
( ( x = $false )
| spl0_101 ),
inference(trivial_inequality_removal,[],[f13171]) ).
thf(f13171,plain,
( ( $true != $true )
| ( x = $false )
| spl0_101 ),
inference(superposition,[],[f12611,f4]) ).
thf(f12611,plain,
( ( x != $true )
| spl0_101 ),
inference(avatar_component_clause,[],[f12610]) ).
thf(f13106,plain,
( spl0_27
| ~ spl0_40
| ~ spl0_42
| ~ spl0_64
| ~ spl0_71
| ~ spl0_78
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f13105]) ).
thf(f13105,plain,
( $false
| spl0_27
| ~ spl0_40
| ~ spl0_42
| ~ spl0_64
| ~ spl0_71
| ~ spl0_78
| ~ spl0_98 ),
inference(subsumption_resolution,[],[f13104,f11947]) ).
thf(f13104,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_42
| ~ spl0_64
| ~ spl0_71
| ~ spl0_78
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13103,f2472]) ).
thf(f13103,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_42
| ~ spl0_64
| ~ spl0_78
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13102,f1112]) ).
thf(f13102,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| ~ spl0_42
| ~ spl0_64
| ~ spl0_78
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13101,f1112]) ).
thf(f13101,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_42
| ~ spl0_64
| ~ spl0_78
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13100,f1112]) ).
thf(f13100,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_42
| ~ spl0_78
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13099,f4808]) ).
thf(f13099,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_42
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13098,f12301]) ).
thf(f13098,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_42
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13097,f12301]) ).
thf(f13097,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_42
| ~ spl0_98 ),
inference(forward_demodulation,[],[f369,f12301]) ).
thf(f13085,plain,
( ~ spl0_34
| spl0_63
| ~ spl0_64
| ~ spl0_78
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f13084]) ).
thf(f13084,plain,
( $false
| ~ spl0_34
| spl0_63
| ~ spl0_64
| ~ spl0_78
| ~ spl0_98 ),
inference(subsumption_resolution,[],[f13083,f1106]) ).
thf(f1106,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_63 ),
inference(avatar_component_clause,[],[f1105]) ).
thf(f13083,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ~ spl0_34
| ~ spl0_64
| ~ spl0_78
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13082,f1112]) ).
thf(f13082,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_34
| ~ spl0_64
| ~ spl0_78
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13081,f1112]) ).
thf(f13081,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_34
| ~ spl0_78
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13080,f4808]) ).
thf(f13080,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_34
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13079,f12301]) ).
thf(f13079,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_34
| ~ spl0_98 ),
inference(forward_demodulation,[],[f13078,f12301]) ).
thf(f13078,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_34
| ~ spl0_98 ),
inference(forward_demodulation,[],[f328,f12301]) ).
thf(f328,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f326]) ).
thf(f326,plain,
( spl0_34
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
thf(f13060,plain,
( spl0_113
| spl0_26
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f12336,f19,f272,f13057]) ).
thf(f12336,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3 ),
inference(superposition,[],[f21,f4]) ).
thf(f13033,plain,
( ~ spl0_24
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_78
| ~ spl0_87 ),
inference(avatar_contradiction_clause,[],[f13032]) ).
thf(f13032,plain,
( $false
| ~ spl0_24
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_78
| ~ spl0_87 ),
inference(subsumption_resolution,[],[f13031,f11947]) ).
thf(f13031,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_24
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_78
| ~ spl0_87 ),
inference(forward_demodulation,[],[f13030,f358]) ).
thf(f13030,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_24
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_78
| ~ spl0_87 ),
inference(forward_demodulation,[],[f13029,f764]) ).
thf(f13029,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_24
| ~ spl0_64
| ~ spl0_71
| ~ spl0_78
| ~ spl0_87 ),
inference(forward_demodulation,[],[f13028,f2472]) ).
thf(f13028,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_24
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87 ),
inference(forward_demodulation,[],[f13027,f1112]) ).
thf(f13027,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_24
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87 ),
inference(forward_demodulation,[],[f13026,f1112]) ).
thf(f13026,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_24
| ~ spl0_64
| ~ spl0_78
| ~ spl0_87 ),
inference(forward_demodulation,[],[f13025,f1112]) ).
thf(f13025,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_24
| ~ spl0_78
| ~ spl0_87 ),
inference(forward_demodulation,[],[f13013,f4808]) ).
thf(f13013,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_24
| ~ spl0_87 ),
inference(backward_demodulation,[],[f265,f6681]) ).
thf(f12923,plain,
( spl0_26
| spl0_110
| ~ spl0_3
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f12918,f12610,f19,f12920,f272]) ).
thf(f12918,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_3
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12336,f12612]) ).
thf(f12894,plain,
( spl0_108
| spl0_109
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f12885,f12610,f356,f282,f19,f12891,f12887]) ).
thf(f12885,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true)))))))))) )
| ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12884,f12612]) ).
thf(f12884,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$true))))))))) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))))))) = $true )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_101 ),
inference(forward_demodulation,[],[f12438,f12612]) ).
thf(f12438,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))))))) = $true )
| ~ spl0_3
| spl0_27
| ~ spl0_40 ),
inference(subsumption_resolution,[],[f12351,f11947]) ).
thf(f12351,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))))))) = $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f12347]) ).
thf(f12347,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))))))) )
| ~ spl0_3 ),
inference(constrained_superposition,[],[f21,f21]) ).
thf(f12813,plain,
( ~ spl0_59
| spl0_96
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f12810,f12299,f10956,f1089]) ).
thf(f12810,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| spl0_96
| ~ spl0_98 ),
inference(backward_demodulation,[],[f10957,f12301]) ).
thf(f12785,plain,
( spl0_44
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f12401,f4852,f2471,f1110,f1101,f762,f356,f282,f19,f702]) ).
thf(f12401,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12400,f12364]) ).
thf(f12364,plain,
( ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f12363,f11947]) ).
thf(f12363,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12362,f358]) ).
thf(f12362,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12361,f764]) ).
thf(f12361,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12360,f2472]) ).
thf(f12360,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12359,f1112]) ).
thf(f12359,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12358,f1112]) ).
thf(f12358,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12357,f1112]) ).
thf(f12357,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_3
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12336,f4854]) ).
thf(f12400,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_64
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f12399,f11947]) ).
thf(f12399,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_3
| ~ spl0_40
| ~ spl0_55
| ~ spl0_62
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12398,f358]) ).
thf(f12398,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_3
| ~ spl0_55
| ~ spl0_62
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12397,f764]) ).
thf(f12397,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_3
| ~ spl0_62
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12396,f2472]) ).
thf(f12396,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_3
| ~ spl0_62
| ~ spl0_64 ),
inference(forward_demodulation,[],[f12340,f1112]) ).
thf(f12340,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_3
| ~ spl0_62 ),
inference(superposition,[],[f21,f1102]) ).
thf(f12784,plain,
( spl0_47
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f12408,f4852,f2471,f1110,f762,f356,f282,f19,f718]) ).
thf(f12408,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12407,f12364]) ).
thf(f12407,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f12406,f11947]) ).
thf(f12406,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12405,f358]) ).
thf(f12405,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12404,f764]) ).
thf(f12404,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12403,f2472]) ).
thf(f12403,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_3
| ~ spl0_64 ),
inference(forward_demodulation,[],[f12341,f1112]) ).
thf(f12756,plain,
( spl0_68
| ~ spl0_25
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f12752,f287,f268,f1711]) ).
thf(f12752,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_25
| ~ spl0_28 ),
inference(backward_demodulation,[],[f289,f270]) ).
thf(f12729,plain,
( ~ spl0_3
| spl0_7
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_68
| ~ spl0_71
| ~ spl0_81
| spl0_94
| spl0_98 ),
inference(avatar_contradiction_clause,[],[f12728]) ).
thf(f12728,plain,
( $false
| ~ spl0_3
| spl0_7
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_68
| ~ spl0_71
| ~ spl0_81
| spl0_94
| spl0_98 ),
inference(subsumption_resolution,[],[f12644,f12690]) ).
thf(f12690,plain,
( ( vAPP($o,$o,f4,vAPP($o,$o,f4,x)) != $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_68
| ~ spl0_71
| ~ spl0_81
| spl0_94 ),
inference(subsumption_resolution,[],[f12565,f1713]) ).
thf(f12565,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,x)) != $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81
| spl0_94 ),
inference(constrained_superposition,[],[f8284,f12364]) ).
thf(f12644,plain,
( ( vAPP($o,$o,f4,vAPP($o,$o,f4,x)) = $false )
| ~ spl0_3
| spl0_7
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81
| spl0_98 ),
inference(subsumption_resolution,[],[f12643,f75]) ).
thf(f12643,plain,
( ( vAPP($o,$o,f4,x) = $false )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,x)) = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81
| spl0_98 ),
inference(subsumption_resolution,[],[f12592,f12300]) ).
thf(f12592,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ( vAPP($o,$o,f4,x) = $false )
| ( vAPP($o,$o,f4,vAPP($o,$o,f4,x)) = $false )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(binary_proxy_clausification,[],[f12556]) ).
thf(f12556,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ( vAPP($o,$o,f4,x) != vAPP($o,$o,f4,vAPP($o,$o,f4,x)) )
| ~ spl0_3
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71
| ~ spl0_81 ),
inference(constrained_superposition,[],[f12364,f12364]) ).
thf(f12297,plain,
( ~ spl0_15
| ~ spl0_21
| ~ spl0_53
| spl0_70
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f12296]) ).
thf(f12296,plain,
( $false
| ~ spl0_15
| ~ spl0_21
| ~ spl0_53
| spl0_70
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f12295,f2468]) ).
thf(f12295,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_15
| ~ spl0_21
| ~ spl0_53
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12294,f2472]) ).
thf(f12294,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_15
| ~ spl0_21
| ~ spl0_53 ),
inference(forward_demodulation,[],[f12293,f752]) ).
thf(f12293,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f139,f112]) ).
thf(f12292,plain,
( ~ spl0_15
| spl0_19
| ~ spl0_53
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f12291]) ).
thf(f12291,plain,
( $false
| ~ spl0_15
| spl0_19
| ~ spl0_53
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f12290,f2472]) ).
thf(f12290,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ~ spl0_15
| spl0_19
| ~ spl0_53 ),
inference(forward_demodulation,[],[f12289,f752]) ).
thf(f12289,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_15
| spl0_19 ),
inference(forward_demodulation,[],[f129,f112]) ).
thf(f129,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))) != $false )
| spl0_19 ),
inference(avatar_component_clause,[],[f128]) ).
thf(f12288,plain,
( ~ spl0_15
| ~ spl0_17
| spl0_70 ),
inference(avatar_contradiction_clause,[],[f12287]) ).
thf(f12287,plain,
( $false
| ~ spl0_15
| ~ spl0_17
| spl0_70 ),
inference(subsumption_resolution,[],[f12286,f2468]) ).
thf(f12286,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f121,f112]) ).
thf(f12240,plain,
( spl0_27
| ~ spl0_29
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f12239]) ).
thf(f12239,plain,
( $false
| spl0_27
| ~ spl0_29
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f12238,f11947]) ).
thf(f12238,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_29
| ~ spl0_40
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12237,f358]) ).
thf(f12237,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_29
| ~ spl0_55
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12236,f764]) ).
thf(f12236,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_29
| ~ spl0_64
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12235,f2472]) ).
thf(f12235,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_29
| ~ spl0_64 ),
inference(forward_demodulation,[],[f12234,f1112]) ).
thf(f12234,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_29
| ~ spl0_64 ),
inference(forward_demodulation,[],[f12230,f1112]) ).
thf(f12230,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_29
| ~ spl0_64 ),
inference(backward_demodulation,[],[f293,f1112]) ).
thf(f12221,plain,
( spl0_14
| ~ spl0_8
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f12220,f4852,f78,f105]) ).
thf(f12220,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_8
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12219,f4854]) ).
thf(f12219,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_8
| ~ spl0_81 ),
inference(forward_demodulation,[],[f12216,f4854]) ).
thf(f12216,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_8
| ~ spl0_81 ),
inference(backward_demodulation,[],[f80,f4854]) ).
thf(f12218,plain,
( spl0_14
| ~ spl0_12
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f12215,f4852,f96,f105]) ).
thf(f12215,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_12
| ~ spl0_81 ),
inference(backward_demodulation,[],[f98,f4854]) ).
thf(f12212,plain,
( ~ spl0_5
| ~ spl0_17
| spl0_70
| ~ spl0_91 ),
inference(avatar_contradiction_clause,[],[f12211]) ).
thf(f12211,plain,
( $false
| ~ spl0_5
| ~ spl0_17
| spl0_70
| ~ spl0_91 ),
inference(subsumption_resolution,[],[f12210,f2468]) ).
thf(f12210,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_5
| ~ spl0_17
| ~ spl0_91 ),
inference(backward_demodulation,[],[f12053,f7916]) ).
thf(f12053,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f121,f67]) ).
thf(f67,plain,
( ( x = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f12200,plain,
( spl0_91
| ~ spl0_5
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f12194,f110,f65,f7914]) ).
thf(f12194,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f112,f67]) ).
thf(f12153,plain,
( ~ spl0_12
| ~ spl0_40
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f12152]) ).
thf(f12152,plain,
( $false
| ~ spl0_12
| ~ spl0_40
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71 ),
inference(trivial_inequality_removal,[],[f12151]) ).
thf(f12151,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_40
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12150,f358]) ).
thf(f12150,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_12
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12149,f752]) ).
thf(f12149,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_12
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71 ),
inference(forward_demodulation,[],[f12148,f2472]) ).
thf(f12148,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_12
| ~ spl0_53
| ~ spl0_67 ),
inference(forward_demodulation,[],[f12137,f752]) ).
thf(f12137,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_12
| ~ spl0_67 ),
inference(backward_demodulation,[],[f98,f1557]) ).
thf(f11970,plain,
( spl0_80
| ~ spl0_91
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f11969,f10956,f7914,f4821]) ).
thf(f11969,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_91
| ~ spl0_96 ),
inference(backward_demodulation,[],[f7916,f10958]) ).
thf(f11936,plain,
( ~ spl0_32
| spl0_36
| ~ spl0_63
| ~ spl0_71
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f11935]) ).
thf(f11935,plain,
( $false
| ~ spl0_32
| spl0_36
| ~ spl0_63
| ~ spl0_71
| ~ spl0_77
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f11934,f2472]) ).
thf(f11934,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ~ spl0_32
| spl0_36
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f11931,f11896]) ).
thf(f11896,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f11895,f1107]) ).
thf(f11895,plain,
( ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f4804,f4808]) ).
thf(f11931,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_32
| spl0_36 ),
inference(backward_demodulation,[],[f338,f316]) ).
thf(f316,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f314]) ).
thf(f338,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))) )
| spl0_36 ),
inference(avatar_component_clause,[],[f337]) ).
thf(f11873,plain,
( ~ spl0_93
| spl0_26
| ~ spl0_63
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11813,f4852,f1105,f272,f8126]) ).
thf(f11813,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_26
| ~ spl0_63
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11812,f1107]) ).
thf(f11812,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_26
| ~ spl0_81 ),
inference(forward_demodulation,[],[f273,f4854]) ).
thf(f11800,plain,
( ~ spl0_34
| ~ spl0_40
| spl0_42
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f11799]) ).
thf(f11799,plain,
( $false
| ~ spl0_34
| ~ spl0_40
| spl0_42
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f11798,f358]) ).
thf(f11798,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| ~ spl0_34
| spl0_42
| ~ spl0_53 ),
inference(forward_demodulation,[],[f11796,f752]) ).
thf(f11796,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_34
| spl0_42 ),
inference(backward_demodulation,[],[f368,f328]) ).
thf(f11744,plain,
( ~ spl0_37
| ~ spl0_53
| ~ spl0_80
| spl0_90 ),
inference(avatar_split_clause,[],[f11743,f7776,f4821,f750,f341]) ).
thf(f7776,plain,
( spl0_90
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
thf(f11743,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_53
| ~ spl0_80
| spl0_90 ),
inference(forward_demodulation,[],[f11742,f752]) ).
thf(f11742,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_80
| spl0_90 ),
inference(forward_demodulation,[],[f7778,f4823]) ).
thf(f7778,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_90 ),
inference(avatar_component_clause,[],[f7776]) ).
thf(f11741,plain,
( ~ spl0_37
| ~ spl0_53
| ~ spl0_80
| spl0_93 ),
inference(avatar_split_clause,[],[f11740,f8126,f4821,f750,f341]) ).
thf(f11740,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_53
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f11739,f752]) ).
thf(f11739,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f11738,f4823]) ).
thf(f11738,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_80
| spl0_93 ),
inference(forward_demodulation,[],[f8128,f4823]) ).
thf(f11708,plain,
( ~ spl0_37
| ~ spl0_53
| spl0_89 ),
inference(avatar_split_clause,[],[f11635,f6948,f750,f341]) ).
thf(f11635,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_53
| spl0_89 ),
inference(forward_demodulation,[],[f6950,f752]) ).
thf(f6950,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_89 ),
inference(avatar_component_clause,[],[f6948]) ).
thf(f11663,plain,
( ~ spl0_63
| spl0_44
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f11657,f4806,f702,f1105]) ).
thf(f11657,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| spl0_44
| ~ spl0_78 ),
inference(backward_demodulation,[],[f703,f4808]) ).
thf(f703,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| spl0_44 ),
inference(avatar_component_clause,[],[f702]) ).
thf(f11661,plain,
( ~ spl0_59
| ~ spl0_78
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f11660]) ).
thf(f11660,plain,
( $false
| ~ spl0_59
| ~ spl0_78
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f11659]) ).
thf(f11659,plain,
( ( $true = $false )
| ~ spl0_59
| ~ spl0_78
| ~ spl0_81 ),
inference(backward_demodulation,[],[f4854,f11658]) ).
thf(f11658,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_59
| ~ spl0_78
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11655,f4854]) ).
thf(f11655,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$true)) )
| ~ spl0_59
| ~ spl0_78 ),
inference(backward_demodulation,[],[f1091,f4808]) ).
thf(f1091,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1089]) ).
thf(f11642,plain,
( ~ spl0_22
| spl0_40
| ~ spl0_53
| ~ spl0_79
| ~ spl0_93 ),
inference(avatar_contradiction_clause,[],[f11641]) ).
thf(f11641,plain,
( $false
| ~ spl0_22
| spl0_40
| ~ spl0_53
| ~ spl0_79
| ~ spl0_93 ),
inference(subsumption_resolution,[],[f11640,f357]) ).
thf(f11640,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_22
| ~ spl0_53
| ~ spl0_79
| ~ spl0_93 ),
inference(forward_demodulation,[],[f11639,f143]) ).
thf(f11639,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_22
| ~ spl0_53
| ~ spl0_79
| ~ spl0_93 ),
inference(forward_demodulation,[],[f11638,f143]) ).
thf(f11638,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_53
| ~ spl0_79
| ~ spl0_93 ),
inference(forward_demodulation,[],[f11513,f752]) ).
thf(f11513,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_79
| ~ spl0_93 ),
inference(forward_demodulation,[],[f8127,f4812]) ).
thf(f11633,plain,
( ~ spl0_76
| spl0_75
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11203,f4852,f3173,f4513]) ).
thf(f11203,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_75
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11202,f4854]) ).
thf(f11202,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_75
| ~ spl0_81 ),
inference(forward_demodulation,[],[f3174,f4854]) ).
thf(f11610,plain,
( spl0_14
| ~ spl0_10
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11251,f4852,f87,f105]) ).
thf(f11251,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_10
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11250,f4854]) ).
thf(f11250,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_10
| ~ spl0_81 ),
inference(forward_demodulation,[],[f89,f4854]) ).
thf(f11512,plain,
( ~ spl0_96
| ~ spl0_5
| spl0_13 ),
inference(avatar_split_clause,[],[f11376,f101,f65,f10956]) ).
thf(f11376,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| spl0_13 ),
inference(forward_demodulation,[],[f102,f67]) ).
thf(f11498,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_19
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f11497]) ).
thf(f11497,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_19
| ~ spl0_95 ),
inference(trivial_inequality_removal,[],[f11496]) ).
thf(f11496,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_19
| ~ spl0_95 ),
inference(backward_demodulation,[],[f11378,f8289]) ).
thf(f11378,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f11279,f11233]) ).
thf(f11233,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f130,f67]) ).
thf(f11279,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f16,f67]) ).
thf(f11495,plain,
( spl0_70
| ~ spl0_5
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f11377,f137,f128,f65,f2467]) ).
thf(f11377,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_5
| ~ spl0_19
| ~ spl0_21 ),
inference(backward_demodulation,[],[f11228,f11233]) ).
thf(f11228,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_demodulation,[],[f139,f67]) ).
thf(f11494,plain,
( ~ spl0_95
| spl0_4
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f11383,f128,f65,f23,f8287]) ).
thf(f11383,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_4
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f11270,f11233]) ).
thf(f11270,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f24,f67]) ).
thf(f11493,plain,
( spl0_29
| ~ spl0_26
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11221,f4852,f272,f291]) ).
thf(f11221,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ~ spl0_26
| ~ spl0_81 ),
inference(forward_demodulation,[],[f274,f4854]) ).
thf(f11403,plain,
( ~ spl0_20
| ~ spl0_22
| ~ spl0_26
| spl0_40
| ~ spl0_64
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f11402]) ).
thf(f11402,plain,
( $false
| ~ spl0_20
| ~ spl0_22
| ~ spl0_26
| spl0_40
| ~ spl0_64
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f11401,f357]) ).
thf(f11401,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_20
| ~ spl0_22
| ~ spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11400,f143]) ).
thf(f11400,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_20
| ~ spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11224,f134]) ).
thf(f134,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f132,plain,
( spl0_20
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f11224,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11223,f1112]) ).
thf(f11223,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11222,f1112]) ).
thf(f11222,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11221,f1112]) ).
thf(f11392,plain,
( spl0_16
| ~ spl0_14
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f11372,f1110,f105,f114]) ).
thf(f11372,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_14
| ~ spl0_64 ),
inference(forward_demodulation,[],[f107,f1112]) ).
thf(f107,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f105]) ).
thf(f11391,plain,
( ~ spl0_50
| spl0_48
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f11390,f1110,f722,f733]) ).
thf(f722,plain,
( spl0_48
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
thf(f11390,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_48
| ~ spl0_64 ),
inference(forward_demodulation,[],[f723,f1112]) ).
thf(f723,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_48 ),
inference(avatar_component_clause,[],[f722]) ).
thf(f11389,plain,
( ~ spl0_50
| spl0_45
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f11388,f1110,f706,f733]) ).
thf(f706,plain,
( spl0_45
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
thf(f11388,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_45
| ~ spl0_64 ),
inference(forward_demodulation,[],[f11387,f1112]) ).
thf(f11387,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_45
| ~ spl0_64 ),
inference(forward_demodulation,[],[f707,f1112]) ).
thf(f707,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_45 ),
inference(avatar_component_clause,[],[f706]) ).
thf(f11382,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_19
| ~ spl0_41
| ~ spl0_42
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f11381]) ).
thf(f11381,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_19
| ~ spl0_41
| ~ spl0_42
| ~ spl0_70 ),
inference(trivial_inequality_removal,[],[f11380]) ).
thf(f11380,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_19
| ~ spl0_41
| ~ spl0_42
| ~ spl0_70 ),
inference(forward_demodulation,[],[f11379,f11218]) ).
thf(f11218,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_41
| ~ spl0_42 ),
inference(backward_demodulation,[],[f364,f369]) ).
thf(f11379,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_19
| ~ spl0_70 ),
inference(forward_demodulation,[],[f11378,f2469]) ).
thf(f11331,plain,
( ~ spl0_64
| spl0_77
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f11330]) ).
thf(f11330,plain,
( $false
| ~ spl0_64
| spl0_77
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f11329,f1112]) ).
thf(f11329,plain,
( ( $true != vAPP($o,$o,f2,$true) )
| ~ spl0_64
| spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f11328,f1112]) ).
thf(f11328,plain,
( ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f4803,f4808]) ).
thf(f4803,plain,
( ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_77 ),
inference(avatar_component_clause,[],[f4802]) ).
thf(f11316,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_17
| ~ spl0_41
| ~ spl0_42
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f11315]) ).
thf(f11315,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_17
| ~ spl0_41
| ~ spl0_42
| ~ spl0_70 ),
inference(trivial_inequality_removal,[],[f11314]) ).
thf(f11314,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_17
| ~ spl0_41
| ~ spl0_42
| ~ spl0_70 ),
inference(forward_demodulation,[],[f11313,f11218]) ).
thf(f11313,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_17
| ~ spl0_70 ),
inference(forward_demodulation,[],[f11312,f2469]) ).
thf(f11312,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_17
| ~ spl0_70 ),
inference(forward_demodulation,[],[f11307,f2469]) ).
