TSTP Solution File: SWW473+6 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW473+6 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:39:34 EDT 2024
% Result : Theorem 21.88s 3.57s
% Output : Refutation 22.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1444
% Syntax : Number of formulae : 4808 (1122 unt; 0 def)
% Number of atoms : 13454 (2774 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 14424 (5778 ~;5858 |; 615 &)
% (1069 <=>;1104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 919 ( 917 usr; 888 prp; 0-5 aty)
% Number of functors : 133 ( 133 usr; 21 con; 0-5 aty)
% Number of variables : 10975 (10701 !; 274 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38787,plain,
$false,
inference(avatar_sat_refutation,[],[f3184,f3189,f3194,f3199,f3204,f3209,f3214,f3219,f3224,f3229,f3234,f3239,f3244,f3249,f3254,f3259,f3264,f3269,f3274,f3279,f3284,f3289,f3294,f3299,f3304,f3309,f3314,f3319,f3324,f3329,f3334,f3338,f3342,f3346,f3350,f3354,f3358,f3362,f3367,f3372,f3376,f3380,f3384,f3388,f3392,f3397,f3402,f3408,f3412,f3416,f3426,f3432,f3438,f3442,f3446,f3450,f3454,f3458,f3462,f3467,f3471,f3475,f3495,f3499,f3503,f3507,f3517,f3522,f3526,f3530,f3534,f3543,f3548,f3553,f3558,f3563,f3567,f3571,f3575,f3579,f3583,f3588,f3592,f3596,f3600,f3604,f3608,f3612,f3617,f3622,f3627,f3634,f3638,f3642,f3646,f3650,f3656,f3660,f3664,f3668,f3672,f3676,f3680,f3684,f3688,f3692,f3696,f3700,f3704,f3714,f3825,f3830,f3834,f3838,f3843,f3847,f3851,f3855,f3859,f3863,f3868,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3930,f3934,f3938,f3942,f3947,f3968,f3972,f3981,f3986,f3991,f3996,f4000,f4004,f4024,f4028,f4032,f4036,f4040,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4099,f4103,f4107,f4111,f4143,f4147,f4151,f4155,f4159,f4163,f4167,f4242,f4246,f4250,f4254,f4259,f4263,f4267,f4271,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4311,f4315,f4319,f4323,f4346,f4410,f4414,f4418,f4422,f4426,f4430,f4434,f4438,f4442,f4654,f4658,f4662,f4666,f4670,f4674,f4678,f4682,f4875,f4879,f4888,f4892,f4896,f4918,f4922,f4926,f4930,f4940,f4944,f4948,f4952,f4956,f4960,f4964,f4968,f4972,f4976,f4981,f4985,f4989,f4993,f4997,f5001,f5005,f5009,f5013,f5017,f5021,f5025,f5029,f5033,f5408,f5795,f5799,f5803,f5807,f5811,f5815,f5819,f6004,f6008,f6012,f6016,f6020,f6024,f6028,f6032,f6039,f6043,f6227,f6299,f6303,f6307,f6342,f6346,f6350,f6355,f6359,f6363,f6367,f6371,f6375,f6379,f6383,f6387,f6391,f6779,f6783,f6787,f6791,f6795,f6799,f6803,f6807,f6850,f7110,f7127,f7131,f7135,f7139,f7143,f7147,f7151,f7155,f7159,f7163,f7410,f7414,f7418,f7422,f7426,f7464,f7468,f7472,f7476,f7625,f7629,f7633,f7637,f7641,f7645,f7649,f7653,f7657,f7661,f7665,f7669,f7673,f7677,f7684,f7690,f7699,f7703,f7839,f8126,f8136,f8140,f8144,f8148,f8152,f8156,f8160,f8164,f8168,f8562,f8566,f8570,f8574,f8578,f8582,f8586,f8691,f8745,f8750,f8759,f8764,f8773,f8918,f8922,f8926,f8930,f8934,f8938,f8942,f8946,f8950,f8979,f9387,f9479,f9486,f9490,f9494,f9498,f9502,f9506,f9510,f9514,f9519,f9534,f9538,f9542,f9547,f9561,f9565,f9569,f9573,f9577,f9587,f9591,f9595,f9599,f9603,f9607,f9611,f10080,f10964,f10972,f10976,f10980,f11055,f11085,f11086,f11092,f11096,f11100,f11104,f11108,f11112,f11116,f11120,f11124,f11128,f11325,f11329,f11333,f11337,f11341,f11345,f11349,f11353,f11637,f11642,f11650,f11655,f11659,f11663,f11667,f11671,f11675,f11679,f11744,f11837,f11843,f11864,f11868,f11872,f11877,f11881,f11886,f11909,f11914,f12390,f12429,f12433,f12437,f12441,f12445,f12449,f12939,f12943,f12947,f12951,f12955,f12959,f12963,f12968,f12972,f12976,f12980,f12984,f12988,f12992,f12996,f13000,f13004,f13008,f13013,f13970,f13974,f13978,f13993,f13997,f14001,f14005,f14009,f14314,f14334,f14338,f14342,f14346,f14350,f14354,f14358,f14362,f14366,f14370,f14374,f14378,f14382,f14386,f14390,f14394,f14398,f14402,f14407,f14411,f14430,f14909,f15406,f15410,f15414,f15450,f15454,f15610,f15614,f15619,f15623,f15627,f15631,f15877,f15975,f15979,f15983,f16084,f16088,f16092,f16096,f16101,f16105,f16109,f16114,f16401,f16406,f16410,f16466,f16470,f16474,f16478,f16482,f16486,f16490,f16777,f16781,f17092,f17096,f17185,f17189,f17193,f17197,f17201,f17206,f17210,f17214,f17219,f17761,f17765,f17769,f17773,f17777,f17781,f17785,f17789,f17793,f17797,f17801,f17805,f17809,f17813,f17818,f18379,f18383,f18388,f18436,f18440,f18444,f18448,f18452,f18456,f18460,f18464,f18468,f18472,f18483,f19166,f19170,f19175,f19218,f19253,f19264,f19268,f19272,f19276,f19280,f20018,f20022,f20026,f20030,f20034,f20038,f20043,f20392,f20396,f20400,f20881,f20885,f20952,f20956,f20960,f20964,f20968,f20972,f20977,f20981,f20985,f23662,f23666,f23712,f23809,f23813,f23817,f23821,f23826,f23844,f24044,f24048,f24053,f24140,f24161,f24166,f24182,f24266,f24270,f24274,f24278,f24282,f24290,f24294,f24298,f24302,f24306,f24310,f24314,f24318,f24322,f24327,f24374,f26447,f26451,f26456,f26502,f26508,f26513,f26517,f26523,f26640,f26644,f26649,f26705,f26711,f26715,f26829,f26834,f26883,f26888,f26928,f26938,f26989,f26994,f27034,f27039,f27123,f27176,f27180,f27184,f27188,f27194,f27297,f27305,f27540,f27581,f27585,f27590,f27634,f27639,f27643,f27766,f27770,f27775,f27885,f27889,f27894,f28124,f28466,f28471,f28510,f28555,f28562,f28566,f28589,f28595,f28618,f28624,f28640,f28646,f28662,f28666,f28671,f28849,f28874,f28879,f28883,f28928,f28933,f28952,f28956,f29021,f29027,f29214,f29218,f29321,f29326,f29575,f29629,f29633,f29659,f29704,f29732,f29791,f29796,f29800,f29862,f29867,f30044,f30140,f30147,f30174,f30180,f30184,f30206,f30210,f30215,f30256,f30262,f30455,f30460,f30481,f30486,f30537,f30542,f30599,f30609,f30613,f30687,f30716,f30841,f30845,f31138,f31191,f31196,f31250,f31255,f31282,f31299,f31303,f31308,f31337,f31342,f31371,f31377,f31403,f31409,f31435,f31488,f31492,f31916,f31921,f31982,f31986,f31990,f31994,f31998,f32002,f32006,f32010,f32041,f32224,f32229,f32233,f32237,f32308,f32438,f33212,f33216,f33220,f33224,f33228,f33232,f33236,f33887,f34018,f34022,f34026,f34030,f34034,f34038,f34042,f34111,f34116,f34185,f34610,f34614,f34624,f34628,f34632,f34636,f34640,f34644,f35143,f35157,f35178,f35182,f35186,f35190,f35194,f35198,f35202,f35206,f35210,f35214,f35218,f35222,f35226,f35231,f35235,f35239,f35243,f35508,f36205,f36218,f36230,f36234,f36238,f36242,f36246,f36250,f36254,f36258,f36262,f36267,f36276,f36284,f36290,f36294,f36298,f36302,f36306,f36310,f36314,f37152,f37156,f37160,f37165,f37170,f37174,f37178,f37182,f37186,f37190,f37194,f37203,f37866,f37874,f37879,f37883,f37922,f37926,f37930,f37950,f37955,f38044,f38048,f38052,f38056,f38060,f38064,f38068,f38072,f38076,f38080,f38084,f38089,f38093,f38097,f38101,f38105,f38109,f38228,f38660,f38698,f38719,f38772,f38776,f38780,f38785,f38786]) ).
fof(f38786,plain,
( ~ spl86_112
| ~ spl86_525
| spl86_882 ),
inference(avatar_split_clause,[],[f38699,f38695,f17199,f3827]) ).
fof(f3827,plain,
( spl86_112
<=> hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_112])]) ).
fof(f17199,plain,
( spl86_525
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_525])]) ).
fof(f38695,plain,
( spl86_882
<=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_882])]) ).
fof(f38699,plain,
( ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| ~ spl86_525
| spl86_882 ),
inference(resolution,[],[f38697,f17200]) ).
fof(f17200,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) )
| ~ spl86_525 ),
inference(avatar_component_clause,[],[f17199]) ).
fof(f38697,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| spl86_882 ),
inference(avatar_component_clause,[],[f38695]) ).
fof(f38785,plain,
( spl86_887
| ~ spl86_4
| ~ spl86_180 ),
inference(avatar_split_clause,[],[f4390,f4293,f3196,f38782]) ).
fof(f38782,plain,
( spl86_887
<=> plus_plus(nat) = hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combi(fun(nat,fun(nat,nat))),plus_plus(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_887])]) ).
fof(f3196,plain,
( spl86_4
<=> ab_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_4])]) ).
fof(f4293,plain,
( spl86_180
<=> ! [X0] :
( plus_plus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),plus_plus(X0))
| ~ ab_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_180])]) ).
fof(f4390,plain,
( plus_plus(nat) = hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combi(fun(nat,fun(nat,nat))),plus_plus(nat))
| ~ spl86_4
| ~ spl86_180 ),
inference(resolution,[],[f4294,f3198]) ).
fof(f3198,plain,
( ab_semigroup_add(nat)
| ~ spl86_4 ),
inference(avatar_component_clause,[],[f3196]) ).
fof(f4294,plain,
( ! [X0] :
( ~ ab_semigroup_add(X0)
| plus_plus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),plus_plus(X0)) )
| ~ spl86_180 ),
inference(avatar_component_clause,[],[f4293]) ).
fof(f38780,plain,
( spl86_886
| ~ spl86_103
| ~ spl86_144 ),
inference(avatar_split_clause,[],[f4045,f4026,f3678,f38778]) ).
fof(f38778,plain,
( spl86_886
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ sP3(X1,hAPP(nat,nat,suc,X0),ord_less_eq(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_886])]) ).
fof(f3678,plain,
( spl86_103
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2,X1),X0))
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_103])]) ).
fof(f4026,plain,
( spl86_144
<=> ! [X0] : hAPP(nat,fun(nat,bool),ord_less(nat),X0) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_144])]) ).
fof(f4045,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ sP3(X1,hAPP(nat,nat,suc,X0),ord_less_eq(nat)) )
| ~ spl86_103
| ~ spl86_144 ),
inference(superposition,[],[f3679,f4027]) ).
fof(f4027,plain,
( ! [X0] : hAPP(nat,fun(nat,bool),ord_less(nat),X0) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0))
| ~ spl86_144 ),
inference(avatar_component_clause,[],[f4026]) ).
fof(f3679,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2,X1),X0))
| ~ sP3(X0,X1,X2) )
| ~ spl86_103 ),
inference(avatar_component_clause,[],[f3678]) ).
fof(f38776,plain,
( spl86_885
| ~ spl86_71
| ~ spl86_141 ),
inference(avatar_split_clause,[],[f4015,f3998,f3532,f38774]) ).
fof(f38774,plain,
( spl86_885
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,combi(bool),X1))
| ~ sP2(X0,hAPP(bool,fun(fun(X0,bool),bool),combk(bool,fun(X0,bool)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_885])]) ).
fof(f3532,plain,
( spl86_71
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,sK60(X0,X1)))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_71])]) ).
fof(f3998,plain,
( spl86_141
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = hAPP(X1,X1,combi(X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_141])]) ).
fof(f4015,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,combi(bool),X1))
| ~ sP2(X0,hAPP(bool,fun(fun(X0,bool),bool),combk(bool,fun(X0,bool)),X1)) )
| ~ spl86_71
| ~ spl86_141 ),
inference(superposition,[],[f3533,f3999]) ).
fof(f3999,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = hAPP(X1,X1,combi(X1),X2)
| ~ spl86_141 ),
inference(avatar_component_clause,[],[f3998]) ).
fof(f3533,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,sK60(X0,X1)))
| ~ sP2(X0,X1) )
| ~ spl86_71 ),
inference(avatar_component_clause,[],[f3532]) ).
fof(f38772,plain,
( spl86_884
| ~ spl86_33
| ~ spl86_66 ),
inference(avatar_split_clause,[],[f3512,f3505,f3340,f38770]) ).
fof(f38770,plain,
( spl86_884
<=> ! [X0,X1] :
( bot_bot(fun(X0,X1)) = hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),bot_bot(fun(X0,X1)))
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_884])]) ).
fof(f3340,plain,
( spl86_33
<=> ! [X0,X1] :
( bot(fun(X0,X1))
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_33])]) ).
fof(f3505,plain,
( spl86_66
<=> ! [X0] :
( bot_bot(X0) = hAPP(X0,X0,combi(X0),bot_bot(X0))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_66])]) ).
fof(f3512,plain,
( ! [X0,X1] :
( bot_bot(fun(X0,X1)) = hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),bot_bot(fun(X0,X1)))
| ~ bot(X1) )
| ~ spl86_33
| ~ spl86_66 ),
inference(resolution,[],[f3506,f3341]) ).
fof(f3341,plain,
( ! [X0,X1] :
( bot(fun(X0,X1))
| ~ bot(X1) )
| ~ spl86_33 ),
inference(avatar_component_clause,[],[f3340]) ).
fof(f3506,plain,
( ! [X0] :
( ~ bot(X0)
| bot_bot(X0) = hAPP(X0,X0,combi(X0),bot_bot(X0)) )
| ~ spl86_66 ),
inference(avatar_component_clause,[],[f3505]) ).
fof(f38719,plain,
( spl86_883
| ~ spl86_112
| ~ spl86_451
| ~ spl86_452 ),
inference(avatar_split_clause,[],[f13956,f13010,f13006,f3827,f38716]) ).
fof(f38716,plain,
( spl86_883
<=> u = hAPP(fun(pname,bool),fun(pname,bool),hAPP(pname,fun(fun(pname,bool),fun(pname,bool)),insert(pname),pn),u) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_883])]) ).
fof(f13006,plain,
( spl86_451
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_451])]) ).
fof(f13010,plain,
( spl86_452
<=> u = hAPP(fun(pname,bool),fun(pname,bool),collect(pname),u) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_452])]) ).
fof(f13956,plain,
( u = hAPP(fun(pname,bool),fun(pname,bool),hAPP(pname,fun(fun(pname,bool),fun(pname,bool)),insert(pname),pn),u)
| ~ spl86_112
| ~ spl86_451
| ~ spl86_452 ),
inference(forward_demodulation,[],[f13941,f13012]) ).
fof(f13012,plain,
( u = hAPP(fun(pname,bool),fun(pname,bool),collect(pname),u)
| ~ spl86_452 ),
inference(avatar_component_clause,[],[f13010]) ).
fof(f13941,plain,
( hAPP(fun(pname,bool),fun(pname,bool),collect(pname),u) = hAPP(fun(pname,bool),fun(pname,bool),hAPP(pname,fun(fun(pname,bool),fun(pname,bool)),insert(pname),pn),u)
| ~ spl86_112
| ~ spl86_451 ),
inference(resolution,[],[f13007,f3829]) ).
fof(f3829,plain,
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| ~ spl86_112 ),
inference(avatar_component_clause,[],[f3827]) ).
fof(f13007,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) )
| ~ spl86_451 ),
inference(avatar_component_clause,[],[f13006]) ).
fof(f38698,plain,
( ~ spl86_882
| ~ spl86_386
| spl86_111
| ~ spl86_619 ),
inference(avatar_split_clause,[],[f26327,f24312,f3822,f11052,f38695]) ).
fof(f11052,plain,
( spl86_386
<=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_386])]) ).
fof(f3822,plain,
( spl86_111
<=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_111])]) ).
fof(f24312,plain,
( spl86_619
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_619])]) ).
fof(f26327,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| spl86_111
| ~ spl86_619 ),
inference(resolution,[],[f24313,f3824]) ).
fof(f3824,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| spl86_111 ),
inference(avatar_component_clause,[],[f3822]) ).
fof(f24313,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) )
| ~ spl86_619 ),
inference(avatar_component_clause,[],[f24312]) ).
fof(f38660,plain,
( spl86_881
| ~ spl86_92
| ~ spl86_131
| ~ spl86_770 ),
inference(avatar_split_clause,[],[f32506,f32435,f3936,f3632,f38657]) ).
fof(f38657,plain,
( spl86_881
<=> zero_zero(nat) = sK48(zero_zero(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_881])]) ).
fof(f3632,plain,
( spl86_92
<=> ! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_92])]) ).
fof(f3936,plain,
( spl86_131
<=> ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),one_one(nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_131])]) ).
fof(f32435,plain,
( spl86_770
<=> one_one(nat) = hAPP(nat,nat,suc,sK48(zero_zero(nat),one_one(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_770])]) ).
fof(f32506,plain,
( zero_zero(nat) = sK48(zero_zero(nat),one_one(nat))
| ~ spl86_92
| ~ spl86_131
| ~ spl86_770 ),
inference(forward_demodulation,[],[f32445,f3633]) ).
fof(f3633,plain,
( ! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X0)
| ~ spl86_92 ),
inference(avatar_component_clause,[],[f3632]) ).
fof(f32445,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),one_one(nat)),one_one(nat)) = sK48(zero_zero(nat),one_one(nat))
| ~ spl86_131
| ~ spl86_770 ),
inference(superposition,[],[f3937,f32437]) ).
fof(f32437,plain,
( one_one(nat) = hAPP(nat,nat,suc,sK48(zero_zero(nat),one_one(nat)))
| ~ spl86_770 ),
inference(avatar_component_clause,[],[f32435]) ).
fof(f3937,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),one_one(nat)) = X0
| ~ spl86_131 ),
inference(avatar_component_clause,[],[f3936]) ).
fof(f38228,plain,
( ~ spl86_880
| ~ spl86_37
| ~ spl86_770 ),
inference(avatar_split_clause,[],[f32439,f32435,f3356,f38225]) ).
fof(f38225,plain,
( spl86_880
<=> one_one(nat) = sK48(zero_zero(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_880])]) ).
fof(f3356,plain,
( spl86_37
<=> ! [X0] : hAPP(nat,nat,suc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_37])]) ).
fof(f32439,plain,
( one_one(nat) != sK48(zero_zero(nat),one_one(nat))
| ~ spl86_37
| ~ spl86_770 ),
inference(superposition,[],[f3357,f32437]) ).
fof(f3357,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) != X0
| ~ spl86_37 ),
inference(avatar_component_clause,[],[f3356]) ).
fof(f38109,plain,
( spl86_879
| ~ spl86_385 ),
inference(avatar_split_clause,[],[f11048,f10978,f38107]) ).
fof(f38107,plain,
( spl86_879
<=> ! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_879])]) ).
fof(f10978,plain,
( spl86_385
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_385])]) ).
fof(f11048,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X1))
| ~ spl86_385 ),
inference(equality_resolution,[],[f10979]) ).
fof(f10979,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) )
| ~ spl86_385 ),
inference(avatar_component_clause,[],[f10978]) ).
fof(f38105,plain,
( spl86_878
| ~ spl86_176
| ~ spl86_332 ),
inference(avatar_split_clause,[],[f8588,f8560,f4277,f38103]) ).
fof(f38103,plain,
( spl86_878
<=> ! [X0] : hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),bot_bot(fun(x_a,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_878])]) ).
fof(f4277,plain,
( spl86_176
<=> ! [X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_176])]) ).
fof(f8560,plain,
( spl86_332
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X0))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_332])]) ).
fof(f8588,plain,
( ! [X0] : hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),bot_bot(fun(x_a,bool))))
| ~ spl86_176
| ~ spl86_332 ),
inference(resolution,[],[f8561,f4278]) ).
fof(f4278,plain,
( ! [X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1))
| ~ spl86_176 ),
inference(avatar_component_clause,[],[f4277]) ).
fof(f8561,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),X1))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X0)) )
| ~ spl86_332 ),
inference(avatar_component_clause,[],[f8560]) ).
fof(f38101,plain,
( spl86_877
| ~ spl86_79
| ~ spl86_283 ),
inference(avatar_split_clause,[],[f7075,f6848,f3573,f38099]) ).
fof(f38099,plain,
( spl86_877
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,X0,sK64(X0,X1)))
| ~ hBOOL(hAPP(nat,bool,X0,X1))
| hBOOL(hAPP(nat,bool,X0,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_877])]) ).
fof(f3573,plain,
( spl86_79
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_79])]) ).
fof(f6848,plain,
( spl86_283
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X1))
| ~ hBOOL(hAPP(nat,bool,X0,sK64(X0,X2)))
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_283])]) ).
fof(f7075,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,X0,sK64(X0,X1)))
| ~ hBOOL(hAPP(nat,bool,X0,X1))
| hBOOL(hAPP(nat,bool,X0,zero_zero(nat))) )
| ~ spl86_79
| ~ spl86_283 ),
inference(resolution,[],[f6849,f3574]) ).
fof(f3574,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X0))
| ~ spl86_79 ),
inference(avatar_component_clause,[],[f3573]) ).
fof(f6849,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,X0,sK64(X0,X2)))
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| hBOOL(hAPP(nat,bool,X0,X1)) )
| ~ spl86_283 ),
inference(avatar_component_clause,[],[f6848]) ).
fof(f38097,plain,
( spl86_876
| ~ spl86_245
| ~ spl86_264 ),
inference(avatar_split_clause,[],[f6494,f6348,f5809,f38095]) ).
fof(f38095,plain,
( spl86_876
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| sP3(X1,X0,ord_less_eq(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_876])]) ).
fof(f5809,plain,
( spl86_245
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_245])]) ).
fof(f6348,plain,
( spl86_264
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X1 = X2
| sP3(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_264])]) ).
fof(f6494,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| sP3(X1,X0,ord_less_eq(nat)) )
| ~ spl86_245
| ~ spl86_264 ),
inference(duplicate_literal_removal,[],[f6463]) ).
fof(f6463,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| sP3(X1,X0,ord_less_eq(nat))
| X0 = X1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) )
| ~ spl86_245
| ~ spl86_264 ),
inference(resolution,[],[f6349,f5810]) ).
fof(f5810,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| X0 = X1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) )
| ~ spl86_245 ),
inference(avatar_component_clause,[],[f5809]) ).
fof(f6349,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
| X1 = X2
| sP3(X1,X2,X0) )
| ~ spl86_264 ),
inference(avatar_component_clause,[],[f6348]) ).
fof(f38093,plain,
( spl86_875
| ~ spl86_264 ),
inference(avatar_split_clause,[],[f6485,f6348,f38091]) ).
fof(f38091,plain,
( spl86_875
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| sP3(X1,X0,ord_less(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_875])]) ).
fof(f6485,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| sP3(X1,X0,ord_less(nat)) )
| ~ spl86_264 ),
inference(factoring,[],[f6349]) ).
fof(f38089,plain,
( spl86_874
| ~ spl86_92
| ~ spl86_131
| ~ spl86_769 ),
inference(avatar_split_clause,[],[f32376,f32305,f3936,f3632,f38086]) ).
fof(f38086,plain,
( spl86_874
<=> zero_zero(nat) = sK20(zero_zero(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_874])]) ).
fof(f32305,plain,
( spl86_769
<=> one_one(nat) = hAPP(nat,nat,suc,sK20(zero_zero(nat),one_one(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_769])]) ).
fof(f32376,plain,
( zero_zero(nat) = sK20(zero_zero(nat),one_one(nat))
| ~ spl86_92
| ~ spl86_131
| ~ spl86_769 ),
inference(forward_demodulation,[],[f32315,f3633]) ).
fof(f32315,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),one_one(nat)),one_one(nat)) = sK20(zero_zero(nat),one_one(nat))
| ~ spl86_131
| ~ spl86_769 ),
inference(superposition,[],[f3937,f32307]) ).
fof(f32307,plain,
( one_one(nat) = hAPP(nat,nat,suc,sK20(zero_zero(nat),one_one(nat)))
| ~ spl86_769 ),
inference(avatar_component_clause,[],[f32305]) ).
fof(f38084,plain,
( spl86_873
| ~ spl86_129
| ~ spl86_223 ),
inference(avatar_split_clause,[],[f5255,f4966,f3928,f38082]) ).
fof(f38082,plain,
( spl86_873
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,suc,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_873])]) ).
fof(f3928,plain,
( spl86_129
<=> ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_129])]) ).
fof(f4966,plain,
( spl86_223
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_223])]) ).
fof(f5255,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,suc,X0))))
| ~ spl86_129
| ~ spl86_223 ),
inference(superposition,[],[f4967,f3929]) ).
fof(f3929,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),one_one(nat))
| ~ spl86_129 ),
inference(avatar_component_clause,[],[f3928]) ).
fof(f4967,plain,
( ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))))
| ~ spl86_223 ),
inference(avatar_component_clause,[],[f4966]) ).
fof(f38080,plain,
( spl86_872
| ~ spl86_147
| ~ spl86_205 ),
inference(avatar_split_clause,[],[f4848,f4680,f4038,f38078]) ).
fof(f38078,plain,
( spl86_872
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| hAPP(nat,nat,suc,sK22(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_872])]) ).
fof(f4038,plain,
( spl86_147
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,suc,sK22(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_147])]) ).
fof(f4680,plain,
( spl86_205
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_205])]) ).
fof(f4848,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| hAPP(nat,nat,suc,sK22(X1)) = X1 )
| ~ spl86_147
| ~ spl86_205 ),
inference(resolution,[],[f4681,f4039]) ).
fof(f4039,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,suc,sK22(X1)) = X1 )
| ~ spl86_147 ),
inference(avatar_component_clause,[],[f4038]) ).
fof(f4681,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) )
| ~ spl86_205 ),
inference(avatar_component_clause,[],[f4680]) ).
fof(f38076,plain,
( spl86_871
| ~ spl86_46
| ~ spl86_202 ),
inference(avatar_split_clause,[],[f4795,f4668,f3394,f38074]) ).
fof(f38074,plain,
( spl86_871
<=> ! [X0] :
( fTrue != hAPP(bool,bool,combi(bool),X0)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fequal(bool),X0),fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_871])]) ).
fof(f3394,plain,
( spl86_46
<=> fTrue = hAPP(bool,bool,combi(bool),fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_46])]) ).
fof(f4668,plain,
( spl86_202
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_202])]) ).
fof(f4795,plain,
( ! [X0] :
( fTrue != hAPP(bool,bool,combi(bool),X0)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fequal(bool),X0),fTrue)) )
| ~ spl86_46
| ~ spl86_202 ),
inference(superposition,[],[f4669,f3396]) ).
fof(f3396,plain,
( fTrue = hAPP(bool,bool,combi(bool),fTrue)
| ~ spl86_46 ),
inference(avatar_component_clause,[],[f3394]) ).
fof(f4669,plain,
( ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2)) )
| ~ spl86_202 ),
inference(avatar_component_clause,[],[f4668]) ).
fof(f38072,plain,
( spl86_870
| ~ spl86_47
| ~ spl86_202 ),
inference(avatar_split_clause,[],[f4794,f4668,f3399,f38070]) ).
fof(f38070,plain,
( spl86_870
<=> ! [X0] :
( fFalse != hAPP(bool,bool,combi(bool),X0)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fequal(bool),X0),fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_870])]) ).
fof(f3399,plain,
( spl86_47
<=> fFalse = hAPP(bool,bool,combi(bool),fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_47])]) ).
fof(f4794,plain,
( ! [X0] :
( fFalse != hAPP(bool,bool,combi(bool),X0)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fequal(bool),X0),fFalse)) )
| ~ spl86_47
| ~ spl86_202 ),
inference(superposition,[],[f4669,f3401]) ).
fof(f3401,plain,
( fFalse = hAPP(bool,bool,combi(bool),fFalse)
| ~ spl86_47 ),
inference(avatar_component_clause,[],[f3399]) ).
fof(f38068,plain,
( spl86_869
| ~ spl86_46
| ~ spl86_202 ),
inference(avatar_split_clause,[],[f4767,f4668,f3394,f38066]) ).
fof(f38066,plain,
( spl86_869
<=> ! [X0] :
( fTrue != hAPP(bool,bool,combi(bool),X0)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fequal(bool),fTrue),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_869])]) ).
fof(f4767,plain,
( ! [X0] :
( fTrue != hAPP(bool,bool,combi(bool),X0)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fequal(bool),fTrue),X0)) )
| ~ spl86_46
| ~ spl86_202 ),
inference(superposition,[],[f4669,f3396]) ).
fof(f38064,plain,
( spl86_868
| ~ spl86_47
| ~ spl86_202 ),
inference(avatar_split_clause,[],[f4766,f4668,f3399,f38062]) ).
fof(f38062,plain,
( spl86_868
<=> ! [X0] :
( fFalse != hAPP(bool,bool,combi(bool),X0)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fequal(bool),fFalse),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_868])]) ).
fof(f4766,plain,
( ! [X0] :
( fFalse != hAPP(bool,bool,combi(bool),X0)
| hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fequal(bool),fFalse),X0)) )
| ~ spl86_47
| ~ spl86_202 ),
inference(superposition,[],[f4669,f3401]) ).
fof(f38060,plain,
( spl86_867
| ~ spl86_100
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3787,f3702,f3666,f38058]) ).
fof(f38058,plain,
( spl86_867
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_867])]) ).
fof(f3666,plain,
( spl86_100
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_100])]) ).
fof(f3702,plain,
( spl86_109
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,hAPP(X0,X0,combi(X0),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_109])]) ).
fof(f3787,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl86_100
| ~ spl86_109 ),
inference(superposition,[],[f3667,f3703]) ).
fof(f3703,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,hAPP(X0,X0,combi(X0),X3))
| ~ spl86_109 ),
inference(avatar_component_clause,[],[f3702]) ).
fof(f3667,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) )
| ~ spl86_100 ),
inference(avatar_component_clause,[],[f3666]) ).
fof(f38056,plain,
( spl86_866
| ~ spl86_102
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3784,f3702,f3674,f38054]) ).
fof(f38054,plain,
( spl86_866
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_866])]) ).
fof(f3674,plain,
( spl86_102
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_102])]) ).
fof(f3784,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0))
| hBOOL(X1) )
| ~ spl86_102
| ~ spl86_109 ),
inference(superposition,[],[f3675,f3703]) ).
fof(f3675,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X0)
| hBOOL(X1) )
| ~ spl86_102 ),
inference(avatar_component_clause,[],[f3674]) ).
fof(f38052,plain,
( spl86_865
| ~ spl86_101
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3781,f3702,f3670,f38050]) ).
fof(f38050,plain,
( spl86_865
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_865])]) ).
fof(f3670,plain,
( spl86_101
<=> ! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_101])]) ).
fof(f3781,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0))
| hBOOL(X1) )
| ~ spl86_101
| ~ spl86_109 ),
inference(superposition,[],[f3671,f3703]) ).
fof(f3671,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(X0)
| hBOOL(X1) )
| ~ spl86_101 ),
inference(avatar_component_clause,[],[f3670]) ).
fof(f38048,plain,
( spl86_864
| ~ spl86_100
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3778,f3702,f3666,f38046]) ).
fof(f38046,plain,
( spl86_864
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1))
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_864])]) ).
fof(f3778,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1))
| ~ hBOOL(X0) )
| ~ spl86_100
| ~ spl86_109 ),
inference(superposition,[],[f3667,f3703]) ).
fof(f38044,plain,
( spl86_863
| ~ spl86_102
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3775,f3702,f3674,f38042]) ).
fof(f38042,plain,
( spl86_863
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X0)
| hBOOL(hAPP(bool,bool,combi(bool),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_863])]) ).
fof(f3775,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X0)
| hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl86_102
| ~ spl86_109 ),
inference(superposition,[],[f3675,f3703]) ).
fof(f37955,plain,
( spl86_862
| spl86_1
| ~ spl86_104
| ~ spl86_209
| ~ spl86_856
| ~ spl86_861 ),
inference(avatar_split_clause,[],[f37951,f37948,f37871,f4885,f3682,f3181,f37953]) ).
fof(f37953,plain,
( spl86_862
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_862])]) ).
fof(f3181,plain,
( spl86_1
<=> hBOOL(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_1])]) ).
fof(f3682,plain,
( spl86_104
<=> ! [X0,X1] : bot_bot(bool) = hAPP(X0,bool,bot_bot(fun(X0,bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_104])]) ).
fof(f4885,plain,
( spl86_209
<=> fFalse = bot_bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_209])]) ).
fof(f37871,plain,
( spl86_856
<=> combi(bool) = bot_bot(fun(bool,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_856])]) ).
fof(f37948,plain,
( spl86_861
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(X0)
| hBOOL(hAPP(bool,bool,combi(bool),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_861])]) ).
fof(f37951,plain,
( ! [X0,X1] :
( hBOOL(fFalse)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(X0) )
| ~ spl86_104
| ~ spl86_209
| ~ spl86_856
| ~ spl86_861 ),
inference(forward_demodulation,[],[f37949,f37912]) ).
fof(f37912,plain,
( ! [X0] : fFalse = hAPP(bool,bool,combi(bool),X0)
| ~ spl86_104
| ~ spl86_209
| ~ spl86_856 ),
inference(forward_demodulation,[],[f37887,f4887]) ).
fof(f4887,plain,
( fFalse = bot_bot(bool)
| ~ spl86_209 ),
inference(avatar_component_clause,[],[f4885]) ).
fof(f37887,plain,
( ! [X0] : hAPP(bool,bool,combi(bool),X0) = bot_bot(bool)
| ~ spl86_104
| ~ spl86_856 ),
inference(superposition,[],[f3683,f37872]) ).
fof(f37872,plain,
( combi(bool) = bot_bot(fun(bool,bool))
| ~ spl86_856 ),
inference(avatar_component_clause,[],[f37871]) ).
fof(f3683,plain,
( ! [X0,X1] : bot_bot(bool) = hAPP(X0,bool,bot_bot(fun(X0,bool)),X1)
| ~ spl86_104 ),
inference(avatar_component_clause,[],[f3682]) ).
fof(f37949,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(X0)
| hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl86_861 ),
inference(avatar_component_clause,[],[f37948]) ).
fof(f37950,plain,
( spl86_861
| ~ spl86_101
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3772,f3702,f3670,f37948]) ).
fof(f3772,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(X0)
| hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl86_101
| ~ spl86_109 ),
inference(superposition,[],[f3671,f3703]) ).
fof(f37930,plain,
( spl86_860
| ~ spl86_40
| ~ spl86_202 ),
inference(avatar_split_clause,[],[f4792,f4668,f3369,f37928]) ).
fof(f37928,plain,
( spl86_860
<=> ! [X0] :
( pn != hAPP(pname,pname,combi(pname),X0)
| hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),fequal(pname),X0),pn)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_860])]) ).
fof(f3369,plain,
( spl86_40
<=> pn = hAPP(pname,pname,combi(pname),pn) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_40])]) ).
fof(f4792,plain,
( ! [X0] :
( pn != hAPP(pname,pname,combi(pname),X0)
| hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),fequal(pname),X0),pn)) )
| ~ spl86_40
| ~ spl86_202 ),
inference(superposition,[],[f4669,f3371]) ).
fof(f3371,plain,
( pn = hAPP(pname,pname,combi(pname),pn)
| ~ spl86_40 ),
inference(avatar_component_clause,[],[f3369]) ).
fof(f37926,plain,
( spl86_859
| ~ spl86_40
| ~ spl86_202 ),
inference(avatar_split_clause,[],[f4764,f4668,f3369,f37924]) ).
fof(f37924,plain,
( spl86_859
<=> ! [X0] :
( pn != hAPP(pname,pname,combi(pname),X0)
| hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),fequal(pname),pn),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_859])]) ).
fof(f4764,plain,
( ! [X0] :
( pn != hAPP(pname,pname,combi(pname),X0)
| hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),fequal(pname),pn),X0)) )
| ~ spl86_40
| ~ spl86_202 ),
inference(superposition,[],[f4669,f3371]) ).
fof(f37922,plain,
( ~ spl86_858
| spl86_729
| ~ spl86_856 ),
inference(avatar_split_clause,[],[f37884,f37871,f30606,f37919]) ).
fof(f37919,plain,
( spl86_858
<=> fNot = combi(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_858])]) ).
fof(f30606,plain,
( spl86_729
<=> fNot = bot_bot(fun(bool,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_729])]) ).
fof(f37884,plain,
( fNot != combi(bool)
| spl86_729
| ~ spl86_856 ),
inference(superposition,[],[f30608,f37872]) ).
fof(f30608,plain,
( fNot != bot_bot(fun(bool,bool))
| spl86_729 ),
inference(avatar_component_clause,[],[f30606]) ).
fof(f37883,plain,
( spl86_856
| ~ spl86_766
| ~ spl86_855 ),
inference(avatar_split_clause,[],[f37880,f37863,f32226,f37871]) ).
fof(f32226,plain,
( spl86_766
<=> combi(bool) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_766])]) ).
fof(f37863,plain,
( spl86_855
<=> bot_bot(fun(bool,bool)) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_855])]) ).
fof(f37880,plain,
( combi(bool) = bot_bot(fun(bool,bool))
| ~ spl86_766
| ~ spl86_855 ),
inference(forward_demodulation,[],[f37865,f32228]) ).
fof(f32228,plain,
( combi(bool) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool))
| ~ spl86_766 ),
inference(avatar_component_clause,[],[f32226]) ).
fof(f37865,plain,
( bot_bot(fun(bool,bool)) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool))
| ~ spl86_855 ),
inference(avatar_component_clause,[],[f37863]) ).
fof(f37879,plain,
( spl86_857
| spl86_855
| ~ spl86_50
| ~ spl86_162 ),
inference(avatar_split_clause,[],[f4186,f4149,f3414,f37863,f37876]) ).
fof(f37876,plain,
( spl86_857
<=> hBOOL(sK51(bool,combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_857])]) ).
fof(f3414,plain,
( spl86_50
<=> ! [X0] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_50])]) ).
fof(f4149,plain,
( spl86_162
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK51(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_162])]) ).
fof(f4186,plain,
( bot_bot(fun(bool,bool)) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool))
| hBOOL(sK51(bool,combi(bool)))
| ~ spl86_50
| ~ spl86_162 ),
inference(resolution,[],[f4150,f3415]) ).
fof(f3415,plain,
( ! [X0] :
( ~ hBOOL(hAPP(bool,bool,combi(bool),X0))
| hBOOL(X0) )
| ~ spl86_50 ),
inference(avatar_component_clause,[],[f3414]) ).
fof(f4150,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X0,bool,X1,sK51(X0,X1)))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) )
| ~ spl86_162 ),
inference(avatar_component_clause,[],[f4149]) ).
fof(f37874,plain,
( ~ spl86_856
| ~ spl86_766
| spl86_855 ),
inference(avatar_split_clause,[],[f37867,f37863,f32226,f37871]) ).
fof(f37867,plain,
( combi(bool) != bot_bot(fun(bool,bool))
| ~ spl86_766
| spl86_855 ),
inference(forward_demodulation,[],[f37864,f32228]) ).
fof(f37864,plain,
( bot_bot(fun(bool,bool)) != hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool))
| spl86_855 ),
inference(avatar_component_clause,[],[f37863]) ).
fof(f37866,plain,
( spl86_854
| spl86_855
| ~ spl86_50
| ~ spl86_161 ),
inference(avatar_split_clause,[],[f4174,f4145,f3414,f37863,f37859]) ).
fof(f37859,plain,
( spl86_854
<=> hBOOL(sK50(bool,combi(bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_854])]) ).
fof(f4145,plain,
( spl86_161
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK50(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_161])]) ).
fof(f4174,plain,
( bot_bot(fun(bool,bool)) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool))
| hBOOL(sK50(bool,combi(bool)))
| ~ spl86_50
| ~ spl86_161 ),
inference(resolution,[],[f4146,f3415]) ).
fof(f4146,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X0,bool,X1,sK50(X0,X1)))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) )
| ~ spl86_161 ),
inference(avatar_component_clause,[],[f4145]) ).
fof(f37203,plain,
( spl86_853
| ~ spl86_176
| ~ spl86_317 ),
inference(avatar_split_clause,[],[f8096,f7675,f4277,f37201]) ).
fof(f37201,plain,
( spl86_853
<=> ! [X0,X1] : ~ sP4(X0,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_853])]) ).
fof(f7675,plain,
( spl86_317
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2))))
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_317])]) ).
fof(f8096,plain,
( ! [X0,X1] : ~ sP4(X0,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1)
| ~ spl86_176
| ~ spl86_317 ),
inference(resolution,[],[f7676,f4278]) ).
fof(f7676,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2))))
| ~ sP4(X0,X1,X2) )
| ~ spl86_317 ),
inference(avatar_component_clause,[],[f7675]) ).
fof(f37194,plain,
( spl86_852
| ~ spl86_97
| ~ spl86_281 ),
inference(avatar_split_clause,[],[f7030,f6801,f3654,f37192]) ).
fof(f37192,plain,
( spl86_852
<=> ! [X0] :
( zero_zero(nat) = X0
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_852])]) ).
fof(f3654,plain,
( spl86_97
<=> ! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_97])]) ).
fof(f6801,plain,
( spl86_281
<=> ! [X0,X1] :
( X0 = X1
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_281])]) ).
fof(f7030,plain,
( ! [X0] :
( zero_zero(nat) = X0
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) )
| ~ spl86_97
| ~ spl86_281 ),
inference(trivial_inequality_removal,[],[f7024]) ).
fof(f7024,plain,
( ! [X0] :
( zero_zero(nat) != zero_zero(nat)
| zero_zero(nat) = X0
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) )
| ~ spl86_97
| ~ spl86_281 ),
inference(superposition,[],[f6802,f3655]) ).
fof(f3655,plain,
( ! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X0)
| ~ spl86_97 ),
inference(avatar_component_clause,[],[f3654]) ).
fof(f6802,plain,
( ! [X0,X1] :
( zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)
| X0 = X1
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) )
| ~ spl86_281 ),
inference(avatar_component_clause,[],[f6801]) ).
fof(f37190,plain,
( spl86_851
| ~ spl86_103
| ~ spl86_225 ),
inference(avatar_split_clause,[],[f5284,f4974,f3678,f37188]) ).
fof(f37188,plain,
( spl86_851
<=> ! [X0,X1] : ~ sP3(hAPP(nat,nat,suc,X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1),ord_less(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_851])]) ).
fof(f4974,plain,
( spl86_225
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),hAPP(nat,nat,suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_225])]) ).
fof(f5284,plain,
( ! [X0,X1] : ~ sP3(hAPP(nat,nat,suc,X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1),ord_less(nat))
| ~ spl86_103
| ~ spl86_225 ),
inference(resolution,[],[f4975,f3679]) ).
fof(f4975,plain,
( ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),hAPP(nat,nat,suc,X0)))
| ~ spl86_225 ),
inference(avatar_component_clause,[],[f4974]) ).
fof(f37186,plain,
( spl86_850
| ~ spl86_103
| ~ spl86_224 ),
inference(avatar_split_clause,[],[f5266,f4970,f3678,f37184]) ).
fof(f37184,plain,
( spl86_850
<=> ! [X0,X1] : ~ sP3(hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1,ord_less(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_850])]) ).
fof(f4970,plain,
( spl86_224
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_224])]) ).
fof(f5266,plain,
( ! [X0,X1] : ~ sP3(hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1,ord_less(nat))
| ~ spl86_103
| ~ spl86_224 ),
inference(resolution,[],[f4971,f3679]) ).
fof(f4971,plain,
( ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0))))
| ~ spl86_224 ),
inference(avatar_component_clause,[],[f4970]) ).
fof(f37182,plain,
( spl86_849
| ~ spl86_103
| ~ spl86_223 ),
inference(avatar_split_clause,[],[f5247,f4966,f3678,f37180]) ).
fof(f37180,plain,
( spl86_849
<=> ! [X0,X1] : ~ sP3(hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0,ord_less(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_849])]) ).
fof(f5247,plain,
( ! [X0,X1] : ~ sP3(hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0,ord_less(nat))
| ~ spl86_103
| ~ spl86_223 ),
inference(resolution,[],[f4967,f3679]) ).
fof(f37178,plain,
( spl86_848
| ~ spl86_130
| ~ spl86_198 ),
inference(avatar_split_clause,[],[f4693,f4652,f3932,f37176]) ).
fof(f37176,plain,
( spl86_848
<=> ! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),one_one(nat)),hAPP(nat,nat,suc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_848])]) ).
fof(f3932,plain,
( spl86_130
<=> ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_130])]) ).
fof(f4652,plain,
( spl86_198
<=> ! [X0,X1] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_198])]) ).
fof(f4693,plain,
( ! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),one_one(nat)),hAPP(nat,nat,suc,X0))
| ~ spl86_130
| ~ spl86_198 ),
inference(superposition,[],[f4653,f3933]) ).
fof(f3933,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X0)
| ~ spl86_130 ),
inference(avatar_component_clause,[],[f3932]) ).
fof(f4653,plain,
( ! [X0,X1] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))
| ~ spl86_198 ),
inference(avatar_component_clause,[],[f4652]) ).
fof(f37174,plain,
( spl86_847
| ~ spl86_159
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4233,f4161,f4109,f37172]) ).
fof(f37172,plain,
( spl86_847
<=> ! [X2,X0,X1] : hAPP(X0,bool,X1,X2) = hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_847])]) ).
fof(f4109,plain,
( spl86_159
<=> ! [X0,X3,X2,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),X2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_159])]) ).
fof(f4161,plain,
( spl86_165
<=> ! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_165])]) ).
fof(f4233,plain,
( ! [X2,X0,X1] : hAPP(X0,bool,X1,X2) = hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1),X2)
| ~ spl86_159
| ~ spl86_165 ),
inference(superposition,[],[f4110,f4162]) ).
fof(f4162,plain,
( ! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ spl86_165 ),
inference(avatar_component_clause,[],[f4161]) ).
fof(f4110,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),X2),X3)
| ~ spl86_159 ),
inference(avatar_component_clause,[],[f4109]) ).
fof(f37170,plain,
( spl86_846
| ~ spl86_149
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4221,f4161,f4068,f37167]) ).
fof(f37167,plain,
( spl86_846
<=> the(bool) = hAPP(fun(fun(bool,bool),bool),fun(fun(bool,bool),bool),collect(fun(bool,bool)),the(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_846])]) ).
fof(f4068,plain,
( spl86_149
<=> ! [X0] : the(X0) = hAPP(fun(fun(X0,bool),X0),fun(fun(X0,bool),X0),combi(fun(fun(X0,bool),X0)),the(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_149])]) ).
fof(f4221,plain,
( the(bool) = hAPP(fun(fun(bool,bool),bool),fun(fun(bool,bool),bool),collect(fun(bool,bool)),the(bool))
| ~ spl86_149
| ~ spl86_165 ),
inference(superposition,[],[f4162,f4069]) ).
fof(f4069,plain,
( ! [X0] : the(X0) = hAPP(fun(fun(X0,bool),X0),fun(fun(X0,bool),X0),combi(fun(fun(X0,bool),X0)),the(X0))
| ~ spl86_149 ),
inference(avatar_component_clause,[],[f4068]) ).
fof(f37165,plain,
( spl86_845
| ~ spl86_148
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4220,f4161,f4064,f37162]) ).
fof(f37162,plain,
( spl86_845
<=> the_elem(bool) = hAPP(fun(fun(bool,bool),bool),fun(fun(bool,bool),bool),collect(fun(bool,bool)),the_elem(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_845])]) ).
fof(f4064,plain,
( spl86_148
<=> ! [X0] : the_elem(X0) = hAPP(fun(fun(X0,bool),X0),fun(fun(X0,bool),X0),combi(fun(fun(X0,bool),X0)),the_elem(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_148])]) ).
fof(f4220,plain,
( the_elem(bool) = hAPP(fun(fun(bool,bool),bool),fun(fun(bool,bool),bool),collect(fun(bool,bool)),the_elem(bool))
| ~ spl86_148
| ~ spl86_165 ),
inference(superposition,[],[f4162,f4065]) ).
fof(f4065,plain,
( ! [X0] : the_elem(X0) = hAPP(fun(fun(X0,bool),X0),fun(fun(X0,bool),X0),combi(fun(fun(X0,bool),X0)),the_elem(X0))
| ~ spl86_148 ),
inference(avatar_component_clause,[],[f4064]) ).
fof(f37160,plain,
( spl86_844
| ~ spl86_152
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4214,f4161,f4080,f37158]) ).
fof(f37158,plain,
( spl86_844
<=> ! [X0] : finite_finite(X0) = hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),finite_finite(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_844])]) ).
fof(f4080,plain,
( spl86_152
<=> ! [X0] : finite_finite(X0) = hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),combi(fun(fun(X0,bool),bool)),finite_finite(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_152])]) ).
fof(f4214,plain,
( ! [X0] : finite_finite(X0) = hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),finite_finite(X0))
| ~ spl86_152
| ~ spl86_165 ),
inference(superposition,[],[f4162,f4081]) ).
fof(f4081,plain,
( ! [X0] : finite_finite(X0) = hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),combi(fun(fun(X0,bool),bool)),finite_finite(X0))
| ~ spl86_152 ),
inference(avatar_component_clause,[],[f4080]) ).
fof(f37156,plain,
( spl86_843
| ~ spl86_108
| ~ spl86_160 ),
inference(avatar_split_clause,[],[f4169,f4141,f3698,f37154]) ).
fof(f37154,plain,
( spl86_843
<=> ! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_843])]) ).
fof(f3698,plain,
( spl86_108
<=> ! [X0,X3,X2,X1] : hAPP(X1,X0,X2,X3) = hAPP(X0,X0,combi(X0),hAPP(X1,X0,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_108])]) ).
fof(f4141,plain,
( spl86_160
<=> ! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_160])]) ).
fof(f4169,plain,
( ! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),bot_bot(fun(X0,bool)))
| ~ spl86_108
| ~ spl86_160 ),
inference(superposition,[],[f3699,f4142]) ).
fof(f4142,plain,
( ! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse))
| ~ spl86_160 ),
inference(avatar_component_clause,[],[f4141]) ).
fof(f3699,plain,
( ! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = hAPP(X0,X0,combi(X0),hAPP(X1,X0,X2,X3))
| ~ spl86_108 ),
inference(avatar_component_clause,[],[f3698]) ).
fof(f37152,plain,
( spl86_842
| ~ spl86_838 ),
inference(avatar_split_clause,[],[f37011,f36300,f37150]) ).
fof(f37150,plain,
( spl86_842
<=> ! [X2,X0,X1] : sP8(X0,X1,X0,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_842])]) ).
fof(f36300,plain,
( spl86_838
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| sP8(X2,X0,X1,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_838])]) ).
fof(f37011,plain,
( ! [X2,X0,X1] : sP8(X0,X1,X0,X2,X2)
| ~ spl86_838 ),
inference(equality_resolution,[],[f36301]) ).
fof(f36301,plain,
( ! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| sP8(X2,X0,X1,X3,X3) )
| ~ spl86_838 ),
inference(avatar_component_clause,[],[f36300]) ).
fof(f36314,plain,
( ~ spl86_22
| spl86_841
| ~ spl86_104
| ~ spl86_176
| ~ spl86_209
| ~ spl86_400 ),
inference(avatar_split_clause,[],[f11434,f11331,f4885,f4277,f3682,f36312,f3286]) ).
fof(f3286,plain,
( spl86_22
<=> ord(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_22])]) ).
fof(f36312,plain,
( spl86_841
<=> ! [X2,X0,X1] : hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),fFalse),hAPP(X0,bool,X2,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_841])]) ).
fof(f11331,plain,
( spl86_400
<=> ! [X2,X3,X0,X5,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),hAPP(X0,X1,X3,X5)))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_400])]) ).
fof(f11434,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),fFalse),hAPP(X0,bool,X2,X1)))
| ~ ord(bool) )
| ~ spl86_104
| ~ spl86_176
| ~ spl86_209
| ~ spl86_400 ),
inference(forward_demodulation,[],[f11433,f4887]) ).
fof(f11433,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),bot_bot(bool)),hAPP(X0,bool,X2,X1)))
| ~ ord(bool) )
| ~ spl86_104
| ~ spl86_176
| ~ spl86_400 ),
inference(forward_demodulation,[],[f11411,f3683]) ).
fof(f11411,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),ord_less_eq(bool),hAPP(X0,bool,bot_bot(fun(X0,bool)),X1)),hAPP(X0,bool,X2,X1)))
| ~ ord(bool) )
| ~ spl86_176
| ~ spl86_400 ),
inference(resolution,[],[f11332,f4278]) ).
fof(f11332,plain,
( ! [X2,X3,X0,X1,X5] :
( ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),hAPP(X0,X1,X3,X5)))
| ~ ord(X1) )
| ~ spl86_400 ),
inference(avatar_component_clause,[],[f11331]) ).
fof(f36310,plain,
( spl86_840
| ~ spl86_176
| ~ spl86_289 ),
inference(avatar_split_clause,[],[f7324,f7141,f4277,f36308]) ).
fof(f36308,plain,
( spl86_840
<=> ! [X0] : ~ sP2(X0,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_840])]) ).
fof(f7141,plain,
( spl86_289
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK59(X0,X1)),sK60(X0,X1))))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_289])]) ).
fof(f7324,plain,
( ! [X0] : ~ sP2(X0,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))))
| ~ spl86_176
| ~ spl86_289 ),
inference(resolution,[],[f7142,f4278]) ).
fof(f7142,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK59(X0,X1)),sK60(X0,X1))))
| ~ sP2(X0,X1) )
| ~ spl86_289 ),
inference(avatar_component_clause,[],[f7141]) ).
fof(f36306,plain,
( spl86_839
| ~ spl86_268 ),
inference(avatar_split_clause,[],[f6717,f6365,f36304]) ).
fof(f36304,plain,
( spl86_839
<=> ! [X0,X3,X2,X1] :
( sP8(X0,X1,X2,X2,X3)
| hAPP(X1,X1,combi(X1),X0) != hAPP(X1,X1,combi(X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_839])]) ).
fof(f6365,plain,
( spl86_268
<=> ! [X4,X0,X3,X2,X1] :
( sP8(X0,X1,X2,X3,X4)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,combi(X1),X0) != hAPP(X1,X1,combi(X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_268])]) ).
fof(f6717,plain,
( ! [X2,X3,X0,X1] :
( sP8(X0,X1,X2,X2,X3)
| hAPP(X1,X1,combi(X1),X0) != hAPP(X1,X1,combi(X1),X3) )
| ~ spl86_268 ),
inference(equality_resolution,[],[f6366]) ).
fof(f6366,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| sP8(X0,X1,X2,X3,X4)
| hAPP(X1,X1,combi(X1),X0) != hAPP(X1,X1,combi(X1),X4) )
| ~ spl86_268 ),
inference(avatar_component_clause,[],[f6365]) ).
fof(f36302,plain,
( spl86_838
| ~ spl86_267 ),
inference(avatar_split_clause,[],[f6598,f6361,f36300]) ).
fof(f6361,plain,
( spl86_267
<=> ! [X4,X0,X3,X2,X1] :
( sP8(X0,X1,X2,X3,X4)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X0)
| hAPP(X1,X1,combi(X1),X3) != hAPP(X1,X1,combi(X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_267])]) ).
fof(f6598,plain,
( ! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| sP8(X2,X0,X1,X3,X3) )
| ~ spl86_267 ),
inference(equality_resolution,[],[f6362]) ).
fof(f6362,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X1,X1,combi(X1),X3) != hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X0)
| sP8(X0,X1,X2,X3,X4) )
| ~ spl86_267 ),
inference(avatar_component_clause,[],[f6361]) ).
fof(f36298,plain,
( spl86_837
| ~ spl86_773
| ~ spl86_810 ),
inference(avatar_split_clause,[],[f35553,f35216,f33218,f36296]) ).
fof(f36296,plain,
( spl86_837
<=> ! [X0] : sK49(zero_zero(nat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_837])]) ).
fof(f33218,plain,
( spl86_773
<=> ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_773])]) ).
fof(f35216,plain,
( spl86_810
<=> ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK49(zero_zero(nat),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_810])]) ).
fof(f35553,plain,
( ! [X0] : sK49(zero_zero(nat),X0) = X0
| ~ spl86_773
| ~ spl86_810 ),
inference(superposition,[],[f35217,f33219]) ).
fof(f33219,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0
| ~ spl86_773 ),
inference(avatar_component_clause,[],[f33218]) ).
fof(f35217,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK49(zero_zero(nat),X0)) = X0
| ~ spl86_810 ),
inference(avatar_component_clause,[],[f35216]) ).
fof(f36294,plain,
( spl86_836
| ~ spl86_129
| ~ spl86_198 ),
inference(avatar_split_clause,[],[f4692,f4652,f3928,f36292]) ).
fof(f36292,plain,
( spl86_836
<=> ! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_836])]) ).
fof(f4692,plain,
( ! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,X0))
| ~ spl86_129
| ~ spl86_198 ),
inference(superposition,[],[f4653,f3929]) ).
fof(f36290,plain,
( spl86_835
| ~ spl86_129
| ~ spl86_190 ),
inference(avatar_split_clause,[],[f4478,f4412,f3928,f36288]) ).
fof(f36288,plain,
( spl86_835
<=> ! [X0] : one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_835])]) ).
fof(f4412,plain,
( spl86_190
<=> ! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_190])]) ).
fof(f4478,plain,
( ! [X0] : one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),X0)
| ~ spl86_129
| ~ spl86_190 ),
inference(superposition,[],[f4413,f3929]) ).
fof(f4413,plain,
( ! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1
| ~ spl86_190 ),
inference(avatar_component_clause,[],[f4412]) ).
fof(f36284,plain,
( ~ spl86_834
| spl86_833
| ~ spl86_43
| ~ spl86_162 ),
inference(avatar_split_clause,[],[f4185,f4149,f3382,f36273,f36281]) ).
fof(f36281,plain,
( spl86_834
<=> hBOOL(sK51(bool,fNot)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_834])]) ).
fof(f36273,plain,
( spl86_833
<=> hAPP(fun(bool,bool),fun(bool,bool),collect(bool),fNot) = bot_bot(fun(bool,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_833])]) ).
fof(f3382,plain,
( spl86_43
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_43])]) ).
fof(f4185,plain,
( hAPP(fun(bool,bool),fun(bool,bool),collect(bool),fNot) = bot_bot(fun(bool,bool))
| ~ hBOOL(sK51(bool,fNot))
| ~ spl86_43
| ~ spl86_162 ),
inference(resolution,[],[f4150,f3383]) ).
fof(f3383,plain,
( ! [X0] :
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(X0) )
| ~ spl86_43 ),
inference(avatar_component_clause,[],[f3382]) ).
fof(f36276,plain,
( ~ spl86_832
| spl86_833
| ~ spl86_43
| ~ spl86_161 ),
inference(avatar_split_clause,[],[f4173,f4145,f3382,f36273,f36269]) ).
fof(f36269,plain,
( spl86_832
<=> hBOOL(sK50(bool,fNot)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_832])]) ).
fof(f4173,plain,
( hAPP(fun(bool,bool),fun(bool,bool),collect(bool),fNot) = bot_bot(fun(bool,bool))
| ~ hBOOL(sK50(bool,fNot))
| ~ spl86_43
| ~ spl86_161 ),
inference(resolution,[],[f4146,f3383]) ).
fof(f36267,plain,
( spl86_831
| ~ spl86_51
| ~ spl86_144 ),
inference(avatar_split_clause,[],[f4041,f4026,f3423,f36264]) ).
fof(f36264,plain,
( spl86_831
<=> hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_831])]) ).
fof(f3423,plain,
( spl86_51
<=> one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_51])]) ).
fof(f4041,plain,
( hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat))
| ~ spl86_51
| ~ spl86_144 ),
inference(superposition,[],[f4027,f3425]) ).
fof(f3425,plain,
( one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat))
| ~ spl86_51 ),
inference(avatar_component_clause,[],[f3423]) ).
fof(f36262,plain,
( spl86_830
| ~ spl86_87
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3790,f3702,f3606,f36260]) ).
fof(f36260,plain,
( spl86_830
<=> ! [X0,X1] :
( hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1)
| hAPP(nat,nat,combi(nat),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_830])]) ).
fof(f3606,plain,
( spl86_87
<=> ! [X0,X1] :
( X0 = X1
| hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_87])]) ).
fof(f3790,plain,
( ! [X0,X1] :
( hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1)
| hAPP(nat,nat,combi(nat),X0) = X1 )
| ~ spl86_87
| ~ spl86_109 ),
inference(superposition,[],[f3607,f3703]) ).
fof(f3607,plain,
( ! [X0,X1] :
( hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1)
| X0 = X1 )
| ~ spl86_87 ),
inference(avatar_component_clause,[],[f3606]) ).
fof(f36258,plain,
( spl86_829
| ~ spl86_86
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3788,f3702,f3602,f36256]) ).
fof(f36256,plain,
( spl86_829
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_829])]) ).
fof(f3602,plain,
( spl86_86
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_86])]) ).
fof(f3788,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl86_86
| ~ spl86_109 ),
inference(superposition,[],[f3603,f3703]) ).
fof(f3603,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(X0) )
| ~ spl86_86 ),
inference(avatar_component_clause,[],[f3602]) ).
fof(f36254,plain,
( spl86_828
| ~ spl86_84
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3785,f3702,f3594,f36252]) ).
fof(f36252,plain,
( spl86_828
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_828])]) ).
fof(f3594,plain,
( spl86_84
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_84])]) ).
fof(f3785,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl86_84
| ~ spl86_109 ),
inference(superposition,[],[f3595,f3703]) ).
fof(f3595,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X0))
| hBOOL(X1) )
| ~ spl86_84 ),
inference(avatar_component_clause,[],[f3594]) ).
fof(f36250,plain,
( spl86_827
| ~ spl86_80
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3783,f3702,f3577,f36248]) ).
fof(f36248,plain,
( spl86_827
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_827])]) ).
fof(f3577,plain,
( spl86_80
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_80])]) ).
fof(f3783,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl86_80
| ~ spl86_109 ),
inference(superposition,[],[f3578,f3703]) ).
fof(f3578,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X0))
| ~ hBOOL(X1) )
| ~ spl86_80 ),
inference(avatar_component_clause,[],[f3577]) ).
fof(f36246,plain,
( spl86_826
| ~ spl86_85
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3780,f3702,f3598,f36244]) ).
fof(f36244,plain,
( spl86_826
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_826])]) ).
fof(f3598,plain,
( spl86_85
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_85])]) ).
fof(f3780,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl86_85
| ~ spl86_109 ),
inference(superposition,[],[f3599,f3703]) ).
fof(f3599,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(X1) )
| ~ spl86_85 ),
inference(avatar_component_clause,[],[f3598]) ).
fof(f36242,plain,
( spl86_825
| ~ spl86_83
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3777,f3702,f3590,f36240]) ).
fof(f36240,plain,
( spl86_825
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_825])]) ).
fof(f3590,plain,
( spl86_83
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_83])]) ).
fof(f3777,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl86_83
| ~ spl86_109 ),
inference(superposition,[],[f3591,f3703]) ).
fof(f3591,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X1) )
| ~ spl86_83 ),
inference(avatar_component_clause,[],[f3590]) ).
fof(f36238,plain,
( spl86_824
| ~ spl86_81
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3773,f3702,f3581,f36236]) ).
fof(f36236,plain,
( spl86_824
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_824])]) ).
fof(f3581,plain,
( spl86_81
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_81])]) ).
fof(f3773,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl86_81
| ~ spl86_109 ),
inference(superposition,[],[f3582,f3703]) ).
fof(f3582,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(X1) )
| ~ spl86_81 ),
inference(avatar_component_clause,[],[f3581]) ).
fof(f36234,plain,
( spl86_823
| ~ spl86_107
| ~ spl86_108 ),
inference(avatar_split_clause,[],[f3754,f3698,f3694,f36232]) ).
fof(f36232,plain,
( spl86_823
<=> ! [X2,X0,X1] :
( fFalse = hAPP(X0,bool,X1,X2)
| fTrue = hAPP(bool,bool,combi(bool),hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_823])]) ).
fof(f3694,plain,
( spl86_107
<=> ! [X0] :
( fFalse = hAPP(bool,bool,combi(bool),X0)
| fTrue = hAPP(bool,bool,combi(bool),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_107])]) ).
fof(f3754,plain,
( ! [X2,X0,X1] :
( fFalse = hAPP(X0,bool,X1,X2)
| fTrue = hAPP(bool,bool,combi(bool),hAPP(X0,bool,X1,X2)) )
| ~ spl86_107
| ~ spl86_108 ),
inference(superposition,[],[f3699,f3695]) ).
fof(f3695,plain,
( ! [X0] :
( fFalse = hAPP(bool,bool,combi(bool),X0)
| fTrue = hAPP(bool,bool,combi(bool),X0) )
| ~ spl86_107 ),
inference(avatar_component_clause,[],[f3694]) ).
fof(f36230,plain,
( spl86_822
| ~ spl86_33
| ~ spl86_70 ),
inference(avatar_split_clause,[],[f3537,f3528,f3340,f36228]) ).
fof(f36228,plain,
( spl86_822
<=> ! [X0,X3,X2,X1] :
( bot_bot(fun(X0,X1)) = hAPP(X2,fun(X0,X1),bot_bot(fun(X2,fun(X0,X1))),X3)
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_822])]) ).
fof(f3528,plain,
( spl86_70
<=> ! [X2,X0,X1] :
( bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2)
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_70])]) ).
fof(f3537,plain,
( ! [X2,X3,X0,X1] :
( bot_bot(fun(X0,X1)) = hAPP(X2,fun(X0,X1),bot_bot(fun(X2,fun(X0,X1))),X3)
| ~ bot(X1) )
| ~ spl86_33
| ~ spl86_70 ),
inference(resolution,[],[f3529,f3341]) ).
fof(f3529,plain,
( ! [X2,X0,X1] :
( ~ bot(X1)
| bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ spl86_70 ),
inference(avatar_component_clause,[],[f3528]) ).
fof(f36218,plain,
( ~ spl86_819
| ~ spl86_820
| ~ spl86_821
| ~ spl86_40
| ~ spl86_195 ),
inference(avatar_split_clause,[],[f4576,f4432,f3369,f36215,f36211,f36207]) ).
fof(f36207,plain,
( spl86_819
<=> bot(pname) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_819])]) ).
fof(f36211,plain,
( spl86_820
<=> hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),ord_less(pname),pn),pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_820])]) ).
fof(f36215,plain,
( spl86_821
<=> pn = bot_bot(pname) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_821])]) ).
fof(f4432,plain,
( spl86_195
<=> ! [X0,X1] :
( bot_bot(X0) != hAPP(X0,X0,combi(X0),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_195])]) ).
fof(f4576,plain,
( pn != bot_bot(pname)
| ~ hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),ord_less(pname),pn),pn))
| ~ bot(pname)
| ~ spl86_40
| ~ spl86_195 ),
inference(inner_rewriting,[],[f4549]) ).
fof(f4549,plain,
( pn != bot_bot(pname)
| ~ hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),ord_less(pname),bot_bot(pname)),pn))
| ~ bot(pname)
| ~ spl86_40
| ~ spl86_195 ),
inference(superposition,[],[f4433,f3371]) ).
fof(f4433,plain,
( ! [X0,X1] :
( bot_bot(X0) != hAPP(X0,X0,combi(X0),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| ~ bot(X0) )
| ~ spl86_195 ),
inference(avatar_component_clause,[],[f4432]) ).
fof(f36205,plain,
( spl86_818
| ~ spl86_105
| ~ spl86_814 ),
inference(avatar_split_clause,[],[f36150,f35233,f3686,f36203]) ).
fof(f36203,plain,
( spl86_818
<=> ! [X0,X1] : ~ sP4(X0,finite_finite(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_818])]) ).
fof(f3686,plain,
( spl86_105
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_105])]) ).
fof(f35233,plain,
( spl86_814
<=> ! [X0,X1] :
( ~ sP4(X0,finite_finite(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK74(X0,finite_finite(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_814])]) ).
fof(f36150,plain,
( ! [X0,X1] : ~ sP4(X0,finite_finite(X0),X1)
| ~ spl86_105
| ~ spl86_814 ),
inference(duplicate_literal_removal,[],[f36134]) ).
fof(f36134,plain,
( ! [X0,X1] :
( ~ sP4(X0,finite_finite(X0),X1)
| ~ sP4(X0,finite_finite(X0),X1) )
| ~ spl86_105
| ~ spl86_814 ),
inference(resolution,[],[f35234,f3687]) ).
fof(f3687,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) )
| ~ spl86_105 ),
inference(avatar_component_clause,[],[f3686]) ).
fof(f35234,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK74(X0,finite_finite(X0),X1)))
| ~ sP4(X0,finite_finite(X0),X1) )
| ~ spl86_814 ),
inference(avatar_component_clause,[],[f35233]) ).
fof(f35508,plain,
( ~ spl86_817
| ~ spl86_410
| spl86_798 ),
inference(avatar_split_clause,[],[f35144,f35140,f11657,f35505]) ).
fof(f35505,plain,
( spl86_817
<=> sP6(hAPP(pname,x_a,mgt_call,pn),x_a,hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u),g) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_817])]) ).
fof(f11657,plain,
( spl86_410
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ sP6(X2,X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_410])]) ).
fof(f35140,plain,
( spl86_798
<=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less(fun(x_a,bool)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_798])]) ).
fof(f35144,plain,
( ~ sP6(hAPP(pname,x_a,mgt_call,pn),x_a,hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u),g)
| ~ spl86_410
| spl86_798 ),
inference(resolution,[],[f35141,f11658]) ).
fof(f11658,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ sP6(X2,X0,X1,X3) )
| ~ spl86_410 ),
inference(avatar_component_clause,[],[f11657]) ).
fof(f35141,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less(fun(x_a,bool)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)))
| spl86_798 ),
inference(avatar_component_clause,[],[f35140]) ).
fof(f35243,plain,
( spl86_816
| ~ spl86_51
| ~ spl86_63
| ~ spl86_78
| ~ spl86_262
| ~ spl86_369
| ~ spl86_668 ),
inference(avatar_split_clause,[],[f28055,f27892,f9545,f6340,f3569,f3493,f3423,f35241]) ).
fof(f35241,plain,
( spl86_816
<=> ! [X0,X1] : one_one(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_816])]) ).
fof(f3493,plain,
( spl86_63
<=> ! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_63])]) ).
fof(f3569,plain,
( spl86_78
<=> ! [X0] : zero_zero(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_78])]) ).
fof(f6340,plain,
( spl86_262
<=> ! [X0,X1] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_262])]) ).
fof(f9545,plain,
( spl86_369
<=> ! [X0,X1] : hAPP(X0,fun(X0,bool),fequal(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_369])]) ).
fof(f27892,plain,
( spl86_668
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_668])]) ).
fof(f28055,plain,
( ! [X0,X1] : one_one(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ spl86_51
| ~ spl86_63
| ~ spl86_78
| ~ spl86_262
| ~ spl86_369
| ~ spl86_668 ),
inference(forward_demodulation,[],[f28054,f3425]) ).
fof(f28054,plain,
( ! [X0,X1] : hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ spl86_63
| ~ spl86_78
| ~ spl86_262
| ~ spl86_369
| ~ spl86_668 ),
inference(forward_demodulation,[],[f28053,f9546]) ).
fof(f9546,plain,
( ! [X0,X1] : hAPP(X0,fun(X0,bool),fequal(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))
| ~ spl86_369 ),
inference(avatar_component_clause,[],[f9545]) ).
fof(f28053,plain,
( ! [X0,X1] : hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ spl86_63
| ~ spl86_78
| ~ spl86_262
| ~ spl86_668 ),
inference(forward_demodulation,[],[f28052,f3570]) ).
fof(f3570,plain,
( ! [X0] : zero_zero(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),bot_bot(fun(X0,bool)))
| ~ spl86_78 ),
inference(avatar_component_clause,[],[f3569]) ).
fof(f28052,plain,
( ! [X0,X1] : hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),bot_bot(fun(X0,bool))))
| ~ spl86_63
| ~ spl86_262
| ~ spl86_668 ),
inference(forward_demodulation,[],[f28026,f6341]) ).
fof(f6341,plain,
( ! [X0,X1] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X1)
| ~ spl86_262 ),
inference(avatar_component_clause,[],[f6340]) ).
fof(f28026,plain,
( ! [X0,X1] : hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ spl86_63
| ~ spl86_668 ),
inference(resolution,[],[f27893,f3494]) ).
fof(f3494,plain,
( ! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),bot_bot(fun(X0,bool))))
| ~ spl86_63 ),
inference(avatar_component_clause,[],[f3493]) ).
fof(f27893,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))) )
| ~ spl86_668 ),
inference(avatar_component_clause,[],[f27892]) ).
fof(f35239,plain,
( spl86_815
| ~ spl86_145
| ~ spl86_332 ),
inference(avatar_split_clause,[],[f8587,f8560,f4030,f35237]) ).
fof(f35237,plain,
( spl86_815
<=> ! [X0] : hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_815])]) ).
fof(f4030,plain,
( spl86_145
<=> ! [X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_145])]) ).
fof(f8587,plain,
( ! [X0] : hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),X0))
| ~ spl86_145
| ~ spl86_332 ),
inference(resolution,[],[f8561,f4031]) ).
fof(f4031,plain,
( ! [X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1))
| ~ spl86_145 ),
inference(avatar_component_clause,[],[f4030]) ).
fof(f35235,plain,
( spl86_814
| ~ spl86_306
| ~ spl86_317 ),
inference(avatar_split_clause,[],[f8093,f7675,f7631,f35233]) ).
fof(f7631,plain,
( spl86_306
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_306])]) ).
fof(f8093,plain,
( ! [X0,X1] :
( ~ sP4(X0,finite_finite(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK74(X0,finite_finite(X0),X1))) )
| ~ spl86_306
| ~ spl86_317 ),
inference(resolution,[],[f7676,f7632]) ).
fof(f7632,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_306 ),
inference(avatar_component_clause,[],[f7631]) ).
fof(f35231,plain,
( spl86_813
| ~ spl86_134
| ~ spl86_293 ),
inference(avatar_split_clause,[],[f7385,f7157,f3966,f35229]) ).
fof(f35229,plain,
( spl86_813
<=> ! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_813])]) ).
fof(f3966,plain,
( spl86_134
<=> ! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_134])]) ).
fof(f7157,plain,
( spl86_293
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK52(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_293])]) ).
fof(f7385,plain,
( ! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),bot_bot(fun(X0,bool)))
| ~ spl86_134
| ~ spl86_293 ),
inference(resolution,[],[f7158,f3967]) ).
fof(f3967,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))
| ~ spl86_134 ),
inference(avatar_component_clause,[],[f3966]) ).
fof(f7158,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK52(X0,X1)),X1))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) )
| ~ spl86_293 ),
inference(avatar_component_clause,[],[f7157]) ).
fof(f35226,plain,
( spl86_812
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_122
| ~ spl86_154
| ~ spl86_282 ),
inference(avatar_split_clause,[],[f7062,f6805,f4088,f3879,f3698,f3636,f3211,f35224]) ).
fof(f35224,plain,
( spl86_812
<=> ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK48(zero_zero(nat),hAPP(nat,nat,suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_812])]) ).
fof(f3211,plain,
( spl86_7
<=> comm_monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_7])]) ).
fof(f3636,plain,
( spl86_93
<=> ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_93])]) ).
fof(f3879,plain,
( spl86_122
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_122])]) ).
fof(f4088,plain,
( spl86_154
<=> ! [X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = hAPP(X0,X0,combi(X0),X1)
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_154])]) ).
fof(f6805,plain,
( spl86_282
<=> ! [X0,X1] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK48(X0,X1))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_282])]) ).
fof(f7062,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK48(zero_zero(nat),hAPP(nat,nat,suc,X0)))
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_122
| ~ spl86_154
| ~ spl86_282 ),
inference(forward_demodulation,[],[f7042,f4120]) ).
fof(f4120,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154 ),
inference(forward_demodulation,[],[f4119,f3752]) ).
fof(f3752,plain,
( ! [X0] : hAPP(nat,nat,combi(nat),X0) = X0
| ~ spl86_93
| ~ spl86_108 ),
inference(superposition,[],[f3699,f3637]) ).
fof(f3637,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) = X0
| ~ spl86_93 ),
inference(avatar_component_clause,[],[f3636]) ).
fof(f4119,plain,
( ! [X0] : hAPP(nat,nat,combi(nat),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X0)
| ~ spl86_7
| ~ spl86_154 ),
inference(resolution,[],[f4089,f3213]) ).
fof(f3213,plain,
( comm_monoid_add(nat)
| ~ spl86_7 ),
inference(avatar_component_clause,[],[f3211]) ).
fof(f4089,plain,
( ! [X0,X1] :
( ~ comm_monoid_add(X0)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = hAPP(X0,X0,combi(X0),X1) )
| ~ spl86_154 ),
inference(avatar_component_clause,[],[f4088]) ).
fof(f7042,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK48(zero_zero(nat),hAPP(nat,nat,suc,X0))))
| ~ spl86_122
| ~ spl86_282 ),
inference(resolution,[],[f6806,f3880]) ).
fof(f3880,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X0)))
| ~ spl86_122 ),
inference(avatar_component_clause,[],[f3879]) ).
fof(f6806,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK48(X0,X1))) = X1 )
| ~ spl86_282 ),
inference(avatar_component_clause,[],[f6805]) ).
fof(f35222,plain,
( spl86_811
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_122
| ~ spl86_154
| ~ spl86_279 ),
inference(avatar_split_clause,[],[f6982,f6793,f4088,f3879,f3698,f3636,f3211,f35220]) ).
fof(f35220,plain,
( spl86_811
<=> ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK20(zero_zero(nat),hAPP(nat,nat,suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_811])]) ).
fof(f6793,plain,
( spl86_279
<=> ! [X0,X1] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK20(X0,X1))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_279])]) ).
fof(f6982,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK20(zero_zero(nat),hAPP(nat,nat,suc,X0)))
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_122
| ~ spl86_154
| ~ spl86_279 ),
inference(forward_demodulation,[],[f6962,f4120]) ).
fof(f6962,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK20(zero_zero(nat),hAPP(nat,nat,suc,X0))))
| ~ spl86_122
| ~ spl86_279 ),
inference(resolution,[],[f6794,f3880]) ).
fof(f6794,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK20(X0,X1))) = X1 )
| ~ spl86_279 ),
inference(avatar_component_clause,[],[f6793]) ).
fof(f35218,plain,
( spl86_810
| ~ spl86_79
| ~ spl86_247 ),
inference(avatar_split_clause,[],[f5973,f5817,f3573,f35216]) ).
fof(f5817,plain,
( spl86_247
<=> ! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK49(X0,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_247])]) ).
fof(f5973,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK49(zero_zero(nat),X0)) = X0
| ~ spl86_79
| ~ spl86_247 ),
inference(resolution,[],[f5818,f3574]) ).
fof(f5818,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK49(X0,X1)) = X1 )
| ~ spl86_247 ),
inference(avatar_component_clause,[],[f5817]) ).
fof(f35214,plain,
( spl86_809
| ~ spl86_131
| ~ spl86_144
| ~ spl86_230 ),
inference(avatar_split_clause,[],[f5422,f4995,f4026,f3936,f35212]) ).
fof(f35212,plain,
( spl86_809
<=> ! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),one_one(nat)))
| zero_zero(nat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_809])]) ).
fof(f4995,plain,
( spl86_230
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_230])]) ).
fof(f5422,plain,
( ! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),one_one(nat)))
| zero_zero(nat) != X0 )
| ~ spl86_131
| ~ spl86_144
| ~ spl86_230 ),
inference(forward_demodulation,[],[f5414,f4027]) ).
fof(f5414,plain,
( ! [X0] :
( zero_zero(nat) != X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),one_one(nat))) )
| ~ spl86_131
| ~ spl86_230 ),
inference(superposition,[],[f4996,f3937]) ).
fof(f4996,plain,
( ! [X0,X1] :
( zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) )
| ~ spl86_230 ),
inference(avatar_component_clause,[],[f4995]) ).
fof(f35210,plain,
( spl86_808
| ~ spl86_93
| ~ spl86_230 ),
inference(avatar_split_clause,[],[f5411,f4995,f3636,f35208]) ).
fof(f35208,plain,
( spl86_808
<=> ! [X0] :
( zero_zero(nat) != X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_808])]) ).
fof(f5411,plain,
( ! [X0] :
( zero_zero(nat) != X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat))) )
| ~ spl86_93
| ~ spl86_230 ),
inference(superposition,[],[f4996,f3637]) ).
fof(f35206,plain,
( spl86_807
| ~ spl86_123
| ~ spl86_205 ),
inference(avatar_split_clause,[],[f4860,f4680,f3883,f35204]) ).
fof(f35204,plain,
( spl86_807
<=> ! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
| zero_zero(nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_807])]) ).
fof(f3883,plain,
( spl86_123
<=> ! [X0] :
( zero_zero(nat) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_123])]) ).
fof(f4860,plain,
( ! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X0))
| zero_zero(nat) = X0 )
| ~ spl86_123
| ~ spl86_205 ),
inference(resolution,[],[f4681,f3884]) ).
fof(f3884,plain,
( ! [X0] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat)))
| zero_zero(nat) = X0 )
| ~ spl86_123 ),
inference(avatar_component_clause,[],[f3883]) ).
fof(f35202,plain,
( spl86_806
| ~ spl86_103
| ~ spl86_205 ),
inference(avatar_split_clause,[],[f4853,f4680,f3678,f35200]) ).
fof(f35200,plain,
( spl86_806
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ sP3(X1,X0,ord_less(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_806])]) ).
fof(f4853,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ sP3(X1,X0,ord_less(nat)) )
| ~ spl86_103
| ~ spl86_205 ),
inference(resolution,[],[f4681,f3679]) ).
fof(f35198,plain,
( spl86_805
| ~ spl86_103
| ~ spl86_199 ),
inference(avatar_split_clause,[],[f4702,f4656,f3678,f35196]) ).
fof(f35196,plain,
( spl86_805
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ sP3(X1,X0,ord_less_eq(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_805])]) ).
fof(f4656,plain,
( spl86_199
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_199])]) ).
fof(f4702,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ sP3(X1,X0,ord_less_eq(nat)) )
| ~ spl86_103
| ~ spl86_199 ),
inference(resolution,[],[f4657,f3679]) ).
fof(f4657,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) )
| ~ spl86_199 ),
inference(avatar_component_clause,[],[f4656]) ).
fof(f35194,plain,
( spl86_804
| ~ spl86_128
| ~ spl86_189 ),
inference(avatar_split_clause,[],[f4452,f4408,f3903,f35192]) ).
fof(f35192,plain,
( spl86_804
<=> ! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)
| sP1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_804])]) ).
fof(f3903,plain,
( spl86_128
<=> ! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| sP1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_128])]) ).
fof(f4408,plain,
( spl86_189
<=> ! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_189])]) ).
fof(f4452,plain,
( ! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)
| sP1(X1,X0) )
| ~ spl86_128
| ~ spl86_189 ),
inference(superposition,[],[f3904,f4409]) ).
fof(f4409,plain,
( ! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)
| ~ spl86_189 ),
inference(avatar_component_clause,[],[f4408]) ).
fof(f3904,plain,
( ! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| sP1(X1,X0) )
| ~ spl86_128 ),
inference(avatar_component_clause,[],[f3903]) ).
fof(f35190,plain,
( spl86_803
| ~ spl86_125
| ~ spl86_189 ),
inference(avatar_split_clause,[],[f4451,f4408,f3891,f35188]) ).
fof(f35188,plain,
( spl86_803
<=> ! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)
| sP0(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_803])]) ).
fof(f3891,plain,
( spl86_125
<=> ! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| sP0(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_125])]) ).
fof(f4451,plain,
( ! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)
| sP0(X1,X0) )
| ~ spl86_125
| ~ spl86_189 ),
inference(superposition,[],[f3892,f4409]) ).
fof(f3892,plain,
( ! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| sP0(X1,X0) )
| ~ spl86_125 ),
inference(avatar_component_clause,[],[f3891]) ).
fof(f35186,plain,
( spl86_802
| ~ spl86_92
| ~ spl86_190
| ~ spl86_784 ),
inference(avatar_split_clause,[],[f34498,f34036,f4412,f3632,f35184]) ).
fof(f35184,plain,
( spl86_802
<=> ! [X0] : zero_zero(nat) = sK49(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_802])]) ).
fof(f34036,plain,
( spl86_784
<=> ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK49(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_784])]) ).
fof(f34498,plain,
( ! [X0] : zero_zero(nat) = sK49(X0,X0)
| ~ spl86_92
| ~ spl86_190
| ~ spl86_784 ),
inference(forward_demodulation,[],[f34378,f3633]) ).
fof(f34378,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X0) = sK49(X0,X0)
| ~ spl86_190
| ~ spl86_784 ),
inference(superposition,[],[f4413,f34037]) ).
fof(f34037,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK49(X0,X0)) = X0
| ~ spl86_784 ),
inference(avatar_component_clause,[],[f34036]) ).
fof(f35182,plain,
( spl86_801
| ~ spl86_129
| ~ spl86_169 ),
inference(avatar_split_clause,[],[f4329,f4248,f3928,f35180]) ).
fof(f35180,plain,
( spl86_801
<=> ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),one_one(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_801])]) ).
fof(f4248,plain,
( spl86_169
<=> ! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_169])]) ).
fof(f4329,plain,
( ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),one_one(nat)))
| ~ spl86_129
| ~ spl86_169 ),
inference(superposition,[],[f4249,f3929]) ).
fof(f4249,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1))
| ~ spl86_169 ),
inference(avatar_component_clause,[],[f4248]) ).
fof(f35178,plain,
( spl86_800
| ~ spl86_52
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4222,f4161,f3430,f35176]) ).
fof(f35176,plain,
( spl86_800
<=> ! [X0] : undefined(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),undefined(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_800])]) ).
fof(f3430,plain,
( spl86_52
<=> ! [X0] : undefined(X0) = hAPP(X0,X0,combi(X0),undefined(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_52])]) ).
fof(f4222,plain,
( ! [X0] : undefined(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),undefined(fun(X0,bool)))
| ~ spl86_52
| ~ spl86_165 ),
inference(superposition,[],[f4162,f3431]) ).
fof(f3431,plain,
( ! [X0] : undefined(X0) = hAPP(X0,X0,combi(X0),undefined(X0))
| ~ spl86_52 ),
inference(avatar_component_clause,[],[f3430]) ).
fof(f35157,plain,
( ~ spl86_48
| spl86_799
| ~ spl86_386
| ~ spl86_539 ),
inference(avatar_split_clause,[],[f18311,f17795,f11052,f35154,f3405]) ).
fof(f3405,plain,
( spl86_48
<=> hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_48])]) ).
fof(f35154,plain,
( spl86_799
<=> hBOOL(hAPP(fun(x_a,bool),bool,finite_finite(x_a),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_799])]) ).
fof(f17795,plain,
( spl86_539
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_539])]) ).
fof(f18311,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,finite_finite(x_a),g))
| ~ hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u))
| ~ spl86_386
| ~ spl86_539 ),
inference(resolution,[],[f17796,f11054]) ).
fof(f11054,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))
| ~ spl86_386 ),
inference(avatar_component_clause,[],[f11052]) ).
fof(f17796,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) )
| ~ spl86_539 ),
inference(avatar_component_clause,[],[f17795]) ).
fof(f35143,plain,
( ~ spl86_797
| spl86_798
| spl86_111
| ~ spl86_212 ),
inference(avatar_split_clause,[],[f5040,f4916,f3822,f35140,f35136]) ).
fof(f35136,plain,
( spl86_797
<=> linorder(fun(x_a,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_797])]) ).
fof(f4916,plain,
( spl86_212
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_212])]) ).
fof(f5040,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less(fun(x_a,bool)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)))
| ~ linorder(fun(x_a,bool))
| spl86_111
| ~ spl86_212 ),
inference(resolution,[],[f4917,f3824]) ).
fof(f4917,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ linorder(X0) )
| ~ spl86_212 ),
inference(avatar_component_clause,[],[f4916]) ).
fof(f34644,plain,
( spl86_796
| ~ spl86_163
| ~ spl86_228 ),
inference(avatar_split_clause,[],[f5328,f4987,f4153,f34642]) ).
fof(f34642,plain,
( spl86_796
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(nat,bool,X0,sK40(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_796])]) ).
fof(f4153,plain,
( spl86_163
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X2,X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_163])]) ).
fof(f4987,plain,
( spl86_228
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK40(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_228])]) ).
fof(f5328,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(nat,bool,X0,sK40(X1,X0))) )
| ~ spl86_163
| ~ spl86_228 ),
inference(resolution,[],[f4988,f4154]) ).
fof(f4154,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| hBOOL(hAPP(X0,bool,X2,X1)) )
| ~ spl86_163 ),
inference(avatar_component_clause,[],[f4153]) ).
fof(f4988,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK40(X0,X1)),X1))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) )
| ~ spl86_228 ),
inference(avatar_component_clause,[],[f4987]) ).
fof(f34640,plain,
( spl86_795
| ~ spl86_163
| ~ spl86_222 ),
inference(avatar_split_clause,[],[f5239,f4962,f4153,f34638]) ).
fof(f34638,plain,
( spl86_795
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(nat,bool,X0,sK14(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_795])]) ).
fof(f4962,plain,
( spl86_222
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK14(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_222])]) ).
fof(f5239,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(nat,bool,X0,sK14(X0,X1))) )
| ~ spl86_163
| ~ spl86_222 ),
inference(resolution,[],[f4963,f4154]) ).
fof(f4963,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK14(X0,X1)),X0))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) )
| ~ spl86_222 ),
inference(avatar_component_clause,[],[f4962]) ).
fof(f34636,plain,
( spl86_794
| ~ spl86_163
| ~ spl86_221 ),
inference(avatar_split_clause,[],[f5234,f4958,f4153,f34634]) ).
fof(f34634,plain,
( spl86_794
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(nat,bool,X0,sK12(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_794])]) ).
fof(f4958,plain,
( spl86_221
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK12(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_221])]) ).
fof(f5234,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(nat,bool,X0,sK12(X0,X1))) )
| ~ spl86_163
| ~ spl86_221 ),
inference(resolution,[],[f4959,f4154]) ).
fof(f4959,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK12(X0,X1)),X0))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) )
| ~ spl86_221 ),
inference(avatar_component_clause,[],[f4958]) ).
fof(f34632,plain,
( spl86_793
| ~ spl86_160
| ~ spl86_187 ),
inference(avatar_split_clause,[],[f4405,f4321,f4141,f34630]) ).
fof(f34630,plain,
( spl86_793
<=> ! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_793])]) ).
fof(f4321,plain,
( spl86_187
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_187])]) ).
fof(f4405,plain,
( ! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse)))
| ~ spl86_160
| ~ spl86_187 ),
inference(trivial_inequality_removal,[],[f4403]) ).
fof(f4403,plain,
( ! [X0] :
( bot_bot(fun(X0,bool)) != bot_bot(fun(X0,bool))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse))) )
| ~ spl86_160
| ~ spl86_187 ),
inference(superposition,[],[f4322,f4142]) ).
fof(f4322,plain,
( ! [X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ spl86_187 ),
inference(avatar_component_clause,[],[f4321]) ).
fof(f34628,plain,
( spl86_792
| ~ spl86_130
| ~ spl86_173 ),
inference(avatar_split_clause,[],[f4353,f4265,f3932,f34626]) ).
fof(f34626,plain,
( spl86_792
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_792])]) ).
fof(f4265,plain,
( spl86_173
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_173])]) ).
fof(f4353,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X0)))
| ~ spl86_130
| ~ spl86_173 ),
inference(superposition,[],[f4266,f3933]) ).
fof(f4266,plain,
( ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)))
| ~ spl86_173 ),
inference(avatar_component_clause,[],[f4265]) ).
fof(f34624,plain,
( spl86_791
| ~ spl86_130
| ~ spl86_169 ),
inference(avatar_split_clause,[],[f4330,f4248,f3932,f34622]) ).
fof(f34622,plain,
( spl86_791
<=> ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_791])]) ).
fof(f4330,plain,
( ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X0))
| ~ spl86_130
| ~ spl86_169 ),
inference(superposition,[],[f4249,f3933]) ).
fof(f34614,plain,
( spl86_790
| ~ spl86_88
| ~ spl86_788 ),
inference(avatar_split_clause,[],[f34605,f34183,f3610,f34612]) ).
fof(f34612,plain,
( spl86_790
<=> ! [X0] : ~ sP2(X0,finite_finite(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_790])]) ).
fof(f3610,plain,
( spl86_88
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK60(X0,X1)))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_88])]) ).
fof(f34183,plain,
( spl86_788
<=> ! [X0] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK60(X0,finite_finite(X0))))
| ~ sP2(X0,finite_finite(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_788])]) ).
fof(f34605,plain,
( ! [X0] : ~ sP2(X0,finite_finite(X0))
| ~ spl86_88
| ~ spl86_788 ),
inference(duplicate_literal_removal,[],[f34592]) ).
fof(f34592,plain,
( ! [X0] :
( ~ sP2(X0,finite_finite(X0))
| ~ sP2(X0,finite_finite(X0)) )
| ~ spl86_88
| ~ spl86_788 ),
inference(resolution,[],[f34184,f3611]) ).
fof(f3611,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK60(X0,X1)))
| ~ sP2(X0,X1) )
| ~ spl86_88 ),
inference(avatar_component_clause,[],[f3610]) ).
fof(f34184,plain,
( ! [X0] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK60(X0,finite_finite(X0))))
| ~ sP2(X0,finite_finite(X0)) )
| ~ spl86_788 ),
inference(avatar_component_clause,[],[f34183]) ).
fof(f34610,plain,
( spl86_789
| ~ spl86_112
| ~ spl86_285 ),
inference(avatar_split_clause,[],[f7164,f7125,f3827,f34607]) ).
fof(f34607,plain,
( spl86_789
<=> hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,pn)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_789])]) ).
fof(f7125,plain,
( spl86_285
<=> ! [X0] :
( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0))))
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X0),u)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_285])]) ).
fof(f7164,plain,
( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,pn))))
| ~ spl86_112
| ~ spl86_285 ),
inference(resolution,[],[f7126,f3829]) ).
fof(f7126,plain,
( ! [X0] :
( ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X0),u))
| hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))) )
| ~ spl86_285 ),
inference(avatar_component_clause,[],[f7125]) ).
fof(f34185,plain,
( spl86_788
| ~ spl86_289
| ~ spl86_306 ),
inference(avatar_split_clause,[],[f7767,f7631,f7141,f34183]) ).
fof(f7767,plain,
( ! [X0] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK60(X0,finite_finite(X0))))
| ~ sP2(X0,finite_finite(X0)) )
| ~ spl86_289
| ~ spl86_306 ),
inference(resolution,[],[f7632,f7142]) ).
fof(f34116,plain,
( ~ spl86_787
| ~ spl86_37
| ~ spl86_769 ),
inference(avatar_split_clause,[],[f32309,f32305,f3356,f34113]) ).
fof(f34113,plain,
( spl86_787
<=> one_one(nat) = sK20(zero_zero(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_787])]) ).
fof(f32309,plain,
( one_one(nat) != sK20(zero_zero(nat),one_one(nat))
| ~ spl86_37
| ~ spl86_769 ),
inference(superposition,[],[f3357,f32307]) ).
fof(f34111,plain,
( ~ spl86_19
| spl86_786
| ~ spl86_7
| ~ spl86_27
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154
| ~ spl86_166
| ~ spl86_196
| ~ spl86_282 ),
inference(avatar_split_clause,[],[f7066,f6805,f4436,f4165,f4088,f3698,f3636,f3311,f3211,f34109,f3271]) ).
fof(f3271,plain,
( spl86_19
<=> bot(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_19])]) ).
fof(f34109,plain,
( spl86_786
<=> ! [X0] :
( zero_zero(nat) = X0
| hAPP(nat,nat,suc,sK48(zero_zero(nat),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_786])]) ).
fof(f3311,plain,
( spl86_27
<=> zero_zero(nat) = bot_bot(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_27])]) ).
fof(f4165,plain,
( spl86_166
<=> ! [X0] : hAPP(nat,nat,combi(nat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_166])]) ).
fof(f4436,plain,
( spl86_196
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| bot_bot(X0) = hAPP(X0,X0,combi(X0),X1)
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_196])]) ).
fof(f7066,plain,
( ! [X0] :
( zero_zero(nat) = X0
| hAPP(nat,nat,suc,sK48(zero_zero(nat),X0)) = X0
| ~ bot(nat) )
| ~ spl86_7
| ~ spl86_27
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154
| ~ spl86_166
| ~ spl86_196
| ~ spl86_282 ),
inference(forward_demodulation,[],[f7065,f3313]) ).
fof(f3313,plain,
( zero_zero(nat) = bot_bot(nat)
| ~ spl86_27 ),
inference(avatar_component_clause,[],[f3311]) ).
fof(f7065,plain,
( ! [X0] :
( bot_bot(nat) = X0
| hAPP(nat,nat,suc,sK48(zero_zero(nat),X0)) = X0
| ~ bot(nat) )
| ~ spl86_7
| ~ spl86_27
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154
| ~ spl86_166
| ~ spl86_196
| ~ spl86_282 ),
inference(forward_demodulation,[],[f7064,f4166]) ).
fof(f4166,plain,
( ! [X0] : hAPP(nat,nat,combi(nat),X0) = X0
| ~ spl86_166 ),
inference(avatar_component_clause,[],[f4165]) ).
fof(f7064,plain,
( ! [X0] :
( hAPP(nat,nat,suc,sK48(zero_zero(nat),X0)) = X0
| bot_bot(nat) = hAPP(nat,nat,combi(nat),X0)
| ~ bot(nat) )
| ~ spl86_7
| ~ spl86_27
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154
| ~ spl86_196
| ~ spl86_282 ),
inference(forward_demodulation,[],[f7063,f4120]) ).
fof(f7063,plain,
( ! [X0] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK48(zero_zero(nat),X0))) = X0
| bot_bot(nat) = hAPP(nat,nat,combi(nat),X0)
| ~ bot(nat) )
| ~ spl86_27
| ~ spl86_196
| ~ spl86_282 ),
inference(forward_demodulation,[],[f7049,f3313]) ).
fof(f7049,plain,
( ! [X0] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),bot_bot(nat)),sK48(bot_bot(nat),X0))) = X0
| bot_bot(nat) = hAPP(nat,nat,combi(nat),X0)
| ~ bot(nat) )
| ~ spl86_196
| ~ spl86_282 ),
inference(resolution,[],[f6806,f4437]) ).
fof(f4437,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| bot_bot(X0) = hAPP(X0,X0,combi(X0),X1)
| ~ bot(X0) )
| ~ spl86_196 ),
inference(avatar_component_clause,[],[f4436]) ).
fof(f34042,plain,
( ~ spl86_19
| spl86_785
| ~ spl86_7
| ~ spl86_27
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154
| ~ spl86_166
| ~ spl86_196
| ~ spl86_279 ),
inference(avatar_split_clause,[],[f6986,f6793,f4436,f4165,f4088,f3698,f3636,f3311,f3211,f34040,f3271]) ).
fof(f34040,plain,
( spl86_785
<=> ! [X0] :
( zero_zero(nat) = X0
| hAPP(nat,nat,suc,sK20(zero_zero(nat),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_785])]) ).
fof(f6986,plain,
( ! [X0] :
( zero_zero(nat) = X0
| hAPP(nat,nat,suc,sK20(zero_zero(nat),X0)) = X0
| ~ bot(nat) )
| ~ spl86_7
| ~ spl86_27
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154
| ~ spl86_166
| ~ spl86_196
| ~ spl86_279 ),
inference(forward_demodulation,[],[f6985,f3313]) ).
fof(f6985,plain,
( ! [X0] :
( bot_bot(nat) = X0
| hAPP(nat,nat,suc,sK20(zero_zero(nat),X0)) = X0
| ~ bot(nat) )
| ~ spl86_7
| ~ spl86_27
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154
| ~ spl86_166
| ~ spl86_196
| ~ spl86_279 ),
inference(forward_demodulation,[],[f6984,f4166]) ).
fof(f6984,plain,
( ! [X0] :
( hAPP(nat,nat,suc,sK20(zero_zero(nat),X0)) = X0
| bot_bot(nat) = hAPP(nat,nat,combi(nat),X0)
| ~ bot(nat) )
| ~ spl86_7
| ~ spl86_27
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154
| ~ spl86_196
| ~ spl86_279 ),
inference(forward_demodulation,[],[f6983,f4120]) ).
fof(f6983,plain,
( ! [X0] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK20(zero_zero(nat),X0))) = X0
| bot_bot(nat) = hAPP(nat,nat,combi(nat),X0)
| ~ bot(nat) )
| ~ spl86_27
| ~ spl86_196
| ~ spl86_279 ),
inference(forward_demodulation,[],[f6969,f3313]) ).
fof(f6969,plain,
( ! [X0] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),bot_bot(nat)),sK20(bot_bot(nat),X0))) = X0
| bot_bot(nat) = hAPP(nat,nat,combi(nat),X0)
| ~ bot(nat) )
| ~ spl86_196
| ~ spl86_279 ),
inference(resolution,[],[f6794,f4437]) ).
fof(f34038,plain,
( spl86_784
| ~ spl86_69
| ~ spl86_247 ),
inference(avatar_split_clause,[],[f5972,f5817,f3524,f34036]) ).
fof(f3524,plain,
( spl86_69
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_69])]) ).
fof(f5972,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK49(X0,X0)) = X0
| ~ spl86_69
| ~ spl86_247 ),
inference(resolution,[],[f5818,f3525]) ).
fof(f3525,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0))
| ~ spl86_69 ),
inference(avatar_component_clause,[],[f3524]) ).
fof(f34034,plain,
( spl86_783
| ~ spl86_164
| ~ spl86_207 ),
inference(avatar_split_clause,[],[f4914,f4877,f4157,f34032]) ).
fof(f34032,plain,
( spl86_783
<=> ! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| ~ hBOOL(hAPP(X0,bool,sK74(X0,X1,X2),sK73(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_783])]) ).
fof(f4157,plain,
( spl86_164
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_164])]) ).
fof(f4877,plain,
( spl86_207
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_207])]) ).
fof(f4914,plain,
( ! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| ~ hBOOL(hAPP(X0,bool,sK74(X0,X1,X2),sK73(X0,X1,X2))) )
| ~ spl86_164
| ~ spl86_207 ),
inference(resolution,[],[f4878,f4158]) ).
fof(f4158,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,X2,X1)) )
| ~ spl86_164 ),
inference(avatar_component_clause,[],[f4157]) ).
fof(f4878,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) )
| ~ spl86_207 ),
inference(avatar_component_clause,[],[f4877]) ).
fof(f34030,plain,
( spl86_782
| ~ spl86_103
| ~ spl86_175 ),
inference(avatar_split_clause,[],[f4370,f4273,f3678,f34028]) ).
fof(f34028,plain,
( spl86_782
<=> ! [X0,X1] : ~ sP3(X0,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1),ord_less_eq(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_782])]) ).
fof(f4273,plain,
( spl86_175
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_175])]) ).
fof(f4370,plain,
( ! [X0,X1] : ~ sP3(X0,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1),ord_less_eq(nat))
| ~ spl86_103
| ~ spl86_175 ),
inference(resolution,[],[f4274,f3679]) ).
fof(f4274,plain,
( ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X0))
| ~ spl86_175 ),
inference(avatar_component_clause,[],[f4273]) ).
fof(f34026,plain,
( spl86_781
| ~ spl86_103
| ~ spl86_174 ),
inference(avatar_split_clause,[],[f4359,f4269,f3678,f34024]) ).
fof(f34024,plain,
( spl86_781
<=> ! [X0,X1] : ~ sP3(hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1),X0,ord_less_eq(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_781])]) ).
fof(f4269,plain,
( spl86_174
<=> ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_174])]) ).
fof(f4359,plain,
( ! [X0,X1] : ~ sP3(hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1),X0,ord_less_eq(nat))
| ~ spl86_103
| ~ spl86_174 ),
inference(resolution,[],[f4270,f3679]) ).
fof(f4270,plain,
( ! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)))
| ~ spl86_174 ),
inference(avatar_component_clause,[],[f4269]) ).
fof(f34022,plain,
( spl86_780
| ~ spl86_103
| ~ spl86_173 ),
inference(avatar_split_clause,[],[f4348,f4265,f3678,f34020]) ).
fof(f34020,plain,
( spl86_780
<=> ! [X0,X1] : ~ sP3(hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1),X1,ord_less_eq(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_780])]) ).
fof(f4348,plain,
( ! [X0,X1] : ~ sP3(hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1),X1,ord_less_eq(nat))
| ~ spl86_103
| ~ spl86_173 ),
inference(resolution,[],[f4266,f3679]) ).
fof(f34018,plain,
( spl86_779
| ~ spl86_115
| ~ spl86_147 ),
inference(avatar_split_clause,[],[f4057,f4038,f3841,f34016]) ).
fof(f34016,plain,
( spl86_779
<=> ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK22(hAPP(nat,nat,suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_779])]) ).
fof(f3841,plain,
( spl86_115
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_115])]) ).
fof(f4057,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK22(hAPP(nat,nat,suc,X0)))
| ~ spl86_115
| ~ spl86_147 ),
inference(resolution,[],[f4039,f3842]) ).
fof(f3842,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X0)))
| ~ spl86_115 ),
inference(avatar_component_clause,[],[f3841]) ).
fof(f33887,plain,
( spl86_778
| ~ spl86_37
| ~ spl86_767 ),
inference(avatar_split_clause,[],[f32239,f32231,f3356,f33885]) ).
fof(f33885,plain,
( spl86_778
<=> ! [X0] :
( sK22(X0) != X0
| zero_zero(nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_778])]) ).
fof(f32231,plain,
( spl86_767
<=> ! [X0] :
( zero_zero(nat) = X0
| hAPP(nat,nat,suc,sK22(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_767])]) ).
fof(f32239,plain,
( ! [X0] :
( sK22(X0) != X0
| zero_zero(nat) = X0 )
| ~ spl86_37
| ~ spl86_767 ),
inference(superposition,[],[f3357,f32232]) ).
fof(f32232,plain,
( ! [X0] :
( hAPP(nat,nat,suc,sK22(X0)) = X0
| zero_zero(nat) = X0 )
| ~ spl86_767 ),
inference(avatar_component_clause,[],[f32231]) ).
fof(f33236,plain,
( spl86_777
| ~ spl86_239 ),
inference(avatar_split_clause,[],[f5772,f5031,f33234]) ).
fof(f33234,plain,
( spl86_777
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_777])]) ).
fof(f5031,plain,
( spl86_239
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_239])]) ).
fof(f5772,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ order(X0) )
| ~ spl86_239 ),
inference(equality_resolution,[],[f5032]) ).
fof(f5032,plain,
( ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ order(X0) )
| ~ spl86_239 ),
inference(avatar_component_clause,[],[f5031]) ).
fof(f33232,plain,
( spl86_776
| ~ spl86_238 ),
inference(avatar_split_clause,[],[f5691,f5027,f33230]) ).
fof(f33230,plain,
( spl86_776
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_776])]) ).
fof(f5027,plain,
( spl86_238
<=> ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_238])]) ).
fof(f5691,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ order(X0) )
| ~ spl86_238 ),
inference(equality_resolution,[],[f5028]) ).
fof(f5028,plain,
( ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ order(X0) )
| ~ spl86_238 ),
inference(avatar_component_clause,[],[f5027]) ).
fof(f33228,plain,
( spl86_775
| ~ spl86_237 ),
inference(avatar_split_clause,[],[f5610,f5023,f33226]) ).