thf(f11307,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_17 ),
inference(backward_demodulation,[],[f11279,f11237]) ).
thf(f11237,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f121,f67]) ).
thf(f11294,plain,
( spl0_37
| ~ spl0_26
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11225,f4852,f1116,f1110,f745,f272,f341]) ).
thf(f11225,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_26
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11224,f10991]) ).
thf(f10991,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65 ),
inference(forward_demodulation,[],[f10990,f1112]) ).
thf(f10990,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65 ),
inference(forward_demodulation,[],[f10988,f1112]) ).
thf(f10988,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_52
| ~ spl0_65 ),
inference(backward_demodulation,[],[f746,f1118]) ).
thf(f11292,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11255,f4852,f1116,f1110,f745,f87,f141]) ).
thf(f11255,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_10
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11254,f10991]) ).
thf(f11254,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_10
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11253,f10991]) ).
thf(f11253,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_10
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11252,f10991]) ).
thf(f11252,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_10
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11251,f1112]) ).
thf(f11290,plain,
( spl0_40
| ~ spl0_3
| ~ spl0_5
| ~ spl0_42
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f11278,f762,f367,f65,f19,f356]) ).
thf(f11278,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_42
| ~ spl0_55 ),
inference(forward_demodulation,[],[f11277,f764]) ).
thf(f11277,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_42 ),
inference(forward_demodulation,[],[f11276,f369]) ).
thf(f11276,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f21,f67]) ).
thf(f11269,plain,
( ~ spl0_8
| ~ spl0_40
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f11268]) ).
thf(f11268,plain,
( $false
| ~ spl0_8
| ~ spl0_40
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f11267]) ).
thf(f11267,plain,
( ( $true = $false )
| ~ spl0_8
| ~ spl0_40
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11266,f358]) ).
thf(f11266,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_8
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11265,f10991]) ).
thf(f11265,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_8
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11264,f10991]) ).
thf(f11264,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_8
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11263,f10991]) ).
thf(f11263,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_8
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11262,f1112]) ).
thf(f11262,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_8
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11261,f4854]) ).
thf(f11261,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_8
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11260,f4854]) ).
thf(f11260,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_8
| ~ spl0_81 ),
inference(forward_demodulation,[],[f80,f4854]) ).
thf(f11258,plain,
( ~ spl0_10
| ~ spl0_40
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f11257]) ).
thf(f11257,plain,
( $false
| ~ spl0_10
| ~ spl0_40
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(trivial_inequality_removal,[],[f11256]) ).
thf(f11256,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_40
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11255,f358]) ).
thf(f11138,plain,
( ~ spl0_5
| spl0_17
| ~ spl0_70
| ~ spl0_80
| ~ spl0_96 ),
inference(avatar_contradiction_clause,[],[f11137]) ).
thf(f11137,plain,
( $false
| ~ spl0_5
| spl0_17
| ~ spl0_70
| ~ spl0_80
| ~ spl0_96 ),
inference(subsumption_resolution,[],[f11120,f2469]) ).
thf(f11120,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_5
| spl0_17
| ~ spl0_80
| ~ spl0_96 ),
inference(backward_demodulation,[],[f11096,f4823]) ).
thf(f11096,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_5
| spl0_17
| ~ spl0_96 ),
inference(backward_demodulation,[],[f10517,f10958]) ).
thf(f10517,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| spl0_17 ),
inference(forward_demodulation,[],[f120,f67]) ).
thf(f11136,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_80
| ~ spl0_96 ),
inference(avatar_contradiction_clause,[],[f11135]) ).
thf(f11135,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_80
| ~ spl0_96 ),
inference(subsumption_resolution,[],[f11134,f10291]) ).
thf(f10291,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f283,f358]) ).
thf(f11134,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_70
| ~ spl0_80
| ~ spl0_96 ),
inference(forward_demodulation,[],[f11133,f2469]) ).
thf(f11133,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_70
| ~ spl0_80
| ~ spl0_96 ),
inference(forward_demodulation,[],[f11132,f2469]) ).
thf(f11132,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_70
| ~ spl0_80
| ~ spl0_96 ),
inference(forward_demodulation,[],[f11119,f2469]) ).
thf(f11119,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_80
| ~ spl0_96 ),
inference(backward_demodulation,[],[f11095,f4823]) ).
thf(f11095,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_96 ),
inference(backward_demodulation,[],[f10467,f10958]) ).
thf(f10467,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f25,f67]) ).
thf(f11111,plain,
( ~ spl0_80
| spl0_91
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f11093,f10956,f7914,f4821]) ).
thf(f11093,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_91
| ~ spl0_96 ),
inference(backward_demodulation,[],[f7915,f10958]) ).
thf(f7915,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| spl0_91 ),
inference(avatar_component_clause,[],[f7914]) ).
thf(f11110,plain,
( ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| spl0_85 ),
inference(avatar_contradiction_clause,[],[f11109]) ).
thf(f11109,plain,
( $false
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| spl0_85 ),
inference(subsumption_resolution,[],[f11108,f10991]) ).
thf(f11108,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_65
| spl0_85 ),
inference(forward_demodulation,[],[f5872,f10991]) ).
thf(f11068,plain,
( ~ spl0_35
| spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11017,f4852,f1110,f272,f330]) ).
thf(f11017,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11016,f1112]) ).
thf(f11016,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11015,f1112]) ).
thf(f11015,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11009,f1112]) ).
thf(f11009,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_26
| ~ spl0_81 ),
inference(backward_demodulation,[],[f273,f4854]) ).
thf(f11067,plain,
( spl0_92
| ~ spl0_64
| ~ spl0_74
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11024,f4852,f3168,f1110,f7918]) ).
thf(f11024,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_64
| ~ spl0_74
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11012,f1112]) ).
thf(f11012,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_74
| ~ spl0_81 ),
inference(backward_demodulation,[],[f3170,f4854]) ).
thf(f11066,plain,
( spl0_92
| ~ spl0_64
| ~ spl0_75
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11029,f4852,f3173,f1110,f7918]) ).
thf(f11029,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_64
| ~ spl0_75
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11028,f1112]) ).
thf(f11028,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_75
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11013,f4854]) ).
thf(f11013,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_75
| ~ spl0_81 ),
inference(backward_demodulation,[],[f3175,f4854]) ).
thf(f3175,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f3173]) ).
thf(f11065,plain,
( spl0_92
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_64
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f11035,f4852,f1110,f74,f65,f23,f7918]) ).
thf(f11035,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11034,f1112]) ).
thf(f11034,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11033,f4854]) ).
thf(f11033,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_81 ),
inference(forward_demodulation,[],[f11014,f4854]) ).
thf(f11014,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_81 ),
inference(backward_demodulation,[],[f10539,f4854]) ).
thf(f10539,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7 ),
inference(subsumption_resolution,[],[f10519,f6228]) ).
thf(f6228,plain,
( ( $false != vAPP($o,$o,f4,$false) )
| ~ spl0_5
| spl0_7 ),
inference(forward_demodulation,[],[f75,f67]) ).
thf(f10519,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ( $false = vAPP($o,$o,f4,$false) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f10467,f4]) ).
thf(f11064,plain,
( ~ spl0_35
| ~ spl0_65
| ~ spl0_68
| spl0_90 ),
inference(avatar_split_clause,[],[f11044,f7776,f1711,f1116,f330]) ).
thf(f11044,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_65
| ~ spl0_68
| spl0_90 ),
inference(backward_demodulation,[],[f7778,f11041]) ).
thf(f11041,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_65
| ~ spl0_68 ),
inference(backward_demodulation,[],[f1118,f1713]) ).
thf(f11008,plain,
( spl0_96
| ~ spl0_5
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f10745,f101,f65,f10956]) ).
thf(f10745,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f103,f67]) ).
thf(f10959,plain,
( spl0_96
| spl0_92
| ~ spl0_4
| ~ spl0_5
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f10711,f1110,f65,f23,f7918,f10956]) ).
thf(f10711,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_64 ),
inference(forward_demodulation,[],[f10525,f1112]) ).
thf(f10525,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f10467,f4]) ).
thf(f10954,plain,
( ~ spl0_28
| ~ spl0_34
| spl0_79
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f10953]) ).
thf(f10953,plain,
( $false
| ~ spl0_28
| ~ spl0_34
| spl0_79
| spl0_80 ),
inference(subsumption_resolution,[],[f10952,f4811]) ).
thf(f4811,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| spl0_79 ),
inference(avatar_component_clause,[],[f4810]) ).
thf(f10952,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_28
| ~ spl0_34
| spl0_79
| spl0_80 ),
inference(subsumption_resolution,[],[f10911,f4822]) ).
thf(f10911,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_28
| ~ spl0_34
| spl0_79 ),
inference(binary_proxy_clausification,[],[f10909]) ).
thf(f10909,plain,
( ( vAPP($o,$o,f2,$false) != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_28
| ~ spl0_34
| spl0_79 ),
inference(trivial_inequality_removal,[],[f10908]) ).
thf(f10908,plain,
( ( $false != $false )
| ( vAPP($o,$o,f2,$false) != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_28
| ~ spl0_34
| spl0_79 ),
inference(constrained_superposition,[],[f4811,f10840]) ).
thf(f10840,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_28
| ~ spl0_34 ),
inference(backward_demodulation,[],[f328,f289]) ).
thf(f10932,plain,
( ~ spl0_28
| ~ spl0_34
| ~ spl0_62
| spl0_63
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f10931]) ).
thf(f10931,plain,
( $false
| ~ spl0_28
| ~ spl0_34
| ~ spl0_62
| spl0_63
| spl0_80 ),
inference(subsumption_resolution,[],[f10930,f4822]) ).
thf(f10930,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_28
| ~ spl0_34
| ~ spl0_62
| spl0_63 ),
inference(subsumption_resolution,[],[f10891,f1106]) ).
thf(f10891,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_28
| ~ spl0_34
| ~ spl0_62 ),
inference(superposition,[],[f10840,f1102]) ).
thf(f10837,plain,
( ~ spl0_5
| spl0_7
| spl0_25
| spl0_28
| ~ spl0_94 ),
inference(avatar_contradiction_clause,[],[f10836]) ).
thf(f10836,plain,
( $false
| ~ spl0_5
| spl0_7
| spl0_25
| spl0_28
| ~ spl0_94 ),
inference(subsumption_resolution,[],[f10835,f10627]) ).
thf(f10627,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$true)) )
| ~ spl0_5
| spl0_7
| spl0_25 ),
inference(subsumption_resolution,[],[f10624,f6228]) ).
thf(f10624,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$true)) )
| ( $false = vAPP($o,$o,f4,$false) )
| spl0_25 ),
inference(superposition,[],[f269,f4]) ).
thf(f10835,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$true)) )
| ~ spl0_5
| spl0_7
| spl0_28
| ~ spl0_94 ),
inference(forward_demodulation,[],[f10834,f10825]) ).
thf(f10825,plain,
( ( $true = vAPP($o,$o,f4,$false) )
| ~ spl0_5
| spl0_7
| spl0_28
| ~ spl0_94 ),
inference(subsumption_resolution,[],[f10814,f10816]) ).
thf(f10816,plain,
( ( $true != vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| spl0_7
| spl0_28
| ~ spl0_94 ),
inference(trivial_inequality_removal,[],[f10810]) ).
thf(f10810,plain,
( ( $false != $false )
| ( $true != vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| spl0_7
| spl0_28
| ~ spl0_94 ),
inference(constrained_superposition,[],[f288,f10715]) ).
thf(f10715,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_5
| spl0_7
| ~ spl0_94 ),
inference(subsumption_resolution,[],[f10697,f6228]) ).
thf(f10697,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f4,$false) )
| ~ spl0_94 ),
inference(superposition,[],[f8285,f4]) ).
thf(f10814,plain,
( ( $true = vAPP($o,$o,f4,$false) )
| ( $true = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| spl0_28
| ~ spl0_94 ),
inference(binary_proxy_clausification,[],[f10813]) ).
thf(f10813,plain,
( ( vAPP($o,$o,f4,$false) != vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| spl0_28
| ~ spl0_94 ),
inference(trivial_inequality_removal,[],[f10811]) ).
thf(f10811,plain,
( ( $false != $false )
| ( vAPP($o,$o,f4,$false) != vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| spl0_28
| ~ spl0_94 ),
inference(constrained_superposition,[],[f288,f8285]) ).
thf(f10834,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| spl0_7
| spl0_28
| ~ spl0_94 ),
inference(subsumption_resolution,[],[f10815,f6228]) ).
thf(f10815,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| spl0_28
| ~ spl0_94 ),
inference(binary_proxy_clausification,[],[f10813]) ).
thf(f10824,plain,
( ~ spl0_5
| spl0_7
| spl0_25
| spl0_28
| ~ spl0_94 ),
inference(avatar_contradiction_clause,[],[f10823]) ).
thf(f10823,plain,
( $false
| ~ spl0_5
| spl0_7
| spl0_25
| spl0_28
| ~ spl0_94 ),
inference(subsumption_resolution,[],[f10817,f269]) ).
thf(f10817,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| spl0_7
| spl0_28
| ~ spl0_94 ),
inference(trivial_inequality_removal,[],[f10808]) ).
thf(f10808,plain,
( ( $false != $false )
| ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| spl0_7
| spl0_28
| ~ spl0_94 ),
inference(superposition,[],[f288,f10749]) ).
thf(f10749,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f3,X0) )
| ( $false = X0 ) )
| ~ spl0_5
| spl0_7
| ~ spl0_94 ),
inference(superposition,[],[f10715,f4]) ).
thf(f10710,plain,
( ~ spl0_5
| spl0_7
| spl0_66
| ~ spl0_78
| ~ spl0_94 ),
inference(avatar_contradiction_clause,[],[f10709]) ).
thf(f10709,plain,
( $false
| ~ spl0_5
| spl0_7
| spl0_66
| ~ spl0_78
| ~ spl0_94 ),
inference(subsumption_resolution,[],[f10708,f6228]) ).
thf(f10708,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| spl0_66
| ~ spl0_78
| ~ spl0_94 ),
inference(subsumption_resolution,[],[f10697,f10331]) ).
thf(f10331,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| spl0_66
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1552,f4808]) ).
thf(f10678,plain,
( ~ spl0_94
| ~ spl0_5
| spl0_9 ),
inference(avatar_split_clause,[],[f10223,f83,f65,f8283]) ).
thf(f10223,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_9 ),
inference(forward_demodulation,[],[f84,f67]) ).
thf(f10668,plain,
( spl0_61
| ~ spl0_78
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f10667]) ).
thf(f10667,plain,
( $false
| spl0_61
| ~ spl0_78
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f10646,f4854]) ).
thf(f10646,plain,
( ( $true != vAPP($o,$o,f3,$true) )
| spl0_61
| ~ spl0_78
| ~ spl0_81 ),
inference(backward_demodulation,[],[f10408,f4854]) ).
thf(f10408,plain,
( ( $true != vAPP($o,$o,f3,vAPP($o,$o,f3,$true)) )
| spl0_61
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1098,f4808]) ).
thf(f1098,plain,
( ( $true != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| spl0_61 ),
inference(avatar_component_clause,[],[f1097]) ).
thf(f10656,plain,
( spl0_26
| ~ spl0_40
| ~ spl0_52
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f10655]) ).
thf(f10655,plain,
( $false
| spl0_26
| ~ spl0_40
| ~ spl0_52
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f10654,f358]) ).
thf(f10654,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_26
| ~ spl0_40
| ~ spl0_52
| ~ spl0_55
| ~ spl0_64
| ~ spl0_78
| ~ spl0_81 ),
inference(forward_demodulation,[],[f10653,f764]) ).
thf(f10653,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_26
| ~ spl0_40
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| ~ spl0_81 ),
inference(forward_demodulation,[],[f10652,f358]) ).
thf(f10652,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| spl0_26
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| ~ spl0_81 ),
inference(forward_demodulation,[],[f10651,f10581]) ).
thf(f10581,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10580,f1112]) ).
thf(f10580,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10579,f1112]) ).
thf(f10579,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10578,f1112]) ).
thf(f10578,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_52
| ~ spl0_78 ),
inference(forward_demodulation,[],[f746,f4808]) ).
thf(f10651,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f10650,f1112]) ).
thf(f10650,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f10649,f1112]) ).
thf(f10649,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_26
| ~ spl0_64
| ~ spl0_81 ),
inference(forward_demodulation,[],[f10640,f1112]) ).
thf(f10640,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_26
| ~ spl0_81 ),
inference(backward_demodulation,[],[f273,f4854]) ).
thf(f10639,plain,
( ~ spl0_5
| spl0_7
| spl0_81
| spl0_94 ),
inference(avatar_contradiction_clause,[],[f10638]) ).
thf(f10638,plain,
( $false
| ~ spl0_5
| spl0_7
| spl0_81
| spl0_94 ),
inference(subsumption_resolution,[],[f10631,f10322]) ).
thf(f10322,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ~ spl0_5
| spl0_7
| spl0_94 ),
inference(subsumption_resolution,[],[f10315,f6228]) ).
thf(f10315,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f4,$false) )
| spl0_94 ),
inference(superposition,[],[f8284,f4]) ).
thf(f10631,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| spl0_81 ),
inference(trivial_inequality_removal,[],[f10630]) ).
thf(f10630,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f3,$true) )
| spl0_81 ),
inference(superposition,[],[f4853,f4]) ).
thf(f10620,plain,
( spl0_62
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f10619,f1110,f1101]) ).
thf(f10619,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f2,X0) )
| ( $false = X0 ) )
| ~ spl0_64 ),
inference(duplicate_literal_removal,[],[f10617]) ).
thf(f10617,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f2,X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl0_64 ),
inference(binary_proxy_clausification,[],[f10612]) ).
thf(f10612,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f2,X0) = X0 )
| ( $false = X0 ) )
| ~ spl0_64 ),
inference(superposition,[],[f1112,f4]) ).
thf(f10592,plain,
( ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| spl0_85 ),
inference(avatar_contradiction_clause,[],[f10591]) ).
thf(f10591,plain,
( $false
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| spl0_85 ),
inference(subsumption_resolution,[],[f10585,f10581]) ).
thf(f10585,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| spl0_85 ),
inference(backward_demodulation,[],[f5872,f10581]) ).
thf(f10590,plain,
( ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| spl0_84 ),
inference(avatar_contradiction_clause,[],[f10589]) ).
thf(f10589,plain,
( $false
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| spl0_84 ),
inference(subsumption_resolution,[],[f10588,f10581]) ).
thf(f10588,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| spl0_84 ),
inference(forward_demodulation,[],[f10584,f10581]) ).
thf(f10584,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_52
| ~ spl0_64
| ~ spl0_78
| spl0_84 ),
inference(backward_demodulation,[],[f5868,f10581]) ).
thf(f5868,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_84 ),
inference(avatar_component_clause,[],[f5867]) ).
thf(f10577,plain,
( spl0_52
| ~ spl0_64
| spl0_71
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f10576]) ).
thf(f10576,plain,
( $false
| spl0_52
| ~ spl0_64
| spl0_71
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f10569,f2473]) ).
thf(f2473,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| spl0_71 ),
inference(avatar_component_clause,[],[f2471]) ).
thf(f10569,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| spl0_52
| ~ spl0_64
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f10568]) ).
thf(f10568,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f1,$true) )
| spl0_52
| ~ spl0_64
| ~ spl0_78 ),
inference(superposition,[],[f10378,f4]) ).
thf(f10378,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| spl0_52
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10377,f1112]) ).
thf(f10377,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| spl0_52
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10359,f1112]) ).
thf(f10359,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| spl0_52
| ~ spl0_64
| ~ spl0_78 ),
inference(backward_demodulation,[],[f10143,f1112]) ).
thf(f10143,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_52
| ~ spl0_78 ),
inference(forward_demodulation,[],[f747,f4808]) ).
thf(f747,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| spl0_52 ),
inference(avatar_component_clause,[],[f745]) ).
thf(f10516,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_21
| spl0_27
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f10515]) ).
thf(f10515,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_21
| spl0_27
| ~ spl0_40 ),
inference(subsumption_resolution,[],[f10514,f10291]) ).
thf(f10514,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_demodulation,[],[f10467,f10199]) ).
thf(f10199,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_demodulation,[],[f139,f67]) ).
thf(f10497,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| spl0_27
| ~ spl0_40
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f10496]) ).
thf(f10496,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| spl0_27
| ~ spl0_40
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f10495,f10291]) ).
thf(f10495,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| ~ spl0_70 ),
inference(forward_demodulation,[],[f10494,f2469]) ).
thf(f10494,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| ~ spl0_70 ),
inference(forward_demodulation,[],[f10491,f2469]) ).
thf(f10491,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17 ),
inference(backward_demodulation,[],[f10467,f10206]) ).
thf(f10206,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f121,f67]) ).
thf(f10484,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_55
| ~ spl0_70
| ~ spl0_91 ),
inference(avatar_contradiction_clause,[],[f10483]) ).
thf(f10483,plain,
( $false
| spl0_2
| ~ spl0_5
| ~ spl0_55
| ~ spl0_70
| ~ spl0_91 ),
inference(subsumption_resolution,[],[f10482,f764]) ).
thf(f10482,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_2
| ~ spl0_5
| ~ spl0_70
| ~ spl0_91 ),
inference(forward_demodulation,[],[f10481,f2469]) ).
thf(f10481,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_2
| ~ spl0_5
| ~ spl0_70
| ~ spl0_91 ),
inference(forward_demodulation,[],[f10480,f2469]) ).
thf(f10480,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_2
| ~ spl0_5
| ~ spl0_70
| ~ spl0_91 ),
inference(forward_demodulation,[],[f10479,f2469]) ).
thf(f10479,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_2
| ~ spl0_5
| ~ spl0_91 ),
inference(forward_demodulation,[],[f10478,f7916]) ).
thf(f10478,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f15,f67]) ).
thf(f10459,plain,
( ~ spl0_5
| spl0_19
| ~ spl0_70
| ~ spl0_91 ),
inference(avatar_contradiction_clause,[],[f10458]) ).
thf(f10458,plain,
( $false
| ~ spl0_5
| spl0_19
| ~ spl0_70
| ~ spl0_91 ),
inference(subsumption_resolution,[],[f10457,f2469]) ).
thf(f10457,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_5
| spl0_19
| ~ spl0_70
| ~ spl0_91 ),
inference(forward_demodulation,[],[f10456,f2469]) ).
thf(f10456,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_5
| spl0_19
| ~ spl0_91 ),
inference(forward_demodulation,[],[f10455,f7916]) ).
thf(f10455,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| spl0_19 ),
inference(forward_demodulation,[],[f129,f67]) ).
thf(f10423,plain,
( ~ spl0_20
| spl0_58
| ~ spl0_64
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f10394,f4806,f1110,f780,f132]) ).
thf(f10394,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_58
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10393,f1112]) ).
thf(f10393,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| spl0_58
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10365,f1112]) ).
thf(f10365,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_58
| ~ spl0_64
| ~ spl0_78 ),
inference(backward_demodulation,[],[f10286,f1112]) ).
thf(f10286,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| spl0_58
| ~ spl0_78 ),
inference(forward_demodulation,[],[f782,f4808]) ).
thf(f782,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| spl0_58 ),
inference(avatar_component_clause,[],[f780]) ).
thf(f10422,plain,
( spl0_73
| ~ spl0_57
| ~ spl0_64
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f10412,f4806,f1110,f774,f3150]) ).
thf(f10412,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_57
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10411,f1112]) ).
thf(f10411,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| ~ spl0_57
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10410,f1112]) ).
thf(f10410,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_57
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10409,f1112]) ).
thf(f10409,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| ~ spl0_57
| ~ spl0_78 ),
inference(forward_demodulation,[],[f776,f4808]) ).
thf(f10390,plain,
( spl0_57
| ~ spl0_64
| ~ spl0_73
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f10389]) ).
thf(f10389,plain,
( $false
| spl0_57
| ~ spl0_64
| ~ spl0_73
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f10388,f3152]) ).
thf(f10388,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_57
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10387,f1112]) ).
thf(f10387,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))) )
| spl0_57
| ~ spl0_64
| ~ spl0_78 ),
inference(forward_demodulation,[],[f10363,f1112]) ).
thf(f10363,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_57
| ~ spl0_64
| ~ spl0_78 ),
inference(backward_demodulation,[],[f10172,f1112]) ).
thf(f10172,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))) )
| spl0_57
| ~ spl0_78 ),
inference(forward_demodulation,[],[f775,f4808]) ).
thf(f10353,plain,
( spl0_63
| spl0_64 ),
inference(avatar_contradiction_clause,[],[f10352]) ).
thf(f10352,plain,
( $false
| spl0_63
| spl0_64 ),
inference(subsumption_resolution,[],[f10346,f1106]) ).
thf(f10346,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| spl0_64 ),
inference(trivial_inequality_removal,[],[f10345]) ).