fof(f33226,plain,
( spl86_775
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_775])]) ).
fof(f5023,plain,
( spl86_237
<=> ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_237])]) ).
fof(f5610,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ linorder(X0) )
| ~ spl86_237 ),
inference(equality_resolution,[],[f5024]) ).
fof(f5024,plain,
( ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ linorder(X0) )
| ~ spl86_237 ),
inference(avatar_component_clause,[],[f5023]) ).
fof(f33224,plain,
( spl86_774
| ~ spl86_213 ),
inference(avatar_split_clause,[],[f5078,f4920,f33222]) ).
fof(f33222,plain,
( spl86_774
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_774])]) ).
fof(f4920,plain,
( spl86_213
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_213])]) ).
fof(f5078,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ linorder(X0) )
| ~ spl86_213 ),
inference(factoring,[],[f4921]) ).
fof(f4921,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ linorder(X0) )
| ~ spl86_213 ),
inference(avatar_component_clause,[],[f4920]) ).
fof(f33220,plain,
( spl86_773
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_154 ),
inference(avatar_split_clause,[],[f4120,f4088,f3698,f3636,f3211,f33218]) ).
fof(f33216,plain,
( spl86_772
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_153 ),
inference(avatar_split_clause,[],[f4118,f4084,f3698,f3636,f3211,f33214]) ).
fof(f33214,plain,
( spl86_772
<=> ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_772])]) ).
fof(f4084,plain,
( spl86_153
<=> ! [X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = hAPP(X0,X0,combi(X0),X1)
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_153])]) ).
fof(f4118,plain,
( ! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_153 ),
inference(forward_demodulation,[],[f4117,f3752]) ).
fof(f4117,plain,
( ! [X0] : hAPP(nat,nat,combi(nat),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),zero_zero(nat))
| ~ spl86_7
| ~ spl86_153 ),
inference(resolution,[],[f4085,f3213]) ).
fof(f4085,plain,
( ! [X0,X1] :
( ~ comm_monoid_add(X0)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = hAPP(X0,X0,combi(X0),X1) )
| ~ spl86_153 ),
inference(avatar_component_clause,[],[f4084]) ).
fof(f33212,plain,
( spl86_771
| ~ spl86_51
| ~ spl86_115 ),
inference(avatar_split_clause,[],[f3871,f3841,f3423,f33209]) ).
fof(f33209,plain,
( spl86_771
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_771])]) ).
fof(f3871,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat)))
| ~ spl86_51
| ~ spl86_115 ),
inference(superposition,[],[f3842,f3425]) ).
fof(f32438,plain,
( ~ spl86_13
| spl86_770
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_118
| ~ spl86_154
| ~ spl86_282 ),
inference(avatar_split_clause,[],[f7067,f6805,f4088,f3853,f3698,f3636,f3211,f32435,f3241]) ).
fof(f3241,plain,
( spl86_13
<=> linordered_semidom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_13])]) ).
fof(f3853,plain,
( spl86_118
<=> ! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_118])]) ).
fof(f7067,plain,
( one_one(nat) = hAPP(nat,nat,suc,sK48(zero_zero(nat),one_one(nat)))
| ~ linordered_semidom(nat)
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_118
| ~ spl86_154
| ~ spl86_282 ),
inference(forward_demodulation,[],[f7051,f4120]) ).
fof(f7051,plain,
( one_one(nat) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK48(zero_zero(nat),one_one(nat))))
| ~ linordered_semidom(nat)
| ~ spl86_118
| ~ spl86_282 ),
inference(resolution,[],[f6806,f3854]) ).
fof(f3854,plain,
( ! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) )
| ~ spl86_118 ),
inference(avatar_component_clause,[],[f3853]) ).
fof(f32308,plain,
( ~ spl86_13
| spl86_769
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_118
| ~ spl86_154
| ~ spl86_279 ),
inference(avatar_split_clause,[],[f6987,f6793,f4088,f3853,f3698,f3636,f3211,f32305,f3241]) ).
fof(f6987,plain,
( one_one(nat) = hAPP(nat,nat,suc,sK20(zero_zero(nat),one_one(nat)))
| ~ linordered_semidom(nat)
| ~ spl86_7
| ~ spl86_93
| ~ spl86_108
| ~ spl86_118
| ~ spl86_154
| ~ spl86_279 ),
inference(forward_demodulation,[],[f6971,f4120]) ).
fof(f6971,plain,
( one_one(nat) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),sK20(zero_zero(nat),one_one(nat))))
| ~ linordered_semidom(nat)
| ~ spl86_118
| ~ spl86_279 ),
inference(resolution,[],[f6794,f3854]) ).
fof(f32237,plain,
( spl86_768
| ~ spl86_103
| ~ spl86_760 ),
inference(avatar_split_clause,[],[f32204,f31996,f3678,f32235]) ).
fof(f32235,plain,
( spl86_768
<=> ! [X0] : ~ sP3(X0,X0,fequal(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_768])]) ).
fof(f31996,plain,
( spl86_760
<=> ! [X0,X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_760])]) ).
fof(f32204,plain,
( ! [X0] : ~ sP3(X0,X0,fequal(nat))
| ~ spl86_103
| ~ spl86_760 ),
inference(resolution,[],[f31997,f3679]) ).
fof(f31997,plain,
( ! [X0,X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X1))
| ~ spl86_760 ),
inference(avatar_component_clause,[],[f31996]) ).
fof(f32233,plain,
( ~ spl86_19
| spl86_767
| ~ spl86_27
| ~ spl86_147
| ~ spl86_166
| ~ spl86_196 ),
inference(avatar_split_clause,[],[f4591,f4436,f4165,f4038,f3311,f32231,f3271]) ).
fof(f4591,plain,
( ! [X0] :
( zero_zero(nat) = X0
| ~ bot(nat)
| hAPP(nat,nat,suc,sK22(X0)) = X0 )
| ~ spl86_27
| ~ spl86_147
| ~ spl86_166
| ~ spl86_196 ),
inference(forward_demodulation,[],[f4590,f3313]) ).
fof(f4590,plain,
( ! [X0] :
( bot_bot(nat) = X0
| ~ bot(nat)
| hAPP(nat,nat,suc,sK22(X0)) = X0 )
| ~ spl86_147
| ~ spl86_166
| ~ spl86_196 ),
inference(forward_demodulation,[],[f4582,f4166]) ).
fof(f4582,plain,
( ! [X0] :
( bot_bot(nat) = hAPP(nat,nat,combi(nat),X0)
| ~ bot(nat)
| hAPP(nat,nat,suc,sK22(X0)) = X0 )
| ~ spl86_147
| ~ spl86_196 ),
inference(resolution,[],[f4437,f4039]) ).
fof(f32229,plain,
( spl86_766
| ~ spl86_106
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4219,f4161,f3690,f32226]) ).
fof(f3690,plain,
( spl86_106
<=> ! [X0] : combi(X0) = hAPP(fun(X0,X0),fun(X0,X0),combi(fun(X0,X0)),combi(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_106])]) ).
fof(f4219,plain,
( combi(bool) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool))
| ~ spl86_106
| ~ spl86_165 ),
inference(superposition,[],[f4162,f3691]) ).
fof(f3691,plain,
( ! [X0] : combi(X0) = hAPP(fun(X0,X0),fun(X0,X0),combi(fun(X0,X0)),combi(X0))
| ~ spl86_106 ),
inference(avatar_component_clause,[],[f3690]) ).
fof(f32224,plain,
( spl86_765
| ~ spl86_107
| ~ spl86_108 ),
inference(avatar_split_clause,[],[f3755,f3698,f3694,f32222]) ).
fof(f32222,plain,
( spl86_765
<=> ! [X2,X0,X1] :
( fFalse = hAPP(X0,bool,X1,X2)
| fTrue = hAPP(X0,bool,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_765])]) ).
fof(f3755,plain,
( ! [X2,X0,X1] :
( fFalse = hAPP(X0,bool,X1,X2)
| fTrue = hAPP(X0,bool,X1,X2) )
| ~ spl86_107
| ~ spl86_108 ),
inference(superposition,[],[f3695,f3699]) ).
fof(f32041,plain,
( spl86_764
| ~ spl86_700 ),
inference(avatar_split_clause,[],[f31922,f29627,f32039]) ).
fof(f32039,plain,
( spl86_764
<=> ! [X2,X0,X1] :
( X0 != X1
| sP8(X2,nat,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_764])]) ).
fof(f29627,plain,
( spl86_700
<=> ! [X0,X3,X2,X1] :
( X2 != X3
| X0 != X1
| sP8(X3,nat,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_700])]) ).
fof(f31922,plain,
( ! [X2,X0,X1] :
( X0 != X1
| sP8(X2,nat,X2,X0,X1) )
| ~ spl86_700 ),
inference(equality_resolution,[],[f29628]) ).
fof(f29628,plain,
( ! [X2,X3,X0,X1] :
( X2 != X3
| X0 != X1
| sP8(X3,nat,X2,X0,X1) )
| ~ spl86_700 ),
inference(avatar_component_clause,[],[f29627]) ).
fof(f32010,plain,
( spl86_763
| ~ spl86_53
| ~ spl86_449 ),
inference(avatar_split_clause,[],[f13891,f12998,f3436,f32008]) ).
fof(f32008,plain,
( spl86_763
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(sum_sum(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_763])]) ).
fof(f3436,plain,
( spl86_53
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_53])]) ).
fof(f12998,plain,
( spl86_449
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_449])]) ).
fof(f13891,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(sum_sum(X0,X2)) )
| ~ spl86_53
| ~ spl86_449 ),
inference(resolution,[],[f12999,f3437]) ).
fof(f3437,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(X0) )
| ~ spl86_53 ),
inference(avatar_component_clause,[],[f3436]) ).
fof(f12999,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_449 ),
inference(avatar_component_clause,[],[f12998]) ).
fof(f32006,plain,
( spl86_762
| ~ spl86_53
| ~ spl86_448 ),
inference(avatar_split_clause,[],[f13884,f12994,f3436,f32004]) ).
fof(f32004,plain,
( spl86_762
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(sum_sum(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_762])]) ).
fof(f12994,plain,
( spl86_448
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_448])]) ).
fof(f13884,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(sum_sum(X2,X0)) )
| ~ spl86_53
| ~ spl86_448 ),
inference(resolution,[],[f12995,f3437]) ).
fof(f12995,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) )
| ~ spl86_448 ),
inference(avatar_component_clause,[],[f12994]) ).
fof(f32002,plain,
( spl86_761
| ~ spl86_192
| ~ spl86_369 ),
inference(avatar_split_clause,[],[f9554,f9545,f4420,f32000]) ).
fof(f32000,plain,
( spl86_761
<=> ! [X0,X1] : bot_bot(fun(X0,bool)) != hAPP(X0,fun(X0,bool),fequal(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_761])]) ).
fof(f4420,plain,
( spl86_192
<=> ! [X2,X0,X1] : bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_192])]) ).
fof(f9554,plain,
( ! [X0,X1] : bot_bot(fun(X0,bool)) != hAPP(X0,fun(X0,bool),fequal(X0),X1)
| ~ spl86_192
| ~ spl86_369 ),
inference(superposition,[],[f4421,f9546]) ).
fof(f4421,plain,
( ! [X2,X0,X1] : bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)
| ~ spl86_192 ),
inference(avatar_component_clause,[],[f4420]) ).
fof(f31998,plain,
( spl86_760
| ~ spl86_202 ),
inference(avatar_split_clause,[],[f4798,f4668,f31996]) ).
fof(f4798,plain,
( ! [X0,X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X1))
| ~ spl86_202 ),
inference(equality_resolution,[],[f4669]) ).
fof(f31994,plain,
( spl86_759
| ~ spl86_163
| ~ spl86_179 ),
inference(avatar_split_clause,[],[f4385,f4289,f4153,f31992]) ).
fof(f31992,plain,
( spl86_759
<=> ! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| hBOOL(hAPP(X0,bool,X2,sK73(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_759])]) ).
fof(f4289,plain,
( spl86_179
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),X2))
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_179])]) ).
fof(f4385,plain,
( ! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| hBOOL(hAPP(X0,bool,X2,sK73(X0,X1,X2))) )
| ~ spl86_163
| ~ spl86_179 ),
inference(resolution,[],[f4290,f4154]) ).
fof(f4290,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),X2))
| ~ sP4(X0,X1,X2) )
| ~ spl86_179 ),
inference(avatar_component_clause,[],[f4289]) ).
fof(f31990,plain,
( spl86_758
| ~ spl86_164
| ~ spl86_178 ),
inference(avatar_split_clause,[],[f4384,f4285,f4157,f31988]) ).
fof(f31988,plain,
( spl86_758
<=> ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ hBOOL(hAPP(X0,bool,sK60(X0,X1),sK59(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_758])]) ).
fof(f4285,plain,
( spl86_178
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK59(X0,X1)),sK60(X0,X1)))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_178])]) ).
fof(f4384,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| ~ hBOOL(hAPP(X0,bool,sK60(X0,X1),sK59(X0,X1))) )
| ~ spl86_164
| ~ spl86_178 ),
inference(resolution,[],[f4286,f4158]) ).
fof(f4286,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK59(X0,X1)),sK60(X0,X1)))
| ~ sP2(X0,X1) )
| ~ spl86_178 ),
inference(avatar_component_clause,[],[f4285]) ).
fof(f31986,plain,
( spl86_757
| ~ spl86_42
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3769,f3702,f3378,f31984]) ).
fof(f31984,plain,
( spl86_757
<=> ! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_757])]) ).
fof(f3378,plain,
( spl86_42
<=> ! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_42])]) ).
fof(f3769,plain,
( ! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl86_42
| ~ spl86_109 ),
inference(superposition,[],[f3379,f3703]) ).
fof(f3379,plain,
( ! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) )
| ~ spl86_42 ),
inference(avatar_component_clause,[],[f3378]) ).
fof(f31982,plain,
( spl86_756
| ~ spl86_43
| ~ spl86_109 ),
inference(avatar_split_clause,[],[f3768,f3702,f3382,f31980]) ).
fof(f31980,plain,
( spl86_756
<=> ! [X0] :
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_756])]) ).
fof(f3768,plain,
( ! [X0] :
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl86_43
| ~ spl86_109 ),
inference(superposition,[],[f3383,f3703]) ).
fof(f31921,plain,
( spl86_755
| ~ spl86_109
| ~ spl86_165
| ~ spl86_754 ),
inference(avatar_split_clause,[],[f31917,f31914,f4161,f3702,f31919]) ).
fof(f31919,plain,
( spl86_755
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,sK72(X0,X1,X2,X3))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_755])]) ).
fof(f31914,plain,
( spl86_754
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,sK72(X0,X1,X2,X3)))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_754])]) ).
fof(f31917,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,sK72(X0,X1,X2,X3))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_754 ),
inference(forward_demodulation,[],[f31915,f4236]) ).
fof(f4236,plain,
( ! [X2,X3,X0,X1] : hAPP(fun(X0,bool),X2,X3,X1) = hAPP(fun(X0,bool),X2,X3,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))
| ~ spl86_109
| ~ spl86_165 ),
inference(superposition,[],[f3703,f4162]) ).
fof(f31915,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,sK72(X0,X1,X2,X3)))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) )
| ~ spl86_754 ),
inference(avatar_component_clause,[],[f31914]) ).
fof(f31916,plain,
spl86_754,
inference(avatar_split_clause,[],[f2601,f31914]) ).
fof(f2601,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,sK72(X0,X1,X2,X3)))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(cnf_transformation,[],[f1869]) ).
fof(f1869,plain,
! [X0,X1,X2,X3] :
( ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,sK72(X0,X1,X2,X3)))))))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK72(X0,X1,X2,X3)),X3)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f1535,f1868]) ).
fof(f1868,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,X4))))))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3)) )
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,sK72(X0,X1,X2,X3)))))))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK72(X0,X1,X2,X3)),X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f1535,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,X4))))))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(flattening,[],[f1534]) ).
fof(f1534,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,X4))))))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(ennf_transformation,[],[f1062]) ).
fof(f1062,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
=> ? [X4] :
( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))),hAPP(X0,fun(X1,bool),hAPP(fun(X1,fun(X0,bool)),fun(X0,fun(X1,bool)),combc(X1,X0,bool),hAPP(fun(X1,X0),fun(X1,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(fun(X1,X0),fun(X1,fun(X0,bool))),combb(X0,fun(X0,bool),X1),fequal(X0)),X2)),hAPP(X1,X0,X2,X4))))))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X3)) ) ) ),
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X1,X0,X11,X7] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X7)))
=> ? [X32] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X7))),hAPP(X1,fun(X0,bool),hAPP(fun(X0,fun(X1,bool)),fun(X1,fun(X0,bool)),combc(X0,X1,bool),hAPP(fun(X0,X1),fun(X0,fun(X1,bool)),hAPP(fun(X1,fun(X1,bool)),fun(fun(X0,X1),fun(X0,fun(X1,bool))),combb(X1,fun(X1,bool),X0),fequal(X1)),X11)),hAPP(X0,X1,X11,X32))))))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pigeonhole__infinite) ).
fof(f31492,plain,
spl86_753,
inference(avatar_split_clause,[],[f2920,f31490]) ).
fof(f31490,plain,
( spl86_753
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))))
| ~ hBOOL(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_753])]) ).
fof(f2920,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))))
| ~ hBOOL(X3) ),
inference(definition_unfolding,[],[f2591,f2190]) ).
fof(f2190,plain,
! [X0,X1] : ti(X0,X1) = hAPP(X0,X0,combi(X0),X1),
inference(cnf_transformation,[],[f784]) ).
fof(f784,plain,
! [X0,X1] : ti(X0,X1) = hAPP(X0,X0,combi(X0),X1),
inference(rectify,[],[f587]) ).
fof(f587,axiom,
! [X2,X79] : hAPP(X2,X2,combi(X2),X79) = ti(X2,X79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
fof(f2591,plain,
! [X2,X3,X0,X1] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))))
| ~ hBOOL(X3) ),
inference(cnf_transformation,[],[f1529]) ).
fof(f1529,plain,
! [X0,X1,X2,X3] :
( ( ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))))
| hBOOL(X3) )
& ( ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))))
| ~ hBOOL(X3) ) ),
inference(ennf_transformation,[],[f1058]) ).
fof(f1058,plain,
! [X0,X1,X2,X3] :
( ( ~ hBOOL(X3)
=> ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))) )
& ( hBOOL(X3)
=> ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))) ) ),
inference(rectify,[],[f261]) ).
fof(f261,axiom,
! [X0,X13,X38,X15] :
( ( ~ hBOOL(X15)
=> ti(X0,X38) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X15)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X13)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X15))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X38)))) )
& ( hBOOL(X15)
=> ti(X0,X13) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X15)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X13)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X15))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X38)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_If__def) ).
fof(f31488,plain,
spl86_752,
inference(avatar_split_clause,[],[f2919,f31486]) ).
fof(f31486,plain,
( spl86_752
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))) = hAPP(X0,X0,combi(X0),X2)
| hBOOL(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_752])]) ).
fof(f2919,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2)))) = hAPP(X0,X0,combi(X0),X2)
| hBOOL(X3) ),
inference(definition_unfolding,[],[f2592,f2190]) ).
fof(f2592,plain,
! [X2,X3,X0,X1] :
( ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,X3)),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,X3))),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))))
| hBOOL(X3) ),
inference(cnf_transformation,[],[f1529]) ).
fof(f31435,plain,
spl86_751,
inference(avatar_split_clause,[],[f2424,f31433]) ).
fof(f31433,plain,
( spl86_751
<=> ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_751])]) ).
fof(f2424,plain,
! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),
inference(cnf_transformation,[],[f947]) ).
fof(f947,plain,
! [X0,X1,X2] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X1))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2)))),
inference(rectify,[],[f258]) ).
fof(f258,axiom,
! [X0,X7,X12] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X7))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X12)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_set__diff__eq) ).
fof(f31409,plain,
( spl86_750
| ~ spl86_109
| ~ spl86_165
| ~ spl86_749 ),
inference(avatar_split_clause,[],[f31405,f31401,f4161,f3702,f31407]) ).
fof(f31407,plain,
( spl86_750
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_750])]) ).
fof(f31401,plain,
( spl86_749
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_749])]) ).
fof(f31405,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_749 ),
inference(forward_demodulation,[],[f31404,f4236]) ).
fof(f31404,plain,
( ! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_749 ),
inference(forward_demodulation,[],[f31402,f4236]) ).
fof(f31402,plain,
( ! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_749 ),
inference(avatar_component_clause,[],[f31401]) ).
fof(f31403,plain,
spl86_749,
inference(avatar_split_clause,[],[f3163,f31401]) ).
fof(f3163,plain,
! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(forward_demodulation,[],[f3162,f2226]) ).
fof(f2226,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(cnf_transformation,[],[f816]) ).
fof(f816,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(rectify,[],[f184]) ).
fof(f184,axiom,
! [X0,X10] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_singleton__conv2) ).
fof(f3162,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(forward_demodulation,[],[f2710,f2226]) ).
fof(f2710,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1613]) ).
fof(f1613,plain,
! [X0,X1,X2,X3,X4] :
( ( ( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) )
& ( ti(X0,X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) ) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(flattening,[],[f1612]) ).
fof(f1612,plain,
! [X0,X1,X2,X3,X4] :
( ( ( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) )
& ( ti(X0,X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) ) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(ennf_transformation,[],[f1124]) ).
fof(f1124,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( ( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
=> hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))) )
& ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
=> ti(X0,X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) ) ) ) ),
inference(rectify,[],[f228]) ).
fof(f228,axiom,
! [X0,X13,X7,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X11),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( ( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))
=> hAPP(fun(X0,bool),X0,X9,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,X13),hAPP(fun(X0,bool),X0,X9,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))))) )
& ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))
=> ti(X0,X13) = hAPP(fun(X0,bool),X0,X9,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_folding__one_Oinsert__remove) ).
fof(f31377,plain,
( spl86_748
| ~ spl86_109
| ~ spl86_165
| ~ spl86_747 ),
inference(avatar_split_clause,[],[f31373,f31369,f4161,f3702,f31375]) ).
fof(f31375,plain,
( spl86_748
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_748])]) ).
fof(f31369,plain,
( spl86_747
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_747])]) ).
fof(f31373,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_747 ),
inference(forward_demodulation,[],[f31372,f4236]) ).
fof(f31372,plain,
( ! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_747 ),
inference(forward_demodulation,[],[f31370,f4236]) ).
fof(f31370,plain,
( ! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_747 ),
inference(avatar_component_clause,[],[f31369]) ).
fof(f31371,plain,
spl86_747,
inference(avatar_split_clause,[],[f3169,f31369]) ).
fof(f3169,plain,
! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(forward_demodulation,[],[f3168,f2226]) ).
fof(f3168,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(forward_demodulation,[],[f2716,f2226]) ).
fof(f2716,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X0,X4,X2)
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1623]) ).
fof(f1623,plain,
! [X0,X1,X2,X3,X4] :
( ( ( hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X0,X4,X2)
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) )
& ( ti(X0,X1) = hAPP(fun(X0,bool),X0,X4,X2)
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) ) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(flattening,[],[f1622]) ).
fof(f1622,plain,
! [X0,X1,X2,X3,X4] :
( ( ( hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X0,X4,X2)
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) )
& ( ti(X0,X1) = hAPP(fun(X0,bool),X0,X4,X2)
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) ) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(ennf_transformation,[],[f1129]) ).
fof(f1129,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> ( ( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
=> hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X0,X4,X2) )
& ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
=> ti(X0,X1) = hAPP(fun(X0,bool),X0,X4,X2) ) ) ) ) ),
inference(rectify,[],[f227]) ).
fof(f227,axiom,
! [X0,X13,X7,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X11),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> ( ( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))
=> hAPP(fun(X0,bool),X0,X9,X7) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,X13),hAPP(fun(X0,bool),X0,X9,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))))) )
& ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))
=> ti(X0,X13) = hAPP(fun(X0,bool),X0,X9,X7) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_folding__one_Oremove) ).
fof(f31342,plain,
( spl86_746
| ~ spl86_109
| ~ spl86_165
| ~ spl86_745 ),
inference(avatar_split_clause,[],[f31338,f31335,f4161,f3702,f31340]) ).
fof(f31340,plain,
( spl86_746
<=> ! [X1,X6,X4,X0,X3,X5,X2,X7] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_746])]) ).
fof(f31335,plain,
( spl86_745
<=> ! [X1,X6,X4,X0,X3,X5,X2,X7] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_745])]) ).
fof(f31338,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_745 ),
inference(forward_demodulation,[],[f31336,f4236]) ).
fof(f31336,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) )
| ~ spl86_745 ),
inference(avatar_component_clause,[],[f31335]) ).
fof(f31337,plain,
spl86_745,
inference(avatar_split_clause,[],[f3178,f31335]) ).
fof(f3178,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(forward_demodulation,[],[f2745,f2226]) ).
fof(f2745,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f1636,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(flattening,[],[f1635]) ).
fof(f1635,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(ennf_transformation,[],[f1144]) ).
fof(f1144,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) ) ),
inference(rectify,[],[f250]) ).
fof(f250,axiom,
! [X1,X0,X13,X7,X11,X41,X39,X9] :
( hBOOL(hAPP(fun(fun(X1,bool),X0),bool,hAPP(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool),hAPP(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)),hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool))),finite1357897459simple(X0,X1),X11),X41),X39),X9))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7))
=> hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,hAPP(X1,X0,X39,X13)),hAPP(fun(X1,bool),X0,X9,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X7),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X13),bot_bot(fun(X1,bool)))))) = hAPP(fun(X1,bool),X0,X9,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X13),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_folding__image__simple_Oinsert__remove) ).
fof(f31308,plain,
( spl86_744
| ~ spl86_109
| ~ spl86_165
| ~ spl86_743 ),
inference(avatar_split_clause,[],[f31304,f31301,f4161,f3702,f31306]) ).
fof(f31306,plain,
( spl86_744
<=> ! [X1,X6,X4,X0,X3,X5,X2,X7] :
( hAPP(fun(X0,bool),X1,X7,X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_744])]) ).
fof(f31301,plain,
( spl86_743
<=> ! [X1,X6,X4,X0,X3,X5,X2,X7] :
( hAPP(fun(X0,bool),X1,X7,X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_743])]) ).
fof(f31304,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(fun(X0,bool),X1,X7,X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_743 ),
inference(forward_demodulation,[],[f31302,f4236]) ).
fof(f31302,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(fun(X0,bool),X1,X7,X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) )
| ~ spl86_743 ),
inference(avatar_component_clause,[],[f31301]) ).
fof(f31303,plain,
spl86_743,
inference(avatar_split_clause,[],[f3179,f31301]) ).
fof(f3179,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(fun(X0,bool),X1,X7,X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(forward_demodulation,[],[f2747,f2226]) ).
fof(f2747,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X1,X7,X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(cnf_transformation,[],[f1640]) ).
fof(f1640,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X1,X7,X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(flattening,[],[f1639]) ).
fof(f1639,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X1,X7,X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(ennf_transformation,[],[f1146]) ).
fof(f1146,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) = hAPP(fun(X0,bool),X1,X7,X3) ) ) ),
inference(rectify,[],[f249]) ).
fof(f249,axiom,
! [X1,X0,X13,X7,X11,X41,X39,X9] :
( hBOOL(hAPP(fun(fun(X1,bool),X0),bool,hAPP(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool),hAPP(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)),hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool))),finite1357897459simple(X0,X1),X11),X41),X39),X9))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X13),X7))
=> hAPP(fun(X1,bool),X0,X9,X7) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,hAPP(X1,X0,X39,X13)),hAPP(fun(X1,bool),X0,X9,hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X7),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X13),bot_bot(fun(X1,bool)))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_folding__image__simple_Oremove) ).
fof(f31299,plain,
( spl86_741
| ~ spl86_742
| ~ spl86_146
| ~ spl86_530 ),
inference(avatar_split_clause,[],[f20865,f17758,f4034,f31296,f31293]) ).
fof(f31293,plain,
( spl86_741
<=> ! [X0] : ~ hBOOL(hAPP(com,bool,wt,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_741])]) ).
fof(f31296,plain,
( spl86_742
<=> wt = bot_bot(fun(com,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_742])]) ).
fof(f4034,plain,
( spl86_146
<=> ! [X0,X1,X3] :
( ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_146])]) ).
fof(f17758,plain,
( spl86_530
<=> wt = hAPP(fun(com,bool),fun(com,bool),collect(com),wt) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_530])]) ).
fof(f20865,plain,
( ! [X0] :
( wt != bot_bot(fun(com,bool))
| ~ hBOOL(hAPP(com,bool,wt,X0)) )
| ~ spl86_146
| ~ spl86_530 ),
inference(superposition,[],[f4035,f17760]) ).
fof(f17760,plain,
( wt = hAPP(fun(com,bool),fun(com,bool),collect(com),wt)
| ~ spl86_530 ),
inference(avatar_component_clause,[],[f17758]) ).
fof(f4035,plain,
( ! [X3,X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(X0,bool,X1,X3)) )
| ~ spl86_146 ),
inference(avatar_component_clause,[],[f4034]) ).
fof(f31282,plain,
spl86_740,
inference(avatar_split_clause,[],[f2028,f31280]) ).
fof(f31280,plain,
( spl86_740
<=> ! [X0] : hBOOL(hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),bool,finite_comp_fun_idem(X0,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,bool),fun(X0,bool))),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),X0),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),combc(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)))),hAPP(fun(X0,bool),fun(X0,fun(X0,bool)),hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_740])]) ).
fof(f2028,plain,
! [X0] : hBOOL(hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),bool,finite_comp_fun_idem(X0,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,bool),fun(X0,bool))),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),X0),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),combc(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)))),hAPP(fun(X0,bool),fun(X0,fun(X0,bool)),hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool)))))),
inference(cnf_transformation,[],[f279]) ).
fof(f279,axiom,
! [X0] : hBOOL(hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),bool,finite_comp_fun_idem(X0,fun(X0,bool)),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,bool),fun(X0,bool))),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,fun(X0,bool)),fun(X0,fun(fun(X0,bool),fun(X0,bool)))),combb(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),X0),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool))),combc(fun(X0,bool),fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)))),hAPP(fun(X0,bool),fun(X0,fun(X0,bool)),hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_comp__fun__idem__remove) ).
fof(f31255,plain,
( spl86_739
| ~ spl86_109
| ~ spl86_165
| ~ spl86_738 ),
inference(avatar_split_clause,[],[f31251,f31248,f4161,f3702,f31253]) ).
fof(f31253,plain,
( spl86_739
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(X0,fun(X0,bool),fequal(X0),sK76(X0,X2)))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_739])]) ).
fof(f31248,plain,
( spl86_738
<=> ! [X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK76(X0,X2))))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_738])]) ).
fof(f31251,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(X0,fun(X0,bool),fequal(X0),sK76(X0,X2)))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_738 ),
inference(forward_demodulation,[],[f31249,f4236]) ).
fof(f31249,plain,
( ! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK76(X0,X2))))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) )
| ~ spl86_738 ),
inference(avatar_component_clause,[],[f31248]) ).
fof(f31250,plain,
spl86_738,
inference(avatar_split_clause,[],[f3143,f31248]) ).
fof(f3143,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK76(X0,X2))))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(forward_demodulation,[],[f3142,f2854]) ).
fof(f2854,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1),
inference(definition_unfolding,[],[f2193,f2190]) ).
fof(f2193,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = ti(fun(X0,bool),X1),
inference(cnf_transformation,[],[f786]) ).
fof(f786,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = ti(fun(X0,bool),X1),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X0,X15] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15) = ti(fun(X0,bool),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
fof(f3142,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK76(X0,X2))))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(forward_demodulation,[],[f2928,f2226]) ).
fof(f2928,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK76(X0,X2)),bot_bot(fun(X0,bool))))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(definition_unfolding,[],[f2638,f2190]) ).
fof(f2638,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK76(X0,X2)),bot_bot(fun(X0,bool))))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1877]) ).
fof(f1877,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK76(X0,X2)),bot_bot(fun(X0,bool))))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75,sK76])],[f1586,f1876]) ).
fof(f1876,plain,
! [X0,X2] :
( ? [X4,X5] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X4),X5)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),bot_bot(fun(X0,bool))))))
=> ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,sK75(X0,X2)),sK76(X0,X2))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK75(X0,X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK76(X0,X2)),bot_bot(fun(X0,bool)))))) ),
introduced(choice_axiom,[]) ).
fof(f1586,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ? [X4,X5] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X4),X5)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),bot_bot(fun(X0,bool))))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(flattening,[],[f1585]) ).
fof(f1585,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1))
| ? [X4,X5] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X4),X5)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),bot_bot(fun(X0,bool))))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(ennf_transformation,[],[f1092]) ).
fof(f1092,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
=> ( ! [X4,X5] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X4),X5)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),bot_bot(fun(X0,bool))))))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X3,X1)),X1)) ) ) ) ),
inference(rectify,[],[f247]) ).
fof(f247,axiom,
! [X0,X7,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X11),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( ti(fun(X0,bool),X7) != bot_bot(fun(X0,bool))
=> ( ! [X32,X60] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,X32),X60)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X32),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X60),bot_bot(fun(X0,bool))))))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(fun(X0,bool),X0,X9,X7)),X7)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_folding__one_Oclosed) ).
fof(f31196,plain,
( spl86_737
| ~ spl86_109
| ~ spl86_165
| ~ spl86_736 ),
inference(avatar_split_clause,[],[f31192,f31189,f4161,f3702,f31194]) ).
fof(f31194,plain,
( spl86_737
<=> ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fimplies),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_737])]) ).
fof(f31189,plain,
( spl86_736
<=> ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fimplies),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_736])]) ).
fof(f31192,plain,
( ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fimplies),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),X2))
| ~ spl86_109
| ~ spl86_165
| ~ spl86_736 ),
inference(forward_demodulation,[],[f31190,f4236]) ).
fof(f31190,plain,
( ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fimplies),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),X2))
| ~ spl86_736 ),
inference(avatar_component_clause,[],[f31189]) ).
fof(f31191,plain,
spl86_736,
inference(avatar_split_clause,[],[f2423,f31189]) ).
fof(f2423,plain,
! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fimplies),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),X2)),
inference(cnf_transformation,[],[f946]) ).
fof(f946,plain,
! [X0,X1,X2] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fimplies),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)))),X2)),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X0,X10,X15] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fimplies),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(bool,bool),fun(fun(X0,bool),fun(X0,bool)),combb(bool,bool,X0),fNot),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X10)))),X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_insert__Collect) ).
fof(f31138,plain,
spl86_735,
inference(avatar_split_clause,[],[f2421,f31136]) ).
fof(f31136,plain,
( spl86_735
<=> ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_735])]) ).
fof(f2421,plain,
! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))),
inference(cnf_transformation,[],[f944]) ).
fof(f944,plain,
! [X0,X1,X2] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X2))),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X0,X32,X42] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X32),X42) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X32))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),X42))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_insert__compr__raw) ).
fof(f30845,plain,
spl86_734,
inference(avatar_split_clause,[],[f3171,f30843]) ).
fof(f30843,plain,
( spl86_734
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(X0,X0,X2,hAPP(fun(X0,bool),X0,X4,X1)) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,sK79(X0,X2,X3)),sK80(X0,X2,X3))) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,sK79(X0,X2,X3))),hAPP(X0,X0,X2,sK80(X0,X2,X3)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_734])]) ).
fof(f3171,plain,
! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(X0,X0,X2,hAPP(fun(X0,bool),X0,X4,X1)) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,sK79(X0,X2,X3)),sK80(X0,X2,X3))) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,sK79(X0,X2,X3))),hAPP(X0,X0,X2,sK80(X0,X2,X3)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(forward_demodulation,[],[f2950,f2854]) ).
fof(f2950,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X0,X0,X2,hAPP(fun(X0,bool),X0,X4,X1)) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X2),X1))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,sK79(X0,X2,X3)),sK80(X0,X2,X3))) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,sK79(X0,X2,X3))),hAPP(X0,X0,X2,sK80(X0,X2,X3)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(definition_unfolding,[],[f2717,f2190]) ).
fof(f2717,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X0,X0,X2,hAPP(fun(X0,bool),X0,X4,X1)) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X2),X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,sK79(X0,X2,X3)),sK80(X0,X2,X3))) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,sK79(X0,X2,X3))),hAPP(X0,X0,X2,sK80(X0,X2,X3)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1909]) ).
fof(f1909,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X0,X0,X2,hAPP(fun(X0,bool),X0,X4,X1)) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X2),X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,sK79(X0,X2,X3)),sK80(X0,X2,X3))) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,sK79(X0,X2,X3))),hAPP(X0,X0,X2,sK80(X0,X2,X3)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f1625,f1908]) ).
fof(f1908,plain,
! [X0,X2,X3] :
( ? [X5,X6] : hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X5),X6)) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,X5)),hAPP(X0,X0,X2,X6))
=> hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,sK79(X0,X2,X3)),sK80(X0,X2,X3))) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,sK79(X0,X2,X3))),hAPP(X0,X0,X2,sK80(X0,X2,X3))) ),
introduced(choice_axiom,[]) ).
fof(f1625,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X0,X0,X2,hAPP(fun(X0,bool),X0,X4,X1)) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X2),X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ? [X5,X6] : hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X5),X6)) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,X5)),hAPP(X0,X0,X2,X6))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(flattening,[],[f1624]) ).
fof(f1624,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X0,X0,X2,hAPP(fun(X0,bool),X0,X4,X1)) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X2),X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ? [X5,X6] : hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X5),X6)) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,X5)),hAPP(X0,X0,X2,X6))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(ennf_transformation,[],[f1130]) ).
fof(f1130,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4))
=> ( ! [X5,X6] : hAPP(X0,X0,X2,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X5),X6)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(X0,X0,X2,X5)),hAPP(X0,X0,X2,X6))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
=> hAPP(X0,X0,X2,hAPP(fun(X0,bool),X0,X4,X1)) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X2),X1)) ) ) ) ),
inference(rectify,[],[f246]) ).
fof(f246,axiom,
! [X0,X47,X8,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X11),X9))
=> ( ! [X32,X60] : hAPP(X0,X0,X8,hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,X32),X60)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,hAPP(X0,X0,X8,X32)),hAPP(X0,X0,X8,X60))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X47))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X47)
=> hAPP(X0,X0,X8,hAPP(fun(X0,bool),X0,X9,X47)) = hAPP(fun(X0,bool),X0,X9,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),X8),X47)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_folding__one__idem_Ohom__commute) ).
fof(f30841,plain,
spl86_733,
inference(avatar_split_clause,[],[f2606,f30839]) ).
fof(f30839,plain,
( spl86_733
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1))),one_one(nat))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_733])]) ).
fof(f2606,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1))),one_one(nat))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(cnf_transformation,[],[f1543]) ).
fof(f1543,plain,
! [X0,X1,X2,X3] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1))),one_one(nat))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(flattening,[],[f1542]) ).
fof(f1542,plain,
! [X0,X1,X2,X3] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1))),one_one(nat))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(ennf_transformation,[],[f1067]) ).
fof(f1067,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1))),one_one(nat)) ) ) ),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X0,X12,X10,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),X7))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),X12))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X12))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12))),one_one(nat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_card__Diff__insert) ).
fof(f30716,plain,
spl86_732,
inference(avatar_split_clause,[],[f2698,f30714]) ).
fof(f30714,plain,
( spl86_732
<=> ! [X4,X0,X3,X2,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_732])]) ).
fof(f2698,plain,
! [X2,X3,X0,X1,X4] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4)))),
inference(cnf_transformation,[],[f1115]) ).
fof(f1115,plain,
! [X0,X1,X2,X3,X4] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X3),X4)))),
inference(rectify,[],[f235]) ).
fof(f235,axiom,
! [X0,X1,X11,X7,X12] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X7)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X12))),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,bool),fun(fun(X1,bool),fun(X1,bool)),minus_minus(fun(X1,bool)),X7),X12)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_image__diff__subset) ).
fof(f30687,plain,
spl86_731,
inference(avatar_split_clause,[],[f2746,f30685]) ).
fof(f30685,plain,
( spl86_731
<=> ! [X2,X6,X4,X0,X3,X5,X1,X7] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_731])]) ).
fof(f2746,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(cnf_transformation,[],[f1638]) ).
fof(f1638,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(flattening,[],[f1637]) ).
fof(f1637,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7)) ),
inference(ennf_transformation,[],[f1145]) ).
fof(f1145,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X4),X5),X6),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> hAPP(fun(X0,bool),X1,X7,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),X4,hAPP(X0,X1,X6,X2)),hAPP(fun(X0,bool),X1,X7,X3)) ) ) ),
inference(rectify,[],[f260]) ).
fof(f260,axiom,
! [X1,X0,X13,X7,X11,X41,X39,X9] :
( hBOOL(hAPP(fun(fun(X1,bool),X0),bool,hAPP(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool),hAPP(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)),hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool))),finite1357897459simple(X0,X1),X11),X41),X39),X9))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7))
=> ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X13),X7))
=> hAPP(fun(X1,bool),X0,X9,hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X13),X7)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,hAPP(X1,X0,X39,X13)),hAPP(fun(X1,bool),X0,X9,X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_folding__image__simple_Oinsert) ).
fof(f30613,plain,
( spl86_730
| ~ spl86_109
| ~ spl86_165
| ~ spl86_727 ),
inference(avatar_split_clause,[],[f30601,f30597,f4161,f3702,f30611]) ).
fof(f30611,plain,
( spl86_730
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_730])]) ).
fof(f30597,plain,
( spl86_727
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_727])]) ).
fof(f30601,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_727 ),
inference(forward_demodulation,[],[f30600,f4236]) ).
fof(f30600,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_727 ),
inference(forward_demodulation,[],[f30598,f4236]) ).
fof(f30598,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))) )
| ~ spl86_727 ),
inference(avatar_component_clause,[],[f30597]) ).
fof(f30609,plain,
( spl86_728
| ~ spl86_729
| ~ spl86_146
| ~ spl86_526 ),
inference(avatar_split_clause,[],[f20126,f17203,f4034,f30606,f30603]) ).
fof(f30603,plain,
( spl86_728
<=> ! [X0] : ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_728])]) ).
fof(f17203,plain,
( spl86_526
<=> fNot = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),fNot) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_526])]) ).
fof(f20126,plain,
( ! [X0] :
( fNot != bot_bot(fun(bool,bool))
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) )
| ~ spl86_146
| ~ spl86_526 ),
inference(superposition,[],[f4035,f17205]) ).
fof(f17205,plain,
( fNot = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),fNot)
| ~ spl86_526 ),
inference(avatar_component_clause,[],[f17203]) ).
fof(f30599,plain,
spl86_727,
inference(avatar_split_clause,[],[f3068,f30597]) ).
fof(f3068,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))) ),
inference(forward_demodulation,[],[f3067,f2226]) ).
fof(f3067,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(forward_demodulation,[],[f2430,f2226]) ).
fof(f2430,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(cnf_transformation,[],[f1411]) ).
fof(f1411,plain,
! [X0,X1,X2] :
( ( hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) )
& ( ti(X0,X2) = hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ) ),
inference(ennf_transformation,[],[f950]) ).
fof(f950,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))
=> hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))
=> ti(X0,X2) = hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) ) ),
inference(rectify,[],[f270]) ).
fof(f270,axiom,
! [X0,X7,X33] :
( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),bot_bot(fun(X0,bool)))))
=> hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X33),X7) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(X0,bool)),combc(X0,fun(X0,bool),bool),member(X0)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),bot_bot(fun(X0,bool)))))) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),bot_bot(fun(X0,bool)))))
=> ti(X0,X33) = hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X33),X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_flat__lub__def) ).
fof(f30542,plain,
( spl86_726
| ~ spl86_109
| ~ spl86_165
| ~ spl86_725 ),
inference(avatar_split_clause,[],[f30538,f30535,f4161,f3702,f30540]) ).
fof(f30540,plain,
( spl86_726
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_726])]) ).
fof(f30535,plain,
( spl86_725
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_725])]) ).
fof(f30538,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_725 ),
inference(forward_demodulation,[],[f30536,f4236]) ).
fof(f30536,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) )
| ~ spl86_725 ),
inference(avatar_component_clause,[],[f30535]) ).
fof(f30537,plain,
spl86_725,
inference(avatar_split_clause,[],[f3135,f30535]) ).
fof(f3135,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(forward_demodulation,[],[f3134,f2226]) ).
fof(f3134,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(forward_demodulation,[],[f3133,f3128]) ).
fof(f3128,plain,
! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))),
inference(forward_demodulation,[],[f2589,f2226]) ).
fof(f2589,plain,
! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f1056]) ).
fof(f1056,plain,
! [X0,X1,X2,X3] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f229]) ).
fof(f229,axiom,
! [X0,X7,X10,X12] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X12)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Diff__insert) ).
fof(f3133,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(forward_demodulation,[],[f2607,f2226]) ).
fof(f2607,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(cnf_transformation,[],[f1545]) ).
fof(f1545,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(flattening,[],[f1544]) ).
fof(f1544,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(ennf_transformation,[],[f1068]) ).
fof(f1068,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X3))) ) ) ),
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X0,X38,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X38),X7))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X38),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X7))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_card__Diff2__less) ).
fof(f30486,plain,
( spl86_724
| ~ spl86_109
| ~ spl86_165
| ~ spl86_723 ),
inference(avatar_split_clause,[],[f30482,f30479,f4161,f3702,f30484]) ).
fof(f30484,plain,
( spl86_724
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_724])]) ).
fof(f30479,plain,
( spl86_723
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_723])]) ).
fof(f30482,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_723 ),
inference(forward_demodulation,[],[f30480,f4236]) ).
fof(f30480,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ~ spl86_723 ),
inference(avatar_component_clause,[],[f30479]) ).
fof(f30481,plain,
spl86_723,
inference(avatar_split_clause,[],[f3145,f30479]) ).
fof(f3145,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(forward_demodulation,[],[f2647,f2226]) ).
fof(f2647,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3)) ),
inference(cnf_transformation,[],[f1596]) ).
fof(f1596,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3)) ),
inference(flattening,[],[f1595]) ).
fof(f1595,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3)) ),
inference(ennf_transformation,[],[f1100]) ).
fof(f1100,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ) ),
inference(rectify,[],[f237]) ).
fof(f237,axiom,
! [X0,X7,X13,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_diff__single__insert) ).
fof(f30460,plain,
( spl86_722
| ~ spl86_109
| ~ spl86_165
| ~ spl86_721 ),
inference(avatar_split_clause,[],[f30456,f30453,f4161,f3702,f30458]) ).
fof(f30458,plain,
( spl86_722
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_722])]) ).
fof(f30453,plain,
( spl86_721
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_721])]) ).
fof(f30456,plain,
( ! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_721 ),
inference(forward_demodulation,[],[f30454,f4236]) ).
fof(f30454,plain,
( ! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_721 ),
inference(avatar_component_clause,[],[f30453]) ).
fof(f30455,plain,
spl86_721,
inference(avatar_split_clause,[],[f3164,f30453]) ).
fof(f3164,plain,
! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(forward_demodulation,[],[f2945,f2226]) ).
fof(f2945,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(definition_unfolding,[],[f2709,f2190]) ).
fof(f2709,plain,
! [X2,X3,X0,X1,X4] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1613]) ).
fof(f30262,plain,
( spl86_720
| ~ spl86_108
| ~ spl86_165
| ~ spl86_719 ),
inference(avatar_split_clause,[],[f30258,f30254,f4161,f3698,f30260]) ).
fof(f30260,plain,
( spl86_720
<=> ! [X2,X0,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_720])]) ).
fof(f30254,plain,
( spl86_719
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_719])]) ).
fof(f30258,plain,
( ! [X2,X0,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)
| ~ hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_108
| ~ spl86_165
| ~ spl86_719 ),
inference(forward_demodulation,[],[f30257,f4223]) ).
fof(f4223,plain,
( ! [X2,X3,X0,X1] : hAPP(X1,fun(X0,bool),X2,X3) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X1,fun(X0,bool),X2,X3))
| ~ spl86_108
| ~ spl86_165 ),
inference(superposition,[],[f4162,f3699]) ).
fof(f30257,plain,
( ! [X2,X0,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_108
| ~ spl86_165
| ~ spl86_719 ),
inference(forward_demodulation,[],[f30255,f4223]) ).
fof(f30255,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_719 ),
inference(avatar_component_clause,[],[f30254]) ).
fof(f30256,plain,
spl86_719,
inference(avatar_split_clause,[],[f3066,f30254]) ).
fof(f3066,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(forward_demodulation,[],[f2427,f2226]) ).
fof(f2427,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1410]) ).
fof(f1410,plain,
! [X0,X1,X2] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1))
| hBOOL(hAPP(X0,bool,X1,X2)) )
& ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
inference(ennf_transformation,[],[f949]) ).
fof(f949,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X0,bool,X1,X2))
=> bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)) )
& ( hBOOL(hAPP(X0,bool,X1,X2))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)) ) ),
inference(rectify,[],[f181]) ).
fof(f181,axiom,
! [X0,X15,X10] :
( ( ~ hBOOL(hAPP(X0,bool,X15,X10))
=> bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X10))),X15)) )
& ( hBOOL(hAPP(X0,bool,X15,X10))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X10))),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Collect__conv__if) ).
fof(f30215,plain,
( spl86_718
| ~ spl86_109
| ~ spl86_165
| ~ spl86_717 ),
inference(avatar_split_clause,[],[f30211,f30208,f4161,f3702,f30213]) ).
fof(f30213,plain,
( spl86_718
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_718])]) ).
fof(f30208,plain,
( spl86_717
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_717])]) ).
fof(f30211,plain,
( ! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_717 ),
inference(forward_demodulation,[],[f30209,f4236]) ).
fof(f30209,plain,
( ! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) )
| ~ spl86_717 ),
inference(avatar_component_clause,[],[f30208]) ).
fof(f30210,plain,
spl86_717,
inference(avatar_split_clause,[],[f3170,f30208]) ).
fof(f3170,plain,
! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(forward_demodulation,[],[f2949,f2226]) ).
fof(f2949,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X4,X2)
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(definition_unfolding,[],[f2715,f2190]) ).
fof(f2715,plain,
! [X2,X3,X0,X1,X4] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,X4,X2)
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1623]) ).
fof(f30206,plain,
spl86_716,
inference(avatar_split_clause,[],[f3167,f30204]) ).
fof(f30204,plain,
( spl86_716
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_716])]) ).
fof(f3167,plain,
! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(forward_demodulation,[],[f2948,f2854]) ).
fof(f2948,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(definition_unfolding,[],[f2713,f2190]) ).
fof(f2713,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1619]) ).
fof(f1619,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(flattening,[],[f1618]) ).
fof(f1618,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4)) ),
inference(ennf_transformation,[],[f1127]) ).
fof(f1127,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X2)
=> hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2)) ) ) ) ),
inference(rectify,[],[f215]) ).
fof(f215,axiom,
! [X0,X13,X7,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X11),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> ( ti(fun(X0,bool),X7) != bot_bot(fun(X0,bool))
=> hAPP(fun(X0,bool),X0,X9,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,X13),hAPP(fun(X0,bool),X0,X9,X7)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_folding__one_Oinsert) ).
fof(f30184,plain,
( spl86_715
| ~ spl86_109
| ~ spl86_165
| ~ spl86_713 ),
inference(avatar_split_clause,[],[f30176,f30172,f4161,f3702,f30182]) ).
fof(f30182,plain,
( spl86_715
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,X0))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_715])]) ).
fof(f30172,plain,
( spl86_713
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_713])]) ).
fof(f30176,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,X0))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_713 ),
inference(forward_demodulation,[],[f30175,f4236]) ).
fof(f30175,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0))))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,X0))))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_713 ),
inference(forward_demodulation,[],[f30173,f4236]) ).
fof(f30173,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,X0))))) )
| ~ spl86_713 ),
inference(avatar_component_clause,[],[f30172]) ).
fof(f30180,plain,
( spl86_714
| spl86_171
| ~ spl86_96
| ~ spl86_104 ),
inference(avatar_split_clause,[],[f6819,f3682,f3648,f4256,f30178]) ).
fof(f30178,plain,
( spl86_714
<=> ! [X0,X1] : ~ sP4(X0,bot_bot(fun(fun(X0,bool),bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_714])]) ).
fof(f4256,plain,
( spl86_171
<=> hBOOL(bot_bot(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_171])]) ).
fof(f3648,plain,
( spl86_96
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_96])]) ).
fof(f6819,plain,
( ! [X0,X1] :
( hBOOL(bot_bot(bool))
| ~ sP4(X0,bot_bot(fun(fun(X0,bool),bool)),X1) )
| ~ spl86_96
| ~ spl86_104 ),
inference(superposition,[],[f3649,f3683]) ).
fof(f3649,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) )
| ~ spl86_96 ),
inference(avatar_component_clause,[],[f3648]) ).
fof(f30174,plain,
spl86_713,
inference(avatar_split_clause,[],[f3016,f30172]) ).
fof(f3016,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,X0))))) ),
inference(forward_demodulation,[],[f3015,f2226]) ).
fof(f3015,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,X0)))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))),bot_bot(fun(x_a,bool))))) ),
inference(forward_demodulation,[],[f2301,f2226]) ).
fof(f2301,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))),bot_bot(fun(x_a,bool))))) ),
inference(cnf_transformation,[],[f1384]) ).
fof(f1384,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))),bot_bot(fun(x_a,bool))))) ),
inference(ennf_transformation,[],[f883]) ).
fof(f883,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),X1)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))),bot_bot(fun(x_a,bool)))))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X0)),bot_bot(fun(x_a,bool))))) ),
inference(rectify,[],[f202]) ).
fof(f202,axiom,
! [X55,X6] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X55)),X6)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X55)))),bot_bot(fun(x_a,bool)))))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X6),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X55)),bot_bot(fun(x_a,bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_assms_I2_J) ).
fof(f30147,plain,
( spl86_712
| ~ spl86_109
| ~ spl86_165
| ~ spl86_711 ),
inference(avatar_split_clause,[],[f30143,f30138,f4161,f3702,f30145]) ).
fof(f30145,plain,
( spl86_712
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_712])]) ).
fof(f30138,plain,
( spl86_711
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_711])]) ).
fof(f30143,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_711 ),
inference(forward_demodulation,[],[f30142,f4236]) ).
fof(f30142,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_711 ),
inference(forward_demodulation,[],[f30141,f4236]) ).
fof(f30141,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_711 ),
inference(forward_demodulation,[],[f30139,f4236]) ).