thf(f10345,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f2,$true) )
| spl0_64 ),
inference(superposition,[],[f1111,f4]) ).
thf(f1111,plain,
( ( $true != vAPP($o,$o,f2,$true) )
| spl0_64 ),
inference(avatar_component_clause,[],[f1110]) ).
thf(f10321,plain,
( ~ spl0_5
| spl0_7
| ~ spl0_66
| ~ spl0_78
| spl0_94 ),
inference(avatar_contradiction_clause,[],[f10320]) ).
thf(f10320,plain,
( $false
| ~ spl0_5
| spl0_7
| ~ spl0_66
| ~ spl0_78
| spl0_94 ),
inference(subsumption_resolution,[],[f10319,f6228]) ).
thf(f10319,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ~ spl0_66
| ~ spl0_78
| spl0_94 ),
inference(subsumption_resolution,[],[f10315,f10129]) ).
thf(f10129,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_66
| ~ spl0_78 ),
inference(backward_demodulation,[],[f1553,f4808]) ).
thf(f10173,plain,
( ~ spl0_86
| ~ spl0_5
| spl0_11 ),
inference(avatar_split_clause,[],[f10156,f92,f65,f6547]) ).
thf(f10156,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| spl0_11 ),
inference(forward_demodulation,[],[f93,f67]) ).
thf(f10166,plain,
( spl0_35
| spl0_55
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f10165]) ).
thf(f10165,plain,
( $false
| spl0_35
| spl0_55
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f10164,f10009]) ).
thf(f10009,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| spl0_55 ),
inference(trivial_inequality_removal,[],[f10008]) ).
thf(f10008,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f0,$false) )
| spl0_55 ),
inference(superposition,[],[f763,f4]) ).
thf(f763,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_55 ),
inference(avatar_component_clause,[],[f762]) ).
thf(f10164,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_35
| spl0_55
| ~ spl0_73 ),
inference(forward_demodulation,[],[f10162,f10009]) ).
thf(f10162,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_35
| ~ spl0_73 ),
inference(backward_demodulation,[],[f331,f3152]) ).
thf(f331,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_35 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f10155,plain,
( ~ spl0_28
| spl0_32
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f10154]) ).
thf(f10154,plain,
( $false
| ~ spl0_28
| spl0_32
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f10153,f4812]) ).
thf(f10153,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_28
| spl0_32 ),
inference(forward_demodulation,[],[f315,f289]) ).
thf(f10115,plain,
( spl0_55
| spl0_56
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[],[f10114]) ).
thf(f10114,plain,
( $false
| spl0_55
| spl0_56
| ~ spl0_57 ),
inference(subsumption_resolution,[],[f10112,f10009]) ).
thf(f10112,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_56
| ~ spl0_57 ),
inference(backward_demodulation,[],[f769,f776]) ).
thf(f769,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))))) )
| spl0_56 ),
inference(avatar_component_clause,[],[f768]) ).
thf(f10061,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_42
| spl0_55 ),
inference(avatar_contradiction_clause,[],[f10060]) ).
thf(f10060,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_42
| spl0_55 ),
inference(subsumption_resolution,[],[f10059,f10009]) ).
thf(f10059,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_3
| ~ spl0_5
| ~ spl0_42
| spl0_55 ),
inference(forward_demodulation,[],[f10056,f10009]) ).
thf(f10056,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_3
| ~ spl0_5
| ~ spl0_42 ),
inference(backward_demodulation,[],[f9848,f369]) ).
thf(f9848,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f20,f67]) ).
thf(f10022,plain,
( spl0_55
| ~ spl0_70
| spl0_95 ),
inference(avatar_contradiction_clause,[],[f10021]) ).
thf(f10021,plain,
( $false
| spl0_55
| ~ spl0_70
| spl0_95 ),
inference(subsumption_resolution,[],[f9608,f10009]) ).
thf(f9608,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_70
| spl0_95 ),
inference(forward_demodulation,[],[f8288,f2469]) ).
thf(f10020,plain,
( spl0_55
| ~ spl0_63
| ~ spl0_70
| spl0_76 ),
inference(avatar_contradiction_clause,[],[f10019]) ).
thf(f10019,plain,
( $false
| spl0_55
| ~ spl0_63
| ~ spl0_70
| spl0_76 ),
inference(subsumption_resolution,[],[f9660,f10009]) ).
thf(f9660,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_63
| ~ spl0_70
| spl0_76 ),
inference(forward_demodulation,[],[f9659,f2469]) ).
thf(f9659,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_63
| ~ spl0_70
| spl0_76 ),
inference(forward_demodulation,[],[f9658,f2469]) ).
thf(f9658,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_63
| ~ spl0_70
| spl0_76 ),
inference(forward_demodulation,[],[f9657,f2469]) ).
thf(f9657,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_63
| spl0_76 ),
inference(forward_demodulation,[],[f4514,f1107]) ).
thf(f4514,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_76 ),
inference(avatar_component_clause,[],[f4513]) ).
thf(f10012,plain,
( spl0_27
| ~ spl0_40
| spl0_55 ),
inference(avatar_contradiction_clause,[],[f10011]) ).
thf(f10011,plain,
( $false
| spl0_27
| ~ spl0_40
| spl0_55 ),
inference(subsumption_resolution,[],[f10009,f9620]) ).
thf(f9620,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f283,f358]) ).
thf(f9741,plain,
( ~ spl0_26
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_63
| ~ spl0_65
| ~ spl0_67
| ~ spl0_68
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f9740]) ).
thf(f9740,plain,
( $false
| ~ spl0_26
| spl0_27
| ~ spl0_40
| ~ spl0_55
| ~ spl0_63
| ~ spl0_65
| ~ spl0_67
| ~ spl0_68
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f9739,f9620]) ).
thf(f9739,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_26
| ~ spl0_40
| ~ spl0_55
| ~ spl0_63
| ~ spl0_65
| ~ spl0_67
| ~ spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9738,f358]) ).
thf(f9738,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_26
| ~ spl0_55
| ~ spl0_63
| ~ spl0_65
| ~ spl0_67
| ~ spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9737,f764]) ).
thf(f9737,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_67
| ~ spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9736,f2469]) ).
thf(f9736,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_67
| ~ spl0_68 ),
inference(forward_demodulation,[],[f9735,f1107]) ).
thf(f9735,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_26
| ~ spl0_65
| ~ spl0_67
| ~ spl0_68 ),
inference(forward_demodulation,[],[f9734,f9668]) ).
thf(f9668,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f1118,f1713]) ).
thf(f9734,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_26
| ~ spl0_67 ),
inference(forward_demodulation,[],[f274,f1557]) ).
thf(f9715,plain,
( spl0_27
| ~ spl0_36
| ~ spl0_40
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f9714]) ).
thf(f9714,plain,
( $false
| spl0_27
| ~ spl0_36
| ~ spl0_40
| ~ spl0_42 ),
inference(subsumption_resolution,[],[f9713,f9620]) ).
thf(f9713,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_36
| ~ spl0_42 ),
inference(forward_demodulation,[],[f369,f339]) ).
thf(f9694,plain,
( spl0_37
| ~ spl0_40
| ~ spl0_55 ),
inference(avatar_contradiction_clause,[],[f9693]) ).
thf(f9693,plain,
( $false
| spl0_37
| ~ spl0_40
| ~ spl0_55 ),
inference(subsumption_resolution,[],[f9689,f358]) ).
thf(f9689,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_37
| ~ spl0_40
| ~ spl0_55 ),
inference(backward_demodulation,[],[f9587,f764]) ).
thf(f9587,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_37
| ~ spl0_40 ),
inference(forward_demodulation,[],[f342,f358]) ).
thf(f342,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| spl0_37 ),
inference(avatar_component_clause,[],[f341]) ).
thf(f9649,plain,
( ~ spl0_70
| ~ spl0_79
| spl0_88
| ~ spl0_93 ),
inference(avatar_contradiction_clause,[],[f9648]) ).
thf(f9648,plain,
( $false
| ~ spl0_70
| ~ spl0_79
| spl0_88
| ~ spl0_93 ),
inference(subsumption_resolution,[],[f9647,f6933]) ).
thf(f9647,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| ~ spl0_79
| ~ spl0_93 ),
inference(forward_demodulation,[],[f9646,f2469]) ).
thf(f9646,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_79
| ~ spl0_93 ),
inference(forward_demodulation,[],[f8127,f4812]) ).
thf(f9633,plain,
( spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_83
| ~ spl0_92 ),
inference(avatar_contradiction_clause,[],[f9632]) ).
thf(f9632,plain,
( $false
| spl0_27
| ~ spl0_40
| ~ spl0_70
| ~ spl0_83
| ~ spl0_92 ),
inference(subsumption_resolution,[],[f9631,f9620]) ).
thf(f9631,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_70
| ~ spl0_83
| ~ spl0_92 ),
inference(forward_demodulation,[],[f9630,f2469]) ).
thf(f9630,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_83
| ~ spl0_92 ),
inference(forward_demodulation,[],[f7920,f5275]) ).
thf(f9629,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_19
| spl0_27
| ~ spl0_40
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f9628]) ).
thf(f9628,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_19
| spl0_27
| ~ spl0_40
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f9473,f9620]) ).
thf(f9473,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_19
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9472,f2469]) ).
thf(f9472,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_19 ),
inference(backward_demodulation,[],[f9423,f9395]) ).
thf(f9395,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f130,f67]) ).
thf(f9423,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f25,f67]) ).
thf(f9627,plain,
( spl0_27
| ~ spl0_40
| ~ spl0_63
| ~ spl0_70
| ~ spl0_76 ),
inference(avatar_contradiction_clause,[],[f9626]) ).
thf(f9626,plain,
( $false
| spl0_27
| ~ spl0_40
| ~ spl0_63
| ~ spl0_70
| ~ spl0_76 ),
inference(subsumption_resolution,[],[f9492,f9620]) ).
thf(f9492,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_63
| ~ spl0_70
| ~ spl0_76 ),
inference(forward_demodulation,[],[f9491,f2469]) ).
thf(f9491,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_63
| ~ spl0_70
| ~ spl0_76 ),
inference(forward_demodulation,[],[f9490,f2469]) ).
thf(f9490,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_63
| ~ spl0_70
| ~ spl0_76 ),
inference(forward_demodulation,[],[f9489,f2469]) ).
thf(f9489,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_63
| ~ spl0_76 ),
inference(forward_demodulation,[],[f4515,f1107]) ).
thf(f9602,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_42
| spl0_46 ),
inference(avatar_contradiction_clause,[],[f9601]) ).
thf(f9601,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_42
| spl0_46 ),
inference(subsumption_resolution,[],[f9600,f714]) ).
thf(f714,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_46 ),
inference(avatar_component_clause,[],[f713]) ).
thf(f713,plain,
( spl0_46
<=> ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
thf(f9600,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_42 ),
inference(forward_demodulation,[],[f9448,f369]) ).
thf(f9448,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f12,f67]) ).
thf(f9590,plain,
( ~ spl0_27
| spl0_37
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f9589]) ).
thf(f9589,plain,
( $false
| ~ spl0_27
| spl0_37
| ~ spl0_40 ),
inference(subsumption_resolution,[],[f9588,f9530]) ).
thf(f9530,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f284,f358]) ).
thf(f9588,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_27
| spl0_37
| ~ spl0_40 ),
inference(forward_demodulation,[],[f9587,f9530]) ).
thf(f9586,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_27
| ~ spl0_34
| ~ spl0_40
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f9585]) ).
thf(f9585,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_27
| ~ spl0_34
| ~ spl0_40
| ~ spl0_70 ),
inference(trivial_inequality_removal,[],[f9584]) ).
thf(f9584,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_27
| ~ spl0_34
| ~ spl0_40
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9583,f9530]) ).
thf(f9583,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_27
| ~ spl0_34
| ~ spl0_40
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9582,f9530]) ).
thf(f9582,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_27
| ~ spl0_34
| ~ spl0_40
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9450,f9530]) ).
thf(f9450,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_34
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9449,f2469]) ).
thf(f9449,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_34 ),
inference(forward_demodulation,[],[f9448,f328]) ).
thf(f9559,plain,
( spl0_26
| ~ spl0_27
| ~ spl0_40
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80 ),
inference(avatar_contradiction_clause,[],[f9558]) ).
thf(f9558,plain,
( $false
| spl0_26
| ~ spl0_27
| ~ spl0_40
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80 ),
inference(subsumption_resolution,[],[f9557,f9530]) ).
thf(f9557,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_26
| ~ spl0_27
| ~ spl0_40
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9556,f9530]) ).
thf(f9556,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_26
| ~ spl0_27
| ~ spl0_40
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9479,f9530]) ).
thf(f9479,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_26
| ~ spl0_67
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9478,f2469]) ).
thf(f9478,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_26
| ~ spl0_67
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9477,f4823]) ).
thf(f9477,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_26
| ~ spl0_67
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9476,f4823]) ).
thf(f9476,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_26
| ~ spl0_67 ),
inference(backward_demodulation,[],[f273,f1557]) ).
thf(f9528,plain,
( ~ spl0_34
| ~ spl0_37
| ~ spl0_40
| ~ spl0_42
| ~ spl0_70
| spl0_88 ),
inference(avatar_contradiction_clause,[],[f9527]) ).
thf(f9527,plain,
( $false
| ~ spl0_34
| ~ spl0_37
| ~ spl0_40
| ~ spl0_42
| ~ spl0_70
| spl0_88 ),
inference(subsumption_resolution,[],[f9526,f9464]) ).
thf(f9464,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_37
| ~ spl0_40
| spl0_88 ),
inference(forward_demodulation,[],[f6933,f9366]) ).
thf(f9366,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_37
| ~ spl0_40 ),
inference(forward_demodulation,[],[f343,f358]) ).
thf(f343,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f341]) ).
thf(f9526,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_34
| ~ spl0_42
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9525,f2469]) ).
thf(f9525,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_34
| ~ spl0_42 ),
inference(forward_demodulation,[],[f369,f328]) ).
thf(f9506,plain,
( ~ spl0_55
| spl0_58
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f9505,f4821,f2467,f1711,f780,f762]) ).
thf(f9505,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_58
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9504,f2469]) ).
thf(f9504,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_58
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9503,f4823]) ).
thf(f9503,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| spl0_58
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9502,f4823]) ).
thf(f9502,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| spl0_58
| ~ spl0_68
| ~ spl0_80 ),
inference(forward_demodulation,[],[f9501,f4823]) ).
thf(f9501,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_58
| ~ spl0_68 ),
inference(forward_demodulation,[],[f782,f1713]) ).
thf(f9486,plain,
( ~ spl0_37
| ~ spl0_40
| ~ spl0_70
| spl0_88
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f9485]) ).
thf(f9485,plain,
( $false
| ~ spl0_37
| ~ spl0_40
| ~ spl0_70
| spl0_88
| ~ spl0_95 ),
inference(subsumption_resolution,[],[f9484,f9464]) ).
thf(f9484,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_70
| ~ spl0_95 ),
inference(forward_demodulation,[],[f8289,f2469]) ).
thf(f9475,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_19
| ~ spl0_37
| ~ spl0_40
| ~ spl0_70
| spl0_88 ),
inference(avatar_contradiction_clause,[],[f9474]) ).
thf(f9474,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_19
| ~ spl0_37
| ~ spl0_40
| ~ spl0_70
| spl0_88 ),
inference(subsumption_resolution,[],[f9473,f9464]) ).
thf(f9459,plain,
( ~ spl0_34
| ~ spl0_37
| ~ spl0_40
| spl0_41
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f9458]) ).
thf(f9458,plain,
( $false
| ~ spl0_34
| ~ spl0_37
| ~ spl0_40
| spl0_41
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f9361,f9366]) ).
thf(f9361,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_34
| spl0_41
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9360,f2469]) ).
thf(f9360,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_34
| spl0_41 ),
inference(forward_demodulation,[],[f363,f328]) ).
thf(f363,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| spl0_41 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f9453,plain,
( ~ spl0_88
| spl0_3
| ~ spl0_5
| ~ spl0_34
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f9435,f2467,f326,f65,f19,f6931]) ).
thf(f9435,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_3
| ~ spl0_5
| ~ spl0_34
| ~ spl0_70 ),
inference(forward_demodulation,[],[f9434,f2469]) ).
thf(f9434,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_3
| ~ spl0_5
| ~ spl0_34 ),
inference(forward_demodulation,[],[f9433,f328]) ).
thf(f9433,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f20,f67]) ).
thf(f9447,plain,
( spl0_2
| ~ spl0_5
| ~ spl0_55
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_94 ),
inference(avatar_contradiction_clause,[],[f9446]) ).
thf(f9446,plain,
( $false
| spl0_2
| ~ spl0_5
| ~ spl0_55
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_94 ),
inference(subsumption_resolution,[],[f9445,f764]) ).
thf(f9445,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_2
| ~ spl0_5
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_94 ),
inference(forward_demodulation,[],[f9444,f2469]) ).
thf(f9444,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_2
| ~ spl0_5
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_94 ),
inference(forward_demodulation,[],[f9443,f2469]) ).
thf(f9443,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_2
| ~ spl0_5
| ~ spl0_68
| ~ spl0_70
| ~ spl0_80
| ~ spl0_94 ),
inference(forward_demodulation,[],[f9442,f2469]) ).
thf(f9442,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_2
| ~ spl0_5
| ~ spl0_68
| ~ spl0_80
| ~ spl0_94 ),
inference(forward_demodulation,[],[f9441,f4823]) ).
thf(f9441,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_2
| ~ spl0_5
| ~ spl0_68
| ~ spl0_94 ),
inference(forward_demodulation,[],[f9440,f1713]) ).
thf(f9440,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| spl0_2
| ~ spl0_5
| ~ spl0_68
| ~ spl0_94 ),
inference(forward_demodulation,[],[f9439,f1713]) ).
thf(f9439,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| spl0_2
| ~ spl0_5
| ~ spl0_94 ),
inference(forward_demodulation,[],[f9438,f8285]) ).
thf(f9438,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f15,f67]) ).
thf(f9328,plain,
( spl0_55
| ~ spl0_20
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f9326,f2471,f132,f762]) ).
thf(f9326,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_20
| ~ spl0_71 ),
inference(backward_demodulation,[],[f134,f2472]) ).
thf(f9293,plain,
( ~ spl0_88
| ~ spl0_70
| spl0_89 ),
inference(avatar_split_clause,[],[f9292,f6948,f2467,f6931]) ).
thf(f9292,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| spl0_89 ),
inference(forward_demodulation,[],[f6950,f2469]) ).
thf(f9287,plain,
( ~ spl0_88
| ~ spl0_70
| ~ spl0_79
| spl0_93 ),
inference(avatar_split_clause,[],[f9286,f8126,f4810,f2467,f6931]) ).
thf(f9286,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_70
| ~ spl0_79
| spl0_93 ),
inference(forward_demodulation,[],[f9285,f2469]) ).
thf(f9285,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_79
| spl0_93 ),
inference(forward_demodulation,[],[f8128,f4812]) ).
thf(f9281,plain,
( spl0_22
| ~ spl0_16
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f9280,f5867,f114,f141]) ).
thf(f9280,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_16
| ~ spl0_84 ),
inference(forward_demodulation,[],[f116,f5869]) ).
thf(f116,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f9274,plain,
( ~ spl0_40
| spl0_56
| ~ spl0_58
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f9273,f1711,f780,f768,f356]) ).
thf(f9273,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_56
| ~ spl0_58
| ~ spl0_68 ),
inference(backward_demodulation,[],[f9095,f9085]) ).
thf(f9085,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_58
| ~ spl0_68 ),
inference(forward_demodulation,[],[f781,f1713]) ).
thf(f781,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f780]) ).
thf(f9095,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_56
| ~ spl0_68 ),
inference(forward_demodulation,[],[f769,f1713]) ).
thf(f8972,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| spl0_55
| ~ spl0_70
| ~ spl0_80 ),
inference(avatar_contradiction_clause,[],[f8971]) ).
thf(f8971,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| spl0_55
| ~ spl0_70
| ~ spl0_80 ),
inference(subsumption_resolution,[],[f8970,f763]) ).
thf(f8970,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f8969,f2469]) ).
thf(f8969,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f8968,f2469]) ).
thf(f8968,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f8965,f2469]) ).
thf(f8965,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13
| ~ spl0_80 ),
inference(backward_demodulation,[],[f8869,f4823]) ).
thf(f8869,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f8743,f8845]) ).
thf(f8845,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f103,f67]) ).
thf(f8743,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f16,f67]) ).
thf(f8958,plain,
( spl0_86
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f8930,f92,f65,f6547]) ).
thf(f8930,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f94,f67]) ).
thf(f8944,plain,
( spl0_93
| ~ spl0_29
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f8680,f1105,f291,f8126]) ).
thf(f8680,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_29
| ~ spl0_63 ),
inference(forward_demodulation,[],[f293,f1107]) ).
thf(f8943,plain,
( spl0_93
| ~ spl0_26
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f8891,f1555,f272,f8126]) ).
thf(f8891,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_26
| ~ spl0_67 ),
inference(backward_demodulation,[],[f274,f1557]) ).
thf(f8858,plain,
( ~ spl0_10
| spl0_55
| ~ spl0_69
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f8857]) ).
thf(f8857,plain,
( $false
| ~ spl0_10
| spl0_55
| ~ spl0_69
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f8856,f763]) ).
thf(f8856,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_10
| ~ spl0_69
| ~ spl0_70 ),
inference(forward_demodulation,[],[f8855,f2469]) ).
thf(f8855,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_10
| ~ spl0_69
| ~ spl0_70 ),
inference(forward_demodulation,[],[f8854,f2469]) ).
thf(f8854,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_10
| ~ spl0_69
| ~ spl0_70 ),
inference(forward_demodulation,[],[f8644,f2469]) ).
thf(f8644,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_10
| ~ spl0_69 ),
inference(backward_demodulation,[],[f89,f1717]) ).
thf(f8836,plain,
( ~ spl0_16
| ~ spl0_92 ),
inference(avatar_contradiction_clause,[],[f8835]) ).
thf(f8835,plain,
( $false
| ~ spl0_16
| ~ spl0_92 ),
inference(trivial_inequality_removal,[],[f8834]) ).
thf(f8834,plain,
( ( $true = $false )
| ~ spl0_16
| ~ spl0_92 ),
inference(forward_demodulation,[],[f116,f7920]) ).
thf(f8829,plain,
( ~ spl0_33
| ~ spl0_63
| ~ spl0_70
| spl0_88 ),
inference(avatar_contradiction_clause,[],[f8828]) ).
thf(f8828,plain,
( $false
| ~ spl0_33
| ~ spl0_63
| ~ spl0_70
| spl0_88 ),
inference(subsumption_resolution,[],[f8827,f6933]) ).
thf(f8827,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_33
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f8826,f2469]) ).
thf(f8826,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_33
| ~ spl0_63 ),
inference(forward_demodulation,[],[f320,f1107]) ).
thf(f320,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f318]) ).
thf(f318,plain,
( spl0_33
<=> ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
thf(f8803,plain,
( spl0_83
| ~ spl0_5
| ~ spl0_19
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f8802,f8283,f4806,f4802,f1551,f1105,f128,f65,f5273]) ).
thf(f8802,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_5
| ~ spl0_19
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78
| ~ spl0_94 ),
inference(forward_demodulation,[],[f8794,f8369]) ).
thf(f8369,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8368,f1107]) ).
thf(f8368,plain,
( ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f4804,f4808]) ).
thf(f8794,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_5
| ~ spl0_19
| ~ spl0_66
| ~ spl0_78
| ~ spl0_94 ),
inference(backward_demodulation,[],[f8705,f8791]) ).
thf(f8791,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_66
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1553,f4808]) ).
thf(f8705,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))) )
| ~ spl0_5
| ~ spl0_19
| ~ spl0_78
| ~ spl0_94 ),
inference(forward_demodulation,[],[f8704,f4808]) ).
thf(f8704,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| ~ spl0_5
| ~ spl0_19
| ~ spl0_94 ),
inference(forward_demodulation,[],[f8703,f8285]) ).
thf(f8703,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| ~ spl0_19 ),
inference(forward_demodulation,[],[f130,f67]) ).
thf(f8801,plain,
( spl0_35
| ~ spl0_26
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f8800,f4806,f4802,f1551,f1105,f272,f330]) ).
thf(f8800,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_26
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8799,f8369]) ).
thf(f8799,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_26
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8798,f1107]) ).
thf(f8798,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_26
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8793,f8369]) ).
thf(f8793,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| ~ spl0_26
| ~ spl0_66
| ~ spl0_78 ),
inference(backward_demodulation,[],[f274,f8791]) ).
thf(f8779,plain,
( spl0_70
| ~ spl0_34
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f8674,f337,f326,f2467]) ).
thf(f8674,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_34
| ~ spl0_36 ),
inference(forward_demodulation,[],[f339,f328]) ).
thf(f8774,plain,
( spl0_12
| ~ spl0_2
| ~ spl0_5
| ~ spl0_78
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f8745,f8283,f4806,f65,f14,f96]) ).
thf(f8745,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_78
| ~ spl0_94 ),
inference(forward_demodulation,[],[f8744,f4808]) ).
thf(f8744,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_94 ),
inference(forward_demodulation,[],[f8743,f8285]) ).
thf(f8764,plain,
( spl0_95
| ~ spl0_34
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f8665,f367,f326,f8287]) ).
thf(f8665,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_34
| ~ spl0_42 ),
inference(forward_demodulation,[],[f369,f328]) ).
thf(f8763,plain,
( spl0_89
| ~ spl0_29
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f8682,f4806,f4802,f1105,f291,f6948]) ).
thf(f8682,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_29
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8681,f1107]) ).
thf(f8681,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_29
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8680,f8369]) ).
thf(f8762,plain,
( spl0_89
| ~ spl0_3
| ~ spl0_5
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f8761,f326,f65,f19,f6948]) ).
thf(f8761,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_34 ),
inference(backward_demodulation,[],[f8734,f328]) ).
thf(f8734,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f21,f67]) ).
thf(f8687,plain,
( ~ spl0_22
| ~ spl0_29
| spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f8686]) ).
thf(f8686,plain,
( $false
| ~ spl0_22
| ~ spl0_29
| spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f8685,f357]) ).
thf(f8685,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_22
| ~ spl0_29
| ~ spl0_53
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8684,f143]) ).
thf(f8684,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_22
| ~ spl0_29
| ~ spl0_53
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8683,f143]) ).
thf(f8683,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ~ spl0_29
| ~ spl0_53
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8682,f752]) ).
thf(f8679,plain,
( ~ spl0_32
| ~ spl0_34
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f8678]) ).
thf(f8678,plain,
( $false
| ~ spl0_32
| ~ spl0_34
| spl0_80 ),
inference(subsumption_resolution,[],[f8677,f4822]) ).
thf(f8677,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_32
| ~ spl0_34 ),
inference(backward_demodulation,[],[f328,f316]) ).
thf(f8631,plain,
( spl0_88
| ~ spl0_35
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f8580,f2471,f330,f6931]) ).
thf(f8580,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_35
| ~ spl0_71 ),
inference(forward_demodulation,[],[f332,f2472]) ).
thf(f8629,plain,
( ~ spl0_55
| spl0_20
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f8616,f2471,f132,f762]) ).
thf(f8616,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_20
| ~ spl0_71 ),
inference(forward_demodulation,[],[f133,f2472]) ).
thf(f133,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_20 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f8628,plain,
( ~ spl0_55
| spl0_16
| ~ spl0_53
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f8620,f2471,f750,f114,f762]) ).
thf(f8620,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_16
| ~ spl0_53
| ~ spl0_71 ),
inference(forward_demodulation,[],[f8619,f2472]) ).
thf(f8619,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_16
| ~ spl0_53
| ~ spl0_71 ),
inference(forward_demodulation,[],[f8618,f752]) ).
thf(f8618,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_16
| ~ spl0_71 ),
inference(forward_demodulation,[],[f115,f2472]) ).
thf(f115,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| spl0_16 ),
inference(avatar_component_clause,[],[f114]) ).
thf(f8615,plain,
( ~ spl0_28
| ~ spl0_34
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f8614]) ).
thf(f8614,plain,
( $false
| ~ spl0_28
| ~ spl0_34
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| spl0_80 ),
inference(subsumption_resolution,[],[f8613,f4822]) ).
thf(f8613,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_28
| ~ spl0_34
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8612,f1107]) ).
thf(f8612,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_28
| ~ spl0_34
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8607,f8369]) ).
thf(f8607,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_28
| ~ spl0_34 ),
inference(backward_demodulation,[],[f328,f289]) ).
thf(f8507,plain,
( spl0_34
| ~ spl0_35
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f6567,f65,f19,f330,f326]) ).
thf(f6567,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f6230,f4]) ).
thf(f6230,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f20,f67]) ).
thf(f8505,plain,
( ~ spl0_35
| spl0_26
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f8439,f4806,f4802,f1551,f1105,f272,f330]) ).
thf(f8439,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_26
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8438,f8369]) ).
thf(f8438,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_26
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8437,f1107]) ).
thf(f8437,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_26
| ~ spl0_63
| ~ spl0_66
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8431,f8369]) ).
thf(f8431,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| spl0_26
| ~ spl0_66
| ~ spl0_78 ),
inference(backward_demodulation,[],[f273,f8385]) ).
thf(f8385,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_66
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1553,f4808]) ).
thf(f8484,plain,
( spl0_40
| ~ spl0_84
| ~ spl0_92 ),
inference(avatar_contradiction_clause,[],[f8483]) ).
thf(f8483,plain,
( $false
| spl0_40
| ~ spl0_84
| ~ spl0_92 ),
inference(subsumption_resolution,[],[f8482,f357]) ).
thf(f8482,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_84
| ~ spl0_92 ),
inference(forward_demodulation,[],[f7920,f5869]) ).
thf(f8481,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_70
| spl0_95 ),
inference(avatar_contradiction_clause,[],[f8480]) ).
thf(f8480,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_70
| spl0_95 ),
inference(subsumption_resolution,[],[f8479,f6530]) ).
thf(f6530,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[],[f6432,f6430]) ).
thf(f6430,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f6425]) ).
thf(f6425,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22 ),
inference(superposition,[],[f5553,f6229]) ).
thf(f6229,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f25,f67]) ).
thf(f5553,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f0,X0) )
| ( $false = X0 ) )
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f5551]) ).
thf(f5551,plain,
( ! [X0: $o] :
( ( $true = vAPP($o,$o,f0,X0) )
| ( $false = X0 )
| ( $false = X0 ) )
| ~ spl0_22 ),
inference(binary_proxy_clausification,[],[f5548]) ).
thf(f5548,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f0,X0) = X0 )
| ( $false = X0 ) )
| ~ spl0_22 ),
inference(superposition,[],[f143,f4]) ).
thf(f6432,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f6423]) ).
thf(f6423,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f6229,f4]) ).
thf(f8479,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_70
| spl0_95 ),
inference(forward_demodulation,[],[f8288,f2469]) ).
thf(f8473,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_44
| spl0_56
| ~ spl0_70
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f8472]) ).
thf(f8472,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_44
| spl0_56
| ~ spl0_70
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f8471,f6530]) ).
thf(f8471,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_44
| spl0_56
| ~ spl0_70
| ~ spl0_79 ),
inference(forward_demodulation,[],[f8470,f6530]) ).
thf(f8470,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_44
| spl0_56
| ~ spl0_70
| ~ spl0_79 ),
inference(forward_demodulation,[],[f8356,f2469]) ).
thf(f8356,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_44
| spl0_56
| ~ spl0_79 ),
inference(backward_demodulation,[],[f8144,f4812]) ).
thf(f8144,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_44
| spl0_56 ),
inference(forward_demodulation,[],[f769,f704]) ).
thf(f8469,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_44
| spl0_57
| ~ spl0_70
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f8468]) ).
thf(f8468,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_44
| spl0_57
| ~ spl0_70
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f8467,f6530]) ).
thf(f8467,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_44
| spl0_57
| ~ spl0_70
| ~ spl0_79 ),
inference(forward_demodulation,[],[f8357,f2469]) ).
thf(f8357,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_44
| spl0_57
| ~ spl0_79 ),
inference(backward_demodulation,[],[f8147,f4812]) ).
thf(f8147,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_44
| spl0_57 ),
inference(forward_demodulation,[],[f775,f704]) ).
thf(f8393,plain,
( ~ spl0_61
| ~ spl0_63
| spl0_69
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f8392]) ).
thf(f8392,plain,
( $false
| ~ spl0_61
| ~ spl0_63
| spl0_69
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f8389,f1107]) ).
thf(f8389,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ~ spl0_61
| spl0_69
| ~ spl0_78 ),
inference(backward_demodulation,[],[f1716,f8388]) ).
thf(f8388,plain,
( ( $true = vAPP($o,$o,f3,vAPP($o,$o,f3,$true)) )
| ~ spl0_61
| ~ spl0_78 ),
inference(forward_demodulation,[],[f1099,f4808]) ).
thf(f8363,plain,
( ~ spl0_44
| spl0_57
| ~ spl0_79
| ~ spl0_95 ),
inference(avatar_contradiction_clause,[],[f8362]) ).
thf(f8362,plain,
( $false
| ~ spl0_44
| spl0_57
| ~ spl0_79
| ~ spl0_95 ),
inference(subsumption_resolution,[],[f8357,f8289]) ).
thf(f8345,plain,
( spl0_94
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f8344,f83,f65,f8283]) ).
thf(f8344,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f85,f67]) ).
thf(f8317,plain,
( ~ spl0_70
| ~ spl0_44
| spl0_51
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f8316,f4821,f739,f702,f2467]) ).
thf(f8316,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_44
| spl0_51
| ~ spl0_80 ),
inference(forward_demodulation,[],[f8309,f4823]) ).
thf(f8309,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| spl0_51
| ~ spl0_80 ),
inference(backward_demodulation,[],[f8140,f4823]) ).
thf(f8140,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| spl0_51 ),
inference(forward_demodulation,[],[f740,f704]) ).
thf(f740,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| spl0_51 ),
inference(avatar_component_clause,[],[f739]) ).
thf(f8313,plain,
( ~ spl0_70
| ~ spl0_32
| spl0_36
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f8307,f4821,f337,f314,f2467]) ).
thf(f8307,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_32
| spl0_36
| ~ spl0_80 ),
inference(backward_demodulation,[],[f8135,f4823]) ).
thf(f8135,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_32
| spl0_36 ),
inference(forward_demodulation,[],[f338,f316]) ).
thf(f8312,plain,
( ~ spl0_95
| ~ spl0_32
| spl0_42
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f8305,f4821,f367,f314,f8287]) ).
thf(f8305,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_32
| spl0_42
| ~ spl0_80 ),
inference(backward_demodulation,[],[f8133,f4823]) ).
thf(f8133,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_32
| spl0_42 ),
inference(forward_demodulation,[],[f368,f316]) ).
thf(f8311,plain,
( spl0_79
| ~ spl0_80 ),
inference(avatar_contradiction_clause,[],[f8310]) ).
thf(f8310,plain,
( $false
| spl0_79
| ~ spl0_80 ),
inference(subsumption_resolution,[],[f8302,f4823]) ).
thf(f8302,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_79
| ~ spl0_80 ),
inference(backward_demodulation,[],[f4811,f4823]) ).
thf(f8300,plain,
( ~ spl0_80
| ~ spl0_32
| spl0_34 ),
inference(avatar_split_clause,[],[f8136,f326,f314,f4821]) ).
thf(f8136,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_32
| spl0_34 ),
inference(forward_demodulation,[],[f327,f316]) ).
thf(f327,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| spl0_34 ),
inference(avatar_component_clause,[],[f326]) ).
thf(f8299,plain,
( ~ spl0_80
| ~ spl0_44
| spl0_47 ),
inference(avatar_split_clause,[],[f8137,f718,f702,f4821]) ).
thf(f8137,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_44
| spl0_47 ),
inference(forward_demodulation,[],[f719,f704]) ).
thf(f719,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47 ),
inference(avatar_component_clause,[],[f718]) ).
thf(f8298,plain,
( spl0_80
| spl0_50
| ~ spl0_1
| ~ spl0_5
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f8195,f314,f65,f10,f733,f4821]) ).
thf(f8195,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_32 ),
inference(superposition,[],[f8130,f4]) ).
thf(f8130,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_32 ),
inference(forward_demodulation,[],[f6238,f316]) ).
thf(f6238,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f12,f67]) ).
thf(f8296,plain,
( spl0_70
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| spl0_73 ),
inference(avatar_split_clause,[],[f7951,f3150,f141,f65,f23,f2467]) ).
thf(f7951,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| spl0_73 ),
inference(backward_demodulation,[],[f6430,f7926]) ).
thf(f7926,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_73 ),
inference(subsumption_resolution,[],[f6418,f3151]) ).
thf(f3151,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_73 ),
inference(avatar_component_clause,[],[f3150]) ).
thf(f6418,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f6229,f4]) ).
thf(f8295,plain,
( spl0_70
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| spl0_73 ),
inference(avatar_split_clause,[],[f7952,f3150,f123,f65,f23,f2467]) ).
thf(f7952,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| spl0_73 ),
inference(backward_demodulation,[],[f7926,f7912]) ).
thf(f7912,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f7911]) ).
thf(f7911,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f6416,f125]) ).
thf(f6416,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f6229,f4]) ).
thf(f8294,plain,
( spl0_70
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f7953,f7914,f123,f65,f23,f2467]) ).
thf(f7953,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_18
| ~ spl0_91 ),
inference(backward_demodulation,[],[f7912,f7916]) ).
thf(f8290,plain,
( spl0_94
| spl0_95
| ~ spl0_4
| ~ spl0_5
| ~ spl0_72
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f8281,f4806,f3146,f65,f23,f8287,f8283]) ).
thf(f3146,plain,
( spl0_72
<=> ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
thf(f8281,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_72
| ~ spl0_78 ),
inference(forward_demodulation,[],[f6411,f8186]) ).
thf(f8186,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| ~ spl0_72
| ~ spl0_78 ),
inference(forward_demodulation,[],[f3148,f4808]) ).
thf(f3148,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f3146]) ).
thf(f6411,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f6229,f4]) ).
thf(f8278,plain,
( ~ spl0_44
| spl0_51
| ~ spl0_63
| ~ spl0_70
| ~ spl0_77
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f8277]) ).
thf(f8277,plain,
( $false
| ~ spl0_44
| spl0_51
| ~ spl0_63
| ~ spl0_70
| ~ spl0_77
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f8276,f2469]) ).
thf(f8276,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_44
| spl0_51
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8260,f1107]) ).
thf(f8260,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$true)) )
| ~ spl0_44
| spl0_51
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(backward_demodulation,[],[f8140,f8252]) ).
thf(f8252,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8251,f1107]) ).
thf(f8251,plain,
( ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_77
| ~ spl0_78 ),
inference(forward_demodulation,[],[f4804,f4808]) ).
thf(f8262,plain,
( ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| spl0_79 ),
inference(avatar_contradiction_clause,[],[f8261]) ).
thf(f8261,plain,
( $false
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| spl0_79 ),
inference(subsumption_resolution,[],[f8253,f1107]) ).
thf(f8253,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ~ spl0_63
| ~ spl0_77
| ~ spl0_78
| spl0_79 ),
inference(backward_demodulation,[],[f4811,f8252]) ).
thf(f8248,plain,
( ~ spl0_44
| spl0_77
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f8247]) ).
thf(f8247,plain,
( $false
| ~ spl0_44
| spl0_77
| spl0_80 ),
inference(subsumption_resolution,[],[f8245,f4822]) ).
thf(f8245,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_44
| spl0_77 ),
inference(trivial_inequality_removal,[],[f8244]) ).
thf(f8244,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_44
| spl0_77 ),
inference(superposition,[],[f8153,f4]) ).
thf(f8153,plain,
( ( $true != vAPP($o,$o,f2,$false) )
| ~ spl0_44
| spl0_77 ),
inference(forward_demodulation,[],[f4803,f704]) ).
thf(f8184,plain,
( ~ spl0_69
| ~ spl0_70
| spl0_72
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f8183]) ).
thf(f8183,plain,
( $false
| ~ spl0_69
| ~ spl0_70
| spl0_72
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f8182,f2469]) ).
thf(f8182,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_69
| ~ spl0_70
| spl0_72
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8181,f2469]) ).
thf(f8181,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_69
| spl0_72
| ~ spl0_78 ),
inference(forward_demodulation,[],[f8180,f1717]) ).
thf(f8180,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))) )
| spl0_72
| ~ spl0_78 ),
inference(forward_demodulation,[],[f3147,f4808]) ).
thf(f3147,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| spl0_72 ),
inference(avatar_component_clause,[],[f3146]) ).
thf(f8166,plain,
( spl0_68
| spl0_78 ),
inference(avatar_contradiction_clause,[],[f8165]) ).
thf(f8165,plain,
( $false
| spl0_68
| spl0_78 ),
inference(subsumption_resolution,[],[f8164,f1712]) ).
thf(f8164,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| spl0_78 ),
inference(trivial_inequality_removal,[],[f8163]) ).
thf(f8163,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f3,$false) )
| spl0_78 ),
inference(superposition,[],[f4807,f4]) ).
thf(f4807,plain,
( ( $true != vAPP($o,$o,f3,$false) )
| spl0_78 ),
inference(avatar_component_clause,[],[f4806]) ).
thf(f8152,plain,
( ~ spl0_79
| ~ spl0_44
| spl0_49 ),
inference(avatar_split_clause,[],[f8151,f729,f702,f4810]) ).
thf(f8151,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| spl0_49 ),
inference(forward_demodulation,[],[f730,f704]) ).
thf(f8129,plain,
( spl0_28
| ~ spl0_93
| spl0_3
| ~ spl0_5
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f6870,f1105,f65,f19,f8126,f287]) ).
thf(f6870,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| spl0_3
| ~ spl0_5
| ~ spl0_63 ),
inference(forward_demodulation,[],[f6564,f1107]) ).
thf(f6564,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f6230,f4]) ).
thf(f8117,plain,
( ~ spl0_44
| ~ spl0_68
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f8116]) ).
thf(f8116,plain,
( $false
| ~ spl0_44
| ~ spl0_68
| spl0_80 ),
inference(subsumption_resolution,[],[f8115,f4822]) ).
thf(f8115,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_44
| ~ spl0_68 ),
inference(forward_demodulation,[],[f704,f1713]) ).
thf(f8114,plain,
( spl0_47
| ~ spl0_68
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f8113]) ).
thf(f8113,plain,
( $false
| spl0_47
| ~ spl0_68
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f8112,f4812]) ).
thf(f8112,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| spl0_47
| ~ spl0_68 ),
inference(forward_demodulation,[],[f719,f1713]) ).
thf(f8091,plain,
( ~ spl0_90
| spl0_31
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f7907,f1105,f305,f7776]) ).
thf(f7907,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_31
| ~ spl0_63 ),
inference(forward_demodulation,[],[f306,f1107]) ).
thf(f306,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_31 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f8077,plain,
( ~ spl0_23
| ~ spl0_5
| spl0_7
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f8055,f268,f74,f65,f259]) ).
thf(f8055,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_7
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f8052]) ).
thf(f8052,plain,
( ( $false != $false )
| ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_7
| ~ spl0_25 ),
inference(constrained_superposition,[],[f6228,f270]) ).
thf(f8076,plain,
( ~ spl0_23
| ~ spl0_5
| spl0_9
| ~ spl0_25
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f8075,f1711,f268,f83,f65,f259]) ).
thf(f8075,plain,
( ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_9
| ~ spl0_25
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f8051,f1713]) ).
thf(f8051,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ( $false != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_9
| ~ spl0_25 ),
inference(constrained_superposition,[],[f7948,f270]) ).
thf(f7948,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_9 ),
inference(forward_demodulation,[],[f84,f67]) ).
thf(f8074,plain,
( spl0_23
| ~ spl0_25
| spl0_87 ),
inference(avatar_split_clause,[],[f8056,f6680,f268,f259]) ).
thf(f8056,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_25
| spl0_87 ),
inference(trivial_inequality_removal,[],[f8050]) ).
thf(f8050,plain,
( ( $false != $false )
| ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_25
| spl0_87 ),
inference(superposition,[],[f6684,f270]) ).
thf(f6684,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f4,X0) )
| ( $false = X0 ) )
| spl0_87 ),
inference(superposition,[],[f6682,f4]) ).
thf(f8071,plain,
( spl0_23
| ~ spl0_5
| spl0_7
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f8070,f268,f74,f65,f259]) ).
thf(f8070,plain,
( ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_7
| ~ spl0_25 ),
inference(subsumption_resolution,[],[f8060,f6228]) ).
thf(f8060,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_25 ),
inference(duplicate_literal_removal,[],[f8059]) ).
thf(f8059,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ( $false = vAPP($o,$o,f4,$false) )
| ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_25 ),
inference(binary_proxy_clausification,[],[f8047]) ).
thf(f8047,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ( vAPP($o,$o,f4,$false) != vAPP($o,$o,f4,vAPP($o,$o,f4,$false)) )
| ~ spl0_25 ),
inference(constrained_superposition,[],[f270,f270]) ).
thf(f8041,plain,
( ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_85 ),
inference(avatar_contradiction_clause,[],[f8040]) ).
thf(f8040,plain,
( $false
| ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_85 ),
inference(subsumption_resolution,[],[f8033,f8026]) ).
thf(f8026,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f8025,f7806]) ).
thf(f7806,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f1118,f1713]) ).
thf(f8025,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f8024,f1107]) ).
thf(f8024,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))) )
| ~ spl0_52
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f8023,f7806]) ).
thf(f8023,plain,
( ( $true = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_52
| ~ spl0_68 ),
inference(forward_demodulation,[],[f746,f1713]) ).
thf(f8033,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_85 ),
inference(backward_demodulation,[],[f5872,f8026]) ).
thf(f8039,plain,
( ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_84 ),
inference(avatar_contradiction_clause,[],[f8038]) ).
thf(f8038,plain,
( $false
| ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_84 ),
inference(subsumption_resolution,[],[f8037,f8026]) ).
thf(f8037,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_84 ),
inference(forward_demodulation,[],[f8032,f8026]) ).
thf(f8032,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_52
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_84 ),
inference(backward_demodulation,[],[f5868,f8026]) ).
thf(f8022,plain,
( spl0_52
| ~ spl0_65
| ~ spl0_68
| spl0_71
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f8021]) ).
thf(f8021,plain,
( $false
| spl0_52
| ~ spl0_65
| ~ spl0_68
| spl0_71
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f8014,f2473]) ).
thf(f8014,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| spl0_52
| ~ spl0_65
| ~ spl0_68
| ~ spl0_79 ),
inference(trivial_inequality_removal,[],[f8013]) ).
thf(f8013,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f1,$true) )
| spl0_52
| ~ spl0_65
| ~ spl0_68
| ~ spl0_79 ),
inference(superposition,[],[f7810,f4]) ).
thf(f7810,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| spl0_52
| ~ spl0_65
| ~ spl0_68
| ~ spl0_79 ),
inference(backward_demodulation,[],[f7784,f7806]) ).
thf(f7784,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| spl0_52
| ~ spl0_68
| ~ spl0_79 ),
inference(backward_demodulation,[],[f7671,f4812]) ).
thf(f7671,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| spl0_52
| ~ spl0_68 ),
inference(forward_demodulation,[],[f747,f1713]) ).
thf(f7933,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_15
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f7932]) ).
thf(f7932,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_15
| spl0_80 ),
inference(subsumption_resolution,[],[f7931,f4822]) ).
thf(f7931,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f7529,f7840]) ).
thf(f7840,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f103,f67]) ).
thf(f7529,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f112,f67]) ).
thf(f7921,plain,
( spl0_91
| spl0_92
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f6414,f65,f23,f7918,f7914]) ).
thf(f6414,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f6229,f4]) ).
thf(f7877,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_18
| ~ spl0_65
| ~ spl0_68
| spl0_71 ),
inference(avatar_contradiction_clause,[],[f7876]) ).
thf(f7876,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_18
| ~ spl0_65
| ~ spl0_68
| spl0_71 ),
inference(trivial_inequality_removal,[],[f7875]) ).
thf(f7875,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_18
| ~ spl0_65
| ~ spl0_68
| spl0_71 ),
inference(forward_demodulation,[],[f125,f7874]) ).
thf(f7874,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_65
| ~ spl0_68
| spl0_71 ),
inference(subsumption_resolution,[],[f7873,f2473]) ).
thf(f7873,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7872,f7806]) ).
thf(f7872,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7871,f1713]) ).
thf(f7871,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7870,f1713]) ).
thf(f7870,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f6416,f6772]) ).
thf(f6772,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f85,f67]) ).
thf(f7852,plain,
( ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_68
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f7851]) ).
thf(f7851,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_68
| spl0_80 ),
inference(subsumption_resolution,[],[f7850,f4822]) ).
thf(f7850,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7849,f1713]) ).
thf(f7849,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7530,f1713]) ).
thf(f7530,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_5
| ~ spl0_9
| ~ spl0_15 ),
inference(forward_demodulation,[],[f7529,f6772]) ).
thf(f7817,plain,
( ~ spl0_20
| spl0_58
| ~ spl0_65
| ~ spl0_68
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f7816]) ).
thf(f7816,plain,
( $false
| ~ spl0_20
| spl0_58
| ~ spl0_65
| ~ spl0_68
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f7808,f134]) ).