fof(f30139,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
| ~ spl86_711 ),
inference(avatar_component_clause,[],[f30138]) ).
fof(f30140,plain,
spl86_711,
inference(avatar_split_clause,[],[f2582,f30138]) ).
fof(f2582,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) ),
inference(cnf_transformation,[],[f1867]) ).
fof(f1867,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) ) ),
inference(flattening,[],[f1866]) ).
fof(f1866,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) ) ),
inference(nnf_transformation,[],[f1049]) ).
fof(f1049,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2))))
<=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) ) ),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X0,X15,X14] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X15)),X14))))
<=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X14)))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__Collect__disjI) ).
fof(f30044,plain,
spl86_710,
inference(avatar_split_clause,[],[f2708,f30042]) ).
fof(f30042,plain,
( spl86_710
<=> ! [X2,X4,X0,X3,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_710])]) ).
fof(f2708,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4)) ),
inference(cnf_transformation,[],[f1611]) ).
fof(f1611,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4)) ),
inference(flattening,[],[f1610]) ).
fof(f1610,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4)) ),
inference(ennf_transformation,[],[f1123]) ).
fof(f1123,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),X1))) ) ),
inference(rectify,[],[f225]) ).
fof(f225,axiom,
! [X0,X45,X12,X7,X40] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X40))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X45),X12))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X40),X45))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_Diff__mono) ).
fof(f29867,plain,
( spl86_709
| ~ spl86_109
| ~ spl86_165
| ~ spl86_708 ),
inference(avatar_split_clause,[],[f29863,f29860,f4161,f3702,f29865]) ).
fof(f29865,plain,
( spl86_709
<=> ! [X0,X3,X2,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_709])]) ).
fof(f29860,plain,
( spl86_708
<=> ! [X0,X3,X2,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_708])]) ).
fof(f29863,plain,
( ! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X3)
| ~ spl86_109
| ~ spl86_165
| ~ spl86_708 ),
inference(forward_demodulation,[],[f29861,f4236]) ).
fof(f29861,plain,
( ! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))),X3)
| ~ spl86_708 ),
inference(avatar_component_clause,[],[f29860]) ).
fof(f29862,plain,
spl86_708,
inference(avatar_split_clause,[],[f3129,f29860]) ).
fof(f3129,plain,
! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))),X3),
inference(forward_demodulation,[],[f2590,f2226]) ).
fof(f2590,plain,
! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3),
inference(cnf_transformation,[],[f1057]) ).
fof(f1057,plain,
! [X0,X1,X2,X3] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3),
inference(rectify,[],[f230]) ).
fof(f230,axiom,
! [X0,X7,X10,X12] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X12)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool))))),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Diff__insert2) ).
fof(f29800,plain,
( spl86_707
| ~ spl86_166
| ~ spl86_268 ),
inference(avatar_split_clause,[],[f6743,f6365,f4165,f29798]) ).
fof(f29798,plain,
( spl86_707
<=> ! [X0,X3,X2,X1] :
( X2 != X3
| X0 != X1
| sP8(X2,nat,X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_707])]) ).
fof(f6743,plain,
( ! [X2,X3,X0,X1] :
( X2 != X3
| X0 != X1
| sP8(X2,nat,X0,X1,X3) )
| ~ spl86_166
| ~ spl86_268 ),
inference(forward_demodulation,[],[f6742,f4166]) ).
fof(f6742,plain,
( ! [X2,X3,X0,X1] :
( hAPP(nat,nat,combi(nat),X2) != X3
| X0 != X1
| sP8(X2,nat,X0,X1,X3) )
| ~ spl86_166
| ~ spl86_268 ),
inference(forward_demodulation,[],[f6741,f4166]) ).
fof(f6741,plain,
( ! [X2,X3,X0,X1] :
( X0 != X1
| sP8(X2,nat,X0,X1,X3)
| hAPP(nat,nat,combi(nat),X2) != hAPP(nat,nat,combi(nat),X3) )
| ~ spl86_166
| ~ spl86_268 ),
inference(forward_demodulation,[],[f6682,f4166]) ).
fof(f6682,plain,
( ! [X2,X3,X0,X1] :
( hAPP(nat,nat,combi(nat),X1) != X0
| sP8(X2,nat,X0,X1,X3)
| hAPP(nat,nat,combi(nat),X2) != hAPP(nat,nat,combi(nat),X3) )
| ~ spl86_166
| ~ spl86_268 ),
inference(superposition,[],[f6366,f4166]) ).
fof(f29796,plain,
( spl86_706
| ~ spl86_108
| ~ spl86_165
| ~ spl86_705 ),
inference(avatar_split_clause,[],[f29792,f29789,f4161,f3698,f29794]) ).
fof(f29794,plain,
( spl86_706
<=> ! [X0,X3,X2,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),hAPP(X0,fun(X0,bool),fequal(X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_706])]) ).
fof(f29789,plain,
( spl86_705
<=> ! [X0,X3,X2,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_705])]) ).
fof(f29792,plain,
( ! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ spl86_108
| ~ spl86_165
| ~ spl86_705 ),
inference(forward_demodulation,[],[f29790,f4223]) ).
fof(f29790,plain,
( ! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| ~ spl86_705 ),
inference(avatar_component_clause,[],[f29789]) ).
fof(f29791,plain,
spl86_705,
inference(avatar_split_clause,[],[f3128,f29789]) ).
fof(f29732,plain,
spl86_704,
inference(avatar_split_clause,[],[f2596,f29730]) ).
fof(f29730,plain,
( spl86_704
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_704])]) ).
fof(f2596,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1531]) ).
fof(f1531,plain,
! [X0,X1,X2,X3] :
( ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) )
& ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
inference(ennf_transformation,[],[f1060]) ).
fof(f1060,plain,
! [X0,X1,X2,X3] :
( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),X3) ) ),
inference(rectify,[],[f223]) ).
fof(f223,axiom,
! [X0,X7,X13,X12] :
( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X12))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)),X12) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X12))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_insert__Diff__if) ).
fof(f29704,plain,
spl86_703,
inference(avatar_split_clause,[],[f2966,f29702]) ).
fof(f29702,plain,
( spl86_703
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( hAPP(fun(X0,bool),X1,X6,X2) = hAPP(X1,X1,combi(X1),X4)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK85(X0,X1,X2,X4,X5)),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_703])]) ).
fof(f2966,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(fun(X0,bool),X1,X6,X2) = hAPP(X1,X1,combi(X1),X4)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK85(X0,X1,X2,X4,X5)),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ),
inference(definition_unfolding,[],[f2743,f2190]) ).
fof(f2743,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ti(X1,X4) = hAPP(fun(X0,bool),X1,X6,X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK85(X0,X1,X2,X4,X5)),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ),
inference(cnf_transformation,[],[f1927]) ).
fof(f1927,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ti(X1,X4) = hAPP(fun(X0,bool),X1,X6,X2)
| ( ti(X1,X4) != hAPP(X0,X1,X5,sK85(X0,X1,X2,X4,X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK85(X0,X1,X2,X4,X5)),X2)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f1634,f1926]) ).
fof(f1926,plain,
! [X0,X1,X2,X4,X5] :
( ? [X7] :
( ti(X1,X4) != hAPP(X0,X1,X5,X7)
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X7),X2)) )
=> ( ti(X1,X4) != hAPP(X0,X1,X5,sK85(X0,X1,X2,X4,X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK85(X0,X1,X2,X4,X5)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1634,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ti(X1,X4) = hAPP(fun(X0,bool),X1,X6,X2)
| ? [X7] :
( ti(X1,X4) != hAPP(X0,X1,X5,X7)
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X7),X2)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ),
inference(flattening,[],[f1633]) ).
fof(f1633,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ti(X1,X4) = hAPP(fun(X0,bool),X1,X6,X2)
| ? [X7] :
( ti(X1,X4) != hAPP(X0,X1,X5,X7)
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X7),X2)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ),
inference(ennf_transformation,[],[f1143]) ).
fof(f1143,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( ! [X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X7),X2))
=> ti(X1,X4) = hAPP(X0,X1,X5,X7) )
=> ti(X1,X4) = hAPP(fun(X0,bool),X1,X6,X2) ) ) ),
inference(rectify,[],[f264]) ).
fof(f264,axiom,
! [X1,X0,X7,X11,X41,X39,X9] :
( hBOOL(hAPP(fun(fun(X1,bool),X0),bool,hAPP(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool),hAPP(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)),hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool))),finite1357897459simple(X0,X1),X11),X41),X39),X9))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X7))
=> ( ! [X32] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X32),X7))
=> ti(X0,X41) = hAPP(X1,X0,X39,X32) )
=> ti(X0,X41) = hAPP(fun(X1,bool),X0,X9,X7) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_folding__image__simple_Oneutral) ).
fof(f29659,plain,
spl86_702,
inference(avatar_split_clause,[],[f2229,f29657]) ).
fof(f29657,plain,
( spl86_702
<=> ! [X0,X1] : hAPP(fun(X0,bool),X0,the_elem(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,fun(X0,bool)),fun(X0,bool),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)),hAPP(fun(X0,bool),fun(X0,fun(X0,bool)),hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_702])]) ).
fof(f2229,plain,
! [X0,X1] : hAPP(fun(X0,bool),X0,the_elem(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,fun(X0,bool)),fun(X0,bool),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)),hAPP(fun(X0,bool),fun(X0,fun(X0,bool)),hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool))))),
inference(cnf_transformation,[],[f819]) ).
fof(f819,plain,
! [X0,X1] : hAPP(fun(X0,bool),X0,the_elem(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,fun(X0,bool)),fun(X0,bool),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X1)),hAPP(fun(X0,bool),fun(X0,fun(X0,bool)),hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool))))),
inference(rectify,[],[f214]) ).
fof(f214,axiom,
! [X0,X59] : hAPP(fun(X0,bool),X0,the_elem(X0),X59) = hAPP(fun(X0,bool),X0,the(X0),hAPP(fun(X0,fun(X0,bool)),fun(X0,bool),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,fun(X0,bool)),fun(X0,bool)),combb(fun(X0,bool),bool,X0),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),fequal(fun(X0,bool)),X59)),hAPP(fun(X0,bool),fun(X0,fun(X0,bool)),hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(fun(X0,bool),fun(X0,fun(X0,bool))),combc(X0,fun(X0,bool),fun(X0,bool)),insert(X0)),bot_bot(fun(X0,bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_the__elem__def) ).
fof(f29633,plain,
spl86_701,
inference(avatar_split_clause,[],[f3166,f29631]) ).
fof(f29631,plain,
( spl86_701
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(fun(X0,bool),X0,X4,X1)),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_701])]) ).
fof(f3166,plain,
! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(fun(X0,bool),X0,X4,X1)),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(forward_demodulation,[],[f2947,f2854]) ).
fof(f2947,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(fun(X0,bool),X0,X4,X1)),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(definition_unfolding,[],[f2712,f2190]) ).
fof(f2712,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(fun(X0,bool),X0,X4,X1)),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1617]) ).
fof(f1617,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(fun(X0,bool),X0,X4,X1)),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(flattening,[],[f1616]) ).
fof(f1616,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(fun(X0,bool),X0,X4,X1)),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(ennf_transformation,[],[f1126]) ).
fof(f1126,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,hAPP(fun(X0,bool),X0,X4,X1)),hAPP(fun(X0,bool),X0,X4,X2)) ) ) ) ),
inference(rectify,[],[f211]) ).
fof(f211,axiom,
! [X0,X12,X7,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X11),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( ti(fun(X0,bool),X12) != bot_bot(fun(X0,bool))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X7))
=> hAPP(fun(X0,bool),X0,X9,X7) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,hAPP(fun(X0,bool),X0,X9,X12)),hAPP(fun(X0,bool),X0,X9,X7)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_folding__one__idem_Osubset__idem) ).
fof(f29629,plain,
( spl86_700
| ~ spl86_166
| ~ spl86_267 ),
inference(avatar_split_clause,[],[f6624,f6361,f4165,f29627]) ).
fof(f6624,plain,
( ! [X2,X3,X0,X1] :
( X2 != X3
| X0 != X1
| sP8(X3,nat,X2,X0,X1) )
| ~ spl86_166
| ~ spl86_267 ),
inference(forward_demodulation,[],[f6623,f4166]) ).
fof(f6623,plain,
( ! [X2,X3,X0,X1] :
( hAPP(nat,nat,combi(nat),X2) != X3
| X0 != X1
| sP8(X3,nat,X2,X0,X1) )
| ~ spl86_166
| ~ spl86_267 ),
inference(forward_demodulation,[],[f6622,f4166]) ).
fof(f6622,plain,
( ! [X2,X3,X0,X1] :
( X0 != X1
| hAPP(nat,nat,combi(nat),X2) != hAPP(nat,nat,combi(nat),X3)
| sP8(X3,nat,X2,X0,X1) )
| ~ spl86_166
| ~ spl86_267 ),
inference(forward_demodulation,[],[f6563,f4166]) ).
fof(f6563,plain,
( ! [X2,X3,X0,X1] :
( hAPP(nat,nat,combi(nat),X1) != X0
| hAPP(nat,nat,combi(nat),X2) != hAPP(nat,nat,combi(nat),X3)
| sP8(X3,nat,X2,X0,X1) )
| ~ spl86_166
| ~ spl86_267 ),
inference(superposition,[],[f6362,f4166]) ).
fof(f29575,plain,
spl86_699,
inference(avatar_split_clause,[],[f3140,f29573]) ).
fof(f29573,plain,
( spl86_699
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_699])]) ).
fof(f3140,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(forward_demodulation,[],[f2925,f2854]) ).
fof(f2925,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(definition_unfolding,[],[f2635,f2190]) ).
fof(f2635,plain,
! [X2,X3,X0,X1] :
( ti(fun(X0,bool),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1582]) ).
fof(f1582,plain,
! [X0,X1,X2,X3] :
( ti(fun(X0,bool),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(flattening,[],[f1581]) ).
fof(f1581,plain,
! [X0,X1,X2,X3] :
( ti(fun(X0,bool),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(ennf_transformation,[],[f1089]) ).
fof(f1089,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
=> ti(fun(X0,bool),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)) ) ),
inference(rectify,[],[f224]) ).
fof(f224,axiom,
! [X0,X40,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X40))
=> ti(fun(X0,bool),X7) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X40),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_double__diff) ).
fof(f29326,plain,
( spl86_698
| ~ spl86_108
| ~ spl86_165
| ~ spl86_697 ),
inference(avatar_split_clause,[],[f29322,f29319,f4161,f3698,f29324]) ).
fof(f29324,plain,
( spl86_698
<=> ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)
| hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_698])]) ).
fof(f29319,plain,
( spl86_697
<=> ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1))
| hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_697])]) ).
fof(f29322,plain,
( ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1)
| hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_108
| ~ spl86_165
| ~ spl86_697 ),
inference(forward_demodulation,[],[f29320,f4223]) ).
fof(f29320,plain,
( ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1))
| hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_697 ),
inference(avatar_component_clause,[],[f29319]) ).
fof(f29321,plain,
spl86_697,
inference(avatar_split_clause,[],[f2428,f29319]) ).
fof(f2428,plain,
! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X2))),X1))
| hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1410]) ).
fof(f29218,plain,
spl86_696,
inference(avatar_split_clause,[],[f3172,f29216]) ).
fof(f29216,plain,
( spl86_696
<=> ! [X2,X3,X4,X0,X5,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) != hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_696])]) ).
fof(f3172,plain,
! [X2,X3,X0,X1,X4,X5] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) != hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ),
inference(forward_demodulation,[],[f2954,f2854]) ).
fof(f2954,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ),
inference(definition_unfolding,[],[f2727,f2190]) ).
fof(f2727,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ti(fun(X0,bool),X2) != hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ),
inference(cnf_transformation,[],[f1921]) ).
fof(f1921,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ! [X5] :
( ti(fun(X0,bool),X2) != hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ) )
& ( ( ti(fun(X0,bool),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),sK84(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),sK84(X0,X1,X2,X3,X4)),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f1919,f1920]) ).
fof(f1920,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( ti(fun(X0,bool),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X6)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X6),X4)) )
=> ( ti(fun(X0,bool),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),sK84(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),sK84(X0,X1,X2,X3,X4)),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f1919,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ! [X5] :
( ti(fun(X0,bool),X2) != hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ) )
& ( ? [X6] :
( ti(fun(X0,bool),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X6)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X6),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
inference(rectify,[],[f1918]) ).
fof(f1918,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ! [X5] :
( ti(fun(X0,bool),X2) != hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ) )
& ( ? [X5] :
( ti(fun(X0,bool),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
inference(nnf_transformation,[],[f1134]) ).
fof(f1134,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
<=> ? [X5] :
( ti(fun(X0,bool),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X5)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X4)) ) ),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X0,X1,X12,X11,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X7)))
<=> ? [X46] :
( ti(fun(X0,bool),X12) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X46)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X46),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_subset__image__iff) ).
fof(f29214,plain,
spl86_695,
inference(avatar_split_clause,[],[f2965,f29212]) ).
fof(f29212,plain,
( spl86_695
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( hAPP(fun(X0,bool),X1,X6,X2) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X0,X1,X5,sK85(X0,X1,X2,X4,X5)) != hAPP(X1,X1,combi(X1),X4)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_695])]) ).
fof(f2965,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(fun(X0,bool),X1,X6,X2) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X0,X1,X5,sK85(X0,X1,X2,X4,X5)) != hAPP(X1,X1,combi(X1),X4)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ),
inference(definition_unfolding,[],[f2744,f2190,f2190]) ).
fof(f2744,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ti(X1,X4) = hAPP(fun(X0,bool),X1,X6,X2)
| ti(X1,X4) != hAPP(X0,X1,X5,sK85(X0,X1,X2,X4,X5))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X3),X4),X5),X6)) ),
inference(cnf_transformation,[],[f1927]) ).
fof(f29027,plain,
( spl86_694
| ~ spl86_108
| ~ spl86_165
| ~ spl86_693 ),
inference(avatar_split_clause,[],[f29023,f29019,f4161,f3698,f29025]) ).
fof(f29025,plain,
( spl86_694
<=> ! [X2,X0,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_694])]) ).
fof(f29019,plain,
( spl86_693
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_693])]) ).
fof(f29023,plain,
( ! [X2,X0,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)
| ~ hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_108
| ~ spl86_165
| ~ spl86_693 ),
inference(forward_demodulation,[],[f29022,f4223]) ).
fof(f29022,plain,
( ! [X2,X0,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_108
| ~ spl86_165
| ~ spl86_693 ),
inference(forward_demodulation,[],[f29020,f4223]) ).
fof(f29020,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_693 ),
inference(avatar_component_clause,[],[f29019]) ).
fof(f29021,plain,
spl86_693,
inference(avatar_split_clause,[],[f3065,f29019]) ).
fof(f3065,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(forward_demodulation,[],[f2425,f2226]) ).
fof(f2425,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1409]) ).
fof(f1409,plain,
! [X0,X1,X2] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1))
| hBOOL(hAPP(X0,bool,X1,X2)) )
& ( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
inference(ennf_transformation,[],[f948]) ).
fof(f948,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X0,bool,X1,X2))
=> bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)) )
& ( hBOOL(hAPP(X0,bool,X1,X2))
=> hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) ) ),
inference(rectify,[],[f182]) ).
fof(f182,axiom,
! [X0,X15,X10] :
( ( ~ hBOOL(hAPP(X0,bool,X15,X10))
=> bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X10))),X15)) )
& ( hBOOL(hAPP(X0,bool,X15,X10))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X10))),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Collect__conv__if2) ).
fof(f28956,plain,
spl86_692,
inference(avatar_split_clause,[],[f3139,f28954]) ).
fof(f28954,plain,
( spl86_692
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_692])]) ).
fof(f3139,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(forward_demodulation,[],[f3138,f2854]) ).
fof(f3138,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(forward_demodulation,[],[f2924,f2854]) ).
fof(f2924,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(definition_unfolding,[],[f2617,f2190,f2190]) ).
fof(f2617,plain,
! [X2,X3,X0,X1] :
( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1874]) ).
fof(f1874,plain,
! [X0,X1,X2,X3] :
( ( ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| ti(fun(X0,bool),X1) != ti(fun(X0,bool),X3) )
& ( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1) ) )
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(nnf_transformation,[],[f1555]) ).
fof(f1555,plain,
! [X0,X1,X2,X3] :
( ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
<=> ti(fun(X0,bool),X1) = ti(fun(X0,bool),X3) )
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(flattening,[],[f1554]) ).
fof(f1554,plain,
! [X0,X1,X2,X3] :
( ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
<=> ti(fun(X0,bool),X1) = ti(fun(X0,bool),X3) )
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(ennf_transformation,[],[f1073]) ).
fof(f1073,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
<=> ti(fun(X0,bool),X1) = ti(fun(X0,bool),X3) ) ) ),
inference(rectify,[],[f117]) ).
fof(f117,axiom,
! [X0,X12,X13,X7] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X12))
=> ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X12)
<=> ti(fun(X0,bool),X7) = ti(fun(X0,bool),X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_insert__ident) ).
fof(f28952,plain,
spl86_691,
inference(avatar_split_clause,[],[f3137,f28950]) ).
fof(f28950,plain,
( spl86_691
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_691])]) ).
fof(f3137,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(forward_demodulation,[],[f3136,f2854]) ).
fof(f3136,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(forward_demodulation,[],[f2923,f2854]) ).
fof(f2923,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X3)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(definition_unfolding,[],[f2618,f2190,f2190]) ).
fof(f2618,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)
| ti(fun(X0,bool),X1) != ti(fun(X0,bool),X3)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1874]) ).
fof(f28933,plain,
( spl86_690
| ~ spl86_109
| ~ spl86_165
| ~ spl86_689 ),
inference(avatar_split_clause,[],[f28929,f28926,f4161,f3702,f28931]) ).
fof(f28931,plain,
( spl86_690
<=> ! [X0,X1] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X0)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_690])]) ).
fof(f28926,plain,
( spl86_689
<=> ! [X0,X1] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X0)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_689])]) ).
fof(f28929,plain,
( ! [X0,X1] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X0)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1))))
| ~ spl86_109
| ~ spl86_165
| ~ spl86_689 ),
inference(forward_demodulation,[],[f28927,f4236]) ).
fof(f28927,plain,
( ! [X0,X1] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X0)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1)))))
| ~ spl86_689 ),
inference(avatar_component_clause,[],[f28926]) ).
fof(f28928,plain,
spl86_689,
inference(avatar_split_clause,[],[f2228,f28926]) ).
fof(f2228,plain,
! [X0,X1] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X0)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1))))),
inference(cnf_transformation,[],[f818]) ).
fof(f818,plain,
! [X0,X1] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X0)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1))))),
inference(rectify,[],[f439]) ).
fof(f439,axiom,
! [X15,X35] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X15)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X35))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_finite__M__bounded__by__nat) ).
fof(f28883,plain,
( spl86_688
| ~ spl86_226
| ~ spl86_317
| ~ spl86_662 ),
inference(avatar_split_clause,[],[f27921,f27641,f7675,f4978,f28881]) ).
fof(f28881,plain,
( spl86_688
<=> ! [X0] : ~ sP4(bool,finite_finite(bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_688])]) ).
fof(f4978,plain,
( spl86_226
<=> hBOOL(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_226])]) ).
fof(f27641,plain,
( spl86_662
<=> ! [X0] : fTrue = hAPP(fun(bool,bool),bool,finite_finite(bool),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_662])]) ).
fof(f27921,plain,
( ! [X0] :
( ~ hBOOL(fTrue)
| ~ sP4(bool,finite_finite(bool),X0) )
| ~ spl86_317
| ~ spl86_662 ),
inference(superposition,[],[f7676,f27642]) ).
fof(f27642,plain,
( ! [X0] : fTrue = hAPP(fun(bool,bool),bool,finite_finite(bool),X0)
| ~ spl86_662 ),
inference(avatar_component_clause,[],[f27641]) ).
fof(f28879,plain,
( spl86_687
| ~ spl86_109
| ~ spl86_165
| ~ spl86_686 ),
inference(avatar_split_clause,[],[f28875,f28872,f4161,f3702,f28877]) ).
fof(f28877,plain,
( spl86_687
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),one_one(nat)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_687])]) ).
fof(f28872,plain,
( spl86_686
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),one_one(nat)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_686])]) ).
fof(f28875,plain,
( ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),one_one(nat)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_686 ),
inference(forward_demodulation,[],[f28873,f4236]) ).
fof(f28873,plain,
( ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),one_one(nat)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_686 ),
inference(avatar_component_clause,[],[f28872]) ).
fof(f28874,plain,
spl86_686,
inference(avatar_split_clause,[],[f3075,f28872]) ).
fof(f3075,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),one_one(nat)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2448,f2226]) ).
fof(f2448,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),one_one(nat))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1426]) ).
fof(f1426,plain,
! [X0,X1,X2] :
( ( ( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) )
& ( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),one_one(nat))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f964]) ).
fof(f964,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),one_one(nat)) ) ) ),
inference(rectify,[],[f272]) ).
fof(f272,axiom,
! [X0,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hAPP(fun(X0,bool),nat,finite_card(X0),X7) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X7)),one_one(nat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_card__Diff__singleton__if) ).
fof(f28849,plain,
spl86_685,
inference(avatar_split_clause,[],[f3165,f28847]) ).
fof(f28847,plain,
( spl86_685
<=> ! [X4,X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_685])]) ).
fof(f3165,plain,
! [X2,X3,X0,X1,X4] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(forward_demodulation,[],[f2946,f2854]) ).
fof(f2946,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(definition_unfolding,[],[f2711,f2190]) ).
fof(f2711,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1615]) ).
fof(f1615,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(flattening,[],[f1614]) ).
fof(f1614,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(ennf_transformation,[],[f1125]) ).
fof(f1125,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X2)
=> hAPP(fun(X0,bool),X0,X4,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2)) ) ) ),
inference(rectify,[],[f212]) ).
fof(f212,axiom,
! [X0,X13,X7,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X11),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( ti(fun(X0,bool),X7) != bot_bot(fun(X0,bool))
=> hAPP(fun(X0,bool),X0,X9,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,X13),hAPP(fun(X0,bool),X0,X9,X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_folding__one__idem_Oinsert__idem) ).
fof(f28671,plain,
( spl86_684
| ~ spl86_109
| ~ spl86_165
| ~ spl86_683 ),
inference(avatar_split_clause,[],[f28667,f28664,f4161,f3702,f28669]) ).
fof(f28669,plain,
( spl86_684
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_684])]) ).
fof(f28664,plain,
( spl86_683
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_683])]) ).
fof(f28667,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_683 ),
inference(forward_demodulation,[],[f28665,f4236]) ).
fof(f28665,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_683 ),
inference(avatar_component_clause,[],[f28664]) ).
fof(f28666,plain,
spl86_683,
inference(avatar_split_clause,[],[f3082,f28664]) ).
fof(f3082,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2467,f2226]) ).
fof(f2467,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1440]) ).
fof(f1440,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1439]) ).
fof(f1439,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f971]) ).
fof(f971,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2))) ) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X0,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X7))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_card__Diff1__less) ).
fof(f28662,plain,
spl86_682,
inference(avatar_split_clause,[],[f2739,f28660]) ).
fof(f28660,plain,
( spl86_682
<=> ! [X3,X4,X0,X5,X2,X1] : hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X3),hAPP(fun(X2,bool),fun(X0,bool),hAPP(fun(X2,X0),fun(fun(X2,bool),fun(X0,bool)),image(X2,X0),X4),X5)) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X0),fun(X2,X1),hAPP(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1)),combb(X0,X1,X2),X3),X4)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_682])]) ).
fof(f2739,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X3),hAPP(fun(X2,bool),fun(X0,bool),hAPP(fun(X2,X0),fun(fun(X2,bool),fun(X0,bool)),image(X2,X0),X4),X5)) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X0),fun(X2,X1),hAPP(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1)),combb(X0,X1,X2),X3),X4)),X5),
inference(cnf_transformation,[],[f1139]) ).
fof(f1139,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X3),hAPP(fun(X2,bool),fun(X0,bool),hAPP(fun(X2,X0),fun(fun(X2,bool),fun(X0,bool)),image(X2,X0),X4),X5)) = hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X0),fun(X2,X1),hAPP(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1)),combb(X0,X1,X2),X3),X4)),X5),
inference(rectify,[],[f136]) ).
fof(f136,axiom,
! [X1,X0,X43,X11,X39,X7] : hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),hAPP(fun(X43,bool),fun(X1,bool),hAPP(fun(X43,X1),fun(fun(X43,bool),fun(X1,bool)),image(X43,X1),X39),X7)) = hAPP(fun(X43,bool),fun(X0,bool),hAPP(fun(X43,X0),fun(fun(X43,bool),fun(X0,bool)),image(X43,X0),hAPP(fun(X43,X1),fun(X43,X0),hAPP(fun(X1,X0),fun(fun(X43,X1),fun(X43,X0)),combb(X1,X0,X43),X11),X39)),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_image__image) ).
fof(f28646,plain,
( spl86_681
| ~ spl86_109
| ~ spl86_165
| ~ spl86_680 ),
inference(avatar_split_clause,[],[f28642,f28638,f4161,f3702,f28644]) ).
fof(f28644,plain,
( spl86_681
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_681])]) ).
fof(f28638,plain,
( spl86_680
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_680])]) ).
fof(f28642,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_680 ),
inference(forward_demodulation,[],[f28641,f4236]) ).
fof(f28641,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_680 ),
inference(forward_demodulation,[],[f28639,f4236]) ).
fof(f28639,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) )
| ~ spl86_680 ),
inference(avatar_component_clause,[],[f28638]) ).
fof(f28640,plain,
spl86_680,
inference(avatar_split_clause,[],[f2581,f28638]) ).
fof(f2581,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) ),
inference(cnf_transformation,[],[f1867]) ).
fof(f28624,plain,
( spl86_679
| ~ spl86_109
| ~ spl86_165
| ~ spl86_678 ),
inference(avatar_split_clause,[],[f28620,f28616,f4161,f3702,f28622]) ).
fof(f28622,plain,
( spl86_679
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_679])]) ).
fof(f28616,plain,
( spl86_678
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_678])]) ).
fof(f28620,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_678 ),
inference(forward_demodulation,[],[f28619,f4236]) ).
fof(f28619,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_678 ),
inference(forward_demodulation,[],[f28617,f4236]) ).
fof(f28617,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) )
| ~ spl86_678 ),
inference(avatar_component_clause,[],[f28616]) ).
fof(f28618,plain,
spl86_678,
inference(avatar_split_clause,[],[f2580,f28616]) ).
fof(f2580,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fdisj),X1)),X2)))) ),
inference(cnf_transformation,[],[f1867]) ).
fof(f28595,plain,
( spl86_677
| ~ spl86_109
| ~ spl86_165
| ~ spl86_676 ),
inference(avatar_split_clause,[],[f28591,f28587,f4161,f3702,f28593]) ).
fof(f28593,plain,
( spl86_677
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_677])]) ).
fof(f28587,plain,
( spl86_676
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_676])]) ).
fof(f28591,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_676 ),
inference(forward_demodulation,[],[f28590,f4236]) ).
fof(f28590,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_676 ),
inference(forward_demodulation,[],[f28588,f4236]) ).
fof(f28588,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) )
| ~ spl86_676 ),
inference(avatar_component_clause,[],[f28587]) ).
fof(f28589,plain,
spl86_676,
inference(avatar_split_clause,[],[f2538,f28587]) ).
fof(f2538,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1))) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f1520,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))))
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)))
& ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2))) ) ),
inference(ennf_transformation,[],[f1031]) ).
fof(f1031,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2))) )
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)))) ),
inference(rectify,[],[f63]) ).
fof(f63,axiom,
! [X0,X14,X15] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X14)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15))) )
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X15)),X14)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__Collect__conjI) ).
fof(f28566,plain,
( spl86_675
| ~ spl86_109
| ~ spl86_165
| ~ spl86_673 ),
inference(avatar_split_clause,[],[f28557,f28553,f4161,f3702,f28564]) ).
fof(f28564,plain,
( spl86_675
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_675])]) ).
fof(f28553,plain,
( spl86_673
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_673])]) ).
fof(f28557,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_673 ),
inference(forward_demodulation,[],[f28556,f4236]) ).
fof(f28556,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_673 ),
inference(forward_demodulation,[],[f28554,f4236]) ).
fof(f28554,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2))) )
| ~ spl86_673 ),
inference(avatar_component_clause,[],[f28553]) ).
fof(f28562,plain,
( ~ spl86_674
| ~ spl86_226
| ~ spl86_289
| ~ spl86_662 ),
inference(avatar_split_clause,[],[f27920,f27641,f7141,f4978,f28559]) ).
fof(f28559,plain,
( spl86_674
<=> sP2(bool,finite_finite(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_674])]) ).
fof(f27920,plain,
( ~ hBOOL(fTrue)
| ~ sP2(bool,finite_finite(bool))
| ~ spl86_289
| ~ spl86_662 ),
inference(superposition,[],[f7142,f27642]) ).
fof(f28555,plain,
spl86_673,
inference(avatar_split_clause,[],[f2537,f28553]) ).
fof(f2537,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),X2)),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2))) ),
inference(cnf_transformation,[],[f1520]) ).
fof(f28510,plain,
spl86_672,
inference(avatar_split_clause,[],[f3160,f28508]) ).
fof(f28508,plain,
( spl86_672
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),sK78(X0,X1,X2,X3,X4)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_672])]) ).
fof(f3160,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),sK78(X0,X1,X2,X3,X4)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(forward_demodulation,[],[f2944,f2854]) ).
fof(f2944,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),sK78(X0,X1,X2,X3,X4)) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(definition_unfolding,[],[f2702,f2190]) ).
fof(f2702,plain,
! [X2,X3,X0,X1,X4] :
( ti(fun(X1,bool),X4) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),sK78(X0,X1,X2,X3,X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(cnf_transformation,[],[f1907]) ).
fof(f1907,plain,
! [X0,X1,X2,X3,X4] :
( ( ti(fun(X1,bool),X4) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),sK78(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK78(X0,X1,X2,X3,X4)))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK78(X0,X1,X2,X3,X4)),X3)) )
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f1604,f1906]) ).
fof(f1906,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ti(fun(X1,bool),X4) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X5)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X5),X3)) )
=> ( ti(fun(X1,bool),X4) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),sK78(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK78(X0,X1,X2,X3,X4)))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK78(X0,X1,X2,X3,X4)),X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f1604,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ti(fun(X1,bool),X4) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X5)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X5),X3)) )
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(flattening,[],[f1603]) ).
fof(f1603,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ti(fun(X1,bool),X4) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X5)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X5),X3)) )
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(ennf_transformation,[],[f1117]) ).
fof(f1117,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
=> ? [X5] :
( ti(fun(X1,bool),X4) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X5)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X5),X3)) ) ) ),
inference(rectify,[],[f100]) ).
fof(f100,axiom,
! [X1,X0,X11,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X7)))
=> ? [X29] :
( ti(fun(X0,bool),X12) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X29)
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X29))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X29),X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite__subset__image) ).
fof(f28471,plain,
( spl86_671
| ~ spl86_109
| ~ spl86_165
| ~ spl86_670 ),
inference(avatar_split_clause,[],[f28467,f28464,f4161,f3702,f28469]) ).
fof(f28469,plain,
( spl86_671
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK39(X1)),hAPP(nat,nat,X1,sK39(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_671])]) ).
fof(f28464,plain,
( spl86_670
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X0))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK39(X1)),hAPP(nat,nat,X1,sK39(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_670])]) ).
fof(f28467,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK39(X1)),hAPP(nat,nat,X1,sK39(X1)))) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_670 ),
inference(forward_demodulation,[],[f28465,f4236]) ).
fof(f28465,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X0))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK39(X1)),hAPP(nat,nat,X1,sK39(X1)))) )
| ~ spl86_670 ),
inference(avatar_component_clause,[],[f28464]) ).
fof(f28466,plain,
spl86_670,
inference(avatar_split_clause,[],[f2322,f28464]) ).
fof(f2322,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X0))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK39(X1)),hAPP(nat,nat,X1,sK39(X1)))) ),
inference(cnf_transformation,[],[f1744]) ).
fof(f1744,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X0))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK39(X1)),hAPP(nat,nat,X1,sK39(X1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f1406,f1743]) ).
fof(f1743,plain,
! [X1] :
( ? [X2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),hAPP(nat,nat,X1,X2)))
=> ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK39(X1)),hAPP(nat,nat,X1,sK39(X1)))) ),
introduced(choice_axiom,[]) ).
fof(f1406,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X0))))
| ? [X2] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),hAPP(nat,nat,X1,X2))) ),
inference(ennf_transformation,[],[f895]) ).
fof(f895,plain,
! [X0,X1] :
( ! [X2] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),hAPP(nat,nat,X1,X2)))
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X0)))) ),
inference(rectify,[],[f205]) ).
fof(f205,axiom,
! [X57,X11] :
( ! [X31] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),hAPP(nat,nat,X11,X31)))
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X11)),X57)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_finite__less__ub) ).
fof(f28124,plain,
spl86_669,
inference(avatar_split_clause,[],[f2697,f28122]) ).
fof(f28122,plain,
( spl86_669
<=> ! [X4,X0,X3,X2,X1] : hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X0,X1,X2,X3)),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_669])]) ).
fof(f2697,plain,
! [X2,X3,X0,X1,X4] : hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X0,X1,X2,X3)),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X4)),
inference(cnf_transformation,[],[f1114]) ).
fof(f1114,plain,
! [X0,X1,X2,X3,X4] : hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X0,X1,X2,X3)),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X4)),
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X1,X0,X11,X10,X12] : hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X10),X12)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(X1,X0,X11,X10)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_image__insert) ).
fof(f27894,plain,
( spl86_668
| ~ spl86_109
| ~ spl86_165
| ~ spl86_667 ),
inference(avatar_split_clause,[],[f27890,f27887,f4161,f3702,f27892]) ).
fof(f27887,plain,
( spl86_667
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_667])]) ).
fof(f27890,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_667 ),
inference(forward_demodulation,[],[f27888,f4236]) ).
fof(f27888,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_667 ),
inference(avatar_component_clause,[],[f27887]) ).
fof(f27889,plain,
spl86_667,
inference(avatar_split_clause,[],[f3071,f27887]) ).
fof(f3071,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2444,f2226]) ).
fof(f2444,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1423]) ).
fof(f1423,plain,
! [X0,X1,X2] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f961]) ).
fof(f961,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))) ),
inference(rectify,[],[f244]) ).
fof(f244,axiom,
! [X0,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_card__insert) ).
fof(f27885,plain,
spl86_666,
inference(avatar_split_clause,[],[f2473,f27883]) ).
fof(f27883,plain,
( spl86_666
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_666])]) ).
fof(f2473,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1452]) ).
fof(f1452,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1451]) ).
fof(f1451,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f977]) ).
fof(f977,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)) ) ),
inference(rectify,[],[f241]) ).
fof(f241,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X7))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X7)),hAPP(fun(X0,bool),nat,finite_card(X0),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_card__Diff__subset) ).
fof(f27775,plain,
( spl86_665
| ~ spl86_109
| ~ spl86_165
| ~ spl86_664 ),
inference(avatar_split_clause,[],[f27771,f27768,f4161,f3702,f27773]) ).
fof(f27773,plain,
( spl86_665
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_665])]) ).
fof(f27768,plain,
( spl86_664
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_664])]) ).
fof(f27771,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_664 ),
inference(forward_demodulation,[],[f27769,f4236]) ).
fof(f27769,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) )
| ~ spl86_664 ),
inference(avatar_component_clause,[],[f27768]) ).
fof(f27770,plain,
spl86_664,
inference(avatar_split_clause,[],[f3100,f27768]) ).
fof(f3100,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(forward_demodulation,[],[f3099,f2226]) ).
fof(f3099,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(forward_demodulation,[],[f2897,f2854]) ).
fof(f2897,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(definition_unfolding,[],[f2522,f2190]) ).
fof(f2522,plain,
! [X2,X0,X1] :
( ti(fun(X0,bool),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(cnf_transformation,[],[f1503]) ).
fof(f1503,plain,
! [X0,X1,X2] :
( ti(fun(X0,bool),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(ennf_transformation,[],[f1017]) ).
fof(f1017,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> ti(fun(X0,bool),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) ),
inference(rectify,[],[f232]) ).
fof(f232,axiom,
! [X0,X13,X7] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> ti(fun(X0,bool),X7) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Diff__insert__absorb) ).
fof(f27766,plain,
spl86_663,
inference(avatar_split_clause,[],[f2706,f27764]) ).
fof(f27764,plain,
( spl86_663
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_663])]) ).
fof(f2706,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(cnf_transformation,[],[f1608]) ).
fof(f1608,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(ennf_transformation,[],[f1121]) ).
fof(f1121,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
=> hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)) ),
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X1,X0,X11,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X7) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),hAPP(X0,X1,X11,X13)),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_insert__image) ).
fof(f27643,plain,
( spl86_662
| ~ spl86_18
| ~ spl86_590 ),
inference(avatar_split_clause,[],[f27299,f23660,f3266,f27641]) ).
fof(f3266,plain,
( spl86_18
<=> finite_finite_1(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_18])]) ).
fof(f23660,plain,
( spl86_590
<=> ! [X0,X1] :
( fTrue = hAPP(fun(X0,bool),bool,finite_finite(X0),X1)
| ~ finite_finite_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_590])]) ).
fof(f27299,plain,
( ! [X0] : fTrue = hAPP(fun(bool,bool),bool,finite_finite(bool),X0)
| ~ spl86_18
| ~ spl86_590 ),
inference(resolution,[],[f23661,f3268]) ).
fof(f3268,plain,
( finite_finite_1(bool)
| ~ spl86_18 ),
inference(avatar_component_clause,[],[f3266]) ).
fof(f23661,plain,
( ! [X0,X1] :
( ~ finite_finite_1(X0)
| fTrue = hAPP(fun(X0,bool),bool,finite_finite(X0),X1) )
| ~ spl86_590 ),
inference(avatar_component_clause,[],[f23660]) ).
fof(f27639,plain,
( spl86_661
| ~ spl86_109
| ~ spl86_165
| ~ spl86_660 ),
inference(avatar_split_clause,[],[f27635,f27632,f4161,f3702,f27637]) ).
fof(f27637,plain,
( spl86_661
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_661])]) ).
fof(f27632,plain,
( spl86_660
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_660])]) ).
fof(f27635,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_660 ),
inference(forward_demodulation,[],[f27633,f4236]) ).
fof(f27633,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0)) )
| ~ spl86_660 ),
inference(avatar_component_clause,[],[f27632]) ).
fof(f27634,plain,
spl86_660,
inference(avatar_split_clause,[],[f3154,f27632]) ).
fof(f3154,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0)) ),
inference(forward_demodulation,[],[f2681,f2226]) ).
fof(f2681,plain,
! [X2,X3,X0,X1] :
( sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0)) ),
inference(cnf_transformation,[],[f1897]) ).
fof(f1897,plain,
! [X0,X1,X2,X3] :
( ( sP5(X0,X1,X2,X3)
| ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
& ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) )
| ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0))
& hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) )
& ( ( ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) )
& ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) )
| ~ sP5(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1896]) ).
fof(f1896,plain,
! [X3,X1,X0,X2] :
( ( sP5(X3,X1,X0,X2)
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
& ( ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
| ~ sP5(X3,X1,X0,X2) ) ),
inference(flattening,[],[f1895]) ).
fof(f1895,plain,
! [X3,X1,X0,X2] :
( ( sP5(X3,X1,X0,X2)
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
& ( ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
| ~ sP5(X3,X1,X0,X2) ) ),
inference(nnf_transformation,[],[f1651]) ).
fof(f1651,plain,
! [X3,X1,X0,X2] :
( sP5(X3,X1,X0,X2)
<=> ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f27590,plain,
( spl86_659
| ~ spl86_109
| ~ spl86_165
| ~ spl86_658 ),
inference(avatar_split_clause,[],[f27586,f27583,f4161,f3702,f27588]) ).
fof(f27588,plain,
( spl86_659
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_659])]) ).
fof(f27583,plain,
( spl86_658
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_658])]) ).
fof(f27586,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_658 ),
inference(forward_demodulation,[],[f27584,f4236]) ).
fof(f27584,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_658 ),
inference(avatar_component_clause,[],[f27583]) ).
fof(f27585,plain,
spl86_658,
inference(avatar_split_clause,[],[f3081,f27583]) ).
fof(f3081,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2466,f2226]) ).
fof(f2466,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1438]) ).
fof(f1438,plain,
! [X0,X1,X2] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1437]) ).
fof(f1437,plain,
! [X0,X1,X2] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f970]) ).
fof(f970,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))) ) ),
inference(rectify,[],[f243]) ).
fof(f243,axiom,
! [X0,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hAPP(fun(X0,bool),nat,finite_card(X0),X7) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_card__Suc__Diff1) ).
fof(f27581,plain,
spl86_657,
inference(avatar_split_clause,[],[f2707,f27579]) ).
fof(f27579,plain,
( spl86_657
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_657])]) ).
fof(f2707,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
inference(cnf_transformation,[],[f1609]) ).
fof(f1609,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4)) ),
inference(ennf_transformation,[],[f1122]) ).
fof(f1122,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X4))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))) ),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X1,X0,X11,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X7)),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_image__mono) ).
fof(f27540,plain,
spl86_656,
inference(avatar_split_clause,[],[f2595,f27538]) ).
fof(f27538,plain,
( spl86_656
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_656])]) ).
fof(f2595,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)),X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1531]) ).
fof(f27305,plain,
( spl86_655
| ~ spl86_108
| ~ spl86_165
| ~ spl86_654 ),
inference(avatar_split_clause,[],[f27298,f27295,f4161,f3698,f27303]) ).
fof(f27303,plain,
( spl86_655
<=> ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)
| hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_655])]) ).
fof(f27295,plain,
( spl86_654
<=> ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1))
| hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_654])]) ).
fof(f27298,plain,
( ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1)
| hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_108
| ~ spl86_165
| ~ spl86_654 ),
inference(forward_demodulation,[],[f27296,f4223]) ).
fof(f27296,plain,
( ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1))
| hBOOL(hAPP(X0,bool,X1,X2)) )
| ~ spl86_654 ),
inference(avatar_component_clause,[],[f27295]) ).
fof(f27297,plain,
spl86_654,
inference(avatar_split_clause,[],[f2426,f27295]) ).
fof(f2426,plain,
! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,fun(bool,bool)),fun(fun(X0,bool),fun(X0,bool)),combs(X0,bool,bool),hAPP(fun(X0,bool),fun(X0,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X0,bool),fun(X0,fun(bool,bool))),combb(bool,fun(bool,bool),X0),fconj),hAPP(X0,fun(X0,bool),fequal(X0),X2))),X1))
| hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1409]) ).
fof(f27194,plain,
( spl86_653
| ~ spl86_109
| ~ spl86_165
| ~ spl86_652 ),
inference(avatar_split_clause,[],[f27190,f27186,f4161,f3702,f27192]) ).
fof(f27192,plain,
( spl86_653
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,sK18(X0)))))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_653])]) ).
fof(f27186,plain,
( spl86_652
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,sK18(X0))))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1)))))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_652])]) ).
fof(f27190,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,sK18(X0)))))
| ~ hBOOL(hAPP(com,bool,wt,X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_652 ),
inference(forward_demodulation,[],[f27189,f4236]) ).
fof(f27189,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,sK18(X0)))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1)))))
| ~ hBOOL(hAPP(com,bool,wt,X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_652 ),
inference(forward_demodulation,[],[f27187,f4236]) ).
fof(f27187,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,sK18(X0))))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1)))))
| ~ hBOOL(hAPP(com,bool,wt,X1)) )
| ~ spl86_652 ),
inference(avatar_component_clause,[],[f27186]) ).
fof(f27188,plain,
spl86_652,
inference(avatar_split_clause,[],[f3008,f27186]) ).
fof(f3008,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(pname,x_a,mgt_call,sK18(X0))))))
| hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1)))))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ),
inference(forward_demodulation,[],[f3007,f2226]) ).
fof(f3007,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1)))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,sK18(X0))),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ),
inference(forward_demodulation,[],[f2260,f2226]) ).
fof(f2260,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X1)),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,sK18(X0))),bot_bot(fun(x_a,bool)))))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ),
inference(cnf_transformation,[],[f1716]) ).
fof(f1716,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X1)),bot_bot(fun(x_a,bool)))))
| ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,sK18(X0))),bot_bot(fun(x_a,bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK18(X0)),u)) )
| ~ hBOOL(hAPP(com,bool,wt,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f1339,f1715]) ).
fof(f1715,plain,
! [X0] :
( ? [X2] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X2)),bot_bot(fun(x_a,bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X2),u)) )
=> ( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,sK18(X0))),bot_bot(fun(x_a,bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK18(X0)),u)) ) ),
introduced(choice_axiom,[]) ).
fof(f1339,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X1)),bot_bot(fun(x_a,bool)))))
| ? [X2] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X2)),bot_bot(fun(x_a,bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X2),u)) )
| ~ hBOOL(hAPP(com,bool,wt,X1)) ),
inference(flattening,[],[f1338]) ).
fof(f1338,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X1)),bot_bot(fun(x_a,bool)))))
| ? [X2] :
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X2)),bot_bot(fun(x_a,bool)))))
& hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X2),u)) )
| ~ hBOOL(hAPP(com,bool,wt,X1)) ),
inference(ennf_transformation,[],[f846]) ).
fof(f846,plain,
! [X0,X1] :
( hBOOL(hAPP(com,bool,wt,X1))
=> ( ! [X2] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X2),u))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X2)),bot_bot(fun(x_a,bool))))) )
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X1)),bot_bot(fun(x_a,bool))))) ) ),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X6,X34] :
( hBOOL(hAPP(com,bool,wt,X34))
=> ( ! [X32] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X32),u))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X6),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,X32)),bot_bot(fun(x_a,bool))))) )
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X6),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X34)),bot_bot(fun(x_a,bool))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_assms_I3_J) ).
fof(f27184,plain,
spl86_651,
inference(avatar_split_clause,[],[f2696,f27182]) ).
fof(f27182,plain,
( spl86_651
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_651])]) ).
fof(f2696,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3))) ),
inference(cnf_transformation,[],[f1905]) ).
fof(f1905,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3))) )
& ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))) ) ),
inference(nnf_transformation,[],[f1113]) ).
fof(f1113,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))))
<=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3))) ),
inference(rectify,[],[f234]) ).
fof(f234,axiom,
! [X0,X7,X10,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X12))))
<=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_finite__Diff__insert) ).
fof(f27180,plain,
spl86_650,
inference(avatar_split_clause,[],[f2695,f27178]) ).
fof(f27178,plain,
( spl86_650
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_650])]) ).
fof(f2695,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))) ),
inference(cnf_transformation,[],[f1905]) ).
fof(f27176,plain,
spl86_649,
inference(avatar_split_clause,[],[f2597,f27174]) ).
fof(f27174,plain,
( spl86_649
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_649])]) ).
fof(f2597,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f1533,plain,
! [X0,X1,X2,X3] :
( ( zero_zero(nat) = hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2))
| ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) )
& ( hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
inference(flattening,[],[f1532]) ).
fof(f1532,plain,
! [X0,X1,X2,X3] :
( ( zero_zero(nat) = hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2))
| ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) )
& ( hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
inference(ennf_transformation,[],[f1061]) ).
fof(f1061,plain,
! [X0,X1,X2,X3] :
( ( ~ ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) )
=> zero_zero(nat) = hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
& hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) )
=> hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)) ) ),
inference(rectify,[],[f499]) ).
fof(f499,axiom,
! [X1,X0,X12,X7] :
( ( ~ ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X12))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7)) )
=> hAPP(fun(sum_sum(X0,X1),bool),nat,finite_card(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X7),X12)) = zero_zero(nat) )
& ( ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X12))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7)) )
=> hAPP(fun(sum_sum(X0,X1),bool),nat,finite_card(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X7),X12)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X7)),hAPP(fun(X1,bool),nat,finite_card(X1),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_card__Plus__conv__if) ).
fof(f27123,plain,
spl86_648,
inference(avatar_split_clause,[],[f3173,f27121]) ).
fof(f27121,plain,
( spl86_648
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),sK84(X0,X1,X2,X3,X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_648])]) ).
fof(f3173,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),sK84(X0,X1,X2,X3,X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(forward_demodulation,[],[f2955,f2854]) ).
fof(f2955,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),sK84(X0,X1,X2,X3,X4)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(definition_unfolding,[],[f2726,f2190]) ).
fof(f2726,plain,
! [X2,X3,X0,X1,X4] :
( ti(fun(X0,bool),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),sK84(X0,X1,X2,X3,X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(cnf_transformation,[],[f1921]) ).
fof(f27039,plain,
( spl86_647
| ~ spl86_109
| ~ spl86_165
| ~ spl86_646 ),
inference(avatar_split_clause,[],[f27035,f27032,f4161,f3702,f27037]) ).
fof(f27037,plain,
( spl86_647
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP7(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_647])]) ).
fof(f27032,plain,
( spl86_646
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP7(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_646])]) ).
fof(f27035,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP7(X0,X1,X2,X3) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_646 ),
inference(forward_demodulation,[],[f27033,f4236]) ).
fof(f27033,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP7(X0,X1,X2,X3) )
| ~ spl86_646 ),
inference(avatar_component_clause,[],[f27032]) ).
fof(f27034,plain,
spl86_646,
inference(avatar_split_clause,[],[f3159,f27032]) ).
fof(f3159,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP7(X0,X1,X2,X3) ),
inference(forward_demodulation,[],[f2684,f2226]) ).
fof(f2684,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1901]) ).
fof(f1901,plain,
! [X0,X1,X2,X3] :
( ( sP7(X0,X1,X2,X3)
| ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
& ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) )
| ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0))
& hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) )
& ( ( ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) )
& ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) )
| ~ sP7(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1900]) ).
fof(f1900,plain,
! [X3,X1,X0,X2] :
( ( sP7(X3,X1,X0,X2)
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
& ( ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
| ~ sP7(X3,X1,X0,X2) ) ),
inference(flattening,[],[f1899]) ).
fof(f1899,plain,
! [X3,X1,X0,X2] :
( ( sP7(X3,X1,X0,X2)
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
& ( ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
| ~ sP7(X3,X1,X0,X2) ) ),
inference(nnf_transformation,[],[f1654]) ).
fof(f1654,plain,
! [X3,X1,X0,X2] :
( sP7(X3,X1,X0,X2)
<=> ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f26994,plain,
( spl86_645
| ~ spl86_109
| ~ spl86_165
| ~ spl86_644 ),
inference(avatar_split_clause,[],[f26990,f26987,f4161,f3702,f26992]) ).
fof(f26992,plain,
( spl86_645
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_645])]) ).
fof(f26987,plain,
( spl86_644
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_644])]) ).
fof(f26990,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_644 ),
inference(forward_demodulation,[],[f26988,f4236]) ).
fof(f26988,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) )
| ~ spl86_644 ),
inference(avatar_component_clause,[],[f26987]) ).
fof(f26989,plain,
spl86_644,
inference(avatar_split_clause,[],[f3158,f26987]) ).
fof(f3158,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ),
inference(forward_demodulation,[],[f2687,f2226]) ).
fof(f2687,plain,
! [X2,X3,X0,X1] :
( sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0)) ),
inference(cnf_transformation,[],[f1901]) ).
fof(f26938,plain,
( spl86_643
| ~ spl86_109
| ~ spl86_165
| ~ spl86_642 ),
inference(avatar_split_clause,[],[f26929,f26926,f4161,f3702,f26936]) ).
fof(f26936,plain,
( spl86_643
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_643])]) ).
fof(f26926,plain,
( spl86_642
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_642])]) ).
fof(f26929,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP5(X0,X1,X2,X3) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_642 ),
inference(forward_demodulation,[],[f26927,f4236]) ).
fof(f26927,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP5(X0,X1,X2,X3) )
| ~ spl86_642 ),
inference(avatar_component_clause,[],[f26926]) ).
fof(f26928,plain,
spl86_642,
inference(avatar_split_clause,[],[f3156,f26926]) ).
fof(f3156,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP5(X0,X1,X2,X3) ),
inference(forward_demodulation,[],[f2676,f2226]) ).
fof(f2676,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1897]) ).
fof(f26888,plain,
( spl86_641
| ~ spl86_109
| ~ spl86_165
| ~ spl86_640 ),
inference(avatar_split_clause,[],[f26884,f26881,f4161,f3702,f26886]) ).
fof(f26886,plain,
( spl86_641
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_641])]) ).
fof(f26881,plain,
( spl86_640
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_640])]) ).
fof(f26884,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(X2,fun(X2,bool),fequal(X2),X3))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_640 ),
inference(forward_demodulation,[],[f26882,f4236]) ).
fof(f26882,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) )
| ~ spl86_640 ),
inference(avatar_component_clause,[],[f26881]) ).
fof(f26883,plain,
spl86_640,
inference(avatar_split_clause,[],[f3155,f26881]) ).
fof(f3155,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),collect(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)))),X0))
| sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ),
inference(forward_demodulation,[],[f2679,f2226]) ).
fof(f2679,plain,
! [X2,X3,X0,X1] :
( sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),hAPP(fun(X2,bool),fun(X2,bool),hAPP(fun(X2,bool),fun(fun(X2,bool),fun(X2,bool)),minus_minus(fun(X2,bool)),X1),hAPP(fun(X2,bool),fun(X2,bool),hAPP(X2,fun(fun(X2,bool),fun(X2,bool)),insert(X2),X3),bot_bot(fun(X2,bool))))),X0)) ),
inference(cnf_transformation,[],[f1897]) ).
fof(f26834,plain,
( spl86_639
| ~ spl86_109
| ~ spl86_165
| ~ spl86_638 ),
inference(avatar_split_clause,[],[f26830,f26827,f4161,f3702,f26832]) ).
fof(f26832,plain,
( spl86_639
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_639])]) ).
fof(f26827,plain,
( spl86_638
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_638])]) ).
fof(f26830,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_638 ),
inference(forward_demodulation,[],[f26828,f4236]) ).
fof(f26828,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_638 ),
inference(avatar_component_clause,[],[f26827]) ).
fof(f26829,plain,
spl86_638,
inference(avatar_split_clause,[],[f3074,f26827]) ).
fof(f3074,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2449,f2226]) ).
fof(f2449,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1426]) ).
fof(f26715,plain,
( spl86_637
| ~ spl86_108
| ~ spl86_109
| ~ spl86_165
| ~ spl86_635 ),
inference(avatar_split_clause,[],[f26707,f26703,f4161,f3702,f3698,f26713]) ).
fof(f26713,plain,
( spl86_637
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(X0,fun(X0,bool),fequal(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_637])]) ).
fof(f26703,plain,
( spl86_635
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_635])]) ).
fof(f26707,plain,
( ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(X0,fun(X0,bool),fequal(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) )
| ~ spl86_108
| ~ spl86_109
| ~ spl86_165
| ~ spl86_635 ),
inference(forward_demodulation,[],[f26706,f4223]) ).
fof(f26706,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_635 ),
inference(forward_demodulation,[],[f26704,f4236]) ).
fof(f26704,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)) )
| ~ spl86_635 ),
inference(avatar_component_clause,[],[f26703]) ).
fof(f26711,plain,
( spl86_636
| ~ spl86_631 ),
inference(avatar_split_clause,[],[f26530,f26521,f26709]) ).
fof(f26709,plain,
( spl86_636
<=> ! [X2,X0,X1] : sP8(X0,X1,X2,X2,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_636])]) ).
fof(f26521,plain,
( spl86_631
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(X0,fun(X0,bool),fequal(X0),X4))
| sP8(X3,X0,X2,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_631])]) ).
fof(f26530,plain,
( ! [X2,X0,X1] : sP8(X0,X1,X2,X2,X0)
| ~ spl86_631 ),
inference(equality_resolution,[],[f26522]) ).
fof(f26522,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(X0,fun(X0,bool),fequal(X0),X4))
| sP8(X3,X0,X2,X4,X1) )
| ~ spl86_631 ),
inference(avatar_component_clause,[],[f26521]) ).
fof(f26705,plain,
spl86_635,
inference(avatar_split_clause,[],[f3111,f26703]) ).
fof(f3111,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)) ),
inference(forward_demodulation,[],[f3110,f2226]) ).
fof(f3110,plain,
! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(forward_demodulation,[],[f3109,f2854]) ).
fof(f3109,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(forward_demodulation,[],[f3108,f2226]) ).
fof(f3108,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(forward_demodulation,[],[f2902,f2854]) ).
fof(f2902,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(definition_unfolding,[],[f2535,f2190,f2190]) ).
fof(f2535,plain,
! [X2,X0,X1] :
( ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(cnf_transformation,[],[f1518]) ).
fof(f1518,plain,
! [X0,X1,X2] :
( ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(flattening,[],[f1517]) ).
fof(f1517,plain,
! [X0,X1,X2] :
( ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(ennf_transformation,[],[f1029]) ).
fof(f1029,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))
=> ( ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ) ),
inference(rectify,[],[f185]) ).
fof(f185,axiom,
! [X0,X7,X13] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))))
=> ( ti(fun(X0,bool),X7) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))
| ti(fun(X0,bool),X7) = bot_bot(fun(X0,bool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_subset__singletonD) ).
fof(f26649,plain,
( spl86_634
| ~ spl86_109
| ~ spl86_165
| ~ spl86_633 ),
inference(avatar_split_clause,[],[f26645,f26642,f4161,f3702,f26647]) ).
fof(f26647,plain,
( spl86_634
<=> ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_634])]) ).
fof(f26642,plain,
( spl86_633
<=> ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_633])]) ).
fof(f26645,plain,
( ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| ~ spl86_109
| ~ spl86_165
| ~ spl86_633 ),
inference(forward_demodulation,[],[f26643,f4236]) ).
fof(f26643,plain,
( ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))
| ~ spl86_633 ),
inference(avatar_component_clause,[],[f26642]) ).
fof(f26644,plain,
spl86_633,
inference(avatar_split_clause,[],[f3064,f26642]) ).
fof(f3064,plain,
! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))),
inference(forward_demodulation,[],[f2420,f2226]) ).
fof(f2420,plain,
! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))),
inference(cnf_transformation,[],[f943]) ).
fof(f943,plain,
! [X0,X1,X2] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))),
inference(rectify,[],[f231]) ).
fof(f231,axiom,
! [X0,X10,X7] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X7) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_insert__Diff__single) ).
fof(f26640,plain,
spl86_632,
inference(avatar_split_clause,[],[f2629,f26638]) ).
fof(f26638,plain,
( spl86_632
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_632])]) ).
fof(f2629,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1570]) ).
fof(f1570,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(ennf_transformation,[],[f1083]) ).
fof(f1083,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3))) ),
inference(rectify,[],[f142]) ).
fof(f142,axiom,
! [X0,X10,X40,X45] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X40),X45))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X40)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insert__mono) ).
fof(f26523,plain,
( spl86_631
| ~ spl86_109
| ~ spl86_165
| ~ spl86_630 ),
inference(avatar_split_clause,[],[f26519,f26515,f4161,f3702,f26521]) ).
fof(f26515,plain,
( spl86_630
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X4)))
| sP8(X3,X0,X2,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_630])]) ).
fof(f26519,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(X0,fun(X0,bool),fequal(X0),X4))
| sP8(X3,X0,X2,X4,X1) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_630 ),
inference(forward_demodulation,[],[f26518,f4236]) ).
fof(f26518,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(X0,fun(X0,bool),fequal(X0),X4))
| sP8(X3,X0,X2,X4,X1) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_630 ),
inference(forward_demodulation,[],[f26516,f4236]) ).
fof(f26516,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X4)))
| sP8(X3,X0,X2,X4,X1) )
| ~ spl86_630 ),
inference(avatar_component_clause,[],[f26515]) ).
fof(f26517,plain,
spl86_630,
inference(avatar_split_clause,[],[f3177,f26515]) ).
fof(f3177,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X4)))
| sP8(X3,X0,X2,X4,X1) ),
inference(forward_demodulation,[],[f3176,f2226]) ).
fof(f3176,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X4)))
| sP8(X3,X0,X2,X4,X1) ),
inference(forward_demodulation,[],[f2734,f2226]) ).
fof(f2734,plain,
! [X2,X3,X0,X1,X4] :
( sP8(X3,X0,X2,X4,X1)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),bot_bot(fun(X0,bool)))) ),
inference(cnf_transformation,[],[f1925]) ).
fof(f1925,plain,
! [X0,X1,X2,X3,X4] :
( ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),bot_bot(fun(X0,bool))))
| ~ sP8(X3,X0,X2,X4,X1) )
& ( sP8(X3,X0,X2,X4,X1)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),bot_bot(fun(X0,bool)))) ) ),
inference(nnf_transformation,[],[f1657]) ).
fof(f1657,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),bot_bot(fun(X0,bool))))
<=> sP8(X3,X0,X2,X4,X1) ),
inference(definition_folding,[],[f1135,f1656]) ).
fof(f1656,plain,
! [X3,X0,X2,X4,X1] :
( sP8(X3,X0,X2,X4,X1)
<=> ( ( ti(X0,X2) = ti(X0,X3)
& ti(X0,X1) = ti(X0,X4) )
| ( ti(X0,X2) = ti(X0,X4)
& ti(X0,X1) = ti(X0,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f1135,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),bot_bot(fun(X0,bool))))
<=> ( ( ti(X0,X2) = ti(X0,X3)
& ti(X0,X1) = ti(X0,X4) )
| ( ti(X0,X2) = ti(X0,X4)
& ti(X0,X1) = ti(X0,X3) ) ) ),
inference(rectify,[],[f173]) ).
fof(f173,axiom,
! [X0,X10,X33,X34,X49] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X34),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X49),bot_bot(fun(X0,bool))))
<=> ( ( ti(X0,X33) = ti(X0,X34)
& ti(X0,X10) = ti(X0,X49) )
| ( ti(X0,X33) = ti(X0,X49)
& ti(X0,X10) = ti(X0,X34) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_doubleton__eq__iff) ).
fof(f26513,plain,
( spl86_629
| ~ spl86_108
| ~ spl86_587 ),
inference(avatar_split_clause,[],[f26146,f20974,f3698,f26510]) ).
fof(f26510,plain,
( spl86_629
<=> fTrue = hAPP(pname,bool,u,pn) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_629])]) ).
fof(f20974,plain,
( spl86_587
<=> fTrue = hAPP(bool,bool,combi(bool),hAPP(pname,bool,u,pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_587])]) ).
fof(f26146,plain,
( fTrue = hAPP(pname,bool,u,pn)
| ~ spl86_108
| ~ spl86_587 ),
inference(superposition,[],[f20976,f3699]) ).
fof(f20976,plain,
( fTrue = hAPP(bool,bool,combi(bool),hAPP(pname,bool,u,pn))
| ~ spl86_587 ),
inference(avatar_component_clause,[],[f20974]) ).
fof(f26508,plain,
( spl86_628
| ~ spl86_109
| ~ spl86_165
| ~ spl86_627 ),
inference(avatar_split_clause,[],[f26504,f26500,f4161,f3702,f26506]) ).
fof(f26506,plain,
( spl86_628
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(X0,fun(X0,bool),fequal(X0),X4))
| ~ sP8(X3,X0,X2,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_628])]) ).
fof(f26500,plain,
( spl86_627
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X4)))
| ~ sP8(X3,X0,X2,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_627])]) ).
fof(f26504,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(X0,fun(X0,bool),fequal(X0),X4))
| ~ sP8(X3,X0,X2,X4,X1) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_627 ),
inference(forward_demodulation,[],[f26503,f4236]) ).
fof(f26503,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(X0,fun(X0,bool),fequal(X0),X4))
| ~ sP8(X3,X0,X2,X4,X1) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_627 ),
inference(forward_demodulation,[],[f26501,f4236]) ).
fof(f26501,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X4)))
| ~ sP8(X3,X0,X2,X4,X1) )
| ~ spl86_627 ),
inference(avatar_component_clause,[],[f26500]) ).
fof(f26502,plain,
spl86_627,
inference(avatar_split_clause,[],[f3175,f26500]) ).
fof(f3175,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X4)))
| ~ sP8(X3,X0,X2,X4,X1) ),
inference(forward_demodulation,[],[f3174,f2226]) ).
fof(f3174,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X4)))
| ~ sP8(X3,X0,X2,X4,X1) ),
inference(forward_demodulation,[],[f2735,f2226]) ).
fof(f2735,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),bot_bot(fun(X0,bool))))
| ~ sP8(X3,X0,X2,X4,X1) ),
inference(cnf_transformation,[],[f1925]) ).
fof(f26456,plain,
( spl86_626
| ~ spl86_109
| ~ spl86_165
| ~ spl86_625 ),
inference(avatar_split_clause,[],[f26452,f26449,f4161,f3702,f26454]) ).
fof(f26454,plain,
( spl86_626
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),sK58(X0,X1)),hAPP(X0,fun(X0,bool),fequal(X0),sK57(X0,X1)))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_626])]) ).
fof(f26449,plain,
( spl86_625
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),sK58(X0,X1)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK57(X0,X1))))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_625])]) ).
fof(f26452,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),sK58(X0,X1)),hAPP(X0,fun(X0,bool),fequal(X0),sK57(X0,X1)))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_625 ),
inference(forward_demodulation,[],[f26450,f4236]) ).
fof(f26450,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),sK58(X0,X1)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK57(X0,X1))))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_625 ),
inference(avatar_component_clause,[],[f26449]) ).
fof(f26451,plain,
spl86_625,
inference(avatar_split_clause,[],[f3076,f26449]) ).
fof(f3076,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),sK58(X0,X1)),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK57(X0,X1))))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2453,f2226]) ).
fof(f2453,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),sK58(X0,X1)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK57(X0,X1)),bot_bot(fun(X0,bool))))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f1822,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),sK58(X0,X1)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK57(X0,X1)),bot_bot(fun(X0,bool))))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,sK58(X0,X1)))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK57(X0,X1)),sK58(X0,X1)))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK58(X0,X1))) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58])],[f1428,f1821]) ).
fof(f1821,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4)) )
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),sK58(X0,X1)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK57(X0,X1)),bot_bot(fun(X0,bool))))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,sK58(X0,X1)))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK57(X0,X1)),sK58(X0,X1)))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK58(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f1428,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ? [X3,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1427]) ).
fof(f1427,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ? [X3,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool))))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f965]) ).
fof(f965,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
=> ( ! [X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
=> hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X4),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))))) ) ) )
=> hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool)))) ) ) ),
inference(rectify,[],[f248]) ).
fof(f248,axiom,
! [X0,X15,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X15,X7))
=> ( ! [X53,X56] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X56))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X53),X56))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X15,X56))
=> hBOOL(hAPP(fun(X0,bool),bool,X15,hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X56),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X53),bot_bot(fun(X0,bool)))))) ) ) )
=> hBOOL(hAPP(fun(X0,bool),bool,X15,bot_bot(fun(X0,bool)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_finite__empty__induct) ).
fof(f26447,plain,
spl86_624,
inference(avatar_split_clause,[],[f2588,f26445]) ).
fof(f26445,plain,
( spl86_624
<=> ! [X0,X3,X2,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_624])]) ).
fof(f2588,plain,
! [X2,X3,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,plain,
! [X0,X1,X2,X3] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X0,X13,X38,X7] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X38),X7)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X38),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_insert__commute) ).
fof(f24374,plain,
spl86_623,
inference(avatar_split_clause,[],[f3087,f24372]) ).
fof(f24372,plain,
( spl86_623
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_623])]) ).
fof(f3087,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f3086,f2854]) ).
fof(f3086,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2891,f2854]) ).
fof(f2891,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(definition_unfolding,[],[f2475,f2190,f2190]) ).
fof(f2475,plain,
! [X2,X0,X1] :
( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1456]) ).
fof(f1456,plain,
! [X0,X1,X2] :
( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1455]) ).
fof(f1455,plain,
! [X0,X1,X2] :
( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f979]) ).
fof(f979,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),X1)))
=> ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2) ) ) ),
inference(rectify,[],[f59]) ).
fof(f59,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X12)),hAPP(fun(X0,bool),nat,finite_card(X0),X7)))
=> ti(fun(X0,bool),X7) = ti(fun(X0,bool),X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_card__seteq) ).
fof(f24327,plain,
( spl86_622
| ~ spl86_109
| ~ spl86_165
| ~ spl86_621 ),
inference(avatar_split_clause,[],[f24323,f24320,f4161,f3702,f24325]) ).
fof(f24325,plain,
( spl86_622
<=> ! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_622])]) ).
fof(f24320,plain,
( spl86_621
<=> ! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_621])]) ).
fof(f24323,plain,
( ! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_621 ),
inference(forward_demodulation,[],[f24321,f4236]) ).
fof(f24321,plain,
( ! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ spl86_621 ),
inference(avatar_component_clause,[],[f24320]) ).
fof(f24322,plain,
spl86_621,
inference(avatar_split_clause,[],[f3023,f24320]) ).
fof(f3023,plain,
! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(forward_demodulation,[],[f2869,f2854]) ).
fof(f2869,plain,
! [X0,X1] :
( hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1)))) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(definition_unfolding,[],[f2334,f2190]) ).
fof(f2334,plain,
! [X0,X1] :
( ti(fun(X0,bool),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(cnf_transformation,[],[f1759]) ).
fof(f1759,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ! [X2,X3] : ti(fun(X0,bool),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))) )
& ( ti(fun(X0,bool),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45])],[f1757,f1758]) ).
fof(f1758,plain,
! [X0,X1] :
( ? [X4,X5] : ti(fun(X0,bool),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X5),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X4)))
=> ti(fun(X0,bool),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),sK45(X0,X1)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),sK44(X0,X1)))) ),
introduced(choice_axiom,[]) ).
fof(f1757,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ! [X2,X3] : ti(fun(X0,bool),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))) )
& ( ? [X4,X5] : ti(fun(X0,bool),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X5),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X4)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(rectify,[],[f1756]) ).
fof(f1756,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ! [X2,X3] : ti(fun(X0,bool),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))) )
& ( ? [X2,X3] : ti(fun(X0,bool),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(nnf_transformation,[],[f900]) ).
fof(f900,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
<=> ? [X2,X3] : ti(fun(X0,bool),X1) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))) ),
inference(rectify,[],[f471]) ).
fof(f471,axiom,
! [X0,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
<=> ? [X31,X69] : ti(fun(X0,bool),X7) = hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X69),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X31))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_finite__conv__nat__seg__image) ).
fof(f24318,plain,
spl86_620,
inference(avatar_split_clause,[],[f2700,f24316]) ).
fof(f24316,plain,
( spl86_620
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK78(X0,X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_620])]) ).
fof(f2700,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),sK78(X0,X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(cnf_transformation,[],[f1907]) ).
fof(f24314,plain,
spl86_619,
inference(avatar_split_clause,[],[f2694,f24312]) ).
fof(f2694,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) ),
inference(cnf_transformation,[],[f1904]) ).
fof(f1904,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3)) ) ),
inference(flattening,[],[f1903]) ).
fof(f1903,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3)) ) ),
inference(nnf_transformation,[],[f1112]) ).
fof(f1112,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3))
<=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) ) ),
inference(rectify,[],[f139]) ).
fof(f139,axiom,
! [X0,X13,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)),X12))
<=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_insert__subset) ).
fof(f24310,plain,
spl86_618,
inference(avatar_split_clause,[],[f2619,f24308]) ).
fof(f24308,plain,
( spl86_618
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_618])]) ).
fof(f2619,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1875]) ).
fof(f1875,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) ) )
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(nnf_transformation,[],[f1556]) ).
fof(f1556,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))
<=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1)) )
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(ennf_transformation,[],[f1074]) ).
fof(f1074,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))
<=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1)) ) ),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X0,X12,X13,X7] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X12)))
<=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_subset__insert) ).
fof(f24306,plain,
spl86_617,
inference(avatar_split_clause,[],[f2474,f24304]) ).
fof(f24304,plain,
( spl86_617
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_617])]) ).
fof(f2474,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1454]) ).
fof(f1454,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1453]) ).
fof(f1453,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f978]) ).
fof(f978,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ) ) ),
inference(rectify,[],[f470]) ).
fof(f470,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X7)),hAPP(fun(X0,bool),nat,finite_card(X0),X12)))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_card__psubset) ).
fof(f24302,plain,
spl86_616,
inference(avatar_split_clause,[],[f2319,f24300]) ).
fof(f24300,plain,
( spl86_616
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,sK38(X0,X1,X3))),hAPP(X0,X1,X3,sK37(X0,X1,X3))))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X4)),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_616])]) ).
fof(f2319,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,sK38(X0,X1,X3))),hAPP(X0,X1,X3,sK37(X0,X1,X3))))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X4)),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1742]) ).
fof(f1742,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,sK38(X0,X1,X3))),hAPP(X0,X1,X3,sK37(X0,X1,X3))))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),sK38(X0,X1,X3)),sK37(X0,X1,X3))) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X4)),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f1404,f1741]) ).
fof(f1741,plain,
! [X0,X1,X3] :
( ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X7)),hAPP(X0,X1,X3,X6)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X7),X6)) )
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,sK38(X0,X1,X3))),hAPP(X0,X1,X3,sK37(X0,X1,X3))))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),sK38(X0,X1,X3)),sK37(X0,X1,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f1404,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X7)),hAPP(X0,X1,X3,X6)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X7),X6)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X4)),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(flattening,[],[f1403]) ).
fof(f1403,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X7)),hAPP(X0,X1,X3,X6)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X7),X6)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X4)),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(ennf_transformation,[],[f893]) ).
fof(f893,plain,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X4)),X5))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X4))
=> ( ! [X6,X7] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X7),X6))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X7)),hAPP(X0,X1,X3,X6))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5)) ) ) ) ),
inference(rectify,[],[f486]) ).
fof(f486,axiom,
! [X1,X0] :
( ( order(X1)
& order(X0) )
=> ! [X34,X11,X33,X10] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X11,X33)),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),X33))
=> ( ! [X32,X60] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X60),X32))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X11,X60)),hAPP(X1,X0,X11,X32))) )
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X11,X34)),X10)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_xt4) ).
fof(f24298,plain,
spl86_615,
inference(avatar_split_clause,[],[f2317,f24296]) ).
fof(f24296,plain,
( spl86_615
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X4,sK35(X0,X1,X4))),hAPP(X1,X0,X4,sK36(X0,X1,X4))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),hAPP(X1,X0,X4,X5)))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_615])]) ).
fof(f2317,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X4,sK35(X0,X1,X4))),hAPP(X1,X0,X4,sK36(X0,X1,X4))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),hAPP(X1,X0,X4,X5)))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1740]) ).
fof(f1740,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X4,sK35(X0,X1,X4))),hAPP(X1,X0,X4,sK36(X0,X1,X4))))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sK35(X0,X1,X4)),sK36(X0,X1,X4))) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),hAPP(X1,X0,X4,X5))) )
| ~ order(X0)
| ~ order(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f1402,f1739]) ).
fof(f1739,plain,
! [X0,X1,X4] :
( ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X4,X6)),hAPP(X1,X0,X4,X7)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7)) )
=> ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X4,sK35(X0,X1,X4))),hAPP(X1,X0,X4,sK36(X0,X1,X4))))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sK35(X0,X1,X4)),sK36(X0,X1,X4))) ) ),
introduced(choice_axiom,[]) ).
fof(f1402,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X4,X6)),hAPP(X1,X0,X4,X7)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7)) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),hAPP(X1,X0,X4,X5))) )
| ~ order(X0)
| ~ order(X1) ),
inference(flattening,[],[f1401]) ).
fof(f1401,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X4,X6)),hAPP(X1,X0,X4,X7)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7)) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),hAPP(X1,X0,X4,X5))) )
| ~ order(X0)
| ~ order(X1) ),
inference(ennf_transformation,[],[f892]) ).
fof(f892,plain,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),hAPP(X1,X0,X4,X5)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
=> ( ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X4,X6)),hAPP(X1,X0,X4,X7))) )
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2))) ) ) ) ),
inference(rectify,[],[f487]) ).
fof(f487,axiom,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X34,X10,X11,X33] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X10),hAPP(X1,X0,X11,X33)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X33),X34))
=> ( ! [X32,X60] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X32),X60))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X11,X32)),hAPP(X1,X0,X11,X60))) )
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X10),hAPP(X1,X0,X11,X34))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_order__le__less__subst1) ).
fof(f24294,plain,
spl86_614,
inference(avatar_split_clause,[],[f2315,f24292]) ).
fof(f24292,plain,
( spl86_614
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X4,sK33(X0,X1,X4))),hAPP(X1,X0,X4,sK34(X0,X1,X4))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X5)))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_614])]) ).
fof(f2315,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X4,sK33(X0,X1,X4))),hAPP(X1,X0,X4,sK34(X0,X1,X4))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X5)))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1738]) ).
fof(f1738,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X4,sK33(X0,X1,X4))),hAPP(X1,X0,X4,sK34(X0,X1,X4))))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sK33(X0,X1,X4)),sK34(X0,X1,X4))) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X5))) )
| ~ order(X0)
| ~ order(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f1400,f1737]) ).
fof(f1737,plain,
! [X0,X1,X4] :
( ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X4,X6)),hAPP(X1,X0,X4,X7)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7)) )
=> ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X4,sK33(X0,X1,X4))),hAPP(X1,X0,X4,sK34(X0,X1,X4))))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sK33(X0,X1,X4)),sK34(X0,X1,X4))) ) ),
introduced(choice_axiom,[]) ).
fof(f1400,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X4,X6)),hAPP(X1,X0,X4,X7)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7)) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X5))) )
| ~ order(X0)
| ~ order(X1) ),
inference(flattening,[],[f1399]) ).
fof(f1399,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X4,X6)),hAPP(X1,X0,X4,X7)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7)) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X5))) )
| ~ order(X0)
| ~ order(X1) ),
inference(ennf_transformation,[],[f891]) ).
fof(f891,plain,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X5)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X2))
=> ( ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X7))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X4,X6)),hAPP(X1,X0,X4,X7))) )
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2))) ) ) ) ),
inference(rectify,[],[f490]) ).
fof(f490,axiom,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X34,X10,X11,X33] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X10),hAPP(X1,X0,X11,X33)))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X33),X34))
=> ( ! [X32,X60] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X32),X60))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X11,X32)),hAPP(X1,X0,X11,X60))) )
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X10),hAPP(X1,X0,X11,X34))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_order__less__le__subst1) ).
fof(f24290,plain,
( spl86_612
| ~ spl86_613
| ~ spl86_146
| ~ spl86_452 ),
inference(avatar_split_clause,[],[f13979,f13010,f4034,f24287,f24284]) ).
fof(f24284,plain,
( spl86_612
<=> ! [X0] : ~ hBOOL(hAPP(pname,bool,u,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_612])]) ).
fof(f24287,plain,
( spl86_613
<=> u = bot_bot(fun(pname,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_613])]) ).
fof(f13979,plain,
( ! [X0] :
( u != bot_bot(fun(pname,bool))
| ~ hBOOL(hAPP(pname,bool,u,X0)) )
| ~ spl86_146
| ~ spl86_452 ),
inference(superposition,[],[f4035,f13012]) ).
fof(f24282,plain,
spl86_611,
inference(avatar_split_clause,[],[f2313,f24280]) ).
fof(f24280,plain,
( spl86_611
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK31(X0,X1,X2))),hAPP(X0,X1,X2,sK32(X0,X1,X2))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X4),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_611])]) ).
fof(f2313,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK31(X0,X1,X2))),hAPP(X0,X1,X2,sK32(X0,X1,X2))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X4),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1736]) ).
fof(f1736,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK31(X0,X1,X2))),hAPP(X0,X1,X2,sK32(X0,X1,X2))))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),sK31(X0,X1,X2)),sK32(X0,X1,X2))) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f1398,f1735]) ).
fof(f1735,plain,
! [X0,X1,X2] :
( ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X6)),hAPP(X0,X1,X2,X7)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X6),X7)) )
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK31(X0,X1,X2))),hAPP(X0,X1,X2,sK32(X0,X1,X2))))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),sK31(X0,X1,X2)),sK32(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f1398,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X6)),hAPP(X0,X1,X2,X7)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X6),X7)) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(flattening,[],[f1397]) ).
fof(f1397,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X6)),hAPP(X0,X1,X2,X7)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X6),X7)) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(ennf_transformation,[],[f890]) ).
fof(f890,plain,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X4),X5))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X5)),X3))
=> ( ! [X6,X7] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X6),X7))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X6)),hAPP(X0,X1,X2,X7))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3)) ) ) ) ),
inference(rectify,[],[f491]) ).
fof(f491,axiom,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X11,X34,X10,X33] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X10),X33))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X11,X33)),X34))
=> ( ! [X32,X60] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X32),X60))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X11,X32)),hAPP(X0,X1,X11,X60))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X11,X10)),X34)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_order__le__less__subst2) ).
fof(f24278,plain,
spl86_610,
inference(avatar_split_clause,[],[f2311,f24276]) ).
fof(f24276,plain,
( spl86_610
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X3,sK30(X0,X1,X3))),hAPP(X1,X0,X3,sK29(X0,X1,X3))))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_610])]) ).
fof(f2311,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X3,sK30(X0,X1,X3))),hAPP(X1,X0,X3,sK29(X0,X1,X3))))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1734]) ).
fof(f1734,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X3,sK30(X0,X1,X3))),hAPP(X1,X0,X3,sK29(X0,X1,X3))))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sK30(X0,X1,X3)),sK29(X0,X1,X3))) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f1396,f1733]) ).
fof(f1733,plain,
! [X0,X1,X3] :
( ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X3,X7)),hAPP(X1,X0,X3,X6)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) )
=> ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X3,sK30(X0,X1,X3))),hAPP(X1,X0,X3,sK29(X0,X1,X3))))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sK30(X0,X1,X3)),sK29(X0,X1,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f1396,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X3,X7)),hAPP(X1,X0,X3,X6)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(flattening,[],[f1395]) ).
fof(f1395,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X3,X7)),hAPP(X1,X0,X3,X6)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(ennf_transformation,[],[f889]) ).
fof(f889,plain,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X4)))
=> ( ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X7),X6))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X3,X7)),hAPP(X1,X0,X3,X6))) )
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5))) ) ) ) ),
inference(rectify,[],[f489]) ).
fof(f489,axiom,
! [X1,X0] :
( ( order(X1)
& order(X0) )
=> ! [X34,X11,X33,X10] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X33),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X0,X1,X11,X33)))
=> ( ! [X32,X60] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X60),X32))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X11,X60)),hAPP(X0,X1,X11,X32))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X0,X1,X11,X10))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_xt7) ).
fof(f24274,plain,
spl86_609,
inference(avatar_split_clause,[],[f2309,f24272]) ).
fof(f24272,plain,
( spl86_609
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,sK27(X0,X1,X2))),hAPP(X0,X1,X2,sK28(X0,X1,X2))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X4),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_609])]) ).
fof(f2309,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,sK27(X0,X1,X2))),hAPP(X0,X1,X2,sK28(X0,X1,X2))))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X4),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1732]) ).
fof(f1732,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,sK27(X0,X1,X2))),hAPP(X0,X1,X2,sK28(X0,X1,X2))))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),sK27(X0,X1,X2)),sK28(X0,X1,X2))) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f1394,f1731]) ).
fof(f1731,plain,
! [X0,X1,X2] :
( ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X6)),hAPP(X0,X1,X2,X7)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X6),X7)) )
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,sK27(X0,X1,X2))),hAPP(X0,X1,X2,sK28(X0,X1,X2))))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),sK27(X0,X1,X2)),sK28(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f1394,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X6)),hAPP(X0,X1,X2,X7)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X6),X7)) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(flattening,[],[f1393]) ).
fof(f1393,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X6)),hAPP(X0,X1,X2,X7)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X6),X7)) )
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(ennf_transformation,[],[f888]) ).
fof(f888,plain,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X4),X5))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),X3))
=> ( ! [X6,X7] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X6),X7))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X6)),hAPP(X0,X1,X2,X7))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3)) ) ) ) ),
inference(rectify,[],[f492]) ).
fof(f492,axiom,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X11,X34,X10,X33] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X10),X33))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X11,X33)),X34))
=> ( ! [X32,X60] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X32),X60))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X11,X32)),hAPP(X0,X1,X11,X60))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X11,X10)),X34)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_order__less__le__subst2) ).
fof(f24270,plain,
spl86_608,
inference(avatar_split_clause,[],[f2307,f24268]) ).
fof(f24268,plain,
( spl86_608
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X3,sK26(X0,X1,X3))),hAPP(X1,X0,X3,sK25(X0,X1,X3))))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_608])]) ).
fof(f2307,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X3,sK26(X0,X1,X3))),hAPP(X1,X0,X3,sK25(X0,X1,X3))))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1730]) ).
fof(f1730,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X3,sK26(X0,X1,X3))),hAPP(X1,X0,X3,sK25(X0,X1,X3))))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sK26(X0,X1,X3)),sK25(X0,X1,X3))) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f1392,f1729]) ).
fof(f1729,plain,
! [X0,X1,X3] :
( ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X3,X7)),hAPP(X1,X0,X3,X6)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) )
=> ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X3,sK26(X0,X1,X3))),hAPP(X1,X0,X3,sK25(X0,X1,X3))))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sK26(X0,X1,X3)),sK25(X0,X1,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f1392,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X3,X7)),hAPP(X1,X0,X3,X6)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(flattening,[],[f1391]) ).
fof(f1391,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X3,X7)),hAPP(X1,X0,X3,X6)))
& hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5)) )
| ~ order(X0)
| ~ order(X1) ),
inference(ennf_transformation,[],[f887]) ).
fof(f887,plain,
! [X0,X1] :
( ( order(X0)
& order(X1) )
=> ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),hAPP(X1,X0,X3,X4)))
=> ( ! [X6,X7] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X3,X7)),hAPP(X1,X0,X3,X6))) )
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5))) ) ) ) ),
inference(rectify,[],[f488]) ).
fof(f488,axiom,
! [X1,X0] :
( ( order(X1)
& order(X0) )
=> ! [X34,X11,X33,X10] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X33),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X34),hAPP(X0,X1,X11,X33)))
=> ( ! [X32,X60] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X60),X32))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X11,X60)),hAPP(X0,X1,X11,X32))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),hAPP(X0,X1,X11,X10))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_xt5) ).
fof(f24266,plain,
spl86_607,
inference(avatar_split_clause,[],[f2305,f24264]) ).
fof(f24264,plain,
( spl86_607
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,sK24(X0,X1,X3))),hAPP(X0,X1,X3,sK23(X0,X1,X3))))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X4)),X5))
| ~ ord(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_607])]) ).
fof(f2305,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,sK24(X0,X1,X3))),hAPP(X0,X1,X3,sK23(X0,X1,X3))))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X4)),X5))
| ~ ord(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1728]) ).
fof(f1728,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,sK24(X0,X1,X3))),hAPP(X0,X1,X3,sK23(X0,X1,X3))))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),sK24(X0,X1,X3)),sK23(X0,X1,X3))) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X4)),X5)) )
| ~ ord(X0)
| ~ order(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f1390,f1727]) ).
fof(f1727,plain,
! [X0,X1,X3] :
( ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X7)),hAPP(X0,X1,X3,X6)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X7),X6)) )
=> ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,sK24(X0,X1,X3))),hAPP(X0,X1,X3,sK23(X0,X1,X3))))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),sK24(X0,X1,X3)),sK23(X0,X1,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f1390,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X7)),hAPP(X0,X1,X3,X6)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X7),X6)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X4)),X5)) )
| ~ ord(X0)
| ~ order(X1) ),
inference(flattening,[],[f1389]) ).
fof(f1389,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| ? [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X7)),hAPP(X0,X1,X3,X6)))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X7),X6)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X4)),X5)) )
| ~ ord(X0)
| ~ order(X1) ),
inference(ennf_transformation,[],[f886]) ).
fof(f886,plain,
! [X0,X1] :
( ( ord(X0)
& order(X1) )
=> ! [X2,X3,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X4)),X5))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X4))
=> ( ! [X6,X7] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X7),X6))
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X7)),hAPP(X0,X1,X3,X6))) )
=> hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5)) ) ) ) ),
inference(rectify,[],[f483]) ).
fof(f483,axiom,
! [X1,X0] :
( ( ord(X1)
& order(X0) )
=> ! [X34,X11,X33,X10] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X1,X0,X11,X33)),X10))
=> ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X34),X33))
=> ( ! [X32,X60] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X60),X32))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X11,X60)),hAPP(X1,X0,X11,X32))) )
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X1,X0,X11,X34)),X10)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_xt6) ).
fof(f24182,plain,
spl86_606,
inference(avatar_split_clause,[],[f2442,f24180]) ).
fof(f24180,plain,
( spl86_606
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_606])]) ).
fof(f2442,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1421]) ).
fof(f1421,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f959]) ).
fof(f959,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)))) ),
inference(rectify,[],[f242]) ).
fof(f242,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X7)),hAPP(fun(X0,bool),nat,finite_card(X0),X12))),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_diff__card__le__card__Diff) ).
fof(f24166,plain,
( spl86_605
| ~ spl86_109
| ~ spl86_165
| ~ spl86_604 ),
inference(avatar_split_clause,[],[f24162,f24159,f4161,f3702,f24164]) ).
fof(f24164,plain,
( spl86_605
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(fun(X0,bool),bool),bool,finite_finite(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_605])]) ).
fof(f24159,plain,
( spl86_604
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(fun(X0,bool),bool),bool,finite_finite(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_604])]) ).
fof(f24162,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(fun(X0,bool),bool),bool,finite_finite(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_604 ),
inference(forward_demodulation,[],[f24160,f4236]) ).
fof(f24160,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(fun(X0,bool),bool),bool,finite_finite(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ spl86_604 ),
inference(avatar_component_clause,[],[f24159]) ).
fof(f24161,plain,
spl86_604,
inference(avatar_split_clause,[],[f2262,f24159]) ).
fof(f2262,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(fun(X0,bool),bool),bool,finite_finite(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(cnf_transformation,[],[f1341]) ).
fof(f1341,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(fun(X0,bool),bool),bool,finite_finite(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(ennf_transformation,[],[f848]) ).
fof(f848,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
=> hBOOL(hAPP(fun(fun(X0,bool),bool),bool,finite_finite(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X1)))) ),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X0,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> hBOOL(hAPP(fun(fun(X0,bool),bool),bool,finite_finite(fun(X0,bool)),hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),hAPP(fun(X0,bool),fun(fun(X0,bool),bool),hAPP(fun(fun(X0,bool),fun(fun(X0,bool),bool)),fun(fun(X0,bool),fun(fun(X0,bool),bool)),combc(fun(X0,bool),fun(X0,bool),bool),ord_less_eq(fun(X0,bool))),X7)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
fof(f24140,plain,
spl86_603,
inference(avatar_split_clause,[],[f2714,f24138]) ).
fof(f24138,plain,
( spl86_603
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_603])]) ).
fof(f2714,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(cnf_transformation,[],[f1621]) ).
fof(f1621,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(flattening,[],[f1620]) ).
fof(f1620,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4)) ),
inference(ennf_transformation,[],[f1128]) ).
fof(f1128,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hAPP(fun(X0,bool),X0,X4,X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X3,X1),hAPP(fun(X0,bool),X0,X4,X2)) ) ) ),
inference(rectify,[],[f236]) ).
fof(f236,axiom,
! [X0,X13,X7,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X11),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hAPP(fun(X0,bool),X0,X9,X7) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,X13),hAPP(fun(X0,bool),X0,X9,X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_folding__one__idem_Oin__idem) ).
fof(f24053,plain,
( spl86_602
| ~ spl86_109
| ~ spl86_165
| ~ spl86_601 ),
inference(avatar_split_clause,[],[f24049,f24046,f4161,f3702,f24051]) ).
fof(f24051,plain,
( spl86_602
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_602])]) ).
fof(f24046,plain,
( spl86_601
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_601])]) ).
fof(f24049,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(X0,fun(X0,bool),fequal(X0),X1)))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_601 ),
inference(forward_demodulation,[],[f24047,f4236]) ).
fof(f24047,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_601 ),
inference(avatar_component_clause,[],[f24046]) ).
fof(f24048,plain,
spl86_601,
inference(avatar_split_clause,[],[f3070,f24046]) ).
fof(f3070,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2443,f2226]) ).
fof(f2443,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1422]) ).
fof(f1422,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f960]) ).
fof(f960,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X2))) ),
inference(rectify,[],[f245]) ).
fof(f245,axiom,
! [X0,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))))),hAPP(fun(X0,bool),nat,finite_card(X0),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_card__Diff1__le) ).
fof(f24044,plain,
spl86_600,
inference(avatar_split_clause,[],[f2964,f24042]) ).
fof(f24042,plain,
( spl86_600
<=> ! [X2,X3,X4,X0,X5,X1] :
( hAPP(fun(X0,bool),X1,X5,bot_bot(fun(X0,bool))) = hAPP(X1,X1,combi(X1),X3)
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X2),X3),X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_600])]) ).
fof(f2964,plain,
! [X2,X3,X0,X1,X4,X5] :
( hAPP(fun(X0,bool),X1,X5,bot_bot(fun(X0,bool))) = hAPP(X1,X1,combi(X1),X3)
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X2),X3),X4),X5)) ),
inference(definition_unfolding,[],[f2742,f2190]) ).
fof(f2742,plain,
! [X2,X3,X0,X1,X4,X5] :
( ti(X1,X3) = hAPP(fun(X0,bool),X1,X5,bot_bot(fun(X0,bool)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X2),X3),X4),X5)) ),
inference(cnf_transformation,[],[f1632]) ).
fof(f1632,plain,
! [X0,X1,X2,X3,X4,X5] :
( ti(X1,X3) = hAPP(fun(X0,bool),X1,X5,bot_bot(fun(X0,bool)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X2),X3),X4),X5)) ),
inference(ennf_transformation,[],[f1142]) ).
fof(f1142,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(fun(fun(X0,bool),X1),bool,hAPP(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool),hAPP(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X0,X1),fun(fun(fun(X0,bool),X1),bool))),finite1357897459simple(X1,X0),X2),X3),X4),X5))
=> ti(X1,X3) = hAPP(fun(X0,bool),X1,X5,bot_bot(fun(X0,bool))) ),
inference(rectify,[],[f259]) ).
fof(f259,axiom,
! [X1,X0,X11,X41,X39,X9] :
( hBOOL(hAPP(fun(fun(X1,bool),X0),bool,hAPP(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool),hAPP(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)),hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool))),finite1357897459simple(X0,X1),X11),X41),X39),X9))
=> ti(X0,X41) = hAPP(fun(X1,bool),X0,X9,bot_bot(fun(X1,bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_folding__image__simple_Oempty) ).
fof(f23844,plain,
( spl86_598
| ~ spl86_599
| ~ spl86_146
| ~ spl86_441 ),
inference(avatar_split_clause,[],[f13674,f12965,f4034,f23841,f23838]) ).
fof(f23838,plain,
( spl86_598
<=> ! [X0] : ~ hBOOL(hAPP(x_a,bool,g,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_598])]) ).
fof(f23841,plain,
( spl86_599
<=> g = bot_bot(fun(x_a,bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_599])]) ).
fof(f12965,plain,
( spl86_441
<=> g = hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),g) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_441])]) ).
fof(f13674,plain,
( ! [X0] :
( g != bot_bot(fun(x_a,bool))
| ~ hBOOL(hAPP(x_a,bool,g,X0)) )
| ~ spl86_146
| ~ spl86_441 ),
inference(superposition,[],[f4035,f12967]) ).
fof(f12967,plain,
( g = hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),g)
| ~ spl86_441 ),
inference(avatar_component_clause,[],[f12965]) ).
fof(f23826,plain,
( spl86_597
| ~ spl86_109
| ~ spl86_165
| ~ spl86_596 ),
inference(avatar_split_clause,[],[f23822,f23819,f4161,f3702,f23824]) ).
fof(f23824,plain,
( spl86_597
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_597])]) ).
fof(f23819,plain,
( spl86_596
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_596])]) ).
fof(f23822,plain,
( ! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_596 ),
inference(forward_demodulation,[],[f23820,f4236]) ).
fof(f23820,plain,
( ! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ spl86_596 ),
inference(avatar_component_clause,[],[f23819]) ).
fof(f23821,plain,
spl86_596,
inference(avatar_split_clause,[],[f3022,f23819]) ).
fof(f3022,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(forward_demodulation,[],[f2868,f2854]) ).
fof(f2868,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(definition_unfolding,[],[f2335,f2190]) ).
fof(f2335,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ti(fun(X0,bool),X1) != hAPP(fun(nat,bool),fun(X0,bool),hAPP(fun(nat,X0),fun(fun(nat,bool),fun(X0,bool)),image(nat,X0),X3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))) ),
inference(cnf_transformation,[],[f1759]) ).
fof(f23817,plain,
spl86_595,
inference(avatar_split_clause,[],[f2623,f23815]) ).
fof(f23815,plain,
( spl86_595
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_595])]) ).
fof(f2623,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1560]) ).
fof(f1560,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(flattening,[],[f1559]) ).
fof(f1559,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1)))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(ennf_transformation,[],[f1077]) ).
fof(f1077,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X3),X1))) ) ),
inference(rectify,[],[f253]) ).
fof(f253,axiom,
! [X0,X12,X34,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),X7))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),X12))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_DiffI) ).
fof(f23813,plain,
spl86_594,
inference(avatar_split_clause,[],[f2516,f23811]) ).
fof(f23811,plain,
( spl86_594
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_594])]) ).
fof(f2516,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1836]) ).
fof(f1836,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1))) ) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(nnf_transformation,[],[f1500]) ).
fof(f1500,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(flattening,[],[f1499]) ).
fof(f1499,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1014]) ).
fof(f1014,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0)) ) ) ),
inference(rectify,[],[f92]) ).
fof(f92,axiom,
! [X19,X18,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X19))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X19),X18)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_le__diff__iff) ).
fof(f23809,plain,
spl86_593,
inference(avatar_split_clause,[],[f2514,f23807]) ).
fof(f23807,plain,
( spl86_593
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_593])]) ).
fof(f2514,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1835]) ).
fof(f1835,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1))) ) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(nnf_transformation,[],[f1498]) ).
fof(f1498,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(flattening,[],[f1497]) ).
fof(f1497,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1013]) ).
fof(f1013,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0)) ) ) ),
inference(rectify,[],[f456]) ).
fof(f456,axiom,
! [X19,X18,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X19))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X19),X18)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X27),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_less__diff__iff) ).
fof(f23712,plain,
spl86_592,
inference(avatar_split_clause,[],[f3097,f23710]) ).
fof(f23710,plain,
( spl86_592
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_592])]) ).
fof(f3097,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(forward_demodulation,[],[f2511,f2415]) ).
fof(f2415,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
inference(cnf_transformation,[],[f938]) ).
fof(f938,plain,
! [X0,X1,X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
inference(rectify,[],[f305]) ).
fof(f305,axiom,
! [X25,X26,X24] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X25),X26)),X24) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X25),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_diff__diff__left) ).
fof(f2511,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1494]) ).
fof(f1494,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(flattening,[],[f1493]) ).
fof(f1493,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1011]) ).
fof(f1011,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)) ) ),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X16,X24,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X16))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X24)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X16),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).
fof(f23666,plain,
spl86_591,
inference(avatar_split_clause,[],[f2419,f23664]) ).
fof(f23664,plain,
( spl86_591
<=> ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_591])]) ).
fof(f2419,plain,
! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X2),
inference(cnf_transformation,[],[f942]) ).
fof(f942,plain,
! [X0,X1,X2] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X2),
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X0,X7,X12] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_Diff__idemp) ).
fof(f23662,plain,
( spl86_590
| ~ spl86_53
| ~ spl86_108
| ~ spl86_339 ),
inference(avatar_split_clause,[],[f8873,f8689,f3698,f3436,f23660]) ).
fof(f8689,plain,
( spl86_339
<=> ! [X0] :
( ~ hBOOL(X0)
| fTrue = hAPP(bool,bool,combi(bool),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_339])]) ).
fof(f8873,plain,
( ! [X0,X1] :
( fTrue = hAPP(fun(X0,bool),bool,finite_finite(X0),X1)
| ~ finite_finite_1(X0) )
| ~ spl86_53
| ~ spl86_108
| ~ spl86_339 ),
inference(forward_demodulation,[],[f8793,f3699]) ).
fof(f8793,plain,
( ! [X0,X1] :
( fTrue = hAPP(bool,bool,combi(bool),hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(X0) )
| ~ spl86_53
| ~ spl86_339 ),
inference(resolution,[],[f8690,f3437]) ).
fof(f8690,plain,
( ! [X0] :
( ~ hBOOL(X0)
| fTrue = hAPP(bool,bool,combi(bool),X0) )
| ~ spl86_339 ),
inference(avatar_component_clause,[],[f8689]) ).
fof(f20985,plain,
spl86_589,
inference(avatar_split_clause,[],[f2318,f20983]) ).
fof(f20983,plain,
( spl86_589
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),sK38(X0,X1,X3)),sK37(X0,X1,X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X4)),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_589])]) ).
fof(f2318,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),sK38(X0,X1,X3)),sK37(X0,X1,X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X4)),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1742]) ).
fof(f20981,plain,
spl86_588,
inference(avatar_split_clause,[],[f2316,f20979]) ).
fof(f20979,plain,
( spl86_588
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sK35(X0,X1,X4)),sK36(X0,X1,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),hAPP(X1,X0,X4,X5)))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_588])]) ).
fof(f2316,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sK35(X0,X1,X4)),sK36(X0,X1,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),hAPP(X1,X0,X4,X5)))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1740]) ).
fof(f20977,plain,
( spl86_587
| ~ spl86_188
| ~ spl86_339 ),
inference(avatar_split_clause,[],[f8816,f8689,f4343,f20974]) ).
fof(f4343,plain,
( spl86_188
<=> hBOOL(hAPP(pname,bool,u,pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_188])]) ).
fof(f8816,plain,
( fTrue = hAPP(bool,bool,combi(bool),hAPP(pname,bool,u,pn))
| ~ spl86_188
| ~ spl86_339 ),
inference(resolution,[],[f8690,f4345]) ).
fof(f4345,plain,
( hBOOL(hAPP(pname,bool,u,pn))
| ~ spl86_188 ),
inference(avatar_component_clause,[],[f4343]) ).
fof(f20972,plain,
spl86_586,
inference(avatar_split_clause,[],[f2314,f20970]) ).
fof(f20970,plain,
( spl86_586
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sK33(X0,X1,X4)),sK34(X0,X1,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X5)))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_586])]) ).
fof(f2314,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X2)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sK33(X0,X1,X4)),sK34(X0,X1,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),hAPP(X1,X0,X4,X5)))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1738]) ).
fof(f20968,plain,
spl86_585,
inference(avatar_split_clause,[],[f2312,f20966]) ).
fof(f20966,plain,
( spl86_585
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),sK31(X0,X1,X2)),sK32(X0,X1,X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X4),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_585])]) ).
fof(f2312,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),sK31(X0,X1,X2)),sK32(X0,X1,X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X4),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1736]) ).
fof(f20964,plain,
spl86_584,
inference(avatar_split_clause,[],[f2310,f20962]) ).
fof(f20962,plain,
( spl86_584
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sK30(X0,X1,X3)),sK29(X0,X1,X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_584])]) ).
fof(f2310,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sK30(X0,X1,X3)),sK29(X0,X1,X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1734]) ).
fof(f20960,plain,
spl86_583,
inference(avatar_split_clause,[],[f2308,f20958]) ).
fof(f20958,plain,
( spl86_583
<=> ! [X5,X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),sK27(X0,X1,X2)),sK28(X0,X1,X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X4),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_583])]) ).
fof(f2308,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X2,X4)),X3))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),sK27(X0,X1,X2)),sK28(X0,X1,X2)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X4),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1732]) ).
fof(f20956,plain,
spl86_582,
inference(avatar_split_clause,[],[f2306,f20954]) ).
fof(f20954,plain,
( spl86_582
<=> ! [X2,X3,X4,X0,X5,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sK26(X0,X1,X3)),sK25(X0,X1,X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ order(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_582])]) ).
fof(f2306,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),hAPP(X1,X0,X3,X5)))
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sK26(X0,X1,X3)),sK25(X0,X1,X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),hAPP(X1,X0,X3,X4)))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
| ~ order(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1730]) ).
fof(f20952,plain,
spl86_581,
inference(avatar_split_clause,[],[f2304,f20950]) ).
fof(f20950,plain,
( spl86_581
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),sK24(X0,X1,X3)),sK23(X0,X1,X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X4)),X5))
| ~ ord(X0)
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_581])]) ).
fof(f2304,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X0,X1,X3,X2)),X5))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),sK24(X0,X1,X3)),sK23(X0,X1,X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X4))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X3,X4)),X5))
| ~ ord(X0)
| ~ order(X1) ),
inference(cnf_transformation,[],[f1728]) ).