thf(f7808,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_58
| ~ spl0_65
| ~ spl0_68
| ~ spl0_79 ),
inference(backward_demodulation,[],[f7782,f7806]) ).
thf(f7782,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| spl0_58
| ~ spl0_68
| ~ spl0_79 ),
inference(backward_demodulation,[],[f7646,f4812]) ).
thf(f7646,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_58
| ~ spl0_68 ),
inference(forward_demodulation,[],[f782,f1713]) ).
thf(f7794,plain,
( ~ spl0_90
| spl0_3
| ~ spl0_5
| ~ spl0_28
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f7789,f4810,f287,f65,f19,f7776]) ).
thf(f7789,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_28
| ~ spl0_79 ),
inference(backward_demodulation,[],[f7702,f4812]) ).
thf(f7702,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_28 ),
inference(backward_demodulation,[],[f6230,f289]) ).
thf(f7769,plain,
( ~ spl0_28
| spl0_41
| ~ spl0_56
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f7768]) ).
thf(f7768,plain,
( $false
| ~ spl0_28
| spl0_41
| ~ spl0_56
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f7657,f7700]) ).
thf(f7700,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_28
| spl0_41 ),
inference(backward_demodulation,[],[f363,f289]) ).
thf(f7657,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_56
| ~ spl0_68 ),
inference(forward_demodulation,[],[f770,f1713]) ).
thf(f7761,plain,
( ~ spl0_5
| ~ spl0_9
| spl0_13
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f7760]) ).
thf(f7760,plain,
( $false
| ~ spl0_5
| ~ spl0_9
| spl0_13
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f7759,f1713]) ).
thf(f7759,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_9
| spl0_13
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7758,f1713]) ).
thf(f7758,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_9
| spl0_13 ),
inference(forward_demodulation,[],[f7757,f6772]) ).
thf(f7757,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| spl0_13 ),
inference(forward_demodulation,[],[f102,f67]) ).
thf(f7727,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_28
| spl0_42
| ~ spl0_70
| ~ spl0_80 ),
inference(avatar_contradiction_clause,[],[f7726]) ).
thf(f7726,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_28
| spl0_42
| ~ spl0_70
| ~ spl0_80 ),
inference(subsumption_resolution,[],[f7725,f6530]) ).
thf(f7725,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_28
| spl0_42
| ~ spl0_70
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7724,f2469]) ).
thf(f7724,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_28
| spl0_42
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7723,f4823]) ).
thf(f7723,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_28
| spl0_42
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7722,f4823]) ).
thf(f7722,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_28
| spl0_42
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7701,f4823]) ).
thf(f7701,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_28
| spl0_42 ),
inference(backward_demodulation,[],[f368,f289]) ).
thf(f7714,plain,
( ~ spl0_28
| spl0_36
| ~ spl0_70
| ~ spl0_80 ),
inference(avatar_contradiction_clause,[],[f7713]) ).
thf(f7713,plain,
( $false
| ~ spl0_28
| spl0_36
| ~ spl0_70
| ~ spl0_80 ),
inference(subsumption_resolution,[],[f7712,f2469]) ).
thf(f7712,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_28
| spl0_36
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7711,f4823]) ).
thf(f7711,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_28
| spl0_36
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7710,f4823]) ).
thf(f7710,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_28
| spl0_36
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7699,f4823]) ).
thf(f7699,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_28
| spl0_36 ),
inference(backward_demodulation,[],[f338,f289]) ).
thf(f7709,plain,
( ~ spl0_28
| spl0_34
| ~ spl0_80 ),
inference(avatar_contradiction_clause,[],[f7708]) ).
thf(f7708,plain,
( $false
| ~ spl0_28
| spl0_34
| ~ spl0_80 ),
inference(subsumption_resolution,[],[f7707,f4823]) ).
thf(f7707,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_28
| spl0_34
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7706,f4823]) ).
thf(f7706,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_28
| spl0_34
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7698,f4823]) ).
thf(f7698,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_28
| spl0_34 ),
inference(backward_demodulation,[],[f327,f289]) ).
thf(f7643,plain,
( spl0_66
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f7642]) ).
thf(f7642,plain,
( $false
| spl0_66
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f7641,f1713]) ).
thf(f7641,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| spl0_66
| ~ spl0_68 ),
inference(forward_demodulation,[],[f1552,f1713]) ).
thf(f7602,plain,
( spl0_32
| ~ spl0_89
| spl0_3
| ~ spl0_5
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f6603,f1105,f65,f19,f6948,f314]) ).
thf(f6603,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_63 ),
inference(forward_demodulation,[],[f6566,f1107]) ).
thf(f6566,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f6230,f4]) ).
thf(f7597,plain,
( spl0_28
| ~ spl0_89
| spl0_3
| ~ spl0_5
| ~ spl0_63
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f7596,f4821,f1105,f65,f19,f6948,f287]) ).
thf(f7596,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| spl0_3
| ~ spl0_5
| ~ spl0_63
| ~ spl0_80 ),
inference(forward_demodulation,[],[f7595,f4823]) ).
thf(f7595,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| spl0_3
| ~ spl0_5
| ~ spl0_63
| ~ spl0_80 ),
inference(forward_demodulation,[],[f6870,f4823]) ).
thf(f7580,plain,
( ~ spl0_68
| ~ spl0_5
| ~ spl0_9
| spl0_86 ),
inference(avatar_split_clause,[],[f7579,f6547,f83,f65,f1711]) ).
thf(f7579,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_9
| spl0_86 ),
inference(forward_demodulation,[],[f6548,f6772]) ).
thf(f7542,plain,
( spl0_18
| ~ spl0_14
| ~ spl0_53
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f7411,f1105,f750,f105,f123]) ).
thf(f7411,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_14
| ~ spl0_53
| ~ spl0_63 ),
inference(forward_demodulation,[],[f7207,f752]) ).
thf(f7207,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_14
| ~ spl0_63 ),
inference(forward_demodulation,[],[f107,f1107]) ).
thf(f7538,plain,
( ~ spl0_18
| spl0_12
| ~ spl0_53
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f7506,f1555,f750,f96,f123]) ).
thf(f7506,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_12
| ~ spl0_53
| ~ spl0_67 ),
inference(forward_demodulation,[],[f7501,f752]) ).
thf(f7501,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_12
| ~ spl0_67 ),
inference(backward_demodulation,[],[f97,f1557]) ).
thf(f97,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| spl0_12 ),
inference(avatar_component_clause,[],[f96]) ).
thf(f7337,plain,
( spl0_80
| ~ spl0_44
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f7336,f718,f702,f4821]) ).
thf(f7336,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_44
| ~ spl0_47 ),
inference(forward_demodulation,[],[f720,f704]) ).
thf(f7334,plain,
( spl0_68
| ~ spl0_5
| ~ spl0_13
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f6771,f6547,f101,f65,f1711]) ).
thf(f6771,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_13
| ~ spl0_86 ),
inference(backward_demodulation,[],[f6554,f6549]) ).
thf(f6554,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f103,f67]) ).
thf(f7320,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| spl0_88 ),
inference(avatar_contradiction_clause,[],[f7319]) ).
thf(f7319,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| spl0_88 ),
inference(subsumption_resolution,[],[f7318,f6530]) ).
thf(f7318,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| spl0_88 ),
inference(forward_demodulation,[],[f7317,f6530]) ).
thf(f7317,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| spl0_88 ),
inference(forward_demodulation,[],[f6933,f6530]) ).
thf(f7282,plain,
( ~ spl0_80
| ~ spl0_5
| ~ spl0_9
| spl0_15
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f6961,f1711,f110,f83,f65,f4821]) ).
thf(f6961,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_9
| spl0_15
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6960,f1713]) ).
thf(f6960,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_9
| spl0_15
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6959,f1713]) ).
thf(f6959,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_5
| ~ spl0_9
| spl0_15 ),
inference(forward_demodulation,[],[f2929,f6772]) ).
thf(f2929,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_5
| spl0_15 ),
inference(forward_demodulation,[],[f111,f67]) ).
thf(f7229,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_71
| spl0_73 ),
inference(avatar_contradiction_clause,[],[f7228]) ).
thf(f7228,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_71
| spl0_73 ),
inference(subsumption_resolution,[],[f7090,f6530]) ).
thf(f7090,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_71
| spl0_73 ),
inference(forward_demodulation,[],[f3151,f2472]) ).
thf(f7227,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_55 ),
inference(avatar_contradiction_clause,[],[f7226]) ).
thf(f7226,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_55 ),
inference(trivial_inequality_removal,[],[f7225]) ).
thf(f7225,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_55 ),
inference(backward_demodulation,[],[f764,f6530]) ).
thf(f7166,plain,
( spl0_55
| ~ spl0_16
| ~ spl0_70
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f7114,f2471,f2467,f114,f762]) ).
thf(f7114,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_16
| ~ spl0_70
| ~ spl0_71 ),
inference(forward_demodulation,[],[f7113,f2469]) ).
thf(f7113,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_16
| ~ spl0_70
| ~ spl0_71 ),
inference(forward_demodulation,[],[f7112,f2469]) ).
thf(f7112,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_16
| ~ spl0_71 ),
inference(forward_demodulation,[],[f116,f2472]) ).
thf(f7118,plain,
( spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_69
| ~ spl0_70
| ~ spl0_71
| ~ spl0_75 ),
inference(avatar_contradiction_clause,[],[f7117]) ).
thf(f7117,plain,
( $false
| spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_69
| ~ spl0_70
| ~ spl0_71
| ~ spl0_75 ),
inference(subsumption_resolution,[],[f7077,f7100]) ).
thf(f7100,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71 ),
inference(forward_demodulation,[],[f7099,f2472]) ).
thf(f7099,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7098,f6312]) ).
thf(f6312,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f1118,f1713]) ).
thf(f7098,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7097,f1107]) ).
thf(f7097,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_57
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f7096,f6312]) ).
thf(f7096,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_57
| ~ spl0_68 ),
inference(forward_demodulation,[],[f775,f1713]) ).
thf(f7077,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_69
| ~ spl0_70
| ~ spl0_75 ),
inference(forward_demodulation,[],[f7076,f2469]) ).
thf(f7076,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_69
| ~ spl0_70
| ~ spl0_75 ),
inference(forward_demodulation,[],[f7075,f2469]) ).
thf(f7075,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_69
| ~ spl0_70
| ~ spl0_75 ),
inference(forward_demodulation,[],[f7074,f2469]) ).
thf(f7074,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_69
| ~ spl0_75 ),
inference(forward_demodulation,[],[f3175,f1717]) ).
thf(f7106,plain,
( ~ spl0_88
| spl0_35
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f7105,f2471,f330,f6931]) ).
thf(f7105,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_35
| ~ spl0_71 ),
inference(forward_demodulation,[],[f331,f2472]) ).
thf(f7079,plain,
( ~ spl0_34
| spl0_42
| ~ spl0_69
| ~ spl0_70
| ~ spl0_75 ),
inference(avatar_contradiction_clause,[],[f7078]) ).
thf(f7078,plain,
( $false
| ~ spl0_34
| spl0_42
| ~ spl0_69
| ~ spl0_70
| ~ spl0_75 ),
inference(subsumption_resolution,[],[f7077,f7010]) ).
thf(f7010,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ~ spl0_34
| spl0_42
| ~ spl0_70 ),
inference(backward_demodulation,[],[f6635,f2469]) ).
thf(f6635,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_34
| spl0_42 ),
inference(backward_demodulation,[],[f368,f328]) ).
thf(f7064,plain,
( spl0_88
| ~ spl0_31
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f6397,f2471,f1711,f1116,f1105,f305,f6931]) ).
thf(f6397,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_31
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6396,f2472]) ).
thf(f6396,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_31
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6395,f6312]) ).
thf(f6395,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_31
| ~ spl0_63 ),
inference(forward_demodulation,[],[f307,f1107]) ).
thf(f7057,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_34
| spl0_42
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f7056]) ).
thf(f7056,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_22
| ~ spl0_34
| spl0_42
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f6530,f7010]) ).
thf(f7047,plain,
( ~ spl0_55
| spl0_14
| ~ spl0_63
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f7043,f2467,f1105,f105,f762]) ).
thf(f7043,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_14
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f7042,f2469]) ).
thf(f7042,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_14
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f7041,f2469]) ).
thf(f7041,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| spl0_14
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f7040,f2469]) ).
thf(f7040,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_14
| ~ spl0_63 ),
inference(forward_demodulation,[],[f106,f1107]) ).
thf(f7037,plain,
( spl0_26
| ~ spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_70
| ~ spl0_71
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f7036]) ).
thf(f7036,plain,
( $false
| spl0_26
| ~ spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_70
| ~ spl0_71
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f7035,f6388]) ).
thf(f6388,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6387,f2472]) ).
thf(f6387,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6386,f6312]) ).
thf(f6386,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6385,f1107]) ).
thf(f6385,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| ~ spl0_57
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6384,f6312]) ).
thf(f6384,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_57
| ~ spl0_68 ),
inference(forward_demodulation,[],[f776,f1713]) ).
thf(f7035,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_26
| ~ spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_70
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7034,f6388]) ).
thf(f7034,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_26
| ~ spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_70
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7033,f6388]) ).
thf(f7033,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_70
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7032,f2469]) ).
thf(f7032,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7031,f1107]) ).
thf(f7031,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7030,f6312]) ).
thf(f7030,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_26
| ~ spl0_63
| ~ spl0_81 ),
inference(forward_demodulation,[],[f7029,f1107]) ).
thf(f7029,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| spl0_26
| ~ spl0_81 ),
inference(forward_demodulation,[],[f273,f4854]) ).
thf(f6952,plain,
( ~ spl0_89
| spl0_3
| ~ spl0_5
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f6636,f326,f65,f19,f6948]) ).
thf(f6636,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_3
| ~ spl0_5
| ~ spl0_34 ),
inference(backward_demodulation,[],[f6230,f328]) ).
thf(f6934,plain,
( spl0_34
| ~ spl0_88
| spl0_3
| ~ spl0_5
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f6607,f2471,f65,f19,f6931,f326]) ).
thf(f6607,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6567,f2472]) ).
thf(f6886,plain,
( ~ spl0_25
| ~ spl0_34
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f6885]) ).
thf(f6885,plain,
( $false
| ~ spl0_25
| ~ spl0_34
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_80 ),
inference(subsumption_resolution,[],[f6884,f4822]) ).
thf(f6884,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_25
| ~ spl0_34
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6883,f1107]) ).
thf(f6883,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ~ spl0_25
| ~ spl0_34
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6882,f6312]) ).
thf(f6882,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_25
| ~ spl0_34
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6881,f1713]) ).
thf(f6881,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_25
| ~ spl0_34 ),
inference(forward_demodulation,[],[f328,f270]) ).
thf(f6879,plain,
( ~ spl0_28
| ~ spl0_30
| spl0_80 ),
inference(avatar_contradiction_clause,[],[f6878]) ).
thf(f6878,plain,
( $false
| ~ spl0_28
| ~ spl0_30
| spl0_80 ),
inference(subsumption_resolution,[],[f6877,f4822]) ).
thf(f6877,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_28
| ~ spl0_30 ),
inference(backward_demodulation,[],[f303,f289]) ).
thf(f303,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f301,plain,
( spl0_30
<=> ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
thf(f6869,plain,
( spl0_25
| ~ spl0_26
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f6562,f65,f19,f272,f268]) ).
thf(f6562,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f6230,f4]) ).
thf(f6859,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_7
| spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f6858]) ).
thf(f6858,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_7
| spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f6857,f357]) ).
thf(f6857,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6856,f752]) ).
thf(f6856,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6855,f2472]) ).
thf(f6855,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_53
| ~ spl0_63
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6854,f752]) ).
thf(f6854,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_63
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6853,f1107]) ).
thf(f6853,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6852,f4854]) ).
thf(f6852,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6825,f4854]) ).
thf(f6825,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_81 ),
inference(backward_demodulation,[],[f6435,f4854]) ).
thf(f6435,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_7 ),
inference(subsumption_resolution,[],[f6410,f6228]) ).
thf(f6410,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ( $false = vAPP($o,$o,f4,$false) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f6229,f4]) ).
thf(f6831,plain,
( spl0_12
| ~ spl0_22
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_81 ),
inference(avatar_contradiction_clause,[],[f6830]) ).
thf(f6830,plain,
( $false
| spl0_12
| ~ spl0_22
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_81 ),
inference(subsumption_resolution,[],[f6829,f143]) ).
thf(f6829,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_12
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6828,f752]) ).
thf(f6828,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_12
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6827,f2472]) ).
thf(f6827,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_12
| ~ spl0_53
| ~ spl0_63
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6826,f752]) ).
thf(f6826,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| spl0_12
| ~ spl0_63
| ~ spl0_81 ),
inference(forward_demodulation,[],[f6820,f1107]) ).
thf(f6820,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_12
| ~ spl0_81 ),
inference(backward_demodulation,[],[f97,f4854]) ).
thf(f6801,plain,
( spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71
| ~ spl0_73
| spl0_81 ),
inference(avatar_contradiction_clause,[],[f6800]) ).
thf(f6800,plain,
( $false
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71
| ~ spl0_73
| spl0_81 ),
inference(subsumption_resolution,[],[f6799,f5903]) ).
thf(f5903,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_71
| ~ spl0_73 ),
inference(backward_demodulation,[],[f3152,f2472]) ).
thf(f6799,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71
| ~ spl0_73
| spl0_81 ),
inference(forward_demodulation,[],[f6798,f5903]) ).
thf(f6798,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71
| ~ spl0_73
| spl0_81 ),
inference(forward_demodulation,[],[f6797,f5903]) ).
thf(f6797,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71
| spl0_81 ),
inference(forward_demodulation,[],[f6796,f2472]) ).
thf(f6796,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_81 ),
inference(forward_demodulation,[],[f6795,f6312]) ).
thf(f6795,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| spl0_26
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| spl0_81 ),
inference(forward_demodulation,[],[f6794,f1107]) ).
thf(f6794,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| spl0_26
| ~ spl0_65
| ~ spl0_68
| spl0_81 ),
inference(forward_demodulation,[],[f6783,f6312]) ).
thf(f6783,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))))) )
| spl0_26
| spl0_81 ),
inference(backward_demodulation,[],[f273,f6777]) ).
thf(f6777,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| spl0_81 ),
inference(trivial_inequality_removal,[],[f6776]) ).
thf(f6776,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f3,$true) )
| spl0_81 ),
inference(superposition,[],[f4853,f4]) ).
thf(f6767,plain,
( ~ spl0_5
| spl0_7
| spl0_9
| ~ spl0_63
| spl0_67 ),
inference(avatar_contradiction_clause,[],[f6766]) ).
thf(f6766,plain,
( $false
| ~ spl0_5
| spl0_7
| spl0_9
| ~ spl0_63
| spl0_67 ),
inference(subsumption_resolution,[],[f6765,f6662]) ).
thf(f6662,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ~ spl0_5
| spl0_7
| spl0_9 ),
inference(subsumption_resolution,[],[f6658,f6228]) ).
thf(f6658,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f4,$false) )
| ~ spl0_5
| spl0_9 ),
inference(superposition,[],[f4712,f4]) ).
thf(f4712,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_9 ),
inference(forward_demodulation,[],[f84,f67]) ).
thf(f6765,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_63
| spl0_67 ),
inference(subsumption_resolution,[],[f6758,f1107]) ).
thf(f6758,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f3,$true) )
| spl0_67 ),
inference(superposition,[],[f1556,f4]) ).
thf(f6611,plain,
( spl0_34
| spl0_3
| ~ spl0_5
| ~ spl0_71
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f6610,f3150,f2471,f65,f19,f326]) ).
thf(f6610,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f6609,f5903]) ).
thf(f6609,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_71
| ~ spl0_73 ),
inference(forward_demodulation,[],[f6608,f5903]) ).
thf(f6608,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_71
| ~ spl0_73 ),
inference(forward_demodulation,[],[f6607,f5903]) ).
thf(f6587,plain,
( ~ spl0_26
| spl0_3
| ~ spl0_5
| spl0_25 ),
inference(avatar_split_clause,[],[f6586,f268,f65,f19,f272]) ).
thf(f6586,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| spl0_3
| ~ spl0_5
| spl0_25 ),
inference(subsumption_resolution,[],[f6562,f269]) ).
thf(f6550,plain,
( spl0_86
| spl0_74
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f6412,f65,f23,f3168,f6547]) ).
thf(f6412,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f6229,f4]) ).
thf(f6539,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_13
| spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f6538]) ).
thf(f6538,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_13
| spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f4709,f6461]) ).
thf(f6461,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_4
| ~ spl0_5
| spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f6460,f357]) ).
thf(f6460,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6459,f752]) ).
thf(f6459,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6458,f2472]) ).
thf(f6458,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_53
| ~ spl0_63 ),
inference(forward_demodulation,[],[f6457,f752]) ).
thf(f6457,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_63 ),
inference(forward_demodulation,[],[f6413,f1107]) ).
thf(f6413,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f6229,f4]) ).
thf(f4709,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| spl0_13 ),
inference(forward_demodulation,[],[f102,f67]) ).
thf(f6440,plain,
( spl0_75
| ~ spl0_4
| ~ spl0_5
| spl0_9 ),
inference(avatar_split_clause,[],[f6439,f83,f65,f23,f3173]) ).
thf(f6439,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_4
| ~ spl0_5
| spl0_9 ),
inference(subsumption_resolution,[],[f6411,f4712]) ).
thf(f6438,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f6437]) ).
thf(f6437,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f6436]) ).
thf(f6436,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_5
| spl0_7
| ~ spl0_8 ),
inference(backward_demodulation,[],[f80,f6435]) ).
thf(f6350,plain,
( spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f6349]) ).
thf(f6349,plain,
( $false
| spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f6348,f5903]) ).
thf(f6348,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6347,f2472]) ).
thf(f6347,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6346,f6312]) ).
thf(f6346,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| spl0_57
| ~ spl0_63
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6345,f1107]) ).
thf(f6345,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))) )
| spl0_57
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6201,f6312]) ).
thf(f6201,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| spl0_57
| ~ spl0_68 ),
inference(forward_demodulation,[],[f775,f1713]) ).
thf(f6269,plain,
( ~ spl0_68
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f6268]) ).
thf(f6268,plain,
( $false
| ~ spl0_68
| ~ spl0_78 ),
inference(trivial_inequality_removal,[],[f6267]) ).
thf(f6267,plain,
( ( $true = $false )
| ~ spl0_68
| ~ spl0_78 ),
inference(forward_demodulation,[],[f4808,f1713]) ).
thf(f6258,plain,
( ~ spl0_80
| spl0_44
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f6179,f1711,f702,f4821]) ).
thf(f6179,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_44
| ~ spl0_68 ),
inference(backward_demodulation,[],[f703,f1713]) ).
thf(f6257,plain,
( spl0_80
| ~ spl0_49
| ~ spl0_68
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f6212,f4810,f1711,f729,f4821]) ).
thf(f6212,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_49
| ~ spl0_68
| ~ spl0_79 ),
inference(forward_demodulation,[],[f6211,f4812]) ).
thf(f6211,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_49
| ~ spl0_68 ),
inference(forward_demodulation,[],[f731,f1713]) ).
thf(f6200,plain,
( ~ spl0_22
| ~ spl0_31
| spl0_40
| ~ spl0_58
| ~ spl0_63
| ~ spl0_68
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f6199]) ).
thf(f6199,plain,
( $false
| ~ spl0_22
| ~ spl0_31
| spl0_40
| ~ spl0_58
| ~ spl0_63
| ~ spl0_68
| ~ spl0_79 ),
inference(subsumption_resolution,[],[f6198,f357]) ).
thf(f6198,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_22
| ~ spl0_31
| ~ spl0_58
| ~ spl0_63
| ~ spl0_68
| ~ spl0_79 ),
inference(forward_demodulation,[],[f6197,f143]) ).
thf(f6197,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_31
| ~ spl0_58
| ~ spl0_63
| ~ spl0_68
| ~ spl0_79 ),
inference(backward_demodulation,[],[f6194,f6196]) ).
thf(f6196,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_58
| ~ spl0_68
| ~ spl0_79 ),
inference(forward_demodulation,[],[f6195,f4812]) ).
thf(f6195,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_58
| ~ spl0_68 ),
inference(forward_demodulation,[],[f781,f1713]) ).
thf(f6194,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_31
| ~ spl0_63 ),
inference(backward_demodulation,[],[f307,f1107]) ).
thf(f6186,plain,
( spl0_59
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f6185]) ).
thf(f6185,plain,
( $false
| spl0_59
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f6184,f1713]) ).
thf(f6184,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| spl0_59
| ~ spl0_68 ),
inference(forward_demodulation,[],[f6180,f1713]) ).
thf(f6180,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| spl0_59
| ~ spl0_68 ),
inference(backward_demodulation,[],[f1090,f1713]) ).