fof(f20885,plain,
spl86_580,
inference(avatar_split_clause,[],[f2725,f20883]) ).
fof(f20883,plain,
( spl86_580
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),sK84(X0,X1,X2,X3,X4)),X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_580])]) ).
fof(f2725,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),sK84(X0,X1,X2,X3,X4)),X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(cnf_transformation,[],[f1921]) ).
fof(f20881,plain,
spl86_579,
inference(avatar_split_clause,[],[f2721,f20879]) ).
fof(f20879,plain,
( spl86_579
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,sK82(X0,X1,X2,X3,X4))),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_579])]) ).
fof(f2721,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,sK82(X0,X1,X2,X3,X4))),X3)) ),
inference(cnf_transformation,[],[f1913]) ).
fof(f1913,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)),X3))
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,sK82(X0,X1,X2,X3,X4))),X3))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK82(X0,X1,X2,X3,X4)),X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f1627,f1912]) ).
fof(f1912,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X5)),X3))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) )
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,sK82(X0,X1,X2,X3,X4))),X3))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK82(X0,X1,X2,X3,X4)),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f1627,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)),X3))
| ? [X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X5)),X3))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ) ),
inference(ennf_transformation,[],[f1132]) ).
fof(f1132,plain,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X5)),X3)) )
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)),X3)) ),
inference(rectify,[],[f149]) ).
fof(f149,axiom,
! [X1,X0,X11,X12,X7] :
( ! [X32] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X7))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X0,X1,X11,X32)),X12)) )
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X7)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_image__subsetI) ).
fof(f20400,plain,
spl86_578,
inference(avatar_split_clause,[],[f2952,f20398]) ).
fof(f20398,plain,
( spl86_578
<=> ! [X2,X4,X0,X3,X5,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| hAPP(X1,X0,X3,X5) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_578])]) ).
fof(f2952,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| hAPP(X1,X0,X3,X5) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(definition_unfolding,[],[f2724,f2190]) ).
fof(f2724,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ti(X0,X2) != hAPP(X1,X0,X3,X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ),
inference(cnf_transformation,[],[f1917]) ).
fof(f1917,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ! [X5] :
( ti(X0,X2) != hAPP(X1,X0,X3,X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ) )
& ( ( ti(X0,X2) = hAPP(X1,X0,X3,sK83(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK83(X0,X1,X2,X3,X4)),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f1915,f1916]) ).
fof(f1916,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( ti(X0,X2) = hAPP(X1,X0,X3,X6)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4)) )
=> ( ti(X0,X2) = hAPP(X1,X0,X3,sK83(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK83(X0,X1,X2,X3,X4)),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f1915,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ! [X5] :
( ti(X0,X2) != hAPP(X1,X0,X3,X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ) )
& ( ? [X6] :
( ti(X0,X2) = hAPP(X1,X0,X3,X6)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
inference(rectify,[],[f1914]) ).
fof(f1914,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ! [X5] :
( ti(X0,X2) != hAPP(X1,X0,X3,X5)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ) )
& ( ? [X5] :
( ti(X0,X2) = hAPP(X1,X0,X3,X5)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
inference(nnf_transformation,[],[f1133]) ).
fof(f1133,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
<=> ? [X5] :
( ti(X0,X2) = hAPP(X1,X0,X3,X5)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ) ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X0,X1,X41,X11,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X41),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X7)))
<=> ? [X32] :
( ti(X0,X41) = hAPP(X1,X0,X11,X32)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X32),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_image__iff) ).
fof(f20396,plain,
spl86_577,
inference(avatar_split_clause,[],[f2506,f20394]) ).
fof(f20394,plain,
( spl86_577
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_577])]) ).
fof(f2506,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1488]) ).
fof(f1488,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1008]) ).
fof(f1008,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))),X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)) ),
inference(rectify,[],[f336]) ).
fof(f336,axiom,
! [X17,X24,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X26))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X24))),X17) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X26)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X24),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_diff__Suc__diff__eq2) ).
fof(f20392,plain,
spl86_576,
inference(avatar_split_clause,[],[f2505,f20390]) ).
fof(f20390,plain,
( spl86_576
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,suc,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_576])]) ).
fof(f2505,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,suc,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1487]) ).
fof(f1487,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,suc,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1007]) ).
fof(f1007,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,suc,X2)) ),
inference(rectify,[],[f337]) ).
fof(f337,axiom,
! [X17,X24,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X26))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X24))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X24)),hAPP(nat,nat,suc,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_diff__Suc__diff__eq1) ).
fof(f20043,plain,
( spl86_575
| ~ spl86_108
| ~ spl86_165
| ~ spl86_574 ),
inference(avatar_split_clause,[],[f20039,f20036,f4161,f3698,f20041]) ).
fof(f20041,plain,
( spl86_575
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_575])]) ).
fof(f20036,plain,
( spl86_574
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X4) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_574])]) ).
fof(f20039,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) )
| ~ spl86_108
| ~ spl86_165
| ~ spl86_574 ),
inference(forward_demodulation,[],[f20037,f4223]) ).
fof(f20037,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X4) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) )
| ~ spl86_574 ),
inference(avatar_component_clause,[],[f20036]) ).
fof(f20038,plain,
spl86_574,
inference(avatar_split_clause,[],[f3161,f20036]) ).
fof(f3161,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X4) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(forward_demodulation,[],[f2705,f2226]) ).
fof(f2705,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(cnf_transformation,[],[f1607]) ).
fof(f1607,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X4)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(ennf_transformation,[],[f1120]) ).
fof(f1120,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X4) ),
inference(rectify,[],[f186]) ).
fof(f186,axiom,
! [X1,X0,X34,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),hAPP(X1,fun(X0,X1),combk(X1,X0),X34)),X7) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),bot_bot(fun(X1,bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_image__constant) ).
fof(f20034,plain,
spl86_573,
inference(avatar_split_clause,[],[f2929,f20032]) ).
fof(f20032,plain,
( spl86_573
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_573])]) ).
fof(f2929,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ),
inference(definition_unfolding,[],[f2639,f2190,f2190]) ).
fof(f2639,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ),
inference(cnf_transformation,[],[f1588]) ).
fof(f1588,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ),
inference(flattening,[],[f1587]) ).
fof(f1587,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ),
inference(ennf_transformation,[],[f1093]) ).
fof(f1093,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
=> ( ti(X0,X1) != ti(X0,X2)
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) ) ),
inference(rectify,[],[f107]) ).
fof(f107,axiom,
! [X0,X10,X33,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),X7)))
=> ( ti(X0,X33) != ti(X0,X10)
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_insertE) ).
fof(f20030,plain,
spl86_572,
inference(avatar_split_clause,[],[f2858,f20028]) ).
fof(f20028,plain,
( spl86_572
<=> ! [X0,X1] : finite1357897459simple(X0,X1) = hAPP(fun(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)))),fun(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)))),combi(fun(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool))))),finite1357897459simple(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_572])]) ).
fof(f2858,plain,
! [X0,X1] : finite1357897459simple(X0,X1) = hAPP(fun(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)))),fun(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)))),combi(fun(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool))))),finite1357897459simple(X0,X1)),
inference(definition_unfolding,[],[f2211,f2190]) ).
fof(f2211,plain,
! [X0,X1] : finite1357897459simple(X0,X1) = ti(fun(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)))),finite1357897459simple(X0,X1)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : finite1357897459simple(X0,X1) = ti(fun(fun(X0,fun(X0,X0)),fun(X0,fun(fun(X1,X0),fun(fun(fun(X1,bool),X0),bool)))),finite1357897459simple(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__image__simple_res) ).
fof(f20026,plain,
spl86_571,
inference(avatar_split_clause,[],[f2701,f20024]) ).
fof(f20024,plain,
( spl86_571
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK78(X0,X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_571])]) ).
fof(f2701,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK78(X0,X1,X2,X3,X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(cnf_transformation,[],[f1907]) ).
fof(f20022,plain,
spl86_570,
inference(avatar_split_clause,[],[f2548,f20020]) ).
fof(f20020,plain,
( spl86_570
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2,X0)),X1)),hAPP(nat,nat,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,sK67(X2))),hAPP(nat,nat,X2,sK68(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_570])]) ).
fof(f2548,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2,X0)),X1)),hAPP(nat,nat,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,sK67(X2))),hAPP(nat,nat,X2,sK68(X2)))) ),
inference(cnf_transformation,[],[f1846]) ).
fof(f1846,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2,X0)),X1)),hAPP(nat,nat,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,sK67(X2))),hAPP(nat,nat,X2,sK68(X2))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK67(X2)),sK68(X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f1524,f1845]) ).
fof(f1845,plain,
! [X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,X3)),hAPP(nat,nat,X2,X4)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) )
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,sK67(X2))),hAPP(nat,nat,X2,sK68(X2))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK67(X2)),sK68(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f1524,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2,X0)),X1)),hAPP(nat,nat,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))))
| ? [X3,X4] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,X3)),hAPP(nat,nat,X2,X4)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ) ),
inference(ennf_transformation,[],[f1034]) ).
fof(f1034,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,X3)),hAPP(nat,nat,X2,X4))) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2,X0)),X1)),hAPP(nat,nat,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)))) ),
inference(rectify,[],[f458]) ).
fof(f458,axiom,
! [X27,X18,X11] :
( ! [X37,X31] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X37),X31))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X11,X37)),hAPP(nat,nat,X11,X31))) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X11,X27)),X18)),hAPP(nat,nat,X11,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X18)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_mono__nat__linear__lb) ).
fof(f20018,plain,
spl86_569,
inference(avatar_split_clause,[],[f2447,f20016]) ).
fof(f20016,plain,
( spl86_569
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),X2))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_569])]) ).
fof(f2447,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),X2))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1425]) ).
fof(f1425,plain,
! [X0,X1,X2] :
( ( ( hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),X2))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) )
& ( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f963]) ).
fof(f963,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),X2)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) ) ) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X0,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)) = hAPP(nat,nat,suc,hAPP(fun(X0,bool),nat,finite_card(X0),X7)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hAPP(fun(X0,bool),nat,finite_card(X0),X7) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_card__insert__if) ).
fof(f19280,plain,
spl86_568,
inference(avatar_split_clause,[],[f2720,f19278]) ).
fof(f19278,plain,
( spl86_568
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK82(X0,X1,X2,X3,X4)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_568])]) ).
fof(f2720,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)),X3))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK82(X0,X1,X2,X3,X4)),X4)) ),
inference(cnf_transformation,[],[f1913]) ).
fof(f19276,plain,
spl86_567,
inference(avatar_split_clause,[],[f2250,f19274]) ).
fof(f19274,plain,
( spl86_567
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
| hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_567])]) ).
fof(f2250,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
| hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f1710]) ).
fof(f1710,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
| hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) )
& ( ( ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
& hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) )
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3)) ) )
| ~ ord(X1) ),
inference(flattening,[],[f1709]) ).
fof(f1709,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
| hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) )
& ( ( ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
& hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) )
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3)) ) )
| ~ ord(X1) ),
inference(nnf_transformation,[],[f1329]) ).
fof(f1329,plain,
! [X0,X1] :
( ! [X2,X3] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
<=> ( ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
& hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) ) )
| ~ ord(X1) ),
inference(ennf_transformation,[],[f838]) ).
fof(f838,plain,
! [X0,X1] :
( ord(X1)
=> ! [X2,X3] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
<=> ( ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
& hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) ) ) ),
inference(rectify,[],[f467]) ).
fof(f467,axiom,
! [X0,X1] :
( ord(X1)
=> ! [X11,X39] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X11),X39))
<=> ( ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X39),X11))
& hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X11),X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_less__fun__def) ).
fof(f19272,plain,
spl86_566,
inference(avatar_split_clause,[],[f2179,f19270]) ).
fof(f19270,plain,
( spl86_566
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,sK11(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK11(X0,X3)))))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_566])]) ).
fof(f2179,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,sK11(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK11(X0,X3)))))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1695]) ).
fof(f1695,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,sK11(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK11(X0,X3))))) )
| ~ order(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f1317,f1694]) ).
fof(f1694,plain,
! [X0,X3] :
( ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4))))
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,sK11(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK11(X0,X3))))) ),
introduced(choice_axiom,[]) ).
fof(f1317,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4)))) )
| ~ order(X0) ),
inference(flattening,[],[f1316]) ).
fof(f1316,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4)))) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f778]) ).
fof(f778,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( ! [X4] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2))) ) ) ),
inference(rectify,[],[f101]) ).
fof(f101,axiom,
! [X0] :
( order(X0)
=> ! [X19,X30,X11] :
( ! [X31] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X11,X31)),hAPP(nat,X0,X11,hAPP(nat,nat,suc,X31))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X30))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(nat,X0,X11,X19)),hAPP(nat,X0,X11,X30))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lift__Suc__mono__le) ).
fof(f19268,plain,
spl86_565,
inference(avatar_split_clause,[],[f2178,f19266]) ).
fof(f19266,plain,
( spl86_565
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK10(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK10(X0,X3)))))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_565])]) ).
fof(f2178,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK10(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK10(X0,X3)))))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1693]) ).
fof(f1693,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2))) ) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK10(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK10(X0,X3))))) )
| ~ order(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f1691,f1692]) ).
fof(f1692,plain,
! [X0,X3] :
( ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4))))
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK10(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK10(X0,X3))))) ),
introduced(choice_axiom,[]) ).
fof(f1691,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2))) ) )
| ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4)))) )
| ~ order(X0) ),
inference(nnf_transformation,[],[f1315]) ).
fof(f1315,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
| ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4)))) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f777]) ).
fof(f777,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( ! [X4] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4))))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ) ),
inference(rectify,[],[f475]) ).
fof(f475,axiom,
! [X0] :
( order(X0)
=> ! [X19,X27,X11] :
( ! [X31] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X11,X31)),hAPP(nat,X0,X11,hAPP(nat,nat,suc,X31))))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X11,X19)),hAPP(nat,X0,X11,X27)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X19),X27)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_lift__Suc__mono__less__iff) ).
fof(f19264,plain,
spl86_564,
inference(avatar_split_clause,[],[f2177,f19262]) ).
fof(f19262,plain,
( spl86_564
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK10(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK10(X0,X3)))))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_564])]) ).
fof(f2177,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK10(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK10(X0,X3)))))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1693]) ).
fof(f19253,plain,
spl86_563,
inference(avatar_split_clause,[],[f2176,f19251]) ).
fof(f19251,plain,
( spl86_563
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK9(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK9(X0,X3)))))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_563])]) ).
fof(f2176,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK9(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK9(X0,X3)))))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1690]) ).
fof(f1690,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK9(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK9(X0,X3))))) )
| ~ order(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f1314,f1689]) ).
fof(f1689,plain,
! [X0,X3] :
( ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4))))
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,sK9(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK9(X0,X3))))) ),
introduced(choice_axiom,[]) ).
fof(f1314,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4)))) )
| ~ order(X0) ),
inference(flattening,[],[f1313]) ).
fof(f1313,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ? [X4] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4)))) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f776]) ).
fof(f776,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( ! [X4] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X4)),hAPP(nat,X0,X3,hAPP(nat,nat,suc,X4))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X3,X1)),hAPP(nat,X0,X3,X2))) ) ) ),
inference(rectify,[],[f472]) ).
fof(f472,axiom,
! [X0] :
( order(X0)
=> ! [X19,X30,X11] :
( ! [X31] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X11,X31)),hAPP(nat,X0,X11,hAPP(nat,nat,suc,X31))))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X19),X30))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(nat,X0,X11,X19)),hAPP(nat,X0,X11,X30))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_lift__Suc__mono__less) ).
fof(f19218,plain,
spl86_562,
inference(avatar_split_clause,[],[f3151,f19216]) ).
fof(f19216,plain,
( spl86_562
<=> ! [X0,X3,X2,X1] :
( bot_bot(fun(X1,bool)) != hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) = bot_bot(fun(sum_sum(X1,X0),bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_562])]) ).
fof(f3151,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X1,bool)) != hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) = bot_bot(fun(sum_sum(X1,X0),bool)) ),
inference(forward_demodulation,[],[f3150,f2854]) ).
fof(f3150,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) = bot_bot(fun(sum_sum(X1,X0),bool))
| bot_bot(fun(X1,bool)) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) ),
inference(forward_demodulation,[],[f2939,f2854]) ).
fof(f2939,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) = bot_bot(fun(sum_sum(X1,X0),bool))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X3)
| bot_bot(fun(X1,bool)) != hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2) ),
inference(definition_unfolding,[],[f2660,f2190,f2190]) ).
fof(f2660,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) = bot_bot(fun(sum_sum(X1,X0),bool))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X3)
| bot_bot(fun(X1,bool)) != ti(fun(X1,bool),X2) ),
inference(cnf_transformation,[],[f1885]) ).
fof(f1885,plain,
! [X0,X1,X2,X3] :
( ( hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) = bot_bot(fun(sum_sum(X1,X0),bool))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X3)
| bot_bot(fun(X1,bool)) != ti(fun(X1,bool),X2) )
& ( ( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X3)
& bot_bot(fun(X1,bool)) = ti(fun(X1,bool),X2) )
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ) ),
inference(flattening,[],[f1884]) ).
fof(f1884,plain,
! [X0,X1,X2,X3] :
( ( hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) = bot_bot(fun(sum_sum(X1,X0),bool))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X3)
| bot_bot(fun(X1,bool)) != ti(fun(X1,bool),X2) )
& ( ( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X3)
& bot_bot(fun(X1,bool)) = ti(fun(X1,bool),X2) )
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ) ),
inference(nnf_transformation,[],[f1106]) ).
fof(f1106,plain,
! [X0,X1,X2,X3] :
( hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) = bot_bot(fun(sum_sum(X1,X0),bool))
<=> ( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X3)
& bot_bot(fun(X1,bool)) = ti(fun(X1,bool),X2) ) ),
inference(rectify,[],[f498]) ).
fof(f498,axiom,
! [X1,X0,X7,X12] :
( hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X7),X12) = bot_bot(fun(sum_sum(X0,X1),bool))
<=> ( bot_bot(fun(X1,bool)) = ti(fun(X1,bool),X12)
& ti(fun(X0,bool),X7) = bot_bot(fun(X0,bool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_Plus__eq__empty__conv) ).
fof(f19175,plain,
( spl86_561
| ~ spl86_108
| ~ spl86_165
| ~ spl86_560 ),
inference(avatar_split_clause,[],[f19171,f19168,f4161,f3698,f19173]) ).
fof(f19173,plain,
( spl86_561
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3)
| bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_561])]) ).
fof(f19168,plain,
( spl86_560
<=> ! [X0,X3,X2,X1] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)
| hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_560])]) ).
fof(f19171,plain,
( ! [X2,X3,X0,X1] :
( hAPP(X0,fun(X0,bool),fequal(X0),X2) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3)
| bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3) )
| ~ spl86_108
| ~ spl86_165
| ~ spl86_560 ),
inference(forward_demodulation,[],[f19169,f4223]) ).
fof(f19169,plain,
( ! [X2,X3,X0,X1] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)
| hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)) )
| ~ spl86_560 ),
inference(avatar_component_clause,[],[f19168]) ).
fof(f19170,plain,
spl86_560,
inference(avatar_split_clause,[],[f3131,f19168]) ).
fof(f3131,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)
| hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2)) ),
inference(forward_demodulation,[],[f3130,f2854]) ).
fof(f3130,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))
| bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(forward_demodulation,[],[f2921,f2226]) ).
fof(f2921,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3)
| bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X3) ),
inference(definition_unfolding,[],[f2594,f2190]) ).
fof(f2594,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3)
| bot_bot(fun(X1,bool)) = ti(fun(X1,bool),X3) ),
inference(cnf_transformation,[],[f1530]) ).
fof(f1530,plain,
! [X0,X1,X2,X3] :
( ( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3)
| bot_bot(fun(X1,bool)) = ti(fun(X1,bool),X3) )
& ( bot_bot(fun(X0,bool)) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3)
| bot_bot(fun(X1,bool)) != ti(fun(X1,bool),X3) ) ),
inference(ennf_transformation,[],[f1059]) ).
fof(f1059,plain,
! [X0,X1,X2,X3] :
( ( bot_bot(fun(X1,bool)) != ti(fun(X1,bool),X3)
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3) )
& ( bot_bot(fun(X1,bool)) = ti(fun(X1,bool),X3)
=> bot_bot(fun(X0,bool)) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),hAPP(X0,fun(X1,X0),combk(X0,X1),X2)),X3) ) ),
inference(rectify,[],[f187]) ).
fof(f187,axiom,
! [X1,X0,X34,X7] :
( ( ti(fun(X0,bool),X7) != bot_bot(fun(X0,bool))
=> hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),hAPP(X1,fun(X0,X1),combk(X1,X0),X34)),X7) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X34),bot_bot(fun(X1,bool))) )
& ( ti(fun(X0,bool),X7) = bot_bot(fun(X0,bool))
=> bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),hAPP(X1,fun(X0,X1),combk(X1,X0),X34)),X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_image__constant__conv) ).
fof(f19166,plain,
spl86_559,
inference(avatar_split_clause,[],[f2526,f19164]) ).
fof(f19164,plain,
( spl86_559
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK65(X0,X1,X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_559])]) ).
fof(f2526,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK65(X0,X1,X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(cnf_transformation,[],[f1840]) ).
fof(f1840,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK65(X0,X1,X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f1507,f1839]) ).
fof(f1839,plain,
! [X0,X1,X2] :
( ? [X3] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK65(X0,X1,X2)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ),
introduced(choice_axiom,[]) ).
fof(f1507,plain,
! [X0,X1,X2] :
( ? [X3] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(ennf_transformation,[],[f1021]) ).
fof(f1021,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
=> ? [X3] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ),
inference(rectify,[],[f479]) ).
fof(f479,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12))
=> ? [X70] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X70),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X12),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_psubset__imp__ex__mem) ).
fof(f18483,plain,
spl86_558,
inference(avatar_split_clause,[],[f3119,f18481]) ).
fof(f18481,plain,
( spl86_558
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_558])]) ).
fof(f3119,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(forward_demodulation,[],[f3118,f2854]) ).
fof(f3118,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(forward_demodulation,[],[f2909,f2854]) ).
fof(f2909,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(definition_unfolding,[],[f2560,f2190,f2190]) ).
fof(f2560,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(cnf_transformation,[],[f1855]) ).
fof(f1855,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) )
& ( ( ti(fun(X0,bool),X1) != ti(fun(X0,bool),X2)
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ) ),
inference(flattening,[],[f1854]) ).
fof(f1854,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) )
& ( ( ti(fun(X0,bool),X1) != ti(fun(X0,bool),X2)
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ) ),
inference(nnf_transformation,[],[f1039]) ).
fof(f1039,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
<=> ( ti(fun(X0,bool),X1) != ti(fun(X0,bool),X2)
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
inference(rectify,[],[f465]) ).
fof(f465,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12))
<=> ( ti(fun(X0,bool),X7) != ti(fun(X0,bool),X12)
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_psubset__eq) ).
fof(f18472,plain,
spl86_557,
inference(avatar_split_clause,[],[f3106,f18470]) ).
fof(f18470,plain,
( spl86_557
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_557])]) ).
fof(f3106,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(forward_demodulation,[],[f3105,f2854]) ).
fof(f3105,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(forward_demodulation,[],[f2900,f2854]) ).
fof(f2900,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(definition_unfolding,[],[f2528,f2190,f2190]) ).
fof(f2528,plain,
! [X2,X0,X1] :
( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(cnf_transformation,[],[f1511]) ).
fof(f1511,plain,
! [X0,X1,X2] :
( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(flattening,[],[f1510]) ).
fof(f1510,plain,
! [X0,X1,X2] :
( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(ennf_transformation,[],[f1023]) ).
fof(f1023,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
=> ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2) ) ),
inference(rectify,[],[f104]) ).
fof(f104,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X7))
=> ti(fun(X0,bool),X7) = ti(fun(X0,bool),X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_equalityI) ).
fof(f18468,plain,
spl86_556,
inference(avatar_split_clause,[],[f2796,f18466]) ).
fof(f18466,plain,
( spl86_556
<=> ! [X2,X0,X1] :
( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| zero_zero(X0) != hAPP(X0,X0,combi(X0),X1)
| zero_zero(X0) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_556])]) ).
fof(f2796,plain,
! [X2,X0,X1] :
( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| zero_zero(X0) != hAPP(X0,X0,combi(X0),X1)
| zero_zero(X0) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ),
inference(definition_unfolding,[],[f2056,f2190,f2190]) ).
fof(f2056,plain,
! [X2,X0,X1] :
( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| zero_zero(X0) != ti(X0,X1)
| zero_zero(X0) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f1662]) ).
fof(f1662,plain,
! [X0] :
( ! [X1,X2] :
( ( ( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| zero_zero(X0) != ti(X0,X1)
| zero_zero(X0) != ti(X0,X2) )
& ( ( zero_zero(X0) = ti(X0,X1)
& zero_zero(X0) = ti(X0,X2) )
| zero_zero(X0) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1) ) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2)) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f1661]) ).
fof(f1661,plain,
! [X0] :
( ! [X1,X2] :
( ( ( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| zero_zero(X0) != ti(X0,X1)
| zero_zero(X0) != ti(X0,X2) )
& ( ( zero_zero(X0) = ti(X0,X1)
& zero_zero(X0) = ti(X0,X2) )
| zero_zero(X0) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1) ) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2)) )
| ~ ordere216010020id_add(X0) ),
inference(nnf_transformation,[],[f1187]) ).
fof(f1187,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
<=> ( zero_zero(X0) = ti(X0,X1)
& zero_zero(X0) = ti(X0,X2) ) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2)) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f1186]) ).
fof(f1186,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
<=> ( zero_zero(X0) = ti(X0,X1)
& zero_zero(X0) = ti(X0,X2) ) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2)) )
| ~ ordere216010020id_add(X0) ),
inference(ennf_transformation,[],[f682]) ).
fof(f682,plain,
! [X0] :
( ordere216010020id_add(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
=> ( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
<=> ( zero_zero(X0) = ti(X0,X1)
& zero_zero(X0) = ti(X0,X2) ) ) ) ) ),
inference(rectify,[],[f515]) ).
fof(f515,axiom,
! [X0] :
( ordere216010020id_add(X0)
=> ! [X38,X13] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X13))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X38))
=> ( zero_zero(X0) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X13),X38)
<=> ( zero_zero(X0) = ti(X0,X38)
& zero_zero(X0) = ti(X0,X13) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_add__nonneg__eq__0__iff) ).
fof(f18464,plain,
spl86_555,
inference(avatar_split_clause,[],[f2634,f18462]) ).
fof(f18462,plain,
( spl86_555
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_555])]) ).
fof(f2634,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1580]) ).
fof(f1580,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(flattening,[],[f1579]) ).
fof(f1579,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(ennf_transformation,[],[f1088]) ).
fof(f1088,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X0,X40,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X40))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_subset__trans) ).
fof(f18460,plain,
spl86_554,
inference(avatar_split_clause,[],[f2633,f18458]) ).
fof(f18458,plain,
( spl86_554
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_554])]) ).
fof(f2633,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1578]) ).
fof(f1578,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(flattening,[],[f1577]) ).
fof(f1577,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(ennf_transformation,[],[f1087]) ).
fof(f1087,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1)) ) ),
inference(rectify,[],[f461]) ).
fof(f461,axiom,
! [X0,X40,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X12),X40))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_subset__psubset__trans) ).
fof(f18456,plain,
spl86_553,
inference(avatar_split_clause,[],[f2627,f18454]) ).
fof(f18454,plain,
( spl86_553
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_553])]) ).
fof(f2627,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1568]) ).
fof(f1568,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(flattening,[],[f1567]) ).
fof(f1567,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(ennf_transformation,[],[f1081]) ).
fof(f1081,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1)) ) ),
inference(rectify,[],[f462]) ).
fof(f462,axiom,
! [X0,X40,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),X40))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_psubset__subset__trans) ).
fof(f18452,plain,
spl86_552,
inference(avatar_split_clause,[],[f2626,f18450]) ).
fof(f18450,plain,
( spl86_552
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_552])]) ).
fof(f2626,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1566]) ).
fof(f1566,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(flattening,[],[f1565]) ).
fof(f1565,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(ennf_transformation,[],[f1080]) ).
fof(f1080,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X3),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X1)) ) ),
inference(rectify,[],[f474]) ).
fof(f474,axiom,
! [X0,X40,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X12),X40))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_psubset__trans) ).
fof(f18448,plain,
spl86_551,
inference(avatar_split_clause,[],[f2069,f18446]) ).
fof(f18446,plain,
( spl86_551
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_551])]) ).
fof(f2069,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f1203]) ).
fof(f1203,plain,
! [X0] :
( ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4)) )
| ~ ordere223160158up_add(X0) ),
inference(flattening,[],[f1202]) ).
fof(f1202,plain,
! [X0] :
( ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4)) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f693]) ).
fof(f693,plain,
! [X0] :
( ordere223160158up_add(X0)
=> ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2))) ) ) ),
inference(rectify,[],[f440]) ).
fof(f440,axiom,
! [X2] :
( ordere223160158up_add(X2)
=> ! [X51,X61,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),X52))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X51),X61))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X61))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_add__le__less__mono) ).
fof(f18444,plain,
spl86_550,
inference(avatar_split_clause,[],[f2068,f18442]) ).
fof(f18442,plain,
( spl86_550
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4))
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_550])]) ).
fof(f2068,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4))
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f1201]) ).
fof(f1201,plain,
! [X0] :
( ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4)) )
| ~ ordere223160158up_add(X0) ),
inference(flattening,[],[f1200]) ).
fof(f1200,plain,
! [X0] :
( ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4)) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f692]) ).
fof(f692,plain,
! [X0] :
( ordere223160158up_add(X0)
=> ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2))) ) ) ),
inference(rectify,[],[f441]) ).
fof(f441,axiom,
! [X2] :
( ordere223160158up_add(X2)
=> ! [X51,X61,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),X52))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X51),X61))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X61))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_add__less__le__mono) ).
fof(f18440,plain,
spl86_549,
inference(avatar_split_clause,[],[f2067,f18438]) ).
fof(f18438,plain,
( spl86_549
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4))
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_549])]) ).
fof(f2067,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4))
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f1199]) ).
fof(f1199,plain,
! [X0] :
( ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4)) )
| ~ ordere223160158up_add(X0) ),
inference(flattening,[],[f1198]) ).
fof(f1198,plain,
! [X0] :
( ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4)) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f691]) ).
fof(f691,plain,
! [X0] :
( ordere223160158up_add(X0)
=> ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X4))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2))) ) ) ),
inference(rectify,[],[f359]) ).
fof(f359,axiom,
! [X2] :
( ordere223160158up_add(X2)
=> ! [X51,X61,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),X52))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X51),X61))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X61))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_add__strict__mono) ).
fof(f18436,plain,
spl86_548,
inference(avatar_split_clause,[],[f2050,f18434]) ).
fof(f18434,plain,
( spl86_548
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
| ~ ordere779506340up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_548])]) ).
fof(f2050,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
| ~ ordere779506340up_add(X0) ),
inference(cnf_transformation,[],[f1180]) ).
fof(f1180,plain,
! [X0] :
( ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4)) )
| ~ ordere779506340up_add(X0) ),
inference(flattening,[],[f1179]) ).
fof(f1179,plain,
! [X0] :
( ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4)) )
| ~ ordere779506340up_add(X0) ),
inference(ennf_transformation,[],[f678]) ).
fof(f678,plain,
! [X0] :
( ordere779506340up_add(X0)
=> ! [X1,X2,X3,X4] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X4))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X4),X2))) ) ) ),
inference(rectify,[],[f285]) ).
fof(f285,axiom,
! [X2] :
( ordere779506340up_add(X2)
=> ! [X51,X61,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),X52))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X51),X61))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X61))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_add__mono) ).
fof(f18388,plain,
( spl86_547
| ~ spl86_109
| ~ spl86_165
| ~ spl86_546 ),
inference(avatar_split_clause,[],[f18384,f18381,f4161,f3702,f18386]) ).
fof(f18386,plain,
( spl86_547
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1))))
| hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK18(X0)),u))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_547])]) ).
fof(f18381,plain,
( spl86_546
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1)))))
| hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK18(X0)),u))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_546])]) ).
fof(f18384,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1))))
| hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK18(X0)),u))
| ~ hBOOL(hAPP(com,bool,wt,X1)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_546 ),
inference(forward_demodulation,[],[f18382,f4236]) ).
fof(f18382,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1)))))
| hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK18(X0)),u))
| ~ hBOOL(hAPP(com,bool,wt,X1)) )
| ~ spl86_546 ),
inference(avatar_component_clause,[],[f18381]) ).
fof(f18383,plain,
spl86_546,
inference(avatar_split_clause,[],[f3009,f18381]) ).
fof(f3009,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),hAPP(x_a,fun(x_a,bool),fequal(x_a),hAPP(com,x_a,mgt,X1)))))
| hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK18(X0)),u))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ),
inference(forward_demodulation,[],[f2259,f2226]) ).
fof(f2259,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(com,x_a,mgt,X1)),bot_bot(fun(x_a,bool)))))
| hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),sK18(X0)),u))
| ~ hBOOL(hAPP(com,bool,wt,X1)) ),
inference(cnf_transformation,[],[f1716]) ).
fof(f18379,plain,
spl86_545,
inference(avatar_split_clause,[],[f2446,f18377]) ).
fof(f18377,plain,
( spl86_545
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_545])]) ).
fof(f2446,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),nat,finite_card(X0),X2) = hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1425]) ).
fof(f17818,plain,
( spl86_544
| ~ spl86_109
| ~ spl86_165
| ~ spl86_543 ),
inference(avatar_split_clause,[],[f17814,f17811,f4161,f3702,f17816]) ).
fof(f17816,plain,
( spl86_544
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(X0,fun(X0,bool),fequal(X0),sK61(X0,X1))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_544])]) ).
fof(f17811,plain,
( spl86_543
<=> ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK61(X0,X1)))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_543])]) ).
fof(f17814,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(X0,fun(X0,bool),fequal(X0),sK61(X0,X1))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_543 ),
inference(forward_demodulation,[],[f17812,f4236]) ).
fof(f17812,plain,
( ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK61(X0,X1)))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
| ~ spl86_543 ),
inference(avatar_component_clause,[],[f17811]) ).
fof(f17813,plain,
spl86_543,
inference(avatar_split_clause,[],[f3079,f17811]) ).
fof(f3079,plain,
! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK61(X0,X1)))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f3078,f2854]) ).
fof(f3078,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),sK61(X0,X1)))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2890,f2226]) ).
fof(f2890,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK61(X0,X1)),bot_bot(fun(X0,bool)))))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(definition_unfolding,[],[f2459,f2190]) ).
fof(f2459,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK61(X0,X1)),bot_bot(fun(X0,bool)))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1828]) ).
fof(f1828,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK61(X0,X1)),bot_bot(fun(X0,bool)))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f1646,f1827]) ).
fof(f1827,plain,
! [X0,X1] :
( ? [X3] : ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))))
=> ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK61(X0,X1)),bot_bot(fun(X0,bool))))) ),
introduced(choice_axiom,[]) ).
fof(f1646,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| sP2(X0,X1)
| ? [X3] : ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(definition_folding,[],[f1430,f1645]) ).
fof(f1645,plain,
! [X0,X1] :
( ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X5)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5)) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f1430,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X5)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5)) )
| ? [X3] : ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1429]) ).
fof(f1429,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X5)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5)) )
| ? [X3] : ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f966]) ).
fof(f966,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X2)
=> ( ! [X3] : hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),bot_bot(fun(X0,bool)))))
=> ( ! [X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X5)
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
=> hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5))) ) ) ) )
=> hBOOL(hAPP(fun(X0,bool),bool,X1,X2)) ) ) ) ),
inference(rectify,[],[f213]) ).
fof(f213,axiom,
! [X0,X15,X9] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X9))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X9)
=> ( ! [X32] : hBOOL(hAPP(fun(X0,bool),bool,X15,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X32),bot_bot(fun(X0,bool)))))
=> ( ! [X32,X54] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X54))
=> ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X54)
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X54))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X15,X54))
=> hBOOL(hAPP(fun(X0,bool),bool,X15,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X32),X54))) ) ) ) )
=> hBOOL(hAPP(fun(X0,bool),bool,X15,X9)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_finite__ne__induct) ).
fof(f17809,plain,
spl86_542,
inference(avatar_split_clause,[],[f2722,f17807]) ).
fof(f17807,plain,
( spl86_542
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK83(X0,X1,X2,X3,X4)),X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_542])]) ).
fof(f2722,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK83(X0,X1,X2,X3,X4)),X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(cnf_transformation,[],[f1917]) ).
fof(f17805,plain,
( ~ spl86_19
| spl86_541
| ~ spl86_27
| ~ spl86_103
| ~ spl86_166
| ~ spl86_196 ),
inference(avatar_split_clause,[],[f4594,f4436,f4165,f3678,f3311,f17803,f3271]) ).
fof(f17803,plain,
( spl86_541
<=> ! [X0] :
( ~ sP3(X0,zero_zero(nat),ord_less(nat))
| zero_zero(nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_541])]) ).
fof(f4594,plain,
( ! [X0] :
( ~ sP3(X0,zero_zero(nat),ord_less(nat))
| zero_zero(nat) = X0
| ~ bot(nat) )
| ~ spl86_27
| ~ spl86_103
| ~ spl86_166
| ~ spl86_196 ),
inference(forward_demodulation,[],[f4593,f3313]) ).
fof(f4593,plain,
( ! [X0] :
( zero_zero(nat) = X0
| ~ bot(nat)
| ~ sP3(X0,bot_bot(nat),ord_less(nat)) )
| ~ spl86_27
| ~ spl86_103
| ~ spl86_166
| ~ spl86_196 ),
inference(forward_demodulation,[],[f4592,f3313]) ).
fof(f4592,plain,
( ! [X0] :
( bot_bot(nat) = X0
| ~ bot(nat)
| ~ sP3(X0,bot_bot(nat),ord_less(nat)) )
| ~ spl86_103
| ~ spl86_166
| ~ spl86_196 ),
inference(forward_demodulation,[],[f4583,f4166]) ).
fof(f4583,plain,
( ! [X0] :
( bot_bot(nat) = hAPP(nat,nat,combi(nat),X0)
| ~ bot(nat)
| ~ sP3(X0,bot_bot(nat),ord_less(nat)) )
| ~ spl86_103
| ~ spl86_196 ),
inference(resolution,[],[f4437,f3679]) ).
fof(f17801,plain,
spl86_540,
inference(avatar_split_clause,[],[f2719,f17799]) ).
fof(f17799,plain,
( spl86_540
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK81(X0,X1,X2,X3,X4)),X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_540])]) ).
fof(f2719,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK81(X0,X1,X2,X3,X4)),X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(cnf_transformation,[],[f1911]) ).
fof(f1911,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK81(X0,X1,X2,X3,X4)),X4))
& ti(X0,X2) = hAPP(X1,X0,X3,sK81(X0,X1,X2,X3,X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f1626,f1910]) ).
fof(f1910,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
& ti(X0,X2) = hAPP(X1,X0,X3,X5) )
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK81(X0,X1,X2,X3,X4)),X4))
& ti(X0,X2) = hAPP(X1,X0,X3,sK81(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f1626,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
& ti(X0,X2) = hAPP(X1,X0,X3,X5) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(ennf_transformation,[],[f1131]) ).
fof(f1131,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
=> ~ ! [X5] :
( ti(X0,X2) = hAPP(X1,X0,X3,X5)
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4)) ) ),
inference(rectify,[],[f147]) ).
fof(f147,axiom,
! [X0,X1,X33,X11,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X33),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X7)))
=> ~ ! [X32] :
( ti(X0,X33) = hAPP(X1,X0,X11,X32)
=> ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X32),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_imageE) ).
fof(f17797,plain,
spl86_539,
inference(avatar_split_clause,[],[f2699,f17795]) ).
fof(f2699,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(cnf_transformation,[],[f1602]) ).
fof(f1602,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(flattening,[],[f1601]) ).
fof(f1601,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4)) ),
inference(ennf_transformation,[],[f1116]) ).
fof(f1116,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4)))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X1,X0,X12,X11,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X12),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X7)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_finite__surj) ).
fof(f17793,plain,
spl86_538,
inference(avatar_split_clause,[],[f2693,f17791]) ).
fof(f17791,plain,
( spl86_538
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_538])]) ).
fof(f2693,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3)) ),
inference(cnf_transformation,[],[f1904]) ).
fof(f17789,plain,
spl86_537,
inference(avatar_split_clause,[],[f2628,f17787]) ).
fof(f17787,plain,
( spl86_537
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_537])]) ).
fof(f2628,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1569]) ).
fof(f1569,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3)) ),
inference(ennf_transformation,[],[f1082]) ).
fof(f1082,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X3))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3))) ),
inference(rectify,[],[f141]) ).
fof(f141,axiom,
! [X0,X33,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_subset__insertI2) ).
fof(f17785,plain,
spl86_536,
inference(avatar_split_clause,[],[f2616,f17783]) ).
fof(f17783,plain,
( spl86_536
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_536])]) ).
fof(f2616,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(cnf_transformation,[],[f1553]) ).
fof(f1553,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(flattening,[],[f1552]) ).
fof(f1552,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
inference(ennf_transformation,[],[f1072]) ).
fof(f1072,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1))) ) ),
inference(rectify,[],[f315]) ).
fof(f315,axiom,
! [X24,X28,X25,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X26))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X28))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X24)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X28))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_add__le__mono) ).
fof(f17781,plain,
spl86_535,
inference(avatar_split_clause,[],[f2614,f17779]) ).
fof(f17779,plain,
( spl86_535
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_535])]) ).
fof(f2614,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(cnf_transformation,[],[f1549]) ).
fof(f1549,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(flattening,[],[f1548]) ).
fof(f1548,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(ennf_transformation,[],[f1070]) ).
fof(f1070,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1))) ) ),
inference(rectify,[],[f350]) ).
fof(f350,axiom,
! [X24,X28,X25,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X26))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X24),X28))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X24)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X28))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_add__less__mono) ).
fof(f17777,plain,
spl86_534,
inference(avatar_split_clause,[],[f2600,f17775]) ).
fof(f17775,plain,
( spl86_534
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK72(X0,X1,X2,X3)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_534])]) ).
fof(f2600,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK72(X0,X1,X2,X3)),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(cnf_transformation,[],[f1869]) ).
fof(f17773,plain,
spl86_533,
inference(avatar_split_clause,[],[f2520,f17771]) ).
fof(f17771,plain,
( spl86_533
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_533])]) ).
fof(f2520,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1838]) ).
fof(f1838,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))) ) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(nnf_transformation,[],[f1502]) ).
fof(f1502,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1016]) ).
fof(f1016,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ) ),
inference(rectify,[],[f327]) ).
fof(f327,axiom,
! [X35,X18,X63] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X63))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X35),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X63),X18)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X18)),X63)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_le__diff__conv2) ).
fof(f17769,plain,
spl86_532,
inference(avatar_split_clause,[],[f2491,f17767]) ).
fof(f17767,plain,
( spl86_532
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_532])]) ).
fof(f2491,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1473]) ).
fof(f1473,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(flattening,[],[f1472]) ).
fof(f1472,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(ennf_transformation,[],[f993]) ).
fof(f993,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0))) ) ),
inference(rectify,[],[f455]) ).
fof(f455,axiom,
! [X51,X48,X52] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X48),X52))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X48))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X48),X51)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X52),X51))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_diff__less__mono) ).
fof(f17765,plain,
spl86_531,
inference(avatar_split_clause,[],[f2490,f17763]) ).
fof(f17763,plain,
( spl86_531
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_531])]) ).
fof(f2490,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1471]) ).
fof(f1471,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(flattening,[],[f1470]) ).
fof(f1470,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(ennf_transformation,[],[f992]) ).
fof(f992,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1))) ) ),
inference(rectify,[],[f381]) ).
fof(f381,axiom,
! [X28,X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X28))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_diff__less__mono2) ).
fof(f17761,plain,
( spl86_530
| ~ spl86_90
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4218,f4161,f3619,f17758]) ).
fof(f3619,plain,
( spl86_90
<=> wt = hAPP(fun(com,bool),fun(com,bool),combi(fun(com,bool)),wt) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_90])]) ).
fof(f4218,plain,
( wt = hAPP(fun(com,bool),fun(com,bool),collect(com),wt)
| ~ spl86_90
| ~ spl86_165 ),
inference(superposition,[],[f4162,f3621]) ).
fof(f3621,plain,
( wt = hAPP(fun(com,bool),fun(com,bool),combi(fun(com,bool)),wt)
| ~ spl86_90 ),
inference(avatar_component_clause,[],[f3619]) ).
fof(f17219,plain,
( spl86_529
| ~ spl86_109
| ~ spl86_165
| ~ spl86_528 ),
inference(avatar_split_clause,[],[f17215,f17212,f4161,f3702,f17217]) ).
fof(f17217,plain,
( spl86_529
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(X0,X0,combi(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_529])]) ).
fof(f17212,plain,
( spl86_528
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(X0,X0,combi(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_528])]) ).
fof(f17215,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(X0,X0,combi(X0),X2) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_528 ),
inference(forward_demodulation,[],[f17213,f4236]) ).
fof(f17213,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(X0,X0,combi(X0),X2) )
| ~ spl86_528 ),
inference(avatar_component_clause,[],[f17212]) ).
fof(f17214,plain,
spl86_528,
inference(avatar_split_clause,[],[f3069,f17212]) ).
fof(f3069,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(X0,X0,combi(X0),X2) ),
inference(forward_demodulation,[],[f2883,f2226]) ).
fof(f2883,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(definition_unfolding,[],[f2429,f2190]) ).
fof(f2429,plain,
! [X2,X0,X1] :
( ti(X0,X2) = hAPP(fun(X0,bool),X0,hAPP(X0,fun(fun(X0,bool),X0),partial_flat_lub(X0),X2),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(cnf_transformation,[],[f1411]) ).
fof(f17210,plain,
spl86_527,
inference(avatar_split_clause,[],[f2903,f17208]) ).
fof(f17208,plain,
( spl86_527
<=> ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_527])]) ).
fof(f2903,plain,
! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) ),
inference(definition_unfolding,[],[f2536,f2190,f2190]) ).
fof(f2536,plain,
! [X2,X0,X1] :
( ti(X0,X1) = ti(X0,X2)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) ),
inference(cnf_transformation,[],[f1519]) ).
fof(f1519,plain,
! [X0,X1,X2] :
( ti(X0,X1) = ti(X0,X2)
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))) ),
inference(ennf_transformation,[],[f1030]) ).
fof(f1030,plain,
! [X0,X1,X2] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))
=> ti(X0,X1) = ti(X0,X2) ),
inference(rectify,[],[f171]) ).
fof(f171,axiom,
! [X0,X10,X33] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),bot_bot(fun(X0,bool)))
=> ti(X0,X33) = ti(X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_singleton__inject) ).
fof(f17206,plain,
( spl86_526
| ~ spl86_91
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4215,f4161,f3624,f17203]) ).
fof(f3624,plain,
( spl86_91
<=> fNot = hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_91])]) ).
fof(f4215,plain,
( fNot = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),fNot)
| ~ spl86_91
| ~ spl86_165 ),
inference(superposition,[],[f4162,f3626]) ).
fof(f3626,plain,
( fNot = hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot)
| ~ spl86_91 ),
inference(avatar_component_clause,[],[f3624]) ).
fof(f17201,plain,
spl86_525,
inference(avatar_split_clause,[],[f2704,f17199]) ).
fof(f2704,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(cnf_transformation,[],[f1606]) ).
fof(f1606,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4)) ),
inference(ennf_transformation,[],[f1119]) ).
fof(f1119,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),hAPP(X1,X0,X2,X3)),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X4))) ),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X1,X0,X11,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X0,X1,X11,X13)),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_imageI) ).
fof(f17197,plain,
spl86_524,
inference(avatar_split_clause,[],[f2503,f17195]) ).
fof(f17195,plain,
( spl86_524
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X0)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_524])]) ).
fof(f2503,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X0)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1485]) ).
fof(f1485,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X0)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1005]) ).
fof(f1005,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)),X0) ),
inference(rectify,[],[f323]) ).
fof(f323,axiom,
! [X25,X24,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X26))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X25)),X24) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X24)),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_add__diff__assoc2) ).
fof(f17193,plain,
spl86_523,
inference(avatar_split_clause,[],[f2501,f17191]) ).
fof(f17191,plain,
( spl86_523
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_523])]) ).
fof(f2501,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1483]) ).
fof(f1483,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1003]) ).
fof(f1003,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) ),
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X25,X24,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X26))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X26)),X24) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_add__diff__assoc) ).
fof(f17189,plain,
spl86_522,
inference(avatar_split_clause,[],[f2500,f17187]) ).
fof(f17187,plain,
( spl86_522
<=> ! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_522])]) ).
fof(f2500,plain,
! [X2,X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1482]) ).
fof(f1482,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1002]) ).
fof(f1002,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2) ),
inference(rectify,[],[f332]) ).
fof(f332,axiom,
! [X25,X24,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X26))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X25),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X24)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X24)),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_diff__diff__right) ).
fof(f17185,plain,
spl86_521,
inference(avatar_split_clause,[],[f2418,f17183]) ).
fof(f17183,plain,
( spl86_521
<=> ! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_521])]) ).
fof(f2418,plain,
! [X2,X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),
inference(cnf_transformation,[],[f941]) ).
fof(f941,plain,
! [X0,X1,X2] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X0,X13,X7] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_insert__absorb2) ).
fof(f17096,plain,
spl86_520,
inference(avatar_split_clause,[],[f3021,f17094]) ).
fof(f17094,plain,
( spl86_520
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK43(X0,X1)),sK42(X0,X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_520])]) ).
fof(f3021,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK43(X0,X1)),sK42(X0,X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(forward_demodulation,[],[f3020,f2854]) ).
fof(f3020,plain,
! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK43(X0,X1)),sK42(X0,X1))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(forward_demodulation,[],[f2867,f2854]) ).
fof(f2867,plain,
! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK43(X0,X1)),sK42(X0,X1)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(definition_unfolding,[],[f2330,f2190,f2190]) ).
fof(f2330,plain,
! [X0,X1] :
( ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK43(X0,X1)),sK42(X0,X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(cnf_transformation,[],[f1755]) ).
fof(f1755,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ( ! [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ) )
& ( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK42(X0,X1)))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK43(X0,X1)),sK42(X0,X1)) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f1753,f1754]) ).
fof(f1754,plain,
! [X0,X1] :
( ? [X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X4) )
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK42(X0,X1)))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK43(X0,X1)),sK42(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1753,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ( ! [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ) )
& ( ? [X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X5),X4) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(rectify,[],[f1752]) ).
fof(f1752,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ( ! [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ) )
& ( ? [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(flattening,[],[f1751]) ).
fof(f1751,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ( ! [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ) )
& ( ? [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(nnf_transformation,[],[f899]) ).
fof(f899,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
<=> ( ? [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ) ),
inference(rectify,[],[f204]) ).
fof(f204,axiom,
! [X0,X10] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X10))
<=> ( ? [X56,X53] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X56))
& ti(fun(X0,bool),X10) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X53),X56) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_finite_Osimps) ).
fof(f17092,plain,
spl86_519,
inference(avatar_split_clause,[],[f2463,f17090]) ).
fof(f17090,plain,
( spl86_519
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK62(X0,X1)),sK63(X0,X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_519])]) ).
fof(f2463,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK62(X0,X1)),sK63(X0,X1))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1830]) ).
fof(f1830,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK62(X0,X1)),sK63(X0,X1))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,sK63(X0,X1)))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK62(X0,X1)),sK63(X0,X1)))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK63(X0,X1))) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63])],[f1432,f1829]) ).
fof(f1829,plain,
! [X0,X1] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4)) )
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK62(X0,X1)),sK63(X0,X1))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,sK63(X0,X1)))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK62(X0,X1)),sK63(X0,X1)))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK63(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f1432,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1431]) ).
fof(f1431,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ? [X3,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f967]) ).
fof(f967,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
=> ( ! [X3,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
=> hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4))) ) ) )
=> hBOOL(hAPP(fun(X0,bool),bool,X1,X2)) ) ) ),
inference(rectify,[],[f203]) ).
fof(f203,axiom,
! [X0,X15,X9] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X15,bot_bot(fun(X0,bool))))
=> ( ! [X32,X54] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X54))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X54))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X15,X54))
=> hBOOL(hAPP(fun(X0,bool),bool,X15,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X32),X54))) ) ) )
=> hBOOL(hAPP(fun(X0,bool),bool,X15,X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_finite__induct) ).
fof(f16781,plain,
spl86_518,
inference(avatar_split_clause,[],[f2603,f16779]) ).
fof(f16779,plain,
( spl86_518
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_518])]) ).
fof(f2603,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(cnf_transformation,[],[f1537]) ).
fof(f1537,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(ennf_transformation,[],[f1064]) ).
fof(f1064,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3))),hAPP(fun(X1,bool),nat,finite_card(X1),X3))) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X1,X0,X11,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X11),X7))),hAPP(fun(X0,bool),nat,finite_card(X0),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_card__image__le) ).
fof(f16777,plain,
spl86_517,
inference(avatar_split_clause,[],[f2547,f16775]) ).
fof(f16775,plain,
( spl86_517
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2,X0)),X1)),hAPP(nat,nat,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK67(X2)),sK68(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_517])]) ).
fof(f2547,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X2,X0)),X1)),hAPP(nat,nat,X2,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK67(X2)),sK68(X2))) ),
inference(cnf_transformation,[],[f1846]) ).
fof(f16490,plain,
spl86_516,
inference(avatar_split_clause,[],[f2692,f16488]) ).
fof(f16488,plain,
( spl86_516
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_516])]) ).
fof(f2692,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)),X3)) ),
inference(cnf_transformation,[],[f1904]) ).
fof(f16486,plain,
spl86_515,
inference(avatar_split_clause,[],[f2643,f16484]) ).
fof(f16484,plain,
( spl86_515
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_515])]) ).
fof(f2643,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))) ),
inference(cnf_transformation,[],[f1592]) ).
fof(f1592,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))) ),
inference(ennf_transformation,[],[f1097]) ).
fof(f1097,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(rectify,[],[f255]) ).
fof(f255,axiom,
! [X0,X34,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_DiffD1) ).
fof(f16482,plain,
spl86_514,
inference(avatar_split_clause,[],[f2642,f16480]) ).
fof(f16480,plain,
( spl86_514
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_514])]) ).