thf(f6173,plain,
( ~ spl0_68
| ~ spl0_25
| spl0_28 ),
inference(avatar_split_clause,[],[f6171,f287,f268,f1711]) ).
thf(f6171,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_25
| spl0_28 ),
inference(backward_demodulation,[],[f288,f270]) ).
thf(f6135,plain,
( ~ spl0_16
| ~ spl0_53
| ~ spl0_71
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f6134]) ).
thf(f6134,plain,
( $false
| ~ spl0_16
| ~ spl0_53
| ~ spl0_71
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f6133]) ).
thf(f6133,plain,
( ( $true = $false )
| ~ spl0_16
| ~ spl0_53
| ~ spl0_71
| ~ spl0_73 ),
inference(forward_demodulation,[],[f6132,f5903]) ).
thf(f6132,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_16
| ~ spl0_53
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6131,f2472]) ).
thf(f6131,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_16
| ~ spl0_53
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6130,f752]) ).
thf(f6130,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_16
| ~ spl0_71 ),
inference(forward_demodulation,[],[f116,f2472]) ).
thf(f6054,plain,
( spl0_18
| ~ spl0_22
| ~ spl0_53
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f6053]) ).
thf(f6053,plain,
( $false
| spl0_18
| ~ spl0_22
| ~ spl0_53
| ~ spl0_71 ),
inference(subsumption_resolution,[],[f6052,f143]) ).
thf(f6052,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_18
| ~ spl0_53
| ~ spl0_71 ),
inference(forward_demodulation,[],[f6051,f752]) ).
thf(f6051,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_18
| ~ spl0_71 ),
inference(forward_demodulation,[],[f124,f2472]) ).
thf(f124,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_18 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f6030,plain,
( spl0_40
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71
| ~ spl0_74 ),
inference(avatar_contradiction_clause,[],[f6029]) ).
thf(f6029,plain,
( $false
| spl0_40
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71
| ~ spl0_74 ),
inference(subsumption_resolution,[],[f6028,f357]) ).
thf(f6028,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71
| ~ spl0_74 ),
inference(forward_demodulation,[],[f6027,f752]) ).
thf(f6027,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_53
| ~ spl0_67
| ~ spl0_71
| ~ spl0_74 ),
inference(forward_demodulation,[],[f6026,f2472]) ).
thf(f6026,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_53
| ~ spl0_67
| ~ spl0_74 ),
inference(forward_demodulation,[],[f5908,f752]) ).
thf(f5908,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_67
| ~ spl0_74 ),
inference(backward_demodulation,[],[f3170,f1557]) ).
thf(f6016,plain,
( spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_76 ),
inference(avatar_contradiction_clause,[],[f6015]) ).
thf(f6015,plain,
( $false
| spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_76 ),
inference(subsumption_resolution,[],[f6014,f357]) ).
thf(f6014,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_76 ),
inference(forward_demodulation,[],[f6013,f752]) ).
thf(f6013,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71
| ~ spl0_76 ),
inference(forward_demodulation,[],[f6012,f2472]) ).
thf(f6012,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_53
| ~ spl0_63
| ~ spl0_76 ),
inference(forward_demodulation,[],[f5918,f752]) ).
thf(f5918,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_63
| ~ spl0_76 ),
inference(backward_demodulation,[],[f4515,f1107]) ).
thf(f6002,plain,
( ~ spl0_72
| ~ spl0_5
| ~ spl0_7
| spl0_19 ),
inference(avatar_split_clause,[],[f6000,f128,f74,f65,f3146]) ).
thf(f6000,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_19 ),
inference(forward_demodulation,[],[f5999,f462]) ).
thf(f462,plain,
( ( $false = vAPP($o,$o,f4,$false) )
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f76,f67]) ).
thf(f5999,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| spl0_19 ),
inference(forward_demodulation,[],[f129,f67]) ).
thf(f5894,plain,
( spl0_71
| spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f5826,f123,f114,f2471]) ).
thf(f5826,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| spl0_16
| ~ spl0_18 ),
inference(subsumption_resolution,[],[f5799,f125]) ).
thf(f5799,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( $false = vAPP($o,$o,f1,$true) )
| spl0_16 ),
inference(superposition,[],[f115,f4]) ).
thf(f5893,plain,
( spl0_44
| ~ spl0_63
| spl0_47 ),
inference(avatar_split_clause,[],[f4748,f718,f1105,f702]) ).
thf(f4748,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| spl0_47 ),
inference(superposition,[],[f719,f4]) ).
thf(f5880,plain,
( spl0_49
| ~ spl0_35
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f5557,f74,f65,f19,f330,f729]) ).
thf(f5557,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f5318,f4]) ).
thf(f5318,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f5317,f462]) ).
thf(f5317,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f5316,f462]) ).
thf(f5316,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f5315,f462]) ).
thf(f5315,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f20,f67]) ).
thf(f5879,plain,
( spl0_49
| spl0_50
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f5597,f74,f65,f10,f733,f729]) ).
thf(f5597,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f5333,f4]) ).
thf(f5333,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f5332,f462]) ).
thf(f5332,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f5331,f462]) ).
thf(f5331,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f5330,f462]) ).
thf(f5330,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f12,f67]) ).
thf(f5877,plain,
( ~ spl0_20
| spl0_16
| spl0_83 ),
inference(avatar_split_clause,[],[f5876,f5273,f114,f132]) ).
thf(f5876,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_16
| spl0_83 ),
inference(subsumption_resolution,[],[f5801,f5274]) ).
thf(f5801,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_16 ),
inference(superposition,[],[f115,f4]) ).
thf(f5865,plain,
( spl0_16
| ~ spl0_20
| ~ spl0_22
| spl0_40 ),
inference(avatar_contradiction_clause,[],[f5864]) ).
thf(f5864,plain,
( $false
| spl0_16
| ~ spl0_20
| ~ spl0_22
| spl0_40 ),
inference(subsumption_resolution,[],[f5863,f357]) ).
thf(f5863,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f5862,f5841]) ).
thf(f5841,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f5840]) ).
thf(f5840,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f1,$true) )
| spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f5816,f5832]) ).
thf(f5832,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16
| ~ spl0_22 ),
inference(subsumption_resolution,[],[f5803,f143]) ).
thf(f5803,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16 ),
inference(superposition,[],[f115,f4]) ).
thf(f5816,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16
| ~ spl0_20 ),
inference(binary_proxy_clausification,[],[f5815]) ).
thf(f5815,plain,
( ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f5808]) ).
thf(f5808,plain,
( ( $true != $true )
| ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16
| ~ spl0_20 ),
inference(constrained_superposition,[],[f115,f134]) ).
thf(f5862,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f5861,f5841]) ).
thf(f5861,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f5811,f5841]) ).
thf(f5811,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| spl0_16 ),
inference(trivial_inequality_removal,[],[f5810]) ).
thf(f5810,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| spl0_16 ),
inference(superposition,[],[f115,f4]) ).
thf(f5860,plain,
( spl0_16
| ~ spl0_18
| ~ spl0_20
| ~ spl0_22
| spl0_71 ),
inference(avatar_contradiction_clause,[],[f5859]) ).
thf(f5859,plain,
( $false
| spl0_16
| ~ spl0_18
| ~ spl0_20
| ~ spl0_22
| spl0_71 ),
inference(subsumption_resolution,[],[f5858,f2473]) ).
thf(f5858,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| spl0_16
| ~ spl0_18
| ~ spl0_20
| ~ spl0_22
| spl0_71 ),
inference(forward_demodulation,[],[f5857,f5841]) ).
thf(f5857,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_16
| ~ spl0_18
| spl0_71 ),
inference(subsumption_resolution,[],[f5814,f5588]) ).
thf(f5588,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f1,X0) )
| ( $false = X0 ) )
| spl0_71 ),
inference(superposition,[],[f2473,f4]) ).
thf(f5814,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16
| ~ spl0_18 ),
inference(binary_proxy_clausification,[],[f5812]) ).
thf(f5812,plain,
( ( vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f5809]) ).
thf(f5809,plain,
( ( $true != $true )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| spl0_16
| ~ spl0_18 ),
inference(constrained_superposition,[],[f115,f125]) ).
thf(f5537,plain,
( spl0_71
| spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f5536,f132,f123,f2471]) ).
thf(f5536,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| spl0_18
| ~ spl0_20 ),
inference(subsumption_resolution,[],[f5087,f134]) ).
thf(f5087,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,$true) )
| spl0_18 ),
inference(superposition,[],[f124,f4]) ).
thf(f5396,plain,
( ~ spl0_55
| spl0_16
| ~ spl0_70
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f5379,f5273,f2467,f114,f762]) ).
thf(f5379,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| spl0_16
| ~ spl0_70
| ~ spl0_83 ),
inference(forward_demodulation,[],[f5377,f2469]) ).
thf(f5377,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| spl0_16
| ~ spl0_83 ),
inference(backward_demodulation,[],[f115,f5275]) ).
thf(f5376,plain,
( spl0_71
| spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f5375,f141,f132,f2471]) ).
thf(f5375,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| spl0_20
| ~ spl0_22 ),
inference(subsumption_resolution,[],[f4896,f143]) ).
thf(f4896,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| spl0_20 ),
inference(superposition,[],[f133,f4]) ).
thf(f5371,plain,
( spl0_71
| spl0_40
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f5370,f3150,f356,f2471]) ).
thf(f5370,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| spl0_40
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5074,f357]) ).
thf(f5074,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_73 ),
inference(superposition,[],[f3152,f4]) ).
thf(f5323,plain,
( spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_51
| ~ spl0_56
| ~ spl0_57 ),
inference(avatar_contradiction_clause,[],[f5322]) ).
thf(f5322,plain,
( $false
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_51
| ~ spl0_56
| ~ spl0_57 ),
inference(subsumption_resolution,[],[f5321,f5283]) ).
thf(f5283,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_56
| ~ spl0_57 ),
inference(forward_demodulation,[],[f770,f776]) ).
thf(f5321,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_51
| ~ spl0_56
| ~ spl0_57 ),
inference(forward_demodulation,[],[f5320,f5283]) ).
thf(f5320,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_51
| ~ spl0_56
| ~ spl0_57 ),
inference(forward_demodulation,[],[f5319,f5283]) ).
thf(f5319,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_51 ),
inference(forward_demodulation,[],[f5318,f741]) ).
thf(f5276,plain,
( spl0_83
| ~ spl0_22
| spl0_18 ),
inference(avatar_split_clause,[],[f5089,f123,f141,f5273]) ).
thf(f5089,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_18 ),
inference(superposition,[],[f124,f4]) ).
thf(f5258,plain,
( ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_63
| spl0_71
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f5257]) ).
thf(f5257,plain,
( $false
| ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_63
| spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5226,f5191]) ).
thf(f5191,plain,
( ! [X0: $o] : ( $false = X0 )
| ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5190,f2473]) ).
thf(f5190,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = X0 ) )
| ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5189,f5172]) ).
thf(f5172,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_16
| ~ spl0_40
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f5171]) ).
thf(f5171,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_16
| ~ spl0_40
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5152,f5168]) ).
thf(f5168,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_16
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f5167]) ).
thf(f5167,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_16
| ~ spl0_40 ),
inference(forward_demodulation,[],[f5130,f358]) ).
thf(f5130,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_16 ),
inference(superposition,[],[f116,f4]) ).
thf(f5152,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_16
| ~ spl0_73 ),
inference(binary_proxy_clausification,[],[f5151]) ).
thf(f5151,plain,
( ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_16
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f5133]) ).
thf(f5133,plain,
( ( $true = $false )
| ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_16
| ~ spl0_73 ),
inference(constrained_superposition,[],[f116,f3152]) ).
thf(f5189,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ( $false = X0 ) )
| ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5188,f5172]) ).
thf(f5188,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) ) )
| ~ spl0_16
| spl0_20
| spl0_71 ),
inference(subsumption_resolution,[],[f5150,f4278]) ).
thf(f4278,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f1,X0) )
| ( $false = X0 ) )
| spl0_71 ),
inference(superposition,[],[f2473,f4]) ).
thf(f5150,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( $false = vAPP($o,$o,f1,X0) ) )
| ~ spl0_16
| spl0_20 ),
inference(binary_proxy_clausification,[],[f5148]) ).
thf(f5148,plain,
( ! [X0: $o] :
( ( $false = X0 )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) != vAPP($o,$o,f1,X0) ) )
| ~ spl0_16
| spl0_20 ),
inference(trivial_inequality_removal,[],[f5134]) ).
thf(f5134,plain,
( ! [X0: $o] :
( ( $true = $false )
| ( $false = X0 )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) != vAPP($o,$o,f1,X0) ) )
| ~ spl0_16
| spl0_20 ),
inference(constrained_superposition,[],[f116,f4908]) ).
thf(f4908,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,X0)) )
| ( $false = X0 ) )
| spl0_20 ),
inference(duplicate_literal_removal,[],[f4907]) ).
thf(f4907,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,X0)) )
| ( $false = X0 )
| ( $false = X0 ) )
| spl0_20 ),
inference(binary_proxy_clausification,[],[f4894]) ).
thf(f4894,plain,
( ! [X0: $o] :
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,X0)) != X0 )
| ( $false = X0 ) )
| spl0_20 ),
inference(superposition,[],[f133,f4]) ).
thf(f5226,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_63
| spl0_71
| ~ spl0_73 ),
inference(backward_demodulation,[],[f1106,f5191]) ).
thf(f5252,plain,
( ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_44
| spl0_71
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f5251]) ).
thf(f5251,plain,
( $false
| ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_44
| spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5220,f5191]) ).
thf(f5220,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_16
| spl0_20
| ~ spl0_40
| spl0_44
| spl0_71
| ~ spl0_73 ),
inference(backward_demodulation,[],[f703,f5191]) ).
thf(f5232,plain,
( ~ spl0_16
| spl0_20
| ~ spl0_40
| ~ spl0_55
| spl0_71
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f5231]) ).
thf(f5231,plain,
( $false
| ~ spl0_16
| spl0_20
| ~ spl0_40
| ~ spl0_55
| spl0_71
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f5219]) ).
thf(f5219,plain,
( ( $true = $false )
| ~ spl0_16
| spl0_20
| ~ spl0_40
| ~ spl0_55
| spl0_71
| ~ spl0_73 ),
inference(backward_demodulation,[],[f764,f5191]) ).
thf(f5185,plain,
( ~ spl0_16
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f5184]) ).
thf(f5184,plain,
( $false
| ~ spl0_16
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5183,f2473]) ).
thf(f5183,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_16
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5182,f5172]) ).
thf(f5182,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_16
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5181,f5172]) ).
thf(f5181,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_16
| spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5153,f2473]) ).
thf(f5153,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_16
| ~ spl0_73 ),
inference(binary_proxy_clausification,[],[f5151]) ).
thf(f5166,plain,
( ~ spl0_16
| spl0_18
| ~ spl0_55
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f5165]) ).
thf(f5165,plain,
( $false
| ~ spl0_16
| spl0_18
| ~ spl0_55
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f5164]) ).
thf(f5164,plain,
( ( $true = $false )
| ~ spl0_16
| spl0_18
| ~ spl0_55
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5163,f3152]) ).
thf(f5163,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_16
| spl0_18
| ~ spl0_55 ),
inference(subsumption_resolution,[],[f5128,f5098]) ).
thf(f5098,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_18
| ~ spl0_55 ),
inference(trivial_inequality_removal,[],[f5091]) ).
thf(f5091,plain,
( ( $true != $true )
| ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| spl0_18
| ~ spl0_55 ),
inference(constrained_superposition,[],[f124,f764]) ).
thf(f5128,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_16 ),
inference(superposition,[],[f116,f4]) ).
thf(f5068,plain,
( ~ spl0_18
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f5067]) ).
thf(f5067,plain,
( $false
| ~ spl0_18
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5066,f2473]) ).
thf(f5066,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_18
| ~ spl0_40
| spl0_71
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5065,f5050]) ).
thf(f5050,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_18
| ~ spl0_40
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f5049]) ).
thf(f5049,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f1,$true) )
| ~ spl0_18
| ~ spl0_40
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5032,f5044]) ).
thf(f5044,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f5043]) ).
thf(f5043,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_40 ),
inference(forward_demodulation,[],[f5018,f358]) ).
thf(f5018,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18 ),
inference(superposition,[],[f125,f4]) ).
thf(f5032,plain,
( ( $true = vAPP($o,$o,f1,$true) )
| ( $true = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_73 ),
inference(binary_proxy_clausification,[],[f5031]) ).
thf(f5031,plain,
( ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f5021]) ).
thf(f5021,plain,
( ( $true = $false )
| ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_73 ),
inference(constrained_superposition,[],[f125,f3152]) ).
thf(f5065,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| spl0_71
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5028,f2473]) ).
thf(f5028,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_73 ),
inference(binary_proxy_clausification,[],[f5026]) ).
thf(f5026,plain,
( ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f5025]) ).
thf(f5025,plain,
( ( $true = $false )
| ( vAPP($o,$o,f1,$true) != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_73 ),
inference(constrained_superposition,[],[f3152,f125]) ).
thf(f5064,plain,
( ~ spl0_18
| ~ spl0_40
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f5063]) ).
thf(f5063,plain,
( $false
| ~ spl0_18
| ~ spl0_40
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f5062,f5050]) ).
thf(f5062,plain,
( ( $true != vAPP($o,$o,f1,$true) )
| ~ spl0_18
| ~ spl0_40
| ~ spl0_73 ),
inference(forward_demodulation,[],[f5029,f5050]) ).
thf(f5029,plain,
( ( $true != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f5024]) ).
thf(f5024,plain,
( ( $true = $false )
| ( $true != vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_18
| ~ spl0_40 ),
inference(constrained_superposition,[],[f358,f125]) ).
thf(f4974,plain,
( ~ spl0_57
| ~ spl0_58 ),
inference(avatar_contradiction_clause,[],[f4973]) ).
thf(f4973,plain,
( $false
| ~ spl0_57
| ~ spl0_58 ),
inference(trivial_inequality_removal,[],[f4972]) ).
thf(f4972,plain,
( ( $true = $false )
| ~ spl0_57
| ~ spl0_58 ),
inference(forward_demodulation,[],[f781,f776]) ).
thf(f4969,plain,
( spl0_57
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f4926,f367,f74,f65,f774]) ).
thf(f4926,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42 ),
inference(forward_demodulation,[],[f4925,f462]) ).
thf(f4925,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42 ),
inference(forward_demodulation,[],[f4924,f462]) ).
thf(f4924,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42 ),
inference(forward_demodulation,[],[f369,f462]) ).
thf(f4941,plain,
( ~ spl0_14
| ~ spl0_76 ),
inference(avatar_contradiction_clause,[],[f4940]) ).
thf(f4940,plain,
( $false
| ~ spl0_14
| ~ spl0_76 ),
inference(trivial_inequality_removal,[],[f4939]) ).
thf(f4939,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_76 ),
inference(forward_demodulation,[],[f107,f4515]) ).
thf(f4935,plain,
( ~ spl0_31
| ~ spl0_45 ),
inference(avatar_contradiction_clause,[],[f4934]) ).
thf(f4934,plain,
( $false
| ~ spl0_31
| ~ spl0_45 ),
inference(trivial_inequality_removal,[],[f4933]) ).
thf(f4933,plain,
( ( $true = $false )
| ~ spl0_31
| ~ spl0_45 ),
inference(backward_demodulation,[],[f708,f307]) ).
thf(f708,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f706]) ).
thf(f4917,plain,
( ~ spl0_53
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f4916]) ).
thf(f4916,plain,
( $false
| ~ spl0_53
| ~ spl0_70 ),
inference(trivial_inequality_removal,[],[f4915]) ).
thf(f4915,plain,
( ( $true = $false )
| ~ spl0_53
| ~ spl0_70 ),
inference(backward_demodulation,[],[f752,f2469]) ).
thf(f4913,plain,
( spl0_73
| spl0_20 ),
inference(avatar_split_clause,[],[f4902,f132,f3150]) ).
thf(f4902,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_20 ),
inference(trivial_inequality_removal,[],[f4901]) ).
thf(f4901,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| spl0_20 ),
inference(superposition,[],[f133,f4]) ).
thf(f4875,plain,
( spl0_72
| spl0_73
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f4290,f74,f65,f23,f3150,f3146]) ).
thf(f4290,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f4067,f4]) ).
thf(f4067,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f4066,f462]) ).
thf(f4066,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f25,f67]) ).
thf(f4858,plain,
( spl0_47
| ~ spl0_49
| spl0_66
| spl0_67
| spl0_68 ),
inference(avatar_contradiction_clause,[],[f4857]) ).
thf(f4857,plain,
( $false
| spl0_47
| ~ spl0_49
| spl0_66
| spl0_67
| spl0_68 ),
inference(subsumption_resolution,[],[f4856,f719]) ).
thf(f4856,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_49
| spl0_66
| spl0_67
| spl0_68 ),
inference(subsumption_resolution,[],[f4777,f4744]) ).
thf(f4744,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| spl0_66
| spl0_68 ),
inference(subsumption_resolution,[],[f4742,f1712]) ).
thf(f4742,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f3,$false) )
| spl0_66 ),
inference(superposition,[],[f1552,f4]) ).
thf(f4777,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_49
| spl0_67 ),
inference(binary_proxy_clausification,[],[f4775]) ).
thf(f4775,plain,
( ( vAPP($o,$o,f3,$true) != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_49
| spl0_67 ),
inference(trivial_inequality_removal,[],[f4771]) ).
thf(f4771,plain,
( ( $false != $false )
| ( vAPP($o,$o,f3,$true) != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_49
| spl0_67 ),
inference(constrained_superposition,[],[f1556,f731]) ).
thf(f4850,plain,
( spl0_47
| ~ spl0_49
| spl0_63
| spl0_68 ),
inference(avatar_contradiction_clause,[],[f4849]) ).
thf(f4849,plain,
( $false
| spl0_47
| ~ spl0_49
| spl0_63
| spl0_68 ),
inference(subsumption_resolution,[],[f4848,f719]) ).
thf(f4848,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49
| spl0_63
| spl0_68 ),
inference(subsumption_resolution,[],[f4780,f1106]) ).
thf(f4780,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49
| spl0_68 ),
inference(binary_proxy_clausification,[],[f4778]) ).
thf(f4778,plain,
( ( vAPP($o,$o,f2,$true) != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49
| spl0_68 ),
inference(trivial_inequality_removal,[],[f4770]) ).
thf(f4770,plain,
( ( $false != $false )
| ( vAPP($o,$o,f2,$true) != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49
| spl0_68 ),
inference(constrained_superposition,[],[f4750,f731]) ).
thf(f4750,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| spl0_47
| spl0_68 ),
inference(subsumption_resolution,[],[f4747,f1712]) ).
thf(f4747,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$true)) )
| ( $false = vAPP($o,$o,f3,$false) )
| spl0_47 ),
inference(superposition,[],[f719,f4]) ).
thf(f4846,plain,
( spl0_44
| spl0_47
| ~ spl0_49 ),
inference(avatar_contradiction_clause,[],[f4845]) ).
thf(f4845,plain,
( $false
| spl0_44
| spl0_47
| ~ spl0_49 ),
inference(subsumption_resolution,[],[f4844,f719]) ).
thf(f4844,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_44
| spl0_47
| ~ spl0_49 ),
inference(subsumption_resolution,[],[f4783,f703]) ).
thf(f4783,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49 ),
inference(binary_proxy_clausification,[],[f4781]) ).
thf(f4781,plain,
( ( vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49 ),
inference(trivial_inequality_removal,[],[f4769]) ).
thf(f4769,plain,
( ( $false != $false )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49 ),
inference(constrained_superposition,[],[f719,f731]) ).
thf(f4838,plain,
( ~ spl0_80
| spl0_47
| ~ spl0_49
| spl0_68 ),
inference(avatar_split_clause,[],[f4837,f1711,f729,f718,f4821]) ).
thf(f4837,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| spl0_47
| ~ spl0_49
| spl0_68 ),
inference(subsumption_resolution,[],[f4836,f719]) ).
thf(f4836,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49
| spl0_68 ),
inference(subsumption_resolution,[],[f4788,f1712]) ).
thf(f4788,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ( $false = vAPP($o,$o,f3,$false) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49 ),
inference(binary_proxy_clausification,[],[f4767]) ).
thf(f4767,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ( vAPP($o,$o,f3,$false) != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| spl0_47
| ~ spl0_49 ),
inference(constrained_superposition,[],[f719,f731]) ).
thf(f4834,plain,
( ~ spl0_77
| ~ spl0_49
| spl0_63 ),
inference(avatar_split_clause,[],[f4789,f1105,f729,f4802]) ).
thf(f4789,plain,
( ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_49
| spl0_63 ),
inference(trivial_inequality_removal,[],[f4766]) ).
thf(f4766,plain,
( ( $false != $false )
| ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))) )
| ~ spl0_49
| spl0_63 ),
inference(constrained_superposition,[],[f1106,f731]) ).
thf(f4718,plain,
( spl0_61
| ~ spl0_66
| spl0_68 ),
inference(avatar_contradiction_clause,[],[f4717]) ).
thf(f4717,plain,
( $false
| spl0_61
| ~ spl0_66
| spl0_68 ),
inference(subsumption_resolution,[],[f4716,f1712]) ).
thf(f4716,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| spl0_61
| ~ spl0_66 ),
inference(trivial_inequality_removal,[],[f4715]) ).
thf(f4715,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f3,$false) )
| spl0_61
| ~ spl0_66 ),
inference(superposition,[],[f4703,f4]) ).
thf(f4703,plain,
( ( $true != vAPP($o,$o,f3,$false) )
| spl0_61
| ~ spl0_66 ),
inference(forward_demodulation,[],[f1098,f1553]) ).
thf(f4702,plain,
( ~ spl0_44
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f4701,f1551,f110,f74,f65,f702]) ).
thf(f4701,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_66 ),
inference(forward_demodulation,[],[f2930,f1553]) ).
thf(f2930,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_5
| ~ spl0_7
| spl0_15 ),
inference(forward_demodulation,[],[f2929,f462]) ).
thf(f4668,plain,
( ~ spl0_8
| spl0_14
| ~ spl0_49
| spl0_63
| spl0_67
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f4667]) ).
thf(f4667,plain,
( $false
| ~ spl0_8
| spl0_14
| ~ spl0_49
| spl0_63
| spl0_67
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f4666,f106]) ).
thf(f4666,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_8
| ~ spl0_49
| spl0_63
| spl0_67
| ~ spl0_68 ),
inference(forward_demodulation,[],[f4665,f4659]) ).
thf(f4659,plain,
( ( $true = vAPP($o,$o,f3,$true) )
| ~ spl0_49
| spl0_63
| spl0_67
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f4632,f4634]) ).
thf(f4634,plain,
( ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_49
| spl0_63
| ~ spl0_68 ),
inference(trivial_inequality_removal,[],[f4625]) ).
thf(f4625,plain,
( ( $false != $false )
| ( $true != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_49
| spl0_63
| ~ spl0_68 ),
inference(constrained_superposition,[],[f1106,f4519]) ).
thf(f4519,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_49
| ~ spl0_68 ),
inference(backward_demodulation,[],[f731,f1713]) ).
thf(f4632,plain,
( ( $true = vAPP($o,$o,f3,$true) )
| ( $true = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_49
| spl0_67
| ~ spl0_68 ),
inference(binary_proxy_clausification,[],[f4631]) ).
thf(f4631,plain,
( ( vAPP($o,$o,f3,$true) != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_49
| spl0_67
| ~ spl0_68 ),
inference(trivial_inequality_removal,[],[f4626]) ).
thf(f4626,plain,
( ( $false != $false )
| ( vAPP($o,$o,f3,$true) != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_49
| spl0_67
| ~ spl0_68 ),
inference(constrained_superposition,[],[f1556,f4519]) ).
thf(f4665,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ~ spl0_8
| ~ spl0_49
| spl0_63
| spl0_67
| ~ spl0_68 ),
inference(forward_demodulation,[],[f4660,f4659]) ).
thf(f4660,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ~ spl0_8
| ~ spl0_49
| spl0_63
| spl0_67
| ~ spl0_68 ),
inference(backward_demodulation,[],[f80,f4659]) ).
thf(f4517,plain,
( spl0_59
| spl0_76
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f4284,f74,f65,f23,f4513,f1089]) ).
thf(f4284,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[],[f4067,f4]) ).
thf(f4507,plain,
( spl0_49
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f4237,f326,f74,f65,f729]) ).
thf(f4237,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34 ),
inference(forward_demodulation,[],[f4236,f462]) ).
thf(f4236,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34 ),
inference(forward_demodulation,[],[f4235,f462]) ).
thf(f4235,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34 ),
inference(forward_demodulation,[],[f328,f462]) ).
thf(f4472,plain,
( spl0_44
| ~ spl0_47
| spl0_63 ),
inference(avatar_contradiction_clause,[],[f4471]) ).
thf(f4471,plain,
( $false
| spl0_44
| ~ spl0_47
| spl0_63 ),
inference(subsumption_resolution,[],[f4450,f703]) ).
thf(f4450,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_47
| spl0_63 ),
inference(trivial_inequality_removal,[],[f4440]) ).
thf(f4440,plain,
( ( $false != $false )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_47
| spl0_63 ),
inference(superposition,[],[f4310,f720]) ).
thf(f4310,plain,
( ! [X0: $o] :
( ( $false != vAPP($o,$o,f2,X0) )
| ( $false = X0 ) )
| spl0_63 ),
inference(superposition,[],[f1106,f4]) ).
thf(f4164,plain,
( spl0_51
| ~ spl0_5
| ~ spl0_7
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f4020,f337,f74,f65,f739]) ).
thf(f4020,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_36 ),
inference(forward_demodulation,[],[f4019,f462]) ).
thf(f4019,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_36 ),
inference(forward_demodulation,[],[f4018,f462]) ).
thf(f4018,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_36 ),
inference(forward_demodulation,[],[f339,f462]) ).
thf(f4163,plain,
( ~ spl0_49
| ~ spl0_5
| ~ spl0_7
| spl0_34 ),
inference(avatar_split_clause,[],[f4027,f326,f74,f65,f729]) ).
thf(f4027,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_5
| ~ spl0_7
| spl0_34 ),
inference(forward_demodulation,[],[f4026,f462]) ).
thf(f4026,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_34 ),
inference(forward_demodulation,[],[f4025,f462]) ).
thf(f4025,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_34 ),
inference(forward_demodulation,[],[f327,f462]) ).
thf(f4160,plain,
( spl0_68
| ~ spl0_63
| spl0_44 ),
inference(avatar_split_clause,[],[f3778,f702,f1105,f1711]) ).
thf(f3778,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f3,$false) )
| spl0_44 ),
inference(superposition,[],[f703,f4]) ).
thf(f3932,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_34
| ~ spl0_47
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f3931]) ).
thf(f3931,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_34
| ~ spl0_47
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f3930,f3800]) ).
thf(f3800,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3799,f1713]) ).
thf(f3799,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3788,f1713]) ).
thf(f3788,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_68 ),
inference(backward_demodulation,[],[f2930,f1713]) ).
thf(f3930,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34
| ~ spl0_47
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3929,f3785]) ).
thf(f3785,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_47
| ~ spl0_68 ),
inference(backward_demodulation,[],[f720,f1713]) ).
thf(f3929,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3928,f1713]) ).
thf(f3928,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34 ),
inference(forward_demodulation,[],[f3927,f462]) ).
thf(f3927,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34 ),
inference(forward_demodulation,[],[f3926,f462]) ).
thf(f3926,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_34 ),
inference(forward_demodulation,[],[f328,f462]) ).
thf(f3909,plain,
( spl0_29
| ~ spl0_40
| ~ spl0_47
| ~ spl0_53
| ~ spl0_55
| ~ spl0_63
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f3908]) ).
thf(f3908,plain,
( $false
| spl0_29
| ~ spl0_40
| ~ spl0_47
| ~ spl0_53
| ~ spl0_55
| ~ spl0_63
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f3907,f358]) ).
thf(f3907,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_29
| ~ spl0_40
| ~ spl0_47
| ~ spl0_53
| ~ spl0_55
| ~ spl0_63
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3906,f764]) ).
thf(f3906,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_29
| ~ spl0_40
| ~ spl0_47
| ~ spl0_53
| ~ spl0_63
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3904,f358]) ).
thf(f3904,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| spl0_29
| ~ spl0_47
| ~ spl0_53
| ~ spl0_63
| ~ spl0_68 ),
inference(backward_demodulation,[],[f3821,f752]) ).
thf(f3821,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_29
| ~ spl0_47
| ~ spl0_63
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3820,f3785]) ).
thf(f3820,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_29
| ~ spl0_63 ),
inference(forward_demodulation,[],[f292,f1107]) ).
thf(f3875,plain,
( spl0_73
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42
| ~ spl0_47
| ~ spl0_65
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f3853,f1711,f1116,f718,f367,f74,f65,f3150]) ).
thf(f3853,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42
| ~ spl0_47
| ~ spl0_65
| ~ spl0_68 ),
inference(backward_demodulation,[],[f3685,f3851]) ).
thf(f3851,plain,
( ( $true = vAPP($o,$o,f2,$false) )
| ~ spl0_65
| ~ spl0_68 ),
inference(forward_demodulation,[],[f1118,f1713]) ).
thf(f3685,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42
| ~ spl0_47 ),
inference(forward_demodulation,[],[f3684,f720]) ).
thf(f3684,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42 ),
inference(forward_demodulation,[],[f3683,f462]) ).
thf(f3683,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42 ),
inference(forward_demodulation,[],[f3682,f462]) ).
thf(f3682,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_42 ),
inference(forward_demodulation,[],[f369,f462]) ).
thf(f3873,plain,
( spl0_71
| ~ spl0_65
| ~ spl0_68
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f3870,f3146,f1711,f1116,f2471]) ).
thf(f3870,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_65
| ~ spl0_68
| ~ spl0_72 ),
inference(duplicate_literal_removal,[],[f3864]) ).
thf(f3864,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_65
| ~ spl0_68
| ~ spl0_72 ),
inference(superposition,[],[f3856,f4]) ).
thf(f3856,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,$true)) )
| ~ spl0_65
| ~ spl0_68
| ~ spl0_72 ),
inference(backward_demodulation,[],[f3802,f3851]) ).
thf(f3802,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))) )
| ~ spl0_68
| ~ spl0_72 ),
inference(forward_demodulation,[],[f3801,f1713]) ).
thf(f3801,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_68
| ~ spl0_72 ),
inference(forward_demodulation,[],[f3789,f1713]) ).
thf(f3789,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))) )
| ~ spl0_68
| ~ spl0_72 ),
inference(backward_demodulation,[],[f3148,f1713]) ).
thf(f3850,plain,
( ~ spl0_47
| spl0_49
| spl0_65
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f3849]) ).
thf(f3849,plain,
( $false
| ~ spl0_47
| spl0_49
| spl0_65
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f3848,f3675]) ).
thf(f3675,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_47
| spl0_49 ),
inference(forward_demodulation,[],[f730,f720]) ).
thf(f3848,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| spl0_65
| ~ spl0_68 ),
inference(trivial_inequality_removal,[],[f3847]) ).
thf(f3847,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f2,$false) )
| spl0_65
| ~ spl0_68 ),
inference(superposition,[],[f3787,f4]) ).
thf(f3787,plain,
( ( $true != vAPP($o,$o,f2,$false) )
| spl0_65
| ~ spl0_68 ),
inference(backward_demodulation,[],[f1117,f1713]) ).
thf(f3841,plain,
( ~ spl0_71
| ~ spl0_55
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f3837,f3150,f762,f2471]) ).
thf(f3837,plain,
( ( $false != vAPP($o,$o,f1,$true) )
| ~ spl0_55
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f3834]) ).
thf(f3834,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f1,$true) )
| ~ spl0_55
| ~ spl0_73 ),
inference(constrained_superposition,[],[f764,f3152]) ).
thf(f3796,plain,
( ~ spl0_29
| spl0_33
| ~ spl0_40
| ~ spl0_47
| ~ spl0_55
| ~ spl0_63
| ~ spl0_68
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f3795]) ).
thf(f3795,plain,
( $false
| ~ spl0_29
| spl0_33
| ~ spl0_40
| ~ spl0_47
| ~ spl0_55
| ~ spl0_63
| ~ spl0_68
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f3794,f3589]) ).
thf(f3589,plain,
( ( $false != vAPP($o,$o,f0,$false) )
| spl0_33
| ~ spl0_40
| ~ spl0_55
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3588,f358]) ).
thf(f3588,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| spl0_33
| ~ spl0_55
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3587,f764]) ).
thf(f3587,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| spl0_33
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3586,f2469]) ).
thf(f3586,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| spl0_33
| ~ spl0_63 ),
inference(forward_demodulation,[],[f319,f1107]) ).
thf(f319,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| spl0_33 ),
inference(avatar_component_clause,[],[f318]) ).
thf(f3794,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_29
| ~ spl0_40
| ~ spl0_47
| ~ spl0_55
| ~ spl0_63
| ~ spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3793,f358]) ).
thf(f3793,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_29
| ~ spl0_47
| ~ spl0_55
| ~ spl0_63
| ~ spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3792,f764]) ).
thf(f3792,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ~ spl0_29
| ~ spl0_47
| ~ spl0_63
| ~ spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3791,f2469]) ).
thf(f3791,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ~ spl0_29
| ~ spl0_47
| ~ spl0_63
| ~ spl0_68 ),
inference(backward_demodulation,[],[f3702,f3785]) ).
thf(f3702,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ~ spl0_29
| ~ spl0_63 ),
inference(forward_demodulation,[],[f293,f1107]) ).
thf(f3708,plain,
( ~ spl0_10
| ~ spl0_75 ),
inference(avatar_contradiction_clause,[],[f3707]) ).
thf(f3707,plain,
( $false
| ~ spl0_10
| ~ spl0_75 ),
inference(trivial_inequality_removal,[],[f3706]) ).
thf(f3706,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_75 ),
inference(forward_demodulation,[],[f89,f3175]) ).
thf(f3537,plain,
( ~ spl0_40
| ~ spl0_50
| ~ spl0_55
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f3536]) ).
thf(f3536,plain,
( $false
| ~ spl0_40
| ~ spl0_50
| ~ spl0_55
| ~ spl0_73 ),
inference(trivial_inequality_removal,[],[f3535]) ).
thf(f3535,plain,
( ( $true = $false )
| ~ spl0_40
| ~ spl0_50
| ~ spl0_55
| ~ spl0_73 ),
inference(forward_demodulation,[],[f3534,f358]) ).
thf(f3534,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_50
| ~ spl0_55
| ~ spl0_73 ),
inference(forward_demodulation,[],[f3530,f764]) ).
thf(f3530,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_50
| ~ spl0_73 ),
inference(backward_demodulation,[],[f735,f3152]) ).
thf(f735,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f733]) ).
thf(f3533,plain,
( spl0_35
| ~ spl0_40
| ~ spl0_55
| ~ spl0_73 ),
inference(avatar_contradiction_clause,[],[f3532]) ).
thf(f3532,plain,
( $false
| spl0_35
| ~ spl0_40
| ~ spl0_55
| ~ spl0_73 ),
inference(subsumption_resolution,[],[f3531,f358]) ).
thf(f3531,plain,
( ( $false != vAPP($o,$o,f0,$true) )
| spl0_35
| ~ spl0_55
| ~ spl0_73 ),
inference(forward_demodulation,[],[f3529,f764]) ).
thf(f3529,plain,
( ( $false != vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| spl0_35
| ~ spl0_73 ),
inference(backward_demodulation,[],[f331,f3152]) ).
thf(f3528,plain,
( ~ spl0_12
| ~ spl0_74 ),
inference(avatar_contradiction_clause,[],[f3527]) ).
thf(f3527,plain,
( $false
| ~ spl0_12
| ~ spl0_74 ),
inference(trivial_inequality_removal,[],[f3526]) ).
thf(f3526,plain,
( ( $true = $false )
| ~ spl0_12
| ~ spl0_74 ),
inference(backward_demodulation,[],[f98,f3170]) ).
thf(f3513,plain,
( ~ spl0_14
| ~ spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f3512]) ).
thf(f3512,plain,
( $false
| ~ spl0_14
| ~ spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(trivial_inequality_removal,[],[f3511]) ).
thf(f3511,plain,
( ( $true = $false )
| ~ spl0_14
| ~ spl0_40
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(forward_demodulation,[],[f3510,f358]) ).
thf(f3510,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_14
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(forward_demodulation,[],[f3509,f752]) ).
thf(f3509,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_14
| ~ spl0_53
| ~ spl0_63
| ~ spl0_71 ),
inference(forward_demodulation,[],[f3402,f2472]) ).
thf(f3402,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ~ spl0_14
| ~ spl0_53
| ~ spl0_63 ),
inference(backward_demodulation,[],[f3089,f752]) ).
thf(f3089,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_14
| ~ spl0_63 ),
inference(forward_demodulation,[],[f107,f1107]) ).
thf(f3508,plain,
( ~ spl0_18
| ~ spl0_40
| ~ spl0_53
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f3507]) ).
thf(f3507,plain,
( $false
| ~ spl0_18
| ~ spl0_40
| ~ spl0_53
| ~ spl0_71 ),
inference(trivial_inequality_removal,[],[f3506]) ).
thf(f3506,plain,
( ( $true = $false )
| ~ spl0_18
| ~ spl0_40
| ~ spl0_53
| ~ spl0_71 ),
inference(forward_demodulation,[],[f3505,f358]) ).
thf(f3505,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_18
| ~ spl0_53
| ~ spl0_71 ),
inference(forward_demodulation,[],[f3502,f752]) ).
thf(f3502,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_18
| ~ spl0_71 ),
inference(backward_demodulation,[],[f125,f2472]) ).
thf(f3498,plain,
( spl0_71
| ~ spl0_20
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f3497,f356,f132,f2471]) ).
thf(f3497,plain,
( ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_20
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f3496]) ).
thf(f3496,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_20
| ~ spl0_40 ),
inference(forward_demodulation,[],[f3484,f358]) ).
thf(f3484,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f1,$true) )
| ~ spl0_20 ),
inference(superposition,[],[f134,f4]) ).
thf(f3394,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_27
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f3393]) ).
thf(f3393,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_27
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f3392]) ).
thf(f3392,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f3389,f3322]) ).
thf(f3322,plain,
( ( $false = vAPP($o,$o,f0,$false) )
| ~ spl0_27
| ~ spl0_40 ),
inference(forward_demodulation,[],[f284,f358]) ).
thf(f3389,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21 ),
inference(backward_demodulation,[],[f3359,f3326]) ).
thf(f3326,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_21 ),
inference(forward_demodulation,[],[f3325,f462]) ).
thf(f3325,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_5
| ~ spl0_21 ),
inference(forward_demodulation,[],[f139,f67]) ).
thf(f3359,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f3358,f462]) ).
thf(f3358,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f16,f67]) ).
thf(f3208,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_44
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f3207]) ).
thf(f3207,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_44
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f3206,f3177]) ).
thf(f3177,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_44
| ~ spl0_68 ),
inference(backward_demodulation,[],[f704,f1713]) ).
thf(f3206,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3205,f1713]) ).
thf(f3205,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3181,f1713]) ).
thf(f3181,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_5
| ~ spl0_7
| spl0_15
| ~ spl0_68 ),
inference(backward_demodulation,[],[f2930,f1713]) ).
thf(f3199,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_44
| ~ spl0_68
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f3198]) ).
thf(f3198,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_44
| ~ spl0_68
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f3197,f2469]) ).
thf(f3197,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_44
| ~ spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3196,f2469]) ).
thf(f3196,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_44
| ~ spl0_68
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3195,f2469]) ).
thf(f3195,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_44
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3194,f3177]) ).
thf(f3194,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3193,f1713]) ).
thf(f3193,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_68 ),
inference(forward_demodulation,[],[f3179,f1713]) ).
thf(f3179,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_21
| ~ spl0_68 ),
inference(backward_demodulation,[],[f2721,f1713]) ).
thf(f2721,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_21 ),
inference(forward_demodulation,[],[f2720,f462]) ).
thf(f2720,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_5
| spl0_21 ),
inference(forward_demodulation,[],[f138,f67]) ).
thf(f3187,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_34
| ~ spl0_44
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f3186]) ).
thf(f3186,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_34
| ~ spl0_44
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f3183,f3177]) ).
thf(f3183,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_34
| ~ spl0_44
| ~ spl0_68 ),
inference(backward_demodulation,[],[f2958,f3177]) ).
thf(f2958,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_34
| ~ spl0_44 ),
inference(forward_demodulation,[],[f2957,f704]) ).
thf(f2957,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))) )
| ~ spl0_5
| ~ spl0_7
| spl0_34 ),
inference(forward_demodulation,[],[f2956,f462]) ).
thf(f2956,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_34 ),
inference(forward_demodulation,[],[f2955,f462]) ).
thf(f2955,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_34 ),
inference(forward_demodulation,[],[f327,f462]) ).
thf(f3060,plain,
( ~ spl0_14
| spl0_55
| ~ spl0_63
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f3059]) ).
thf(f3059,plain,
( $false
| ~ spl0_14
| spl0_55
| ~ spl0_63
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f3058,f763]) ).
thf(f3058,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_14
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3057,f2469]) ).
thf(f3057,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_14
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3056,f2469]) ).
thf(f3056,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_14
| ~ spl0_63
| ~ spl0_70 ),
inference(forward_demodulation,[],[f2873,f2469]) ).
thf(f2873,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_14
| ~ spl0_63 ),
inference(forward_demodulation,[],[f107,f1107]) ).
thf(f3055,plain,
( ~ spl0_12
| spl0_55
| ~ spl0_67
| ~ spl0_70 ),
inference(avatar_contradiction_clause,[],[f3054]) ).
thf(f3054,plain,
( $false
| ~ spl0_12
| spl0_55
| ~ spl0_67
| ~ spl0_70 ),
inference(subsumption_resolution,[],[f3053,f763]) ).
thf(f3053,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_12
| ~ spl0_67
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3052,f2469]) ).
thf(f3052,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_12
| ~ spl0_67
| ~ spl0_70 ),
inference(forward_demodulation,[],[f3051,f2469]) ).
thf(f3051,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_12
| ~ spl0_67
| ~ spl0_70 ),
inference(backward_demodulation,[],[f2875,f2469]) ).
thf(f2875,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_12
| ~ spl0_67 ),
inference(forward_demodulation,[],[f98,f1557]) ).
thf(f3047,plain,
( spl0_70
| spl0_53 ),
inference(avatar_split_clause,[],[f3044,f750,f2467]) ).
thf(f3044,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| spl0_53 ),
inference(trivial_inequality_removal,[],[f3043]) ).
thf(f3043,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f1,$false) )
| spl0_53 ),
inference(superposition,[],[f751,f4]) ).
thf(f751,plain,
( ( $true != vAPP($o,$o,f1,$false) )
| spl0_53 ),
inference(avatar_component_clause,[],[f750]) ).
thf(f2969,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f2968]) ).
thf(f2968,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f2967]) ).
thf(f2967,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(backward_demodulation,[],[f2893,f2966]) ).
thf(f2966,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f2965,f462]) ).
thf(f2965,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f25,f67]) ).
thf(f2893,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f2892,f462]) ).
thf(f2892,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f16,f67]) ).
thf(f2931,plain,
( spl0_70
| ~ spl0_44
| ~ spl0_49
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f2920,f739,f729,f702,f2467]) ).
thf(f2920,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_44
| ~ spl0_49
| ~ spl0_51 ),
inference(backward_demodulation,[],[f2817,f2919]) ).
thf(f2919,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| ~ spl0_49 ),
inference(forward_demodulation,[],[f731,f704]) ).
thf(f2817,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| ~ spl0_51 ),
inference(forward_demodulation,[],[f741,f704]) ).
thf(f2854,plain,
( ~ spl0_20
| ~ spl0_22
| ~ spl0_35
| spl0_40 ),
inference(avatar_contradiction_clause,[],[f2853]) ).
thf(f2853,plain,
( $false
| ~ spl0_20
| ~ spl0_22
| ~ spl0_35
| spl0_40 ),
inference(subsumption_resolution,[],[f2852,f357]) ).
thf(f2852,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_20
| ~ spl0_22
| ~ spl0_35 ),
inference(forward_demodulation,[],[f2851,f143]) ).
thf(f2851,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_20
| ~ spl0_35 ),
inference(forward_demodulation,[],[f332,f134]) ).
thf(f2824,plain,
( ~ spl0_20
| ~ spl0_22
| spl0_50 ),
inference(avatar_contradiction_clause,[],[f2823]) ).
thf(f2823,plain,
( $false
| ~ spl0_20
| ~ spl0_22
| spl0_50 ),
inference(subsumption_resolution,[],[f2822,f143]) ).
thf(f2822,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| ~ spl0_20
| ~ spl0_22
| spl0_50 ),
inference(forward_demodulation,[],[f2821,f143]) ).
thf(f2821,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_20
| spl0_50 ),
inference(forward_demodulation,[],[f734,f134]) ).
thf(f734,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| spl0_50 ),
inference(avatar_component_clause,[],[f733]) ).
thf(f2643,plain,
( spl0_22
| ~ spl0_46
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f2642,f762,f713,f141]) ).
thf(f2642,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_46
| ~ spl0_55 ),
inference(forward_demodulation,[],[f715,f764]) ).
thf(f715,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f713]) ).