fof(f2642,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))) ),
inference(cnf_transformation,[],[f1591]) ).
fof(f1591,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3))) ),
inference(ennf_transformation,[],[f1096]) ).
fof(f1096,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X3)))
=> ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) ),
inference(rectify,[],[f254]) ).
fof(f254,axiom,
! [X0,X34,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)))
=> ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_DiffD2) ).
fof(f16478,plain,
spl86_513,
inference(avatar_split_clause,[],[f2604,f16476]) ).
fof(f16476,plain,
( spl86_513
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(sum_sum(X1,X0),bool),bool,finite_finite(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_513])]) ).
fof(f2604,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(sum_sum(X1,X0),bool),bool,finite_finite(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(cnf_transformation,[],[f1539]) ).
fof(f1539,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(sum_sum(X1,X0),bool),bool,finite_finite(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(flattening,[],[f1538]) ).
fof(f1538,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(sum_sum(X1,X0),bool),bool,finite_finite(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(ennf_transformation,[],[f1065]) ).
fof(f1065,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> hBOOL(hAPP(fun(sum_sum(X1,X0),bool),bool,finite_finite(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2))) ) ),
inference(rectify,[],[f495]) ).
fof(f495,axiom,
! [X1,X0,X12,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X12))
=> hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X7),X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_finite__Plus) ).
fof(f16474,plain,
spl86_512,
inference(avatar_split_clause,[],[f2550,f16472]) ).
fof(f16472,plain,
( spl86_512
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2,X0)),hAPP(nat,nat,X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,sK69(X2))),hAPP(nat,nat,X2,sK70(X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_512])]) ).
fof(f2550,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2,X0)),hAPP(nat,nat,X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,sK69(X2))),hAPP(nat,nat,X2,sK70(X2)))) ),
inference(cnf_transformation,[],[f1848]) ).
fof(f1848,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2,X0)),hAPP(nat,nat,X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,sK69(X2))),hAPP(nat,nat,X2,sK70(X2))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(X2)),sK70(X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f1526,f1847]) ).
fof(f1847,plain,
! [X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,X3)),hAPP(nat,nat,X2,X4)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) )
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,sK69(X2))),hAPP(nat,nat,X2,sK70(X2))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(X2)),sK70(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f1526,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2,X0)),hAPP(nat,nat,X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,X3)),hAPP(nat,nat,X2,X4)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ) ),
inference(flattening,[],[f1525]) ).
fof(f1525,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2,X0)),hAPP(nat,nat,X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ? [X3,X4] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,X3)),hAPP(nat,nat,X2,X4)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ) ),
inference(ennf_transformation,[],[f1035]) ).
fof(f1035,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X2,X3)),hAPP(nat,nat,X2,X4))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2,X0)),hAPP(nat,nat,X2,X1))) ) ),
inference(rectify,[],[f480]) ).
fof(f480,axiom,
! [X35,X63,X11] :
( ! [X68,X71] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X68),X71))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X11,X68)),hAPP(nat,nat,X11,X71))) )
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X35),X63))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X11,X35)),hAPP(nat,nat,X11,X63))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_less__mono__imp__le__mono) ).
fof(f16470,plain,
spl86_511,
inference(avatar_split_clause,[],[f2472,f16468]) ).
fof(f16468,plain,
( spl86_511
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_511])]) ).
fof(f2472,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1450]) ).
fof(f1450,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1449]) ).
fof(f1449,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f976]) ).
fof(f976,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))) ) ),
inference(rectify,[],[f58]) ).
fof(f58,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X7)),hAPP(fun(X0,bool),nat,finite_card(X0),X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_card__mono) ).
fof(f16466,plain,
spl86_510,
inference(avatar_split_clause,[],[f2470,f16464]) ).
fof(f16464,plain,
( spl86_510
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_510])]) ).
fof(f2470,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1446]) ).
fof(f1446,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1445]) ).
fof(f1445,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f974]) ).
fof(f974,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X1)),hAPP(fun(X0,bool),nat,finite_card(X0),X2))) ) ),
inference(rectify,[],[f468]) ).
fof(f468,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X7)),hAPP(fun(X0,bool),nat,finite_card(X0),X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_psubset__card__mono) ).
fof(f16410,plain,
spl86_509,
inference(avatar_split_clause,[],[f2953,f16408]) ).
fof(f16408,plain,
( spl86_509
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X1,X0,X3,sK83(X0,X1,X2,X3,X4)) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_509])]) ).
fof(f2953,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X0,X3,sK83(X0,X1,X2,X3,X4)) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(definition_unfolding,[],[f2723,f2190]) ).
fof(f2723,plain,
! [X2,X3,X0,X1,X4] :
( ti(X0,X2) = hAPP(X1,X0,X3,sK83(X0,X1,X2,X3,X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(cnf_transformation,[],[f1917]) ).
fof(f16406,plain,
( spl86_508
| ~ spl86_92
| ~ spl86_131
| ~ spl86_491 ),
inference(avatar_split_clause,[],[f15937,f15616,f3936,f3632,f16403]) ).
fof(f16403,plain,
( spl86_508
<=> zero_zero(nat) = sK22(one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_508])]) ).
fof(f15616,plain,
( spl86_491
<=> one_one(nat) = hAPP(nat,nat,suc,sK22(one_one(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_491])]) ).
fof(f15937,plain,
( zero_zero(nat) = sK22(one_one(nat))
| ~ spl86_92
| ~ spl86_131
| ~ spl86_491 ),
inference(forward_demodulation,[],[f15907,f3633]) ).
fof(f15907,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),one_one(nat)),one_one(nat)) = sK22(one_one(nat))
| ~ spl86_131
| ~ spl86_491 ),
inference(superposition,[],[f3937,f15618]) ).
fof(f15618,plain,
( one_one(nat) = hAPP(nat,nat,suc,sK22(one_one(nat)))
| ~ spl86_491 ),
inference(avatar_component_clause,[],[f15616]) ).
fof(f16401,plain,
spl86_507,
inference(avatar_split_clause,[],[f2951,f16399]) ).
fof(f16399,plain,
( spl86_507
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X1,X0,X3,sK81(X0,X1,X2,X3,X4)) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_507])]) ).
fof(f2951,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X0,X3,sK81(X0,X1,X2,X3,X4)) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(definition_unfolding,[],[f2718,f2190]) ).
fof(f2718,plain,
! [X2,X3,X0,X1,X4] :
( ti(X0,X2) = hAPP(X1,X0,X3,sK81(X0,X1,X2,X3,X4))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X3),X4))) ),
inference(cnf_transformation,[],[f1911]) ).
fof(f16114,plain,
( spl86_506
| ~ spl86_109
| ~ spl86_165
| ~ spl86_505 ),
inference(avatar_split_clause,[],[f16110,f16107,f4161,f3702,f16112]) ).
fof(f16112,plain,
( spl86_506
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X3,hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_506])]) ).
fof(f16107,plain,
( spl86_505
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X3,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_505])]) ).
fof(f16110,plain,
( ! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X3,hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_505 ),
inference(forward_demodulation,[],[f16108,f4236]) ).
fof(f16108,plain,
( ! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X3,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) )
| ~ spl86_505 ),
inference(avatar_component_clause,[],[f16107]) ).
fof(f16109,plain,
spl86_505,
inference(avatar_split_clause,[],[f3141,f16107]) ).
fof(f3141,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X3,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(forward_demodulation,[],[f2927,f2226]) ).
fof(f2927,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,X3,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(definition_unfolding,[],[f2637,f2190]) ).
fof(f2637,plain,
! [X2,X3,X0,X1] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,X3,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1584]) ).
fof(f1584,plain,
! [X0,X1,X2,X3] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,X3,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3)) ),
inference(ennf_transformation,[],[f1091]) ).
fof(f1091,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X2),X3))
=> ti(X0,X1) = hAPP(fun(X0,bool),X0,X3,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) ),
inference(rectify,[],[f240]) ).
fof(f240,axiom,
! [X0,X13,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite_folding_one(X0),X11),X9))
=> ti(X0,X13) = hAPP(fun(X0,bool),X0,X9,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_folding__one_Osingleton) ).
fof(f16105,plain,
spl86_504,
inference(avatar_split_clause,[],[f3063,f16103]) ).
fof(f16103,plain,
( spl86_504
<=> ! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),X1)),hAPP(nat,nat,suc,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_504])]) ).
fof(f3063,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),X1)),hAPP(nat,nat,suc,X2)),
inference(forward_demodulation,[],[f2417,f2415]) ).
fof(f2417,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),X1)),hAPP(nat,nat,suc,X2)),
inference(cnf_transformation,[],[f940]) ).
fof(f940,plain,
! [X0,X1,X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),X1)),hAPP(nat,nat,suc,X2)),
inference(rectify,[],[f90]) ).
fof(f90,axiom,
! [X17,X16,X24] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X17)),X16)),hAPP(nat,nat,suc,X24)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16)),X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Suc__diff__diff) ).
fof(f16101,plain,
( ~ spl86_503
| ~ spl86_37
| ~ spl86_491 ),
inference(avatar_split_clause,[],[f15901,f15616,f3356,f16098]) ).
fof(f16098,plain,
( spl86_503
<=> one_one(nat) = sK22(one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_503])]) ).
fof(f15901,plain,
( one_one(nat) != sK22(one_one(nat))
| ~ spl86_37
| ~ spl86_491 ),
inference(superposition,[],[f3357,f15618]) ).
fof(f16096,plain,
spl86_502,
inference(avatar_split_clause,[],[f2625,f16094]) ).
fof(f16094,plain,
( spl86_502
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_502])]) ).
fof(f2625,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1564]) ).
fof(f1564,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(flattening,[],[f1563]) ).
fof(f1563,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3)) ),
inference(ennf_transformation,[],[f1079]) ).
fof(f1079,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X3)) ) ),
inference(rectify,[],[f473]) ).
fof(f473,axiom,
! [X0,X34,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_psubsetD) ).
fof(f16092,plain,
spl86_501,
inference(avatar_split_clause,[],[f2624,f16090]) ).
fof(f16090,plain,
( spl86_501
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_501])]) ).
fof(f2624,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1562]) ).
fof(f1562,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(flattening,[],[f1561]) ).
fof(f1561,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(ennf_transformation,[],[f1078]) ).
fof(f1078,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(rectify,[],[f125]) ).
fof(f125,axiom,
! [X0,X12,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_set__rev__mp) ).
fof(f16088,plain,
spl86_500,
inference(avatar_split_clause,[],[f2441,f16086]) ).
fof(f16086,plain,
( spl86_500
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_500])]) ).
fof(f2441,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1420]) ).
fof(f1420,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f958]) ).
fof(f958,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X2)),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)))) ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X0,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X0,bool),nat,finite_card(X0),X7)),hAPP(fun(X0,bool),nat,finite_card(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_card__insert__le) ).
fof(f16084,plain,
spl86_499,
inference(avatar_split_clause,[],[f2052,f16082]) ).
fof(f16082,plain,
( spl86_499
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),zero_zero(X0)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_499])]) ).
fof(f2052,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),zero_zero(X0)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f1183]) ).
fof(f1183,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),zero_zero(X0)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0))) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f1182]) ).
fof(f1182,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),zero_zero(X0)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0))) )
| ~ ordere216010020id_add(X0) ),
inference(ennf_transformation,[],[f680]) ).
fof(f680,plain,
! [X0] :
( ordere216010020id_add(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),zero_zero(X0)))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),zero_zero(X0)))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),zero_zero(X0))) ) ) ),
inference(rectify,[],[f518]) ).
fof(f518,axiom,
! [X2] :
( ordere216010020id_add(X2)
=> ! [X52,X48] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),zero_zero(X2)))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X52),zero_zero(X2)))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X52)),zero_zero(X2))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_add__nonpos__nonpos) ).
fof(f15983,plain,
spl86_498,
inference(avatar_split_clause,[],[f2798,f15981]) ).
fof(f15981,plain,
( spl86_498
<=> ! [X2,X0,X1] :
( zero_zero(X0) = hAPP(X0,X0,combi(X0),X2)
| zero_zero(X0) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_498])]) ).
fof(f2798,plain,
! [X2,X0,X1] :
( zero_zero(X0) = hAPP(X0,X0,combi(X0),X2)
| zero_zero(X0) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ),
inference(definition_unfolding,[],[f2054,f2190]) ).
fof(f2054,plain,
! [X2,X0,X1] :
( zero_zero(X0) = ti(X0,X2)
| zero_zero(X0) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f1662]) ).
fof(f15979,plain,
spl86_497,
inference(avatar_split_clause,[],[f2797,f15977]) ).
fof(f15977,plain,
( spl86_497
<=> ! [X2,X0,X1] :
( zero_zero(X0) = hAPP(X0,X0,combi(X0),X1)
| zero_zero(X0) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_497])]) ).
fof(f2797,plain,
! [X2,X0,X1] :
( zero_zero(X0) = hAPP(X0,X0,combi(X0),X1)
| zero_zero(X0) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ),
inference(definition_unfolding,[],[f2055,f2190]) ).
fof(f2055,plain,
! [X2,X0,X1] :
( zero_zero(X0) = ti(X0,X1)
| zero_zero(X0) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X2))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f1662]) ).
fof(f15975,plain,
spl86_496,
inference(avatar_split_clause,[],[f2512,f15973]) ).
fof(f15973,plain,
( spl86_496
<=> ! [X2,X0,X1] :
( X0 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_496])]) ).
fof(f2512,plain,
! [X2,X0,X1] :
( X0 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1834]) ).
fof(f1834,plain,
! [X0,X1,X2] :
( ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)
| X0 != X2 )
& ( X0 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1) ) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(nnf_transformation,[],[f1496]) ).
fof(f1496,plain,
! [X0,X1,X2] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)
<=> X0 = X2 )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(flattening,[],[f1495]) ).
fof(f1495,plain,
! [X0,X1,X2] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)
<=> X0 = X2 )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1012]) ).
fof(f1012,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X1)
<=> X0 = X2 ) ) ),
inference(rectify,[],[f94]) ).
fof(f94,axiom,
! [X19,X18,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X27))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X18),X19))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X18) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X19),X18)
<=> X19 = X27 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_eq__diff__iff) ).
fof(f15877,plain,
spl86_495,
inference(avatar_split_clause,[],[f1940,f15874]) ).
fof(f15874,plain,
( spl86_495
<=> hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_495])]) ).
fof(f1940,plain,
hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
inference(cnf_transformation,[],[f606]) ).
fof(f606,axiom,
hAPP(fun(x_a,bool),nat,finite_card(x_a),g) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),hAPP(nat,nat,suc,na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(f15631,plain,
spl86_494,
inference(avatar_split_clause,[],[f2621,f15629]) ).
fof(f15629,plain,
( spl86_494
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_494])]) ).
fof(f2621,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1557]) ).
fof(f1557,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(ennf_transformation,[],[f1075]) ).
fof(f1075,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3))) ),
inference(rectify,[],[f118]) ).
fof(f118,axiom,
! [X0,X33,X10,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),X12))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_insertI2) ).
fof(f15627,plain,
spl86_493,
inference(avatar_split_clause,[],[f2613,f15625]) ).
fof(f15625,plain,
( spl86_493
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X3))
| sP4(X0,X1,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_493])]) ).
fof(f2613,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X3))
| sP4(X0,X1,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(cnf_transformation,[],[f1650]) ).
fof(f1650,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X3))
| sP4(X0,X1,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(definition_folding,[],[f1547,f1649]) ).
fof(f1649,plain,
! [X0,X1,X2] :
( ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X2))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5)) )
| ~ sP4(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f1547,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X3))
| ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X2))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(flattening,[],[f1546]) ).
fof(f1546,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X3))
| ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X2))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) ),
inference(ennf_transformation,[],[f1069]) ).
fof(f1069,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X3),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
=> ( ! [X4,X5] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X2))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
=> hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5))) ) ) ) )
=> hBOOL(hAPP(fun(X0,bool),bool,X1,X3)) ) ) ) ),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X0,X15,X7,X9] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X9))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X9),X7))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X15,bot_bot(fun(X0,bool))))
=> ( ! [X53,X54] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X54))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X53),X7))
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X53),X54))
=> ( hBOOL(hAPP(fun(X0,bool),bool,X15,X54))
=> hBOOL(hAPP(fun(X0,bool),bool,X15,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X53),X54))) ) ) ) )
=> hBOOL(hAPP(fun(X0,bool),bool,X15,X9)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_finite__subset__induct) ).
fof(f15623,plain,
spl86_492,
inference(avatar_split_clause,[],[f2075,f15621]) ).
fof(f15621,plain,
( spl86_492
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X3))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_492])]) ).
fof(f2075,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X3))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f1210]) ).
fof(f1210,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X3)) )
| ~ linordered_semidom(X0) ),
inference(flattening,[],[f1209]) ).
fof(f1209,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X3)) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f699]) ).
fof(f699,plain,
! [X0] :
( linordered_semidom(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2))) ) ) ),
inference(rectify,[],[f507]) ).
fof(f507,axiom,
! [X2] :
( linordered_semidom(X2)
=> ! [X52,X51,X48] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),X48))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X52),X51))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X52),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_pos__add__strict) ).
fof(f15619,plain,
( ~ spl86_13
| spl86_491
| ~ spl86_118
| ~ spl86_147 ),
inference(avatar_split_clause,[],[f4059,f4038,f3853,f15616,f3241]) ).
fof(f4059,plain,
( one_one(nat) = hAPP(nat,nat,suc,sK22(one_one(nat)))
| ~ linordered_semidom(nat)
| ~ spl86_118
| ~ spl86_147 ),
inference(resolution,[],[f4039,f3854]) ).
fof(f15614,plain,
spl86_490,
inference(avatar_split_clause,[],[f2060,f15612]) ).
fof(f15612,plain,
( spl86_490
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_490])]) ).
fof(f2060,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f1193]) ).
fof(f1193,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3)) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f1192]) ).
fof(f1192,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3)) )
| ~ ordere216010020id_add(X0) ),
inference(ennf_transformation,[],[f686]) ).
fof(f686,plain,
! [X0] :
( ordere216010020id_add(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3))) ) ) ),
inference(rectify,[],[f517]) ).
fof(f517,axiom,
! [X2] :
( ordere216010020id_add(X2)
=> ! [X52,X48,X51] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),zero_zero(X2)),X51))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X52),X48))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X52),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_add__increasing2) ).
fof(f15610,plain,
spl86_489,
inference(avatar_split_clause,[],[f2059,f15608]) ).
fof(f15608,plain,
( spl86_489
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_489])]) ).
fof(f2059,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f1191]) ).
fof(f1191,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3)) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f1190]) ).
fof(f1190,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3)) )
| ~ ordere216010020id_add(X0) ),
inference(ennf_transformation,[],[f685]) ).
fof(f685,plain,
! [X0] :
( ordere216010020id_add(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2))) ) ) ),
inference(rectify,[],[f516]) ).
fof(f516,axiom,
! [X2] :
( ordere216010020id_add(X2)
=> ! [X52,X51,X48] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),zero_zero(X2)),X48))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X52),X51))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X52),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_add__increasing) ).
fof(f15454,plain,
spl86_488,
inference(avatar_split_clause,[],[f2252,f15452]) ).
fof(f15452,plain,
( spl86_488
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK17(X0,X1,X2,X3))),hAPP(X0,X1,X3,sK17(X0,X1,X2,X3))))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_488])]) ).
fof(f2252,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK17(X0,X1,X2,X3))),hAPP(X0,X1,X3,sK17(X0,X1,X2,X3))))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f1714]) ).
fof(f1714,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK17(X0,X1,X2,X3))),hAPP(X0,X1,X3,sK17(X0,X1,X2,X3)))) )
& ( ! [X5] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),hAPP(X0,X1,X3,X5)))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) ) )
| ~ ord(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f1712,f1713]) ).
fof(f1713,plain,
! [X0,X1,X2,X3] :
( ? [X4] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4)))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK17(X0,X1,X2,X3))),hAPP(X0,X1,X3,sK17(X0,X1,X2,X3)))) ),
introduced(choice_axiom,[]) ).
fof(f1712,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ? [X4] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4))) )
& ( ! [X5] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),hAPP(X0,X1,X3,X5)))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) ) )
| ~ ord(X1) ),
inference(rectify,[],[f1711]) ).
fof(f1711,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ? [X4] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4))) )
& ( ! [X4] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4)))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) ) )
| ~ ord(X1) ),
inference(nnf_transformation,[],[f1330]) ).
fof(f1330,plain,
! [X0,X1] :
( ! [X2,X3] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
<=> ! [X4] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4))) )
| ~ ord(X1) ),
inference(ennf_transformation,[],[f839]) ).
fof(f839,plain,
! [X0,X1] :
( ord(X1)
=> ! [X2,X3] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
<=> ! [X4] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4))) ) ),
inference(rectify,[],[f153]) ).
fof(f153,axiom,
! [X0,X1] :
( ord(X1)
=> ! [X11,X39] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X11),X39))
<=> ! [X32] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X11,X32)),hAPP(X0,X1,X39,X32))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_le__fun__def) ).
fof(f15450,plain,
spl86_487,
inference(avatar_split_clause,[],[f2247,f15448]) ).
fof(f15448,plain,
( spl86_487
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK16(X0,X1,X2,X3))),hAPP(X0,X1,X3,sK16(X0,X1,X2,X3))))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_487])]) ).
fof(f2247,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK16(X0,X1,X2,X3))),hAPP(X0,X1,X3,sK16(X0,X1,X2,X3))))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f1708]) ).
fof(f1708,plain,
! [X0,X1] :
( ! [X2,X3] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK16(X0,X1,X2,X3))),hAPP(X0,X1,X3,sK16(X0,X1,X2,X3)))) )
| ~ ord(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f1328,f1707]) ).
fof(f1707,plain,
! [X0,X1,X2,X3] :
( ? [X4] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4)))
=> ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,sK16(X0,X1,X2,X3))),hAPP(X0,X1,X3,sK16(X0,X1,X2,X3)))) ),
introduced(choice_axiom,[]) ).
fof(f1328,plain,
! [X0,X1] :
( ! [X2,X3] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ? [X4] : ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4))) )
| ~ ord(X1) ),
inference(ennf_transformation,[],[f837]) ).
fof(f837,plain,
! [X0,X1] :
( ord(X1)
=> ! [X2,X3] :
( ! [X4] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4)))
=> hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3)) ) ),
inference(rectify,[],[f208]) ).
fof(f208,axiom,
! [X0,X1] :
( ord(X1)
=> ! [X11,X39] :
( ! [X32] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X11,X32)),hAPP(X0,X1,X39,X32)))
=> hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X11),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_le__funI) ).
fof(f15414,plain,
spl86_486,
inference(avatar_split_clause,[],[f2615,f15412]) ).
fof(f15412,plain,
( spl86_486
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_486])]) ).
fof(f2615,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(cnf_transformation,[],[f1551]) ).
fof(f1551,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(flattening,[],[f1550]) ).
fof(f1550,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
inference(ennf_transformation,[],[f1071]) ).
fof(f1071,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
inference(rectify,[],[f349]) ).
fof(f349,axiom,
! [X17,X16,X24,X28] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X24),X28))
=> ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X24),X16) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X28)
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_less__add__eq__less) ).
fof(f15410,plain,
spl86_485,
inference(avatar_split_clause,[],[f2241,f15408]) ).
fof(f15408,plain,
( spl86_485
<=> ! [X2,X4,X0,X3,X1] :
( hAPP(X0,X1,hAPP(fun(X0,X1),fun(X0,X1),hAPP(fun(X0,X1),fun(fun(X0,X1),fun(X0,X1)),minus_minus(fun(X0,X1)),X2),X3),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4))
| ~ minus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_485])]) ).
fof(f2241,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X0,X1,hAPP(fun(X0,X1),fun(X0,X1),hAPP(fun(X0,X1),fun(fun(X0,X1),fun(X0,X1)),minus_minus(fun(X0,X1)),X2),X3),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4))
| ~ minus(X1) ),
inference(cnf_transformation,[],[f1322]) ).
fof(f1322,plain,
! [X0,X1] :
( ! [X2,X3,X4] : hAPP(X0,X1,hAPP(fun(X0,X1),fun(X0,X1),hAPP(fun(X0,X1),fun(fun(X0,X1),fun(X0,X1)),minus_minus(fun(X0,X1)),X2),X3),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4))
| ~ minus(X1) ),
inference(ennf_transformation,[],[f831]) ).
fof(f831,plain,
! [X0,X1] :
( minus(X1)
=> ! [X2,X3,X4] : hAPP(X0,X1,hAPP(fun(X0,X1),fun(X0,X1),hAPP(fun(X0,X1),fun(fun(X0,X1),fun(X0,X1)),minus_minus(fun(X0,X1)),X2),X3),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),minus_minus(X1),hAPP(X0,X1,X2,X4)),hAPP(X0,X1,X3,X4)) ),
inference(rectify,[],[f266]) ).
fof(f266,axiom,
! [X1,X0] :
( minus(X0)
=> ! [X7,X12,X13] : hAPP(X1,X0,hAPP(fun(X1,X0),fun(X1,X0),hAPP(fun(X1,X0),fun(fun(X1,X0),fun(X1,X0)),minus_minus(fun(X1,X0)),X7),X12),X13) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),minus_minus(X0),hAPP(X1,X0,X7,X13)),hAPP(X1,X0,X12,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_minus__apply) ).
fof(f15406,plain,
( spl86_484
| ~ spl86_125
| ~ spl86_130 ),
inference(avatar_split_clause,[],[f3955,f3932,f3891,f15404]) ).
fof(f15404,plain,
( spl86_484
<=> ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| sP0(X0,one_one(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_484])]) ).
fof(f3955,plain,
( ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| sP0(X0,one_one(nat)) )
| ~ spl86_125
| ~ spl86_130 ),
inference(superposition,[],[f3892,f3933]) ).
fof(f14909,plain,
( spl86_483
| ~ spl86_128
| ~ spl86_130 ),
inference(avatar_split_clause,[],[f3954,f3932,f3903,f14907]) ).
fof(f14907,plain,
( spl86_483
<=> ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| sP1(X0,one_one(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_483])]) ).
fof(f3954,plain,
( ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| sP1(X0,one_one(nat)) )
| ~ spl86_128
| ~ spl86_130 ),
inference(superposition,[],[f3904,f3933]) ).
fof(f14430,plain,
spl86_482,
inference(avatar_split_clause,[],[f3029,f14428]) ).
fof(f14428,plain,
( spl86_482
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK46(X0,X1)),sK47(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_482])]) ).
fof(f3029,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK46(X0,X1)),sK47(X0,X1)) ),
inference(forward_demodulation,[],[f3028,f2854]) ).
fof(f3028,plain,
! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK46(X0,X1)),sK47(X0,X1))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(forward_demodulation,[],[f2872,f2854]) ).
fof(f2872,plain,
! [X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK46(X0,X1)),sK47(X0,X1)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(definition_unfolding,[],[f2336,f2190,f2190]) ).
fof(f2336,plain,
! [X0,X1] :
( ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK46(X0,X1)),sK47(X0,X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ),
inference(cnf_transformation,[],[f1763]) ).
fof(f1763,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
| ! [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) ) )
& ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK46(X0,X1)),sK47(X0,X1)))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK46(X0,X1)),sK47(X0,X1)) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47])],[f1761,f1762]) ).
fof(f1762,plain,
! [X0,X1] :
( ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) )
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK46(X0,X1)),sK47(X0,X1)))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK46(X0,X1)),sK47(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1761,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
| ! [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) ) )
& ( ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ) ),
inference(rectify,[],[f1760]) ).
fof(f1760,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
| ! [X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) ) )
& ( ? [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) )
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ) ),
inference(nnf_transformation,[],[f901]) ).
fof(f901,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
<=> ? [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
& ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3) ) ),
inference(rectify,[],[f207]) ).
fof(f207,axiom,
! [X0,X7] :
( ti(fun(X0,bool),X7) != bot_bot(fun(X0,bool))
<=> ? [X32,X58] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X58))
& ti(fun(X0,bool),X7) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X32),X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_nonempty__iff) ).
fof(f14411,plain,
( spl86_481
| ~ spl86_108
| ~ spl86_165
| ~ spl86_479 ),
inference(avatar_split_clause,[],[f14403,f14400,f4161,f3698,f14409]) ).
fof(f14409,plain,
( spl86_481
<=> ! [X0,X1] : hAPP(X0,fun(X0,bool),fequal(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_481])]) ).
fof(f14400,plain,
( spl86_479
<=> ! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_479])]) ).
fof(f14403,plain,
( ! [X0,X1] : hAPP(X0,fun(X0,bool),fequal(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))
| ~ spl86_108
| ~ spl86_165
| ~ spl86_479 ),
inference(forward_demodulation,[],[f14401,f4223]) ).
fof(f14401,plain,
( ! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1))
| ~ spl86_479 ),
inference(avatar_component_clause,[],[f14400]) ).
fof(f14407,plain,
( spl86_480
| ~ spl86_125
| ~ spl86_129 ),
inference(avatar_split_clause,[],[f3950,f3928,f3891,f14405]) ).
fof(f14405,plain,
( spl86_480
<=> ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| sP0(one_one(nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_480])]) ).
fof(f3950,plain,
( ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| sP0(one_one(nat),X0) )
| ~ spl86_125
| ~ spl86_129 ),
inference(superposition,[],[f3892,f3929]) ).
fof(f14402,plain,
spl86_479,
inference(avatar_split_clause,[],[f3006,f14400]) ).
fof(f3006,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(forward_demodulation,[],[f2227,f2226]) ).
fof(f2227,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(cnf_transformation,[],[f817]) ).
fof(f817,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(rectify,[],[f183]) ).
fof(f183,axiom,
! [X0,X10] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_singleton__conv) ).
fof(f14398,plain,
spl86_478,
inference(avatar_split_clause,[],[f2881,f14396]) ).
fof(f14396,plain,
( spl86_478
<=> ! [X2,X0,X1] : combs(X0,X1,X2) = hAPP(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))),fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))),combi(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)))),combs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_478])]) ).
fof(f2881,plain,
! [X2,X0,X1] : combs(X0,X1,X2) = hAPP(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))),fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))),combi(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2)))),combs(X0,X1,X2)),
inference(definition_unfolding,[],[f2403,f2190]) ).
fof(f2403,plain,
! [X2,X0,X1] : combs(X0,X1,X2) = ti(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))),combs(X0,X1,X2)),
inference(cnf_transformation,[],[f926]) ).
fof(f926,plain,
! [X0,X1,X2] : combs(X0,X1,X2) = ti(fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))),combs(X0,X1,X2)),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X0,X1] : combs(X2,X0,X1) = ti(fun(fun(X2,fun(X0,X1)),fun(fun(X2,X0),fun(X2,X1))),combs(X2,X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
fof(f14394,plain,
spl86_477,
inference(avatar_split_clause,[],[f2599,f14392]) ).
fof(f14392,plain,
( spl86_477
<=> ! [X0,X3,X2,X1] :
( zero_zero(nat) = hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_477])]) ).
fof(f2599,plain,
! [X2,X3,X0,X1] :
( zero_zero(nat) = hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f14390,plain,
spl86_476,
inference(avatar_split_clause,[],[f2598,f14388]) ).
fof(f14388,plain,
( spl86_476
<=> ! [X0,X3,X2,X1] :
( zero_zero(nat) = hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_476])]) ).
fof(f2598,plain,
! [X2,X3,X0,X1] :
( zero_zero(nat) = hAPP(fun(sum_sum(X1,X0),bool),nat,finite_card(sum_sum(X1,X0)),hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X3),X2))
| hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f14386,plain,
spl86_475,
inference(avatar_split_clause,[],[f2476,f14384]) ).
fof(f14384,plain,
( spl86_475
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_475])]) ).
fof(f2476,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1831]) ).
fof(f1831,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2))) ) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(nnf_transformation,[],[f1457]) ).
fof(f1457,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)))
<=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) )
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f980]) ).
fof(f980,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)))
<=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(rectify,[],[f221]) ).
fof(f221,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)))
<=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_finite__Diff2) ).
fof(f14382,plain,
spl86_474,
inference(avatar_split_clause,[],[f2087,f14380]) ).
fof(f14380,plain,
( spl86_474
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_474])]) ).
fof(f2087,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f1668]) ).
fof(f1668,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
& ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3))) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f1218]) ).
fof(f1218,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f707]) ).
fof(f707,plain,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) ) ),
inference(rectify,[],[f282]) ).
fof(f282,axiom,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X34,X10,X33] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X34),X10)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X34),X33)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X10),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_add__le__cancel__left) ).
fof(f14378,plain,
spl86_473,
inference(avatar_split_clause,[],[f2085,f14376]) ).
fof(f14376,plain,
( spl86_473
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_473])]) ).
fof(f2085,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f1667]) ).
fof(f1667,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3)) )
& ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2))) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f1217]) ).
fof(f1217,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f706]) ).
fof(f706,plain,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3)) ) ),
inference(rectify,[],[f281]) ).
fof(f281,axiom,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X10,X34,X33] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X10),X34)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X33),X34)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X10),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_add__le__cancel__right) ).
fof(f14374,plain,
spl86_472,
inference(avatar_split_clause,[],[f2083,f14372]) ).
fof(f14372,plain,
( spl86_472
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_472])]) ).
fof(f2083,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f1666]) ).
fof(f1666,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3)) )
& ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2))) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f1216]) ).
fof(f1216,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f705]) ).
fof(f705,plain,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3)) ) ),
inference(rectify,[],[f363]) ).
fof(f363,axiom,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X10,X34,X33] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X10),X34)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X33),X34)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X10),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_add__less__cancel__right) ).
fof(f14370,plain,
spl86_471,
inference(avatar_split_clause,[],[f2081,f14368]) ).
fof(f14368,plain,
( spl86_471
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_471])]) ).
fof(f2081,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f1665]) ).
fof(f1665,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
& ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3))) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f1215]) ).
fof(f1215,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f704]) ).
fof(f704,plain,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) ) ),
inference(rectify,[],[f362]) ).
fof(f362,axiom,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X34,X10,X33] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X34),X10)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X34),X33)))
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X10),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_add__less__cancel__left) ).
fof(f14366,plain,
spl86_470,
inference(avatar_split_clause,[],[f2079,f14364]) ).
fof(f14364,plain,
( spl86_470
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_470])]) ).
fof(f2079,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f1214]) ).
fof(f1214,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3))) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f703]) ).
fof(f703,plain,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) ) ),
inference(rectify,[],[f287]) ).
fof(f287,axiom,
! [X2] :
( ordere236663937imp_le(X2)
=> ! [X51,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X48)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X52)))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_add__le__imp__le__left) ).
fof(f14362,plain,
( spl86_469
| ~ spl86_128
| ~ spl86_129 ),
inference(avatar_split_clause,[],[f3949,f3928,f3903,f14360]) ).
fof(f14360,plain,
( spl86_469
<=> ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| sP1(one_one(nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_469])]) ).
fof(f3949,plain,
( ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| sP1(one_one(nat),X0) )
| ~ spl86_128
| ~ spl86_129 ),
inference(superposition,[],[f3904,f3929]) ).
fof(f14358,plain,
spl86_468,
inference(avatar_split_clause,[],[f2078,f14356]) ).
fof(f14356,plain,
( spl86_468
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_468])]) ).
fof(f2078,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f1213]) ).
fof(f1213,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2))) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f702]) ).
fof(f702,plain,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3)) ) ),
inference(rectify,[],[f286]) ).
fof(f286,axiom,
! [X2] :
( ordere236663937imp_le(X2)
=> ! [X48,X51,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X51)))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_add__le__imp__le__right) ).
fof(f14354,plain,
spl86_467,
inference(avatar_split_clause,[],[f2077,f14352]) ).
fof(f14352,plain,
( spl86_467
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_467])]) ).
fof(f2077,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f1212]) ).
fof(f1212,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3))) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f701]) ).
fof(f701,plain,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) ) ),
inference(rectify,[],[f357]) ).
fof(f357,axiom,
! [X2] :
( ordere236663937imp_le(X2)
=> ! [X51,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X48)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X52)))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_add__less__imp__less__left) ).
fof(f14350,plain,
spl86_466,
inference(avatar_split_clause,[],[f2076,f14348]) ).
fof(f14348,plain,
( spl86_466
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_466])]) ).
fof(f2076,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f1211]) ).
fof(f1211,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2))) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f700]) ).
fof(f700,plain,
! [X0] :
( ordere236663937imp_le(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3)) ) ),
inference(rectify,[],[f358]) ).
fof(f358,axiom,
! [X2] :
( ordere236663937imp_le(X2)
=> ! [X48,X51,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X51)))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_add__less__imp__less__right) ).
fof(f14346,plain,
spl86_465,
inference(avatar_split_clause,[],[f2058,f14344]) ).
fof(f14344,plain,
( spl86_465
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_465])]) ).
fof(f2058,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f1189]) ).
fof(f1189,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f684]) ).
fof(f684,plain,
! [X0] :
( ordere223160158up_add(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3))) ) ),
inference(rectify,[],[f360]) ).
fof(f360,axiom,
! [X2] :
( ordere223160158up_add(X2)
=> ! [X51,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),X52))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X48)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X52))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_add__strict__left__mono) ).
fof(f14342,plain,
spl86_464,
inference(avatar_split_clause,[],[f2057,f14340]) ).
fof(f14340,plain,
( spl86_464
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_464])]) ).
fof(f2057,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f1188]) ).
fof(f1188,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f683]) ).
fof(f683,plain,
! [X0] :
( ordere223160158up_add(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1))) ) ),
inference(rectify,[],[f361]) ).
fof(f361,axiom,
! [X2] :
( ordere223160158up_add(X2)
=> ! [X51,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),X52))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X51))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_add__strict__right__mono) ).
fof(f14338,plain,
spl86_463,
inference(avatar_split_clause,[],[f2049,f14336]) ).
fof(f14336,plain,
( spl86_463
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ ordere779506340up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_463])]) ).
fof(f2049,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ ordere779506340up_add(X0) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f1178,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ ordere779506340up_add(X0) ),
inference(ennf_transformation,[],[f677]) ).
fof(f677,plain,
! [X0] :
( ordere779506340up_add(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X1)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X1))) ) ),
inference(rectify,[],[f283]) ).
fof(f283,axiom,
! [X2] :
( ordere779506340up_add(X2)
=> ! [X51,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),X52))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X51))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_add__right__mono) ).
fof(f14334,plain,
spl86_462,
inference(avatar_split_clause,[],[f2048,f14332]) ).
fof(f14332,plain,
( spl86_462
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ ordere779506340up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_462])]) ).
fof(f2048,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ ordere779506340up_add(X0) ),
inference(cnf_transformation,[],[f1177]) ).
fof(f1177,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ ordere779506340up_add(X0) ),
inference(ennf_transformation,[],[f676]) ).
fof(f676,plain,
! [X0] :
( ordere779506340up_add(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3))) ) ),
inference(rectify,[],[f284]) ).
fof(f284,axiom,
! [X2] :
( ordere779506340up_add(X2)
=> ! [X51,X48,X52] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),X52))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X48)),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X52))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_add__left__mono) ).
fof(f14314,plain,
( spl86_461
| ~ spl86_51
| ~ spl86_87 ),
inference(avatar_split_clause,[],[f3628,f3606,f3423,f14312]) ).
fof(f14312,plain,
( spl86_461
<=> ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| zero_zero(nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_461])]) ).
fof(f3628,plain,
( ! [X0] :
( one_one(nat) != hAPP(nat,nat,suc,X0)
| zero_zero(nat) = X0 )
| ~ spl86_51
| ~ spl86_87 ),
inference(superposition,[],[f3607,f3425]) ).
fof(f14009,plain,
spl86_460,
inference(avatar_split_clause,[],[f3153,f14007]) ).
fof(f14007,plain,
( spl86_460
<=> ! [X0,X3,X2,X1] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_460])]) ).
fof(f3153,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ),
inference(forward_demodulation,[],[f2941,f2854]) ).
fof(f2941,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),combi(fun(X1,bool)),X2)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ),
inference(definition_unfolding,[],[f2658,f2190]) ).
fof(f2658,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X1,bool)) = ti(fun(X1,bool),X2)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ),
inference(cnf_transformation,[],[f1885]) ).
fof(f14005,plain,
spl86_459,
inference(avatar_split_clause,[],[f3152,f14003]) ).
fof(f14003,plain,
( spl86_459
<=> ! [X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_459])]) ).
fof(f3152,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ),
inference(forward_demodulation,[],[f2940,f2854]) ).
fof(f2940,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X3)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ),
inference(definition_unfolding,[],[f2659,f2190]) ).
fof(f2659,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X3)
| hAPP(fun(X0,bool),fun(sum_sum(X1,X0),bool),hAPP(fun(X1,bool),fun(fun(X0,bool),fun(sum_sum(X1,X0),bool)),sum_Plus(X1,X0),X2),X3) != bot_bot(fun(sum_sum(X1,X0),bool)) ),
inference(cnf_transformation,[],[f1885]) ).
fof(f14001,plain,
spl86_458,
inference(avatar_split_clause,[],[f3017,f13999]) ).
fof(f13999,plain,
( spl86_458
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_458])]) ).
fof(f3017,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(forward_demodulation,[],[f2864,f2854]) ).
fof(f2864,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(definition_unfolding,[],[f2333,f2190]) ).
fof(f2333,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ti(fun(X0,bool),X1) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X2) ),
inference(cnf_transformation,[],[f1755]) ).
fof(f13997,plain,
spl86_457,
inference(avatar_split_clause,[],[f2931,f13995]) ).
fof(f13995,plain,
( spl86_457
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_457])]) ).
fof(f2931,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) ),
inference(definition_unfolding,[],[f2649,f2190,f2190]) ).
fof(f2649,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ti(X0,X1) != ti(X0,X2) ),
inference(cnf_transformation,[],[f1597]) ).
fof(f1597,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3)))
| ( ti(X0,X1) != ti(X0,X2)
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
inference(ennf_transformation,[],[f1101]) ).
fof(f1101,plain,
! [X0,X1,X2,X3] :
( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> ti(X0,X1) = ti(X0,X2) )
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X3))) ),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X0,X33,X10,X12] :
( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),X12))
=> ti(X0,X33) = ti(X0,X10) )
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X33),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insertCI) ).
fof(f13993,plain,
spl86_456,
inference(avatar_split_clause,[],[f2549,f13991]) ).
fof(f13991,plain,
( spl86_456
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2,X0)),hAPP(nat,nat,X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(X2)),sK70(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_456])]) ).
fof(f2549,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X2,X0)),hAPP(nat,nat,X2,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK69(X2)),sK70(X2))) ),
inference(cnf_transformation,[],[f1848]) ).
fof(f13978,plain,
spl86_455,
inference(avatar_split_clause,[],[f2461,f13976]) ).
fof(f13976,plain,
( spl86_455
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK62(X0,X1)),sK63(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_455])]) ).
fof(f2461,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK62(X0,X1)),sK63(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1830]) ).
fof(f13974,plain,
spl86_454,
inference(avatar_split_clause,[],[f2451,f13972]) ).
fof(f13972,plain,
( spl86_454
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK57(X0,X1)),sK58(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_454])]) ).
fof(f2451,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK57(X0,X1)),sK58(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f13970,plain,
spl86_453,
inference(avatar_split_clause,[],[f2044,f13968]) ).
fof(f13968,plain,
( spl86_453
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),X3) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3))
| ~ ab_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_453])]) ).
fof(f2044,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),X3) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3))
| ~ ab_semigroup_add(X0) ),
inference(cnf_transformation,[],[f1173]) ).
fof(f1173,plain,
! [X0] :
( ! [X1,X2,X3] : hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),X3) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3))
| ~ ab_semigroup_add(X0) ),
inference(ennf_transformation,[],[f672]) ).
fof(f672,plain,
! [X0] :
( ab_semigroup_add(X0)
=> ! [X1,X2,X3] : hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2)),X3) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X2),X3)) ),
inference(rectify,[],[f302]) ).
fof(f302,axiom,
! [X2] :
( ab_semigroup_add(X2)
=> ! [X48,X52,X51] : hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X52)),X51) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(f13013,plain,
( spl86_452
| ~ spl86_73
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4217,f4161,f3545,f13010]) ).
fof(f3545,plain,
( spl86_73
<=> u = hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_73])]) ).
fof(f4217,plain,
( u = hAPP(fun(pname,bool),fun(pname,bool),collect(pname),u)
| ~ spl86_73
| ~ spl86_165 ),
inference(superposition,[],[f4162,f3547]) ).
fof(f3547,plain,
( u = hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u)
| ~ spl86_73 ),
inference(avatar_component_clause,[],[f3545]) ).
fof(f13008,plain,
spl86_451,
inference(avatar_split_clause,[],[f3101,f13006]) ).
fof(f3101,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(forward_demodulation,[],[f2898,f2854]) ).
fof(f2898,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(definition_unfolding,[],[f2523,f2190]) ).
fof(f2523,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(cnf_transformation,[],[f1504]) ).
fof(f1504,plain,
! [X0,X1,X2] :
( hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(ennf_transformation,[],[f1018]) ).
fof(f1018,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2) = ti(fun(X0,bool),X2) ),
inference(rectify,[],[f119]) ).
fof(f119,axiom,
! [X0,X10,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),X7))
=> hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X7) = ti(fun(X0,bool),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_insert__absorb) ).
fof(f13004,plain,
spl86_450,
inference(avatar_split_clause,[],[f2857,f13002]) ).
fof(f13002,plain,
( spl86_450
<=> ! [X0,X1] : sum_Plus(X0,X1) = hAPP(fun(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool))),fun(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool))),combi(fun(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)))),sum_Plus(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_450])]) ).
fof(f2857,plain,
! [X0,X1] : sum_Plus(X0,X1) = hAPP(fun(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool))),fun(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool))),combi(fun(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)))),sum_Plus(X0,X1)),
inference(definition_unfolding,[],[f2198,f2190]) ).
fof(f2198,plain,
! [X0,X1] : sum_Plus(X0,X1) = ti(fun(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool))),sum_Plus(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] : sum_Plus(X0,X1) = ti(fun(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool))),sum_Plus(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Sum__Type_OPlus_res) ).
fof(f13000,plain,
spl86_449,
inference(avatar_split_clause,[],[f2641,f12998]) ).
fof(f2641,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3))) ),
inference(cnf_transformation,[],[f1590]) ).
fof(f1590,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3))) ),
inference(ennf_transformation,[],[f1095]) ).
fof(f1095,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3)))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(rectify,[],[f496]) ).
fof(f496,axiom,
! [X0,X1,X7,X12] :
( hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X7),X12)))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_finite__PlusD_I1_J) ).
fof(f12996,plain,
spl86_448,
inference(avatar_split_clause,[],[f2640,f12994]) ).
fof(f2640,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3))) ),
inference(cnf_transformation,[],[f1589]) ).
fof(f1589,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
| ~ hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3))) ),
inference(ennf_transformation,[],[f1094]) ).
fof(f1094,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X2),X3)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(rectify,[],[f497]) ).
fof(f497,axiom,
! [X0,X1,X7,X12] :
( hBOOL(hAPP(fun(sum_sum(X0,X1),bool),bool,finite_finite(sum_sum(X0,X1)),hAPP(fun(X1,bool),fun(sum_sum(X0,X1),bool),hAPP(fun(X0,bool),fun(fun(X1,bool),fun(sum_sum(X0,X1),bool)),sum_Plus(X0,X1),X7),X12)))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_finite__PlusD_I2_J) ).
fof(f12992,plain,
spl86_447,
inference(avatar_split_clause,[],[f2577,f12990]) ).
fof(f12990,plain,
( spl86_447
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_447])]) ).
fof(f2577,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1864]) ).
fof(f1864,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2))) ) ),
inference(nnf_transformation,[],[f1047]) ).
fof(f1047,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(rectify,[],[f311]) ).
fof(f311,axiom,
! [X18,X27,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X27)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X19)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_nat__add__left__cancel__le) ).
fof(f12988,plain,
spl86_446,
inference(avatar_split_clause,[],[f2576,f12986]) ).
fof(f12986,plain,
( spl86_446
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_446])]) ).
fof(f2576,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2))) ),
inference(cnf_transformation,[],[f1864]) ).
fof(f12984,plain,
spl86_445,
inference(avatar_split_clause,[],[f2575,f12982]) ).
fof(f12982,plain,
( spl86_445
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_445])]) ).
fof(f2575,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1863]) ).
fof(f1863,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2))) ) ),
inference(nnf_transformation,[],[f1046]) ).
fof(f1046,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(rectify,[],[f354]) ).
fof(f354,axiom,
! [X18,X27,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X27)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X19)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X27),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_nat__add__left__cancel__less) ).
fof(f12980,plain,
spl86_444,
inference(avatar_split_clause,[],[f2574,f12978]) ).
fof(f12978,plain,
( spl86_444
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_444])]) ).
fof(f2574,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2))) ),
inference(cnf_transformation,[],[f1863]) ).
fof(f12976,plain,
spl86_443,
inference(avatar_split_clause,[],[f2567,f12974]) ).
fof(f12974,plain,
( spl86_443
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_443])]) ).
fof(f2567,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))) ),
inference(cnf_transformation,[],[f1859]) ).
fof(f1859,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2)) ) ),
inference(nnf_transformation,[],[f1042]) ).
fof(f1042,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))) ),
inference(rectify,[],[f331]) ).
fof(f331,axiom,
! [X63,X18,X35] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X63),X18)),X35))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X63),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X18))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_le__diff__conv) ).
fof(f12972,plain,
spl86_442,
inference(avatar_split_clause,[],[f2566,f12970]) ).
fof(f12970,plain,
( spl86_442
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_442])]) ).
fof(f2566,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2)) ),
inference(cnf_transformation,[],[f1859]) ).
fof(f12968,plain,
( spl86_441
| ~ spl86_72
| ~ spl86_165 ),
inference(avatar_split_clause,[],[f4216,f4161,f3540,f12965]) ).
fof(f3540,plain,
( spl86_72
<=> g = hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_72])]) ).
fof(f4216,plain,
( g = hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),g)
| ~ spl86_72
| ~ spl86_165 ),
inference(superposition,[],[f4162,f3542]) ).
fof(f3542,plain,
( g = hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g)
| ~ spl86_72 ),
inference(avatar_component_clause,[],[f3540]) ).
fof(f12963,plain,
spl86_440,
inference(avatar_split_clause,[],[f2565,f12961]) ).
fof(f12961,plain,
( spl86_440
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_440])]) ).
fof(f2565,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1)) ),
inference(cnf_transformation,[],[f1858]) ).
fof(f1858,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ) ),
inference(nnf_transformation,[],[f1041]) ).
fof(f1041,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1)) ),
inference(rectify,[],[f454]) ).
fof(f454,axiom,
! [X35,X63,X18] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X63),X18)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X35),X18)),X63)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_less__diff__conv) ).
fof(f12959,plain,
spl86_439,
inference(avatar_split_clause,[],[f2564,f12957]) ).
fof(f12957,plain,
( spl86_439
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_439])]) ).
fof(f2564,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2))) ),
inference(cnf_transformation,[],[f1858]) ).
fof(f12955,plain,
spl86_438,
inference(avatar_split_clause,[],[f2499,f12953]) ).
fof(f12953,plain,
( spl86_438
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_438])]) ).
fof(f2499,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1481]) ).
fof(f1481,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1001]) ).
fof(f1001,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1))) ),
inference(rectify,[],[f97]) ).
fof(f97,axiom,
! [X28,X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X28),X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_diff__le__mono2) ).
fof(f12951,plain,
spl86_437,
inference(avatar_split_clause,[],[f2498,f12949]) ).
fof(f12949,plain,
( spl86_437
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_437])]) ).
fof(f2498,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1480]) ).
fof(f1480,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1000]) ).
fof(f1000,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0))) ),
inference(rectify,[],[f96]) ).
fof(f96,axiom,
! [X28,X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X28)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X16),X28))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_diff__le__mono) ).
fof(f12947,plain,
spl86_436,
inference(avatar_split_clause,[],[f2497,f12945]) ).
fof(f12945,plain,
( spl86_436
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_436])]) ).
fof(f2497,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1479]) ).
fof(f1479,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f999]) ).
fof(f999,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0))) ),
inference(rectify,[],[f314]) ).
fof(f314,axiom,
! [X24,X25,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X26))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X24)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_add__le__mono1) ).
fof(f12943,plain,
spl86_435,
inference(avatar_split_clause,[],[f2496,f12941]) ).
fof(f12941,plain,
( spl86_435
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_435])]) ).
fof(f2496,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1478]) ).
fof(f1478,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f998]) ).
fof(f998,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)),X1))) ),
inference(rectify,[],[f330]) ).
fof(f330,axiom,
! [X17,X24,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X17)),X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_le__add__diff) ).
fof(f12939,plain,
spl86_434,
inference(avatar_split_clause,[],[f2488,f12937]) ).
fof(f12937,plain,
( spl86_434
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_434])]) ).
fof(f2488,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1467]) ).
fof(f1467,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(ennf_transformation,[],[f990]) ).
fof(f990,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0))) ),
inference(rectify,[],[f351]) ).
fof(f351,axiom,
! [X24,X25,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X26))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X24)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X24))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_add__less__mono1) ).
fof(f12449,plain,
spl86_433,
inference(avatar_split_clause,[],[f3062,f12447]) ).
fof(f12447,plain,
( spl86_433
<=> ! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_433])]) ).
fof(f3062,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),
inference(forward_demodulation,[],[f2416,f2415]) ).
fof(f2416,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),X1),
inference(cnf_transformation,[],[f939]) ).
fof(f939,plain,
! [X0,X1,X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2)),X1),
inference(rectify,[],[f78]) ).
fof(f78,axiom,
! [X25,X26,X24] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X25),X26)),X24) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X25),X24)),X26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_diff__commute) ).
fof(f12445,plain,
spl86_432,
inference(avatar_split_clause,[],[f2415,f12443]) ).
fof(f12443,plain,
( spl86_432
<=> ! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_432])]) ).
fof(f12441,plain,
spl86_431,
inference(avatar_split_clause,[],[f2414,f12439]) ).
fof(f12439,plain,
( spl86_431
<=> ! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_431])]) ).
fof(f2414,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2),
inference(cnf_transformation,[],[f937]) ).
fof(f937,plain,
! [X0,X1,X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2),
inference(rectify,[],[f294]) ).
fof(f294,axiom,
! [X17,X16,X24] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X16)),X24) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_nat__add__assoc) ).
fof(f12437,plain,
spl86_430,
inference(avatar_split_clause,[],[f2413,f12435]) ).
fof(f12435,plain,
( spl86_430
<=> ! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_430])]) ).