thf(f2600,plain,
( ~ spl0_55
| ~ spl0_20
| ~ spl0_40
| spl0_50 ),
inference(avatar_split_clause,[],[f2492,f733,f356,f132,f762]) ).
thf(f2492,plain,
( ( $true != vAPP($o,$o,f0,$false) )
| ~ spl0_20
| ~ spl0_40
| spl0_50 ),
inference(forward_demodulation,[],[f2491,f358]) ).
thf(f2491,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_20
| spl0_50 ),
inference(forward_demodulation,[],[f734,f134]) ).
thf(f2503,plain,
( ~ spl0_70
| ~ spl0_5
| ~ spl0_7
| spl0_36
| ~ spl0_44
| ~ spl0_47
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f2502,f1711,f718,f702,f337,f74,f65,f2467]) ).
thf(f2502,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_36
| ~ spl0_44
| ~ spl0_47
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2501,f2207]) ).
thf(f2207,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_44
| ~ spl0_47 ),
inference(forward_demodulation,[],[f720,f704]) ).
thf(f2501,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_36
| ~ spl0_44
| ~ spl0_47
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2500,f2207]) ).
thf(f2500,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_5
| ~ spl0_7
| spl0_36
| ~ spl0_44
| ~ spl0_47
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2499,f2207]) ).
thf(f2499,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_5
| ~ spl0_7
| spl0_36
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2498,f1713]) ).
thf(f2498,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_36 ),
inference(forward_demodulation,[],[f2497,f462]) ).
thf(f2497,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_36 ),
inference(forward_demodulation,[],[f2496,f462]) ).
thf(f2496,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_5
| ~ spl0_7
| spl0_36 ),
inference(forward_demodulation,[],[f338,f462]) ).
thf(f2490,plain,
( ~ spl0_70
| ~ spl0_44
| ~ spl0_47
| spl0_51
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f2489,f1711,f739,f718,f702,f2467]) ).
thf(f2489,plain,
( ( $false != vAPP($o,$o,f1,$false) )
| ~ spl0_44
| ~ spl0_47
| spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2488,f2207]) ).
thf(f2488,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| ~ spl0_47
| spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2487,f2207]) ).
thf(f2487,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| ~ spl0_47
| spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2486,f2207]) ).
thf(f2486,plain,
( ( $false != vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f740,f1713]) ).
thf(f2417,plain,
( spl0_55
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_44
| ~ spl0_47
| ~ spl0_51
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f2398,f1711,f739,f718,f702,f74,f65,f14,f762]) ).
thf(f2398,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_44
| ~ spl0_47
| ~ spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2397,f2321]) ).
thf(f2321,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_44
| ~ spl0_47
| ~ spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2320,f2207]) ).
thf(f2320,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| ~ spl0_47
| ~ spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2319,f2207]) ).
thf(f2319,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))) )
| ~ spl0_44
| ~ spl0_47
| ~ spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2318,f2207]) ).
thf(f2318,plain,
( ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))) )
| ~ spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f741,f1713]) ).
thf(f2397,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_44
| ~ spl0_47
| ~ spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2396,f2321]) ).
thf(f2396,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_44
| ~ spl0_47
| ~ spl0_51
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2395,f2321]) ).
thf(f2395,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_44
| ~ spl0_47
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2394,f2207]) ).
thf(f2394,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2393,f1713]) ).
thf(f2393,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2392,f1713]) ).
thf(f2392,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2391,f1713]) ).
thf(f2391,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f2390,f462]) ).
thf(f2390,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f16,f67]) ).
thf(f2317,plain,
( ~ spl0_22
| ~ spl0_44
| ~ spl0_47
| ~ spl0_53
| spl0_54
| ~ spl0_68 ),
inference(avatar_contradiction_clause,[],[f2316]) ).
thf(f2316,plain,
( $false
| ~ spl0_22
| ~ spl0_44
| ~ spl0_47
| ~ spl0_53
| spl0_54
| ~ spl0_68 ),
inference(subsumption_resolution,[],[f2315,f143]) ).
thf(f2315,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| ~ spl0_22
| ~ spl0_44
| ~ spl0_47
| ~ spl0_53
| spl0_54
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2314,f143]) ).
thf(f2314,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_44
| ~ spl0_47
| ~ spl0_53
| spl0_54
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2313,f752]) ).
thf(f2313,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false))) )
| ~ spl0_44
| ~ spl0_47
| spl0_54
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2312,f2207]) ).
thf(f2312,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false)))) )
| ~ spl0_44
| ~ spl0_47
| spl0_54
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2311,f2207]) ).
thf(f2311,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false))))) )
| ~ spl0_44
| ~ spl0_47
| spl0_54
| ~ spl0_68 ),
inference(forward_demodulation,[],[f2310,f2207]) ).
thf(f2310,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| spl0_54
| ~ spl0_68 ),
inference(forward_demodulation,[],[f759,f1713]) ).
thf(f759,plain,
( ( $true != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))))) )
| spl0_54 ),
inference(avatar_component_clause,[],[f758]) ).
thf(f2233,plain,
( spl0_68
| spl0_63
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f2145,f702,f1105,f1711]) ).
thf(f2145,plain,
( ( $false = vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_44 ),
inference(superposition,[],[f704,f4]) ).
thf(f2232,plain,
( spl0_68
| ~ spl0_59
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f2197,f1551,f1089,f1711]) ).
thf(f2197,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_59
| ~ spl0_66 ),
inference(forward_demodulation,[],[f1091,f1553]) ).
thf(f2231,plain,
( spl0_68
| ~ spl0_5
| ~ spl0_7
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f2215,f287,f74,f65,f1711]) ).
thf(f2215,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_28 ),
inference(forward_demodulation,[],[f2214,f462]) ).
thf(f2214,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_28 ),
inference(forward_demodulation,[],[f2213,f462]) ).
thf(f2213,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_28 ),
inference(forward_demodulation,[],[f289,f462]) ).
thf(f2230,plain,
( spl0_68
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f2220,f1551,f101,f74,f65,f1711]) ).
thf(f2220,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13
| ~ spl0_66 ),
inference(forward_demodulation,[],[f2219,f1553]) ).
thf(f2219,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f2218,f462]) ).
thf(f2218,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f103,f67]) ).
thf(f2124,plain,
( spl0_22
| spl0_40 ),
inference(avatar_contradiction_clause,[],[f2123]) ).
thf(f2123,plain,
( $false
| spl0_22
| spl0_40 ),
inference(subsumption_resolution,[],[f2118,f357]) ).
thf(f2118,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| spl0_22 ),
inference(trivial_inequality_removal,[],[f2117]) ).
thf(f2117,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f0,$true) )
| spl0_22 ),
inference(superposition,[],[f142,f4]) ).
thf(f142,plain,
( ( $true != vAPP($o,$o,f0,$true) )
| spl0_22 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f1777,plain,
( ~ spl0_68
| ~ spl0_5
| ~ spl0_7
| spl0_9 ),
inference(avatar_split_clause,[],[f1776,f83,f74,f65,f1711]) ).
thf(f1776,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_9 ),
inference(forward_demodulation,[],[f1775,f462]) ).
thf(f1775,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_9 ),
inference(forward_demodulation,[],[f84,f67]) ).
thf(f1758,plain,
( ~ spl0_68
| ~ spl0_5
| ~ spl0_7
| spl0_28 ),
inference(avatar_split_clause,[],[f1757,f287,f74,f65,f1711]) ).
thf(f1757,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_28 ),
inference(forward_demodulation,[],[f1756,f462]) ).
thf(f1756,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_28 ),
inference(forward_demodulation,[],[f1755,f462]) ).
thf(f1755,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| ~ spl0_7
| spl0_28 ),
inference(forward_demodulation,[],[f288,f462]) ).
thf(f1718,plain,
( spl0_68
| spl0_69
| ~ spl0_5
| ~ spl0_7
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f968,f110,f74,f65,f1715,f1711]) ).
thf(f968,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))) )
| ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_15 ),
inference(superposition,[],[f501,f4]) ).
thf(f501,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false)))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_15 ),
inference(forward_demodulation,[],[f500,f462]) ).
thf(f500,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))) )
| ~ spl0_5
| ~ spl0_15 ),
inference(forward_demodulation,[],[f112,f67]) ).
thf(f1709,plain,
( spl0_44
| ~ spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1708,f1551,f110,f74,f65,f702]) ).
thf(f1708,plain,
( ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_15
| ~ spl0_66 ),
inference(backward_demodulation,[],[f501,f1553]) ).
thf(f1663,plain,
( ~ spl0_33
| ~ spl0_48 ),
inference(avatar_contradiction_clause,[],[f1662]) ).
thf(f1662,plain,
( $false
| ~ spl0_33
| ~ spl0_48 ),
inference(trivial_inequality_removal,[],[f1661]) ).
thf(f1661,plain,
( ( $true = $false )
| ~ spl0_33
| ~ spl0_48 ),
inference(forward_demodulation,[],[f724,f320]) ).
thf(f724,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f722]) ).
thf(f1584,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f1583]) ).
thf(f1583,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_28 ),
inference(subsumption_resolution,[],[f1582,f1523]) ).
thf(f1523,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_28 ),
inference(forward_demodulation,[],[f1522,f462]) ).
thf(f1522,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_28 ),
inference(forward_demodulation,[],[f1521,f462]) ).
thf(f1521,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| ~ spl0_7
| spl0_28 ),
inference(forward_demodulation,[],[f288,f462]) ).
thf(f1582,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1581,f462]) ).
thf(f1581,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f85,f67]) ).
thf(f1442,plain,
( ~ spl0_22
| ~ spl0_27
| spl0_40 ),
inference(avatar_contradiction_clause,[],[f1441]) ).
thf(f1441,plain,
( $false
| ~ spl0_22
| ~ spl0_27
| spl0_40 ),
inference(subsumption_resolution,[],[f1440,f357]) ).
thf(f1440,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_22
| ~ spl0_27 ),
inference(forward_demodulation,[],[f284,f143]) ).
thf(f1426,plain,
( ~ spl0_35
| ~ spl0_50 ),
inference(avatar_contradiction_clause,[],[f1425]) ).
thf(f1425,plain,
( $false
| ~ spl0_35
| ~ spl0_50 ),
inference(trivial_inequality_removal,[],[f1424]) ).
thf(f1424,plain,
( ( $true = $false )
| ~ spl0_35
| ~ spl0_50 ),
inference(backward_demodulation,[],[f735,f332]) ).
thf(f1423,plain,
( ~ spl0_22
| ~ spl0_37
| spl0_40 ),
inference(avatar_contradiction_clause,[],[f1422]) ).
thf(f1422,plain,
( $false
| ~ spl0_22
| ~ spl0_37
| spl0_40 ),
inference(subsumption_resolution,[],[f1421,f357]) ).
thf(f1421,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ~ spl0_22
| ~ spl0_37 ),
inference(forward_demodulation,[],[f1420,f143]) ).
thf(f1420,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ~ spl0_22
| ~ spl0_37 ),
inference(forward_demodulation,[],[f343,f143]) ).
thf(f1220,plain,
( ~ spl0_22
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f1219]) ).
thf(f1219,plain,
( $false
| ~ spl0_22
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f1218]) ).
thf(f1218,plain,
( ( $true = $false )
| ~ spl0_22
| ~ spl0_40 ),
inference(forward_demodulation,[],[f143,f358]) ).
thf(f1172,plain,
( ~ spl0_44
| ~ spl0_47
| spl0_49 ),
inference(avatar_contradiction_clause,[],[f1171]) ).
thf(f1171,plain,
( $false
| ~ spl0_44
| ~ spl0_47
| spl0_49 ),
inference(subsumption_resolution,[],[f1162,f1159]) ).
thf(f1159,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_44
| ~ spl0_47 ),
inference(forward_demodulation,[],[f720,f704]) ).
thf(f1162,plain,
( ( $false != vAPP($o,$o,f2,$false) )
| ~ spl0_44
| ~ spl0_47
| spl0_49 ),
inference(backward_demodulation,[],[f1125,f1159]) ).
thf(f1125,plain,
( ( $false != vAPP($o,$o,f2,vAPP($o,$o,f2,$false)) )
| ~ spl0_44
| spl0_49 ),
inference(backward_demodulation,[],[f730,f704]) ).
thf(f1123,plain,
( spl0_44
| ~ spl0_63
| spl0_47 ),
inference(avatar_split_clause,[],[f951,f718,f1105,f702]) ).
thf(f951,plain,
( ( $false != vAPP($o,$o,f2,$true) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,$false)) )
| spl0_47 ),
inference(superposition,[],[f719,f4]) ).
thf(f915,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_9
| spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f914]) ).
thf(f914,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_9
| spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f913,f845]) ).
thf(f845,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ~ spl0_5
| ~ spl0_7
| spl0_9
| spl0_11 ),
inference(subsumption_resolution,[],[f843,f637]) ).
thf(f637,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_9 ),
inference(forward_demodulation,[],[f636,f462]) ).
thf(f636,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| spl0_9 ),
inference(forward_demodulation,[],[f84,f67]) ).
thf(f843,plain,
( ( $false != vAPP($o,$o,f3,$true) )
| ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_11 ),
inference(superposition,[],[f645,f4]) ).
thf(f645,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_11 ),
inference(forward_demodulation,[],[f644,f462]) ).
thf(f644,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| spl0_11 ),
inference(forward_demodulation,[],[f93,f67]) ).
thf(f913,plain,
( ( $false = vAPP($o,$o,f3,$true) )
| ~ spl0_5
| ~ spl0_7
| spl0_9
| spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f912,f899]) ).
thf(f899,plain,
( ( $true = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| spl0_9
| spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f880,f882]) ).
thf(f882,plain,
( ( $true != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_9
| spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f877]) ).
thf(f877,plain,
( ( $false != $false )
| ( $true != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_9
| spl0_11
| ~ spl0_13 ),
inference(constrained_superposition,[],[f845,f557]) ).
thf(f557,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f556,f462]) ).
thf(f556,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| ~ spl0_13 ),
inference(forward_demodulation,[],[f103,f67]) ).
thf(f880,plain,
( ( $true = vAPP($o,$o,f3,$false) )
| ( $true = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_11
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f879]) ).
thf(f879,plain,
( ( vAPP($o,$o,f3,$false) != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f878]) ).
thf(f878,plain,
( ( $false != $false )
| ( vAPP($o,$o,f3,$false) != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_11
| ~ spl0_13 ),
inference(constrained_superposition,[],[f645,f557]) ).
thf(f912,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_9
| spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f881,f637]) ).
thf(f881,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| spl0_11
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f879]) ).
thf(f822,plain,
( ~ spl0_40
| ~ spl0_46
| ~ spl0_55 ),
inference(avatar_contradiction_clause,[],[f821]) ).
thf(f821,plain,
( $false
| ~ spl0_40
| ~ spl0_46
| ~ spl0_55 ),
inference(trivial_inequality_removal,[],[f820]) ).
thf(f820,plain,
( ( $true = $false )
| ~ spl0_40
| ~ spl0_46
| ~ spl0_55 ),
inference(forward_demodulation,[],[f819,f358]) ).
thf(f819,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ~ spl0_46
| ~ spl0_55 ),
inference(forward_demodulation,[],[f715,f764]) ).
thf(f743,plain,
( spl0_51
| spl0_46
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f666,f356,f74,f65,f10,f713,f739]) ).
thf(f666,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,$false)) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7
| ~ spl0_40 ),
inference(superposition,[],[f469,f653]) ).
thf(f653,plain,
( ! [X0: $o] :
( ( $false = vAPP($o,$o,f0,X0) )
| ( $false = X0 ) )
| ~ spl0_40 ),
inference(superposition,[],[f358,f4]) ).
thf(f469,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f468,f462]) ).
thf(f468,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f465,f462]) ).
thf(f465,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(backward_demodulation,[],[f417,f462]) ).
thf(f417,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| ~ spl0_1
| ~ spl0_5 ),
inference(forward_demodulation,[],[f12,f67]) ).
thf(f639,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_9
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f638]) ).
thf(f638,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| spl0_9
| ~ spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[],[f637,f611]) ).
thf(f611,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_13 ),
inference(backward_demodulation,[],[f557,f493]) ).
thf(f493,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11 ),
inference(forward_demodulation,[],[f492,f462]) ).
thf(f492,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))) )
| ~ spl0_5
| ~ spl0_11 ),
inference(forward_demodulation,[],[f94,f67]) ).
thf(f531,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_13 ),
inference(avatar_contradiction_clause,[],[f530]) ).
thf(f530,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_13 ),
inference(subsumption_resolution,[],[f529,f467]) ).
thf(f467,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(backward_demodulation,[],[f218,f462]) ).
thf(f218,plain,
( ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,$false)) )
| ~ spl0_5
| ~ spl0_9 ),
inference(forward_demodulation,[],[f85,f67]) ).
thf(f529,plain,
( ( $false != vAPP($o,$o,f3,$false) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_13 ),
inference(forward_demodulation,[],[f528,f467]) ).
thf(f528,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,$false)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_13 ),
inference(forward_demodulation,[],[f527,f467]) ).
thf(f527,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))) )
| ~ spl0_5
| ~ spl0_7
| spl0_13 ),
inference(forward_demodulation,[],[f526,f462]) ).
thf(f526,plain,
( ( $false != vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false)))) )
| ~ spl0_5
| spl0_13 ),
inference(forward_demodulation,[],[f102,f67]) ).
thf(f382,plain,
( spl0_41
| spl0_40
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f246,f65,f19,f356,f362]) ).
thf(f246,plain,
( ( $false = vAPP($o,$o,f0,$true) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f216,f4]) ).
thf(f216,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f21,f67]) ).
thf(f370,plain,
( spl0_42
| spl0_27
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f243,f65,f19,f282,f367]) ).
thf(f243,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f216,f4]) ).
thf(f344,plain,
( spl0_36
| spl0_37
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f240,f65,f19,f341,f337]) ).
thf(f240,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$true))) )
| ( $false = vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f216,f4]) ).
thf(f333,plain,
( spl0_34
| spl0_35
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f238,f65,f19,f330,f326]) ).
thf(f238,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$true)))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f216,f4]) ).
thf(f321,plain,
( spl0_32
| spl0_33
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f236,f65,f19,f318,f314]) ).
thf(f236,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f216,f4]) ).
thf(f308,plain,
( spl0_30
| spl0_31
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f234,f65,f19,f305,f301]) ).
thf(f234,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$true)))))) )
| ( $false = vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f216,f4]) ).
thf(f299,plain,
( ~ spl0_28
| spl0_27
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13
| ~ spl0_15
| ~ spl0_19
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f298,f137,f128,f110,f101,f92,f83,f65,f19,f14,f282,f287]) ).
thf(f298,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,$true)) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13
| ~ spl0_15
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f297,f225]) ).
thf(f225,plain,
( ( $true = vAPP($o,$o,f0,$false) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13
| ~ spl0_15
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f224,f148]) ).
thf(f148,plain,
( ( $false = vAPP($o,$o,f1,$false) )
| ~ spl0_19
| ~ spl0_21 ),
inference(backward_demodulation,[],[f139,f130]) ).
thf(f224,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$false)) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13
| ~ spl0_15
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f223,f148]) ).
thf(f223,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$false))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13
| ~ spl0_15
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f222,f148]) ).
thf(f222,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$false)))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f221,f151]) ).
thf(f151,plain,
( ( $false = vAPP($o,$o,f2,$false) )
| ~ spl0_13
| ~ spl0_15 ),
inference(backward_demodulation,[],[f112,f103]) ).
thf(f221,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f220,f152]) ).
thf(f152,plain,
( ( $false = vAPP($o,$o,f3,$false) )
| ~ spl0_11
| ~ spl0_13 ),
inference(backward_demodulation,[],[f103,f94]) ).
thf(f220,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$false)))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f219,f152]) ).
thf(f219,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$false))))))) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_9 ),
inference(backward_demodulation,[],[f164,f218]) ).
thf(f164,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$false))))))))) )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f16,f67]) ).
thf(f297,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,$false))) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_15
| ~ spl0_19
| ~ spl0_21 ),
inference(forward_demodulation,[],[f296,f148]) ).
thf(f296,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,$false)))) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f295,f151]) ).
thf(f295,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,$false))))) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_demodulation,[],[f233,f151]) ).
thf(f233,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,$false)))))) )
| ( $false != vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_13
| ~ spl0_15 ),
inference(constrained_superposition,[],[f216,f151]) ).
thf(f294,plain,
( spl0_28
| spl0_29
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f232,f65,f19,f291,f287]) ).
thf(f232,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,$true))))))) )
| ( $false = vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false)))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f216,f4]) ).
thf(f275,plain,
( spl0_25
| spl0_26
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f230,f65,f19,f272,f268]) ).
thf(f230,plain,
( ( $false = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))))) )
| ( $false = vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,$false))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(superposition,[],[f216,f4]) ).
thf(f147,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f146]) ).
thf(f146,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f145]) ).
thf(f145,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f12,f21]) ).
thf(f144,plain,
( spl0_21
| spl0_22
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f63,f14,f141,f137]) ).
thf(f63,plain,
( ( $true = vAPP($o,$o,f0,$true) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))))))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f135,plain,
( spl0_19
| spl0_20
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f62,f14,f132,f128]) ).
thf(f62,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,$true)) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f126,plain,
( spl0_17
| spl0_18
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f61,f14,f123,f119]) ).
thf(f61,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,$true))) )
| ( vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f117,plain,
( spl0_15
| spl0_16
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f60,f14,f114,f110]) ).
thf(f60,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,$true)))) )
| ( vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f108,plain,
( spl0_13
| spl0_14
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f59,f14,f105,f101]) ).
thf(f59,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,$true))))) )
| ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x)))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f99,plain,
( spl0_11
| spl0_12
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f58,f14,f96,f92]) ).
thf(f58,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,$true)))))) )
| ( vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f90,plain,
( spl0_9
| spl0_10
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f57,f14,f87,f83]) ).
thf(f57,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,$true))))))) )
| ( vAPP($o,$o,f3,vAPP($o,$o,f4,x)) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f81,plain,
( spl0_7
| spl0_8
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f56,f14,f78,f74]) ).
thf(f56,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,$true)))))))) )
| ( vAPP($o,$o,f4,x) = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f72,plain,
( spl0_5
| spl0_6
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f55,f14,f69,f65]) ).
thf(f55,plain,
( ( $true = vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,$true))))))))) )
| ( x = $false )
| ~ spl0_2 ),
inference(superposition,[],[f16,f4]) ).
thf(f26,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f23,f19]) ).
thf(f8,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) = $false )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))) = $false ) ),
inference(binary_proxy_clausification,[],[f6]) ).
thf(f6,plain,
vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))),
inference(flattening,[],[f2]) ).
thf(f2,negated_conjecture,
vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) != vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) = vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kaminski5) ).
thf(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f7,f14,f10]) ).
thf(f7,plain,
( ( vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f3,vAPP($o,$o,f4,x))))))))) = $true )
| ( vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f0,vAPP($o,$o,f1,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f2,vAPP($o,$o,f3,vAPP($o,$o,f4,vAPP($o,$o,f4,vAPP($o,$o,f4,x))))))))))) = $true ) ),
inference(binary_proxy_clausification,[],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SYO500^1.005 : TPTP v8.2.0. Released v4.1.0.
% 0.09/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.37 % Computer : n015.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 10:23:08 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 % (30259)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.39 % (30262)WARNING: value z3 for option sas not known
% 0.16/0.39 % (30260)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.39 % (30261)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.39 % (30264)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)
% 0.16/0.39 % (30265)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)
% 0.16/0.39 % (30263)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.39 % (30266)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)
% 0.16/0.39 % (30262)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)
% 0.16/0.39 % (30266)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.39 % Exception at run slice level
% 0.16/0.39 User error: % Exception at run slice levelFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.39
% 0.16/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.39 % Exception at run slice level
% 0.16/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.41 % (30267)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.16/0.41 % (30268)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)
% 0.16/0.41 % (30269)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)
% 0.16/0.41 % (30268)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.41 % (30267)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.41 % Exception at run slice level
% 0.16/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.43 % (30270)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)
% 2.48/0.75 % (30269)First to succeed.
% 2.99/0.78 % (30269)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30259"
% 2.99/0.79 % (30269)Refutation found. Thanks to Tanya!
% 2.99/0.79 % SZS status Theorem for theBenchmark
% 2.99/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.99/0.80 % (30269)------------------------------
% 2.99/0.80 % (30269)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.99/0.80 % (30269)Termination reason: Refutation
% 2.99/0.80
% 2.99/0.80 % (30269)Memory used [KB]: 4809
% 2.99/0.80 % (30269)Time elapsed: 0.395 s
% 2.99/0.80 % (30269)Instructions burned: 1320 (million)
% 2.99/0.80 % (30259)Success in time 0.413 s
%------------------------------------------------------------------------------