fof(f2413,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),
inference(cnf_transformation,[],[f936]) ).
fof(f936,plain,
! [X0,X1,X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),
inference(rectify,[],[f295]) ).
fof(f295,axiom,
! [X20,X21,X50] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X20),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),X50)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X20),X50)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_nat__add__left__commute) ).
fof(f12433,plain,
spl86_429,
inference(avatar_split_clause,[],[f2412,f12431]) ).
fof(f12431,plain,
( spl86_429
<=> ! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_429])]) ).
fof(f2412,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),
inference(cnf_transformation,[],[f935]) ).
fof(f935,plain,
! [X0,X1,X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)),
inference(rectify,[],[f306]) ).
fof(f306,axiom,
! [X24,X17,X16] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X24),X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X24),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_diff__cancel) ).
fof(f12429,plain,
spl86_428,
inference(avatar_split_clause,[],[f2411,f12427]) ).
fof(f12427,plain,
( spl86_428
<=> ! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_428])]) ).
fof(f2411,plain,
! [X2,X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),
inference(cnf_transformation,[],[f934]) ).
fof(f934,plain,
! [X0,X1,X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)),
inference(rectify,[],[f307]) ).
fof(f307,axiom,
! [X17,X24,X16] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X24)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X24)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_diff__cancel2) ).
fof(f12390,plain,
( spl86_427
| ~ spl86_176
| ~ spl86_411 ),
inference(avatar_split_clause,[],[f11726,f11661,f4277,f12388]) ).
fof(f12388,plain,
( spl86_427
<=> ! [X2,X0,X1] : sP7(X0,bot_bot(fun(X1,bool)),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_427])]) ).
fof(f11661,plain,
( spl86_411
<=> ! [X0,X3,X2,X1] :
( sP7(X3,X1,X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_411])]) ).
fof(f11726,plain,
( ! [X2,X0,X1] : sP7(X0,bot_bot(fun(X1,bool)),X1,X2)
| ~ spl86_176
| ~ spl86_411 ),
inference(resolution,[],[f11662,f4278]) ).
fof(f11662,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| sP7(X3,X1,X0,X2) )
| ~ spl86_411 ),
inference(avatar_component_clause,[],[f11661]) ).
fof(f11914,plain,
( spl86_426
| ~ spl86_109
| ~ spl86_165
| ~ spl86_425 ),
inference(avatar_split_clause,[],[f11910,f11907,f4161,f3702,f11912]) ).
fof(f11912,plain,
( spl86_426
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_426])]) ).
fof(f11907,plain,
( spl86_425
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_425])]) ).
fof(f11910,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_425 ),
inference(forward_demodulation,[],[f11908,f4236]) ).
fof(f11908,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) )
| ~ spl86_425 ),
inference(avatar_component_clause,[],[f11907]) ).
fof(f11909,plain,
spl86_425,
inference(avatar_split_clause,[],[f3126,f11907]) ).
fof(f3126,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) ),
inference(forward_demodulation,[],[f2913,f2226]) ).
fof(f2913,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) ),
inference(definition_unfolding,[],[f2579,f2190,f2190]) ).
fof(f2579,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))
| ti(X0,X1) != ti(X0,X2) ),
inference(cnf_transformation,[],[f1865]) ).
fof(f1865,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))
| ti(X0,X1) != ti(X0,X2) )
& ( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ) ),
inference(nnf_transformation,[],[f1048]) ).
fof(f1048,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))
<=> ti(X0,X1) = ti(X0,X2) ),
inference(rectify,[],[f174]) ).
fof(f174,axiom,
! [X0,X33,X10] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X33),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool)))))
<=> ti(X0,X33) = ti(X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_singleton__iff) ).
fof(f11886,plain,
( spl86_424
| ~ spl86_109
| ~ spl86_165
| ~ spl86_423 ),
inference(avatar_split_clause,[],[f11882,f11879,f4161,f3702,f11884]) ).
fof(f11884,plain,
( spl86_424
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_424])]) ).
fof(f11879,plain,
( spl86_423
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_423])]) ).
fof(f11882,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(X0,fun(X0,bool),fequal(X0),X2)))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2) )
| ~ spl86_109
| ~ spl86_165
| ~ spl86_423 ),
inference(forward_demodulation,[],[f11880,f4236]) ).
fof(f11880,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2) )
| ~ spl86_423 ),
inference(avatar_component_clause,[],[f11879]) ).
fof(f11881,plain,
spl86_423,
inference(avatar_split_clause,[],[f3107,f11879]) ).
fof(f3107,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X2))))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2) ),
inference(forward_demodulation,[],[f2901,f2226]) ).
fof(f2901,plain,
! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(definition_unfolding,[],[f2534,f2190,f2190]) ).
fof(f2534,plain,
! [X2,X0,X1] :
( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(cnf_transformation,[],[f1516]) ).
fof(f1516,plain,
! [X0,X1,X2] :
( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))) ),
inference(ennf_transformation,[],[f1028]) ).
fof(f1028,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool)))))
=> ti(X0,X1) = ti(X0,X2) ),
inference(rectify,[],[f172]) ).
fof(f172,axiom,
! [X0,X33,X10] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X33),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),bot_bot(fun(X0,bool)))))
=> ti(X0,X33) = ti(X0,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_singletonE) ).
fof(f11877,plain,
spl86_422,
inference(avatar_split_clause,[],[f2780,f11875]) ).
fof(f11875,plain,
( spl86_422
<=> ! [X0] : finite_folding_one(X0) = hAPP(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),combi(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool))),finite_folding_one(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_422])]) ).
fof(f2780,plain,
! [X0] : finite_folding_one(X0) = hAPP(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),combi(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool))),finite_folding_one(X0)),
inference(definition_unfolding,[],[f2017,f2190]) ).
fof(f2017,plain,
! [X0] : finite_folding_one(X0) = ti(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),finite_folding_one(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : finite_folding_one(X0) = ti(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),finite_folding_one(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one_res) ).
fof(f11872,plain,
spl86_421,
inference(avatar_split_clause,[],[f2779,f11870]) ).
fof(f11870,plain,
( spl86_421
<=> ! [X0] : finite2073411215e_idem(X0) = hAPP(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),combi(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool))),finite2073411215e_idem(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_421])]) ).
fof(f2779,plain,
! [X0] : finite2073411215e_idem(X0) = hAPP(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),combi(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool))),finite2073411215e_idem(X0)),
inference(definition_unfolding,[],[f2016,f2190]) ).
fof(f2016,plain,
! [X0] : finite2073411215e_idem(X0) = ti(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),finite2073411215e_idem(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] : finite2073411215e_idem(X0) = ti(fun(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool)),finite2073411215e_idem(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofolding__one__idem_res) ).
fof(f11868,plain,
spl86_420,
inference(avatar_split_clause,[],[f2738,f11866]) ).
fof(f11866,plain,
( spl86_420
<=> ! [X3,X4,X0,X5,X2,X1] : hAPP(X0,X1,hAPP(fun(X0,X2),fun(X0,X1),hAPP(fun(X0,fun(X2,X1)),fun(fun(X0,X2),fun(X0,X1)),combs(X0,X2,X1),X3),X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),hAPP(X0,X2,X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_420])]) ).
fof(f2738,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(X0,X1,hAPP(fun(X0,X2),fun(X0,X1),hAPP(fun(X0,fun(X2,X1)),fun(fun(X0,X2),fun(X0,X1)),combs(X0,X2,X1),X3),X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),hAPP(X0,X2,X4,X5)),
inference(cnf_transformation,[],[f1138]) ).
fof(f1138,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(X0,X1,hAPP(fun(X0,X2),fun(X0,X1),hAPP(fun(X0,fun(X2,X1)),fun(fun(X0,X2),fun(X0,X1)),combs(X0,X2,X1),X3),X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),hAPP(X0,X2,X4,X5)),
inference(rectify,[],[f589]) ).
fof(f589,axiom,
! [X2,X1,X0,X79,X80,X81] : hAPP(X2,X1,hAPP(fun(X2,X0),fun(X2,X1),hAPP(fun(X2,fun(X0,X1)),fun(fun(X2,X0),fun(X2,X1)),combs(X2,X0,X1),X79),X80),X81) = hAPP(X0,X1,hAPP(X2,fun(X0,X1),X79,X81),hAPP(X2,X0,X80,X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
fof(f11864,plain,
spl86_419,
inference(avatar_split_clause,[],[f2285,f11862]) ).
fof(f11862,plain,
( spl86_419
<=> ! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X0) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_419])]) ).
fof(f2285,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X0) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1365]) ).
fof(f1365,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X0) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f869]) ).
fof(f869,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X1)),X0) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) ),
inference(rectify,[],[f64]) ).
fof(f64,axiom,
! [X16,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X17)),X16) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Suc__diff__le) ).
fof(f11843,plain,
( spl86_418
| ~ spl86_144
| ~ spl86_417 ),
inference(avatar_split_clause,[],[f11838,f11834,f4026,f11840]) ).
fof(f11840,plain,
( spl86_418
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),na),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_418])]) ).
fof(f11834,plain,
( spl86_417
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_417])]) ).
fof(f11838,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),na),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))))
| ~ spl86_144
| ~ spl86_417 ),
inference(forward_demodulation,[],[f11836,f4027]) ).
fof(f11836,plain,
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))))
| ~ spl86_417 ),
inference(avatar_component_clause,[],[f11834]) ).
fof(f11837,plain,
spl86_417,
inference(avatar_split_clause,[],[f1939,f11834]) ).
fof(f1939,plain,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
inference(cnf_transformation,[],[f605]) ).
fof(f605,axiom,
hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,na)),hAPP(fun(x_a,bool),nat,finite_card(x_a),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f11744,plain,
( spl86_416
| ~ spl86_346
| ~ spl86_411 ),
inference(avatar_split_clause,[],[f11724,f11661,f8920,f11742]) ).
fof(f11742,plain,
( spl86_416
<=> ! [X2,X0,X1] : sP7(X0,X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_416])]) ).
fof(f8920,plain,
( spl86_346
<=> ! [X2,X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_346])]) ).
fof(f11724,plain,
( ! [X2,X0,X1] : sP7(X0,X0,X1,X2)
| ~ spl86_346
| ~ spl86_411 ),
inference(resolution,[],[f11662,f8921]) ).
fof(f8921,plain,
( ! [X2,X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1)))
| ~ spl86_346 ),
inference(avatar_component_clause,[],[f8920]) ).
fof(f11679,plain,
spl86_415,
inference(avatar_split_clause,[],[f3037,f11677]) ).
fof(f11677,plain,
( spl86_415
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_415])]) ).
fof(f3037,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1)) ),
inference(forward_demodulation,[],[f2373,f2022]) ).
fof(f2022,plain,
! [X0] : hAPP(nat,fun(nat,bool),ord_less(nat),X0) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),
inference(cnf_transformation,[],[f640]) ).
fof(f640,plain,
! [X0] : hAPP(nat,fun(nat,bool),ord_less(nat),X0) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),
inference(rectify,[],[f457]) ).
fof(f457,axiom,
! [X32] : hAPP(nat,fun(nat,bool),ord_less(nat),X32) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_less__eq__Suc__le__raw) ).
fof(f2373,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(cnf_transformation,[],[f1795]) ).
fof(f1795,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1)) )
& ( hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1)) ) ),
inference(nnf_transformation,[],[f917]) ).
fof(f917,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1))
<=> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1)) ),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X27,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X27)),X19))
<=> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27)),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_less__eq__nat_Osimps_I2_J) ).
fof(f11675,plain,
spl86_414,
inference(avatar_split_clause,[],[f3036,f11673]) ).
fof(f11673,plain,
( spl86_414
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_414])]) ).
fof(f3036,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1)) ),
inference(forward_demodulation,[],[f2374,f2022]) ).
fof(f2374,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0)),X1)) ),
inference(cnf_transformation,[],[f1795]) ).
fof(f11671,plain,
spl86_413,
inference(avatar_split_clause,[],[f2703,f11669]) ).
fof(f11669,plain,
( spl86_413
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),X3) = hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),X3))
| ~ hBOOL(hAPP(fun(X0,fun(X1,X1)),bool,finite_comp_fun_idem(X0,X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_413])]) ).
fof(f2703,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),X3) = hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),X3))
| ~ hBOOL(hAPP(fun(X0,fun(X1,X1)),bool,finite_comp_fun_idem(X0,X1),X4)) ),
inference(cnf_transformation,[],[f1605]) ).
fof(f1605,plain,
! [X0,X1,X2,X3,X4] :
( hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),X3) = hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),X3))
| ~ hBOOL(hAPP(fun(X0,fun(X1,X1)),bool,finite_comp_fun_idem(X0,X1),X4)) ),
inference(ennf_transformation,[],[f1118]) ).
fof(f1118,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(fun(X0,fun(X1,X1)),bool,finite_comp_fun_idem(X0,X1),X4))
=> hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),X3) = hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),hAPP(X1,X1,hAPP(X0,fun(X1,X1),X4,X2),X3)) ),
inference(rectify,[],[f291]) ).
fof(f291,axiom,
! [X0,X1,X13,X41,X11] :
( hBOOL(hAPP(fun(X0,fun(X1,X1)),bool,finite_comp_fun_idem(X0,X1),X11))
=> hAPP(X1,X1,hAPP(X0,fun(X1,X1),X11,X13),X41) = hAPP(X1,X1,hAPP(X0,fun(X1,X1),X11,X13),hAPP(X1,X1,hAPP(X0,fun(X1,X1),X11,X13),X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_comp__fun__idem_Ofun__left__idem) ).
fof(f11667,plain,
spl86_412,
inference(avatar_split_clause,[],[f2691,f11665]) ).
fof(f11665,plain,
( spl86_412
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ sP7(X3,X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_412])]) ).
fof(f2691,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ sP7(X3,X1,X0,X2) ),
inference(cnf_transformation,[],[f1902]) ).
fof(f1902,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ sP7(X3,X1,X0,X2) )
& ( sP7(X3,X1,X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ) ),
inference(nnf_transformation,[],[f1655]) ).
fof(f1655,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
<=> sP7(X3,X1,X0,X2) ),
inference(definition_folding,[],[f1600,f1654]) ).
fof(f1600,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
<=> ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ) ),
inference(ennf_transformation,[],[f1111]) ).
fof(f1111,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
<=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3)) ) ) ),
inference(rectify,[],[f238]) ).
fof(f238,axiom,
! [X0,X7,X13,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X12)))
<=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))),X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_subset__insert__iff) ).
fof(f11663,plain,
spl86_411,
inference(avatar_split_clause,[],[f2690,f11661]) ).
fof(f2690,plain,
! [X2,X3,X0,X1] :
( sP7(X3,X1,X0,X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ),
inference(cnf_transformation,[],[f1902]) ).
fof(f11659,plain,
spl86_410,
inference(avatar_split_clause,[],[f2683,f11657]) ).
fof(f2683,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ sP6(X2,X0,X1,X3) ),
inference(cnf_transformation,[],[f1898]) ).
fof(f1898,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
| ~ sP6(X2,X0,X1,X3) )
& ( sP6(X2,X0,X1,X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ) ),
inference(nnf_transformation,[],[f1653]) ).
fof(f1653,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
<=> sP6(X2,X0,X1,X3) ),
inference(definition_folding,[],[f1599,f1652,f1651]) ).
fof(f1652,plain,
! [X2,X0,X1,X3] :
( sP6(X2,X0,X1,X3)
<=> ( ( sP5(X3,X1,X0,X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f1599,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
<=> ( ( ( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) )
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ) ),
inference(ennf_transformation,[],[f1110]) ).
fof(f1110,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
<=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X3)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),bot_bot(fun(X0,bool))))),X3)) ) ) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X3)) ) ) ),
inference(rectify,[],[f469]) ).
fof(f469,axiom,
! [X0,X7,X13,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X12)))
<=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X12))
=> ( ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool))))),X12)) ) ) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X12))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_psubset__insert__iff) ).
fof(f11655,plain,
spl86_409,
inference(avatar_split_clause,[],[f2682,f11653]) ).
fof(f11653,plain,
( spl86_409
<=> ! [X0,X3,X2,X1] :
( sP6(X2,X0,X1,X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_409])]) ).
fof(f2682,plain,
! [X2,X3,X0,X1] :
( sP6(X2,X0,X1,X3)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3))) ),
inference(cnf_transformation,[],[f1898]) ).
fof(f11650,plain,
( spl86_408
| spl86_171
| ~ spl86_354 ),
inference(avatar_split_clause,[],[f9390,f8977,f4256,f11647]) ).
fof(f11647,plain,
( spl86_408
<=> fTrue = hAPP(bool,bool,fNot,bot_bot(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_408])]) ).
fof(f8977,plain,
( spl86_354
<=> ! [X0] :
( fTrue = hAPP(bool,bool,fNot,X0)
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_354])]) ).
fof(f9390,plain,
( fTrue = hAPP(bool,bool,fNot,bot_bot(bool))
| spl86_171
| ~ spl86_354 ),
inference(resolution,[],[f8978,f4258]) ).
fof(f4258,plain,
( ~ hBOOL(bot_bot(bool))
| spl86_171 ),
inference(avatar_component_clause,[],[f4256]) ).
fof(f8978,plain,
( ! [X0] :
( hBOOL(X0)
| fTrue = hAPP(bool,bool,fNot,X0) )
| ~ spl86_354 ),
inference(avatar_component_clause,[],[f8977]) ).
fof(f11642,plain,
( spl86_407
| ~ spl86_108
| ~ spl86_165
| ~ spl86_406 ),
inference(avatar_split_clause,[],[f11638,f11635,f4161,f3698,f11640]) ).
fof(f11640,plain,
( spl86_407
<=> ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_407])]) ).
fof(f11635,plain,
( spl86_406
<=> ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_406])]) ).
fof(f11638,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0))
| ~ spl86_108
| ~ spl86_165
| ~ spl86_406 ),
inference(forward_demodulation,[],[f11636,f4223]) ).
fof(f11636,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0)))
| ~ spl86_406 ),
inference(avatar_component_clause,[],[f11635]) ).
fof(f11637,plain,
spl86_406,
inference(avatar_split_clause,[],[f2027,f11635]) ).
fof(f2027,plain,
! [X0] : hAPP(nat,nat,suc,X0) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0))),
inference(cnf_transformation,[],[f644]) ).
fof(f644,plain,
! [X0] : hAPP(nat,nat,suc,X0) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0))),
inference(rectify,[],[f66]) ).
fof(f66,axiom,
! [X19] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X19))) = hAPP(nat,nat,suc,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_card__Collect__le__nat) ).
fof(f11353,plain,
spl86_405,
inference(avatar_split_clause,[],[f2934,f11351]) ).
fof(f11351,plain,
( spl86_405
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,X2,X3))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X3)
| ~ hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_405])]) ).
fof(f2934,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,X2,X3))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X3)
| ~ hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3)) ),
inference(definition_unfolding,[],[f2651,f2190,f2190]) ).
fof(f2651,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,X2,X3))
| ti(X0,X1) = ti(X0,X3)
| ~ hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3)) ),
inference(cnf_transformation,[],[f1881]) ).
fof(f1881,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3))
| ( ~ hBOOL(hAPP(X0,bool,X2,X3))
& ti(X0,X1) != ti(X0,X3) ) )
& ( hBOOL(hAPP(X0,bool,X2,X3))
| ti(X0,X1) = ti(X0,X3)
| ~ hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3)) ) ),
inference(flattening,[],[f1880]) ).
fof(f1880,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3))
| ( ~ hBOOL(hAPP(X0,bool,X2,X3))
& ti(X0,X1) != ti(X0,X3) ) )
& ( hBOOL(hAPP(X0,bool,X2,X3))
| ti(X0,X1) = ti(X0,X3)
| ~ hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3)) ) ),
inference(nnf_transformation,[],[f1103]) ).
fof(f1103,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3))
<=> ( hBOOL(hAPP(X0,bool,X2,X3))
| ti(X0,X1) = ti(X0,X3) ) ),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X0,X38,X7,X13] :
( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X38),X7),X13))
<=> ( hBOOL(hAPP(X0,bool,X7,X13))
| ti(X0,X38) = ti(X0,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_insert__code) ).
fof(f11349,plain,
spl86_404,
inference(avatar_split_clause,[],[f2932,f11347]) ).
fof(f11347,plain,
( spl86_404
<=> ! [X0,X3,X2,X1] :
( hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),X2) = hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),X3)
| hAPP(X0,X1,X2,sK77(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK77(X0,X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_404])]) ).
fof(f2932,plain,
! [X2,X3,X0,X1] :
( hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),X2) = hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),X3)
| hAPP(X0,X1,X2,sK77(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK77(X0,X1,X2,X3)) ),
inference(definition_unfolding,[],[f2650,f2190,f2190]) ).
fof(f2650,plain,
! [X2,X3,X0,X1] :
( ti(fun(X0,X1),X2) = ti(fun(X0,X1),X3)
| hAPP(X0,X1,X2,sK77(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK77(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f1879]) ).
fof(f1879,plain,
! [X0,X1,X2,X3] :
( ti(fun(X0,X1),X2) = ti(fun(X0,X1),X3)
| hAPP(X0,X1,X2,sK77(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK77(X0,X1,X2,X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77])],[f1598,f1878]) ).
fof(f1878,plain,
! [X0,X1,X2,X3] :
( ? [X4] : hAPP(X0,X1,X2,X4) != hAPP(X0,X1,X3,X4)
=> hAPP(X0,X1,X2,sK77(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK77(X0,X1,X2,X3)) ),
introduced(choice_axiom,[]) ).
fof(f1598,plain,
! [X0,X1,X2,X3] :
( ti(fun(X0,X1),X2) = ti(fun(X0,X1),X3)
| ? [X4] : hAPP(X0,X1,X2,X4) != hAPP(X0,X1,X3,X4) ),
inference(ennf_transformation,[],[f1102]) ).
fof(f1102,plain,
! [X0,X1,X2,X3] :
( ! [X4] : hAPP(X0,X1,X2,X4) = hAPP(X0,X1,X3,X4)
=> ti(fun(X0,X1),X2) = ti(fun(X0,X1),X3) ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X0,X1,X11,X39] :
( ! [X32] : hAPP(X0,X1,X11,X32) = hAPP(X0,X1,X39,X32)
=> ti(fun(X0,X1),X11) = ti(fun(X0,X1),X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
fof(f11345,plain,
spl86_403,
inference(avatar_split_clause,[],[f2880,f11343]) ).
fof(f11343,plain,
( spl86_403
<=> ! [X2,X0,X1] : combc(X0,X1,X2) = hAPP(fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))),fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))),combi(fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2)))),combc(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_403])]) ).
fof(f2880,plain,
! [X2,X0,X1] : combc(X0,X1,X2) = hAPP(fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))),fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))),combi(fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2)))),combc(X0,X1,X2)),
inference(definition_unfolding,[],[f2402,f2190]) ).
fof(f2402,plain,
! [X2,X0,X1] : combc(X0,X1,X2) = ti(fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))),combc(X0,X1,X2)),
inference(cnf_transformation,[],[f925]) ).
fof(f925,plain,
! [X0,X1,X2] : combc(X0,X1,X2) = ti(fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))),combc(X0,X1,X2)),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X0,X1] : combc(X2,X0,X1) = ti(fun(fun(X2,fun(X0,X1)),fun(X0,fun(X2,X1))),combc(X2,X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
fof(f11341,plain,
spl86_402,
inference(avatar_split_clause,[],[f2879,f11339]) ).
fof(f11339,plain,
( spl86_402
<=> ! [X2,X0,X1] : combb(X0,X1,X2) = hAPP(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))),fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))),combi(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1)))),combb(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_402])]) ).
fof(f2879,plain,
! [X2,X0,X1] : combb(X0,X1,X2) = hAPP(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))),fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))),combi(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1)))),combb(X0,X1,X2)),
inference(definition_unfolding,[],[f2401,f2190]) ).
fof(f2401,plain,
! [X2,X0,X1] : combb(X0,X1,X2) = ti(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))),combb(X0,X1,X2)),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] : combb(X0,X1,X2) = ti(fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))),combb(X0,X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
fof(f11337,plain,
spl86_401,
inference(avatar_split_clause,[],[f2410,f11335]) ).
fof(f11335,plain,
( spl86_401
<=> ! [X2,X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_401])]) ).
fof(f2410,plain,
! [X2,X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X1)),
inference(cnf_transformation,[],[f933]) ).
fof(f933,plain,
! [X0,X1,X2] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X2)),X1)),
inference(rectify,[],[f226]) ).
fof(f226,axiom,
! [X0,X7,X12] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12)),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Diff__subset) ).
fof(f11333,plain,
spl86_400,
inference(avatar_split_clause,[],[f2251,f11331]) ).
fof(f2251,plain,
! [X2,X3,X0,X1,X5] :
( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X0,X1,X2,X5)),hAPP(X0,X1,X3,X5)))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f1714]) ).
fof(f11329,plain,
spl86_399,
inference(avatar_split_clause,[],[f2249,f11327]) ).
fof(f11327,plain,
( spl86_399
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_399])]) ).
fof(f2249,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X3),X2))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f1710]) ).
fof(f11325,plain,
spl86_398,
inference(avatar_split_clause,[],[f2248,f11323]) ).
fof(f11323,plain,
( spl86_398
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_398])]) ).
fof(f2248,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less_eq(fun(X0,X1)),X2),X3))
| ~ hBOOL(hAPP(fun(X0,X1),bool,hAPP(fun(X0,X1),fun(fun(X0,X1),bool),ord_less(fun(X0,X1)),X2),X3))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f1710]) ).
fof(f11128,plain,
spl86_397,
inference(avatar_split_clause,[],[f3147,f11126]) ).
fof(f11126,plain,
( spl86_397
<=> ! [X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| bot_bot(fun(X1,bool)) != hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_397])]) ).
fof(f3147,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| bot_bot(fun(X1,bool)) != hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3) ),
inference(forward_demodulation,[],[f2936,f2854]) ).
fof(f2936,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X3)
| bot_bot(fun(X1,bool)) != hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3) ),
inference(definition_unfolding,[],[f2654,f2190]) ).
fof(f2654,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X3)
| bot_bot(fun(X1,bool)) != hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3) ),
inference(cnf_transformation,[],[f1882]) ).
fof(f1882,plain,
! [X0,X1,X2,X3] :
( ( bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X3) )
& ( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X3)
| bot_bot(fun(X1,bool)) != hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3) ) ),
inference(nnf_transformation,[],[f1104]) ).
fof(f1104,plain,
! [X0,X1,X2,X3] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)
<=> bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X3) ),
inference(rectify,[],[f178]) ).
fof(f178,axiom,
! [X1,X0,X11,X7] :
( hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),X7) = bot_bot(fun(X0,bool))
<=> ti(fun(X1,bool),X7) = bot_bot(fun(X1,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_image__is__empty) ).
fof(f11124,plain,
spl86_396,
inference(avatar_split_clause,[],[f3146,f11122]) ).
fof(f11122,plain,
( spl86_396
<=> ! [X0,X3,X2,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_396])]) ).
fof(f3146,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X3)
| bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3) ),
inference(forward_demodulation,[],[f2935,f2854]) ).
fof(f2935,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X3) ),
inference(definition_unfolding,[],[f2655,f2190]) ).
fof(f2655,plain,
! [X2,X3,X0,X1] :
( bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),X3)
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X3) ),
inference(cnf_transformation,[],[f1882]) ).
fof(f11120,plain,
spl86_395,
inference(avatar_split_clause,[],[f2926,f11118]) ).
fof(f11118,plain,
( spl86_395
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X1),X1)
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_395])]) ).
fof(f2926,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X1),X1)
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X2),X3)) ),
inference(definition_unfolding,[],[f2636,f2190]) ).
fof(f2636,plain,
! [X2,X3,X0,X1] :
( ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X1),X1)
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X2),X3)) ),
inference(cnf_transformation,[],[f1583]) ).
fof(f1583,plain,
! [X0,X1,X2,X3] :
( ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X1),X1)
| ~ hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X2),X3)) ),
inference(ennf_transformation,[],[f1090]) ).
fof(f1090,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X2),X3))
=> ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X2,X1),X1) ),
inference(rectify,[],[f217]) ).
fof(f217,axiom,
! [X0,X13,X11,X9] :
( hBOOL(hAPP(fun(fun(X0,bool),X0),bool,hAPP(fun(X0,fun(X0,X0)),fun(fun(fun(X0,bool),X0),bool),finite2073411215e_idem(X0),X11),X9))
=> ti(X0,X13) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),X11,X13),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_folding__one__idem_Oidem) ).
fof(f11116,plain,
spl86_394,
inference(avatar_split_clause,[],[f2904,f11114]) ).
fof(f11114,plain,
( spl86_394
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| hAPP(X0,X0,combi(X0),X3) != hAPP(X0,X0,combi(X0),sK71(X0,X2,X3))
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_394])]) ).
fof(f2904,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| hAPP(X0,X0,combi(X0),X3) != hAPP(X0,X0,combi(X0),sK71(X0,X2,X3))
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ),
inference(definition_unfolding,[],[f2552,f2190,f2190,f2190]) ).
fof(f2552,plain,
! [X2,X3,X0,X1] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| ti(X0,X3) != ti(X0,sK71(X0,X2,X3))
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ),
inference(cnf_transformation,[],[f1850]) ).
fof(f1850,plain,
! [X0,X1,X2] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| ! [X3] :
( ( ti(X0,X3) != ti(X0,sK71(X0,X2,X3))
& hBOOL(hAPP(X0,bool,X2,sK71(X0,X2,X3))) )
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71])],[f1528,f1849]) ).
fof(f1849,plain,
! [X0,X2,X3] :
( ? [X4] :
( ti(X0,X3) != ti(X0,X4)
& hBOOL(hAPP(X0,bool,X2,X4)) )
=> ( ti(X0,X3) != ti(X0,sK71(X0,X2,X3))
& hBOOL(hAPP(X0,bool,X2,sK71(X0,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f1528,plain,
! [X0,X1,X2] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| ! [X3] :
( ? [X4] :
( ti(X0,X3) != ti(X0,X4)
& hBOOL(hAPP(X0,bool,X2,X4)) )
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ) ),
inference(flattening,[],[f1527]) ).
fof(f1527,plain,
! [X0,X1,X2] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| ! [X3] :
( ? [X4] :
( ti(X0,X3) != ti(X0,X4)
& hBOOL(hAPP(X0,bool,X2,X4)) )
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ) ),
inference(ennf_transformation,[],[f1036]) ).
fof(f1036,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( hBOOL(hAPP(X0,bool,X2,X4))
=> ti(X0,X3) = ti(X0,X4) )
& hBOOL(hAPP(X0,bool,X2,X3)) )
=> ( hBOOL(hAPP(X0,bool,X2,X1))
=> ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),X2) ) ),
inference(rectify,[],[f269]) ).
fof(f269,axiom,
! [X0,X10,X15] :
( ? [X32] :
( ! [X60] :
( hBOOL(hAPP(X0,bool,X15,X60))
=> ti(X0,X32) = ti(X0,X60) )
& hBOOL(hAPP(X0,bool,X15,X32)) )
=> ( hBOOL(hAPP(X0,bool,X15,X10))
=> ti(X0,X10) = hAPP(fun(X0,bool),X0,the(X0),X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_the1__equality) ).
fof(f11112,plain,
spl86_393,
inference(avatar_split_clause,[],[f2688,f11110]) ).
fof(f11110,plain,
( spl86_393
<=> ! [X0,X3,X2,X1] :
( sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_393])]) ).
fof(f2688,plain,
! [X2,X3,X0,X1] :
( sP7(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ),
inference(cnf_transformation,[],[f1901]) ).
fof(f11108,plain,
spl86_392,
inference(avatar_split_clause,[],[f2685,f11106]) ).
fof(f11106,plain,
( spl86_392
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP7(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_392])]) ).
fof(f2685,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP7(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1901]) ).
fof(f11104,plain,
spl86_391,
inference(avatar_split_clause,[],[f2680,f11102]) ).
fof(f11102,plain,
( spl86_391
<=> ! [X0,X3,X2,X1] :
( sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_391])]) ).
fof(f2680,plain,
! [X2,X3,X0,X1] :
( sP5(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1)) ),
inference(cnf_transformation,[],[f1897]) ).
fof(f11100,plain,
spl86_390,
inference(avatar_split_clause,[],[f2677,f11098]) ).
fof(f11098,plain,
( spl86_390
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_390])]) ).
fof(f2677,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X1),X0))
| hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X3),X1))
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1897]) ).
fof(f11096,plain,
spl86_389,
inference(avatar_split_clause,[],[f2673,f11094]) ).
fof(f11094,plain,
( spl86_389
<=> ! [X0,X3,X2,X1] :
( sP6(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_389])]) ).
fof(f2673,plain,
! [X2,X3,X0,X1] :
( sP6(X0,X1,X2,X3)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1894]) ).
fof(f1894,plain,
! [X0,X1,X2,X3] :
( ( sP6(X0,X1,X2,X3)
| ( ~ sP5(X3,X2,X1,X0)
& ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3)) )
| ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3)) ) )
& ( ( ( sP5(X3,X2,X1,X0)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3)) )
& ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3)) ) )
| ~ sP6(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1893]) ).
fof(f1893,plain,
! [X2,X0,X1,X3] :
( ( sP6(X2,X0,X1,X3)
| ( ~ sP5(X3,X1,X0,X2)
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) )
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) )
& ( ( ( sP5(X3,X1,X0,X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) )
| ~ sP6(X2,X0,X1,X3) ) ),
inference(flattening,[],[f1892]) ).
fof(f1892,plain,
! [X2,X0,X1,X3] :
( ( sP6(X2,X0,X1,X3)
| ( ~ sP5(X3,X1,X0,X2)
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) )
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X3))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) )
& ( ( ( sP5(X3,X1,X0,X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X3))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) )
| ~ sP6(X2,X0,X1,X3) ) ),
inference(nnf_transformation,[],[f1652]) ).
fof(f11092,plain,
spl86_388,
inference(avatar_split_clause,[],[f2670,f11090]) ).
fof(f11090,plain,
( spl86_388
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3))
| ~ sP6(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_388])]) ).
fof(f2670,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1894]) ).
fof(f11086,plain,
( spl86_1
| spl86_226
| ~ spl86_42
| ~ spl86_365 ),
inference(avatar_split_clause,[],[f10966,f9516,f3378,f4978,f3181]) ).
fof(f9516,plain,
( spl86_365
<=> fTrue = hAPP(bool,bool,fNot,fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_365])]) ).
fof(f10966,plain,
( hBOOL(fTrue)
| hBOOL(fFalse)
| ~ spl86_42
| ~ spl86_365 ),
inference(superposition,[],[f3379,f9518]) ).
fof(f9518,plain,
( fTrue = hAPP(bool,bool,fNot,fFalse)
| ~ spl86_365 ),
inference(avatar_component_clause,[],[f9516]) ).
fof(f11085,plain,
spl86_387,
inference(avatar_split_clause,[],[f2489,f11083]) ).
fof(f11083,plain,
( spl86_387
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_387])]) ).
fof(f2489,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1469]) ).
fof(f1469,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(flattening,[],[f1468]) ).
fof(f1468,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(ennf_transformation,[],[f991]) ).
fof(f991,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X0)) ) ),
inference(rectify,[],[f368]) ).
fof(f368,axiom,
! [X24,X25,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X26))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X24))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X25)),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_less__trans__Suc) ).
fof(f11055,plain,
spl86_386,
inference(avatar_split_clause,[],[f1938,f11052]) ).
fof(f1938,plain,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cnf_transformation,[],[f604]) ).
fof(f604,axiom,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f10980,plain,
spl86_385,
inference(avatar_split_clause,[],[f3121,f10978]) ).
fof(f3121,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(forward_demodulation,[],[f3120,f2854]) ).
fof(f3120,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(forward_demodulation,[],[f2910,f2854]) ).
fof(f2910,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(definition_unfolding,[],[f2559,f2190,f2190]) ).
fof(f2559,plain,
! [X2,X0,X1] :
( ti(fun(X0,bool),X1) != ti(fun(X0,bool),X2)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(cnf_transformation,[],[f1855]) ).
fof(f10976,plain,
spl86_384,
inference(avatar_split_clause,[],[f3090,f10974]) ).
fof(f10974,plain,
( spl86_384
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_384])]) ).
fof(f3090,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(forward_demodulation,[],[f3089,f2854]) ).
fof(f3089,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X2) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(forward_demodulation,[],[f2893,f2854]) ).
fof(f2893,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X2) ),
inference(definition_unfolding,[],[f2479,f2190,f2190]) ).
fof(f2479,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ti(fun(X0,bool),X1) != ti(fun(X0,bool),X2) ),
inference(cnf_transformation,[],[f1459]) ).
fof(f1459,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ti(fun(X0,bool),X1) != ti(fun(X0,bool),X2) ),
inference(ennf_transformation,[],[f982]) ).
fof(f982,plain,
! [X0,X1,X2] :
( ti(fun(X0,bool),X1) = ti(fun(X0,bool),X2)
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X0,X7,X12] :
( ti(fun(X0,bool),X7) = ti(fun(X0,bool),X12)
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_equalityD1) ).
fof(f10972,plain,
spl86_383,
inference(avatar_split_clause,[],[f2855,f10970]) ).
fof(f10970,plain,
( spl86_383
<=> ! [X0,X1] : image(X0,X1) = hAPP(fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool))),fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool))),combi(fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)))),image(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_383])]) ).
fof(f2855,plain,
! [X0,X1] : image(X0,X1) = hAPP(fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool))),fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool))),combi(fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)))),image(X0,X1)),
inference(definition_unfolding,[],[f2194,f2190]) ).
fof(f2194,plain,
! [X0,X1] : image(X0,X1) = ti(fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool))),image(X0,X1)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] : image(X0,X1) = ti(fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool))),image(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).
fof(f10964,plain,
spl86_382,
inference(avatar_split_clause,[],[f2525,f10962]) ).
fof(f10962,plain,
( spl86_382
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_382])]) ).
fof(f2525,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(cnf_transformation,[],[f1506]) ).
fof(f1506,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2)) ),
inference(ennf_transformation,[],[f1020]) ).
fof(f1020,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),X2))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2)) ),
inference(rectify,[],[f463]) ).
fof(f463,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),X12))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_psubset__imp__subset) ).
fof(f10080,plain,
( spl86_365
| spl86_1
| ~ spl86_354 ),
inference(avatar_split_clause,[],[f9391,f8977,f3181,f9516]) ).
fof(f9391,plain,
( fTrue = hAPP(bool,bool,fNot,fFalse)
| spl86_1
| ~ spl86_354 ),
inference(resolution,[],[f8978,f3183]) ).
fof(f3183,plain,
( ~ hBOOL(fFalse)
| spl86_1 ),
inference(avatar_component_clause,[],[f3181]) ).
fof(f9611,plain,
spl86_381,
inference(avatar_split_clause,[],[f2850,f9609]) ).
fof(f9609,plain,
( spl86_381
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_381])]) ).
fof(f2850,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ order(X0) ),
inference(definition_unfolding,[],[f2173,f2190,f2190]) ).
fof(f2173,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1308]) ).
fof(f1308,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ order(X0) ),
inference(flattening,[],[f1307]) ).
fof(f1307,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f773]) ).
fof(f773,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
=> ( ti(X0,X1) = ti(X0,X2)
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3)) ) ) ),
inference(rectify,[],[f193]) ).
fof(f193,axiom,
! [X2] :
( order(X2)
=> ! [X51,X52,X48] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X52),X48))
=> ( ti(X2,X52) = ti(X2,X51)
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X51),X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_xt1_I4_J) ).
fof(f9607,plain,
spl86_380,
inference(avatar_split_clause,[],[f2849,f9605]) ).
fof(f9605,plain,
( spl86_380
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_380])]) ).
fof(f2849,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ order(X0) ),
inference(definition_unfolding,[],[f2170,f2190,f2190]) ).
fof(f2170,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1302]) ).
fof(f1302,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ order(X0) ),
inference(flattening,[],[f1301]) ).
fof(f1301,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f770]) ).
fof(f770,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
=> ( ti(X0,X1) = ti(X0,X2)
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3)) ) ) ),
inference(rectify,[],[f400]) ).
fof(f400,axiom,
! [X2] :
( order(X2)
=> ! [X51,X52,X48] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X52),X48))
=> ( ti(X2,X52) = ti(X2,X51)
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X51),X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_xt1_I2_J) ).
fof(f9603,plain,
spl86_379,
inference(avatar_split_clause,[],[f2848,f9601]) ).
fof(f9601,plain,
( spl86_379
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),X3)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_379])]) ).
fof(f2848,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),X3)
| ~ order(X0) ),
inference(definition_unfolding,[],[f2169,f2190,f2190]) ).
fof(f2169,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ti(X0,X2) != ti(X0,X3)
| ~ order(X0) ),
inference(cnf_transformation,[],[f1300]) ).
fof(f1300,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ti(X0,X2) != ti(X0,X3) )
| ~ order(X0) ),
inference(flattening,[],[f1299]) ).
fof(f1299,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ti(X0,X2) != ti(X0,X3) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f769]) ).
fof(f769,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( ti(X0,X2) = ti(X0,X3)
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) ) ),
inference(rectify,[],[f195]) ).
fof(f195,axiom,
! [X2] :
( order(X2)
=> ! [X51,X48,X52] :
( ti(X2,X48) = ti(X2,X52)
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X51),X52))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X51),X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_xt1_I3_J) ).
fof(f9599,plain,
spl86_378,
inference(avatar_split_clause,[],[f2847,f9597]) ).
fof(f9597,plain,
( spl86_378
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),X3)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_378])]) ).
fof(f2847,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),X3)
| ~ order(X0) ),
inference(definition_unfolding,[],[f2168,f2190,f2190]) ).
fof(f2168,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ti(X0,X2) != ti(X0,X3)
| ~ order(X0) ),
inference(cnf_transformation,[],[f1298]) ).
fof(f1298,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ti(X0,X2) != ti(X0,X3) )
| ~ order(X0) ),
inference(flattening,[],[f1297]) ).
fof(f1297,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ti(X0,X2) != ti(X0,X3) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f768]) ).
fof(f768,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( ti(X0,X2) = ti(X0,X3)
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) ) ),
inference(rectify,[],[f398]) ).
fof(f398,axiom,
! [X2] :
( order(X2)
=> ! [X51,X48,X52] :
( ti(X2,X48) = ti(X2,X52)
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X51),X52))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X51),X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_xt1_I1_J) ).
fof(f9595,plain,
spl86_377,
inference(avatar_split_clause,[],[f2836,f9593]) ).
fof(f9593,plain,
( spl86_377
<=> ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_377])]) ).
fof(f2836,plain,
! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ order(X0) ),
inference(definition_unfolding,[],[f2155,f2190,f2190]) ).
fof(f2155,plain,
! [X2,X0,X1] :
( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1290]) ).
fof(f1290,plain,
! [X0] :
( ! [X1,X2] :
( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ order(X0) ),
inference(flattening,[],[f1289]) ).
fof(f1289,plain,
! [X0] :
( ! [X1,X2] :
( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f762]) ).
fof(f762,plain,
! [X0] :
( order(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
=> ti(X0,X1) = ti(X0,X2) ) ) ),
inference(rectify,[],[f190]) ).
fof(f190,axiom,
! [X2] :
( order(X2)
=> ! [X21,X20] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X21),X20))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X21))
=> ti(X2,X20) = ti(X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_xt1_I5_J) ).
fof(f9591,plain,
spl86_376,
inference(avatar_split_clause,[],[f2828,f9589]) ).
fof(f9589,plain,
( spl86_376
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_376])]) ).
fof(f2828,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ order(X0) ),
inference(definition_unfolding,[],[f2146,f2190,f2190]) ).
fof(f2146,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ti(X0,X1) = ti(X0,X2)
| ~ order(X0) ),
inference(cnf_transformation,[],[f1276]) ).
fof(f1276,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ti(X0,X1) = ti(X0,X2) )
| ~ order(X0) ),
inference(flattening,[],[f1275]) ).
fof(f1275,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ti(X0,X1) = ti(X0,X2) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f753]) ).
fof(f753,plain,
! [X0] :
( order(X0)
=> ! [X1,X2] :
( ti(X0,X1) != ti(X0,X2)
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) ) ),
inference(rectify,[],[f424]) ).
fof(f424,axiom,
! [X2] :
( order(X2)
=> ! [X48,X52] :
( ti(X2,X48) != ti(X2,X52)
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),X52))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),X52)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_order__neq__le__trans) ).
fof(f9587,plain,
spl86_375,
inference(avatar_split_clause,[],[f2811,f9585]) ).
fof(f9585,plain,
( spl86_375
<=> ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_375])]) ).
fof(f2811,plain,
! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ),
inference(definition_unfolding,[],[f2096,f2190,f2190]) ).
fof(f2096,plain,
! [X2,X0,X1] :
( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f1670,plain,
! [X0] :
( ! [X1,X2] :
( ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ti(X0,X1) != ti(X0,X2) )
& ( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) )
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f1228]) ).
fof(f1228,plain,
! [X0] :
( ! [X1,X2] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
<=> ti(X0,X1) = ti(X0,X2) )
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f715]) ).
fof(f715,plain,
! [X0] :
( linorder(X0)
=> ! [X1,X2] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
<=> ti(X0,X1) = ti(X0,X2) ) ) ),
inference(rectify,[],[f423]) ).
fof(f423,axiom,
! [X0] :
( linorder(X0)
=> ! [X13,X38] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X13),X38))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X13),X38))
<=> ti(X0,X38) = ti(X0,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_linorder__antisym__conv1) ).
fof(f9577,plain,
spl86_374,
inference(avatar_split_clause,[],[f2810,f9575]) ).
fof(f9575,plain,
( spl86_374
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_374])]) ).
fof(f2810,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ),
inference(definition_unfolding,[],[f2097,f2190,f2190]) ).
fof(f2097,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ti(X0,X1) != ti(X0,X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f9573,plain,
spl86_373,
inference(avatar_split_clause,[],[f2805,f9571]) ).
fof(f9571,plain,
( spl86_373
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_373])]) ).
fof(f2805,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ),
inference(definition_unfolding,[],[f2088,f2190,f2190]) ).
fof(f2088,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ti(X0,X1) = ti(X0,X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f1219]) ).
fof(f1219,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ti(X0,X1) = ti(X0,X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f708]) ).
fof(f708,plain,
! [X0] :
( linorder(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ti(X0,X1) = ti(X0,X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) ),
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X2] :
( linorder(X2)
=> ! [X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X21),X20))
| ti(X2,X20) = ti(X2,X21)
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_linorder__less__linear) ).
fof(f9569,plain,
spl86_372,
inference(avatar_split_clause,[],[f2546,f9567]) ).
fof(f9567,plain,
( spl86_372
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK66(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_372])]) ).
fof(f2546,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK66(X0,X1,X2)),X1)) ),
inference(cnf_transformation,[],[f1844]) ).
fof(f1844,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK66(X0,X1,X2)),X1))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK66(X0,X1,X2)),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f1523,f1843]) ).
fof(f1843,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK66(X0,X1,X2)),X1))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK66(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1523,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| ? [X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ) ),
inference(ennf_transformation,[],[f1033]) ).
fof(f1033,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) )
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1)) ),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X0,X12,X7] :
( ! [X32] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X12)) )
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_subsetI) ).
fof(f9565,plain,
spl86_371,
inference(avatar_split_clause,[],[f2545,f9563]) ).
fof(f9563,plain,
( spl86_371
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK66(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_371])]) ).
fof(f2545,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X2),X1))
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK66(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f1844]) ).
fof(f9561,plain,
spl86_370,
inference(avatar_split_clause,[],[f2440,f9559]) ).
fof(f9559,plain,
( spl86_370
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_370])]) ).
fof(f2440,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1419]) ).
fof(f1419,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f957]) ).
fof(f957,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X2),X1))) ),
inference(rectify,[],[f216]) ).
fof(f216,axiom,
! [X0,X12,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_finite__Diff) ).
fof(f9547,plain,
( spl86_369
| ~ spl86_108
| ~ spl86_165
| ~ spl86_368 ),
inference(avatar_split_clause,[],[f9543,f9540,f4161,f3698,f9545]) ).
fof(f9540,plain,
( spl86_368
<=> ! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_368])]) ).
fof(f9543,plain,
( ! [X0,X1] : hAPP(X0,fun(X0,bool),fequal(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))
| ~ spl86_108
| ~ spl86_165
| ~ spl86_368 ),
inference(forward_demodulation,[],[f9541,f4223]) ).
fof(f9541,plain,
( ! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ spl86_368 ),
inference(avatar_component_clause,[],[f9540]) ).
fof(f9542,plain,
spl86_368,
inference(avatar_split_clause,[],[f2226,f9540]) ).
fof(f9538,plain,
spl86_367,
inference(avatar_split_clause,[],[f2225,f9536]) ).
fof(f9536,plain,
( spl86_367
<=> ! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),one_one(nat))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_367])]) ).
fof(f2225,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),one_one(nat))),X1),
inference(cnf_transformation,[],[f815]) ).
fof(f815,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,suc,X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),one_one(nat))),X1),
inference(rectify,[],[f274]) ).
fof(f274,axiom,
! [X17,X16] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),hAPP(nat,nat,suc,X16)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),one_one(nat))),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_diff__Suc__eq__diff__pred) ).
fof(f9534,plain,
spl86_366,
inference(avatar_split_clause,[],[f2175,f9532]) ).
fof(f9532,plain,
( spl86_366
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_366])]) ).
fof(f2175,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1312]) ).
fof(f1312,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ order(X0) ),
inference(flattening,[],[f1311]) ).
fof(f1311,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f775]) ).
fof(f775,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X3)) ) ) ),
inference(rectify,[],[f189]) ).
fof(f189,axiom,
! [X2] :
( order(X2)
=> ! [X50,X21,X20] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X21),X20))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X50),X21))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X50),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_xt1_I6_J) ).
fof(f9519,plain,
( spl86_365
| spl86_171
| ~ spl86_209
| ~ spl86_354 ),
inference(avatar_split_clause,[],[f9474,f8977,f4885,f4256,f9516]) ).
fof(f9474,plain,
( fTrue = hAPP(bool,bool,fNot,fFalse)
| spl86_171
| ~ spl86_209
| ~ spl86_354 ),
inference(forward_demodulation,[],[f9390,f4887]) ).
fof(f9514,plain,
spl86_364,
inference(avatar_split_clause,[],[f2174,f9512]) ).
fof(f9512,plain,
( spl86_364
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_364])]) ).
fof(f2174,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1310]) ).
fof(f1310,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ order(X0) ),
inference(flattening,[],[f1309]) ).
fof(f1309,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f774]) ).
fof(f774,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3)) ) ) ),
inference(rectify,[],[f435]) ).
fof(f435,axiom,
! [X2] :
( order(X2)
=> ! [X50,X21,X20] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X21),X20))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X50),X21))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X50),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_xt1_I8_J) ).
fof(f9510,plain,
spl86_363,
inference(avatar_split_clause,[],[f2172,f9508]) ).
fof(f9508,plain,
( spl86_363
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_363])]) ).
fof(f2172,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ order(X0) ),
inference(flattening,[],[f1305]) ).
fof(f1305,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f772]) ).
fof(f772,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3)) ) ) ),
inference(rectify,[],[f433]) ).
fof(f433,axiom,
! [X2] :
( order(X2)
=> ! [X50,X21,X20] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X21),X20))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X50),X21))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X50),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_xt1_I7_J) ).
fof(f9506,plain,
spl86_362,
inference(avatar_split_clause,[],[f2171,f9504]) ).
fof(f9504,plain,
( spl86_362
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_362])]) ).
fof(f2171,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1304]) ).
fof(f1304,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ order(X0) ),
inference(flattening,[],[f1303]) ).
fof(f1303,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f771]) ).
fof(f771,plain,
! [X0] :
( order(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X3)) ) ) ),
inference(rectify,[],[f402]) ).
fof(f402,axiom,
! [X2] :
( order(X2)
=> ! [X50,X21,X20] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X21),X20))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X50),X21))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X50),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_xt1_I10_J) ).
fof(f9502,plain,
spl86_361,
inference(avatar_split_clause,[],[f2145,f9500]) ).
fof(f9500,plain,
( spl86_361
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_361])]) ).
fof(f2145,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1274]) ).
fof(f1274,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ preorder(X0) ),
inference(flattening,[],[f1273]) ).
fof(f1273,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f752]) ).
fof(f752,plain,
! [X0] :
( preorder(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1)) ) ) ),
inference(rectify,[],[f191]) ).
fof(f191,axiom,
! [X2] :
( preorder(X2)
=> ! [X50,X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X21))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X21),X50))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order__trans) ).
fof(f9498,plain,
spl86_360,
inference(avatar_split_clause,[],[f2144,f9496]) ).
fof(f9496,plain,
( spl86_360
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_360])]) ).
fof(f2144,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1272]) ).
fof(f1272,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ preorder(X0) ),
inference(flattening,[],[f1271]) ).
fof(f1271,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3)) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f751]) ).
fof(f751,plain,
! [X0] :
( preorder(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ) ),
inference(rectify,[],[f434]) ).
fof(f434,axiom,
! [X2] :
( preorder(X2)
=> ! [X50,X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X21))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X21),X50))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_order__le__less__trans) ).
fof(f9494,plain,
spl86_359,
inference(avatar_split_clause,[],[f2143,f9492]) ).
fof(f9492,plain,
( spl86_359
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_359])]) ).
fof(f2143,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1270]) ).
fof(f1270,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ preorder(X0) ),
inference(flattening,[],[f1269]) ).
fof(f1269,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f750]) ).
fof(f750,plain,
! [X0] :
( preorder(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X3),X1))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ) ),
inference(rectify,[],[f432]) ).
fof(f432,axiom,
! [X2] :
( preorder(X2)
=> ! [X50,X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X21))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X21),X50))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_order__less__le__trans) ).
fof(f9490,plain,
spl86_358,
inference(avatar_split_clause,[],[f2142,f9488]) ).
fof(f9488,plain,
( spl86_358
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_358])]) ).
fof(f2142,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1268]) ).
fof(f1268,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ preorder(X0) ),
inference(flattening,[],[f1267]) ).
fof(f1267,plain,
! [X0] :
( ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3)) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f749]) ).
fof(f749,plain,
! [X0] :
( preorder(X0)
=> ! [X1,X2,X3] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X3))
=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X3),X1))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ) ),
inference(rectify,[],[f401]) ).
fof(f401,axiom,
! [X2] :
( preorder(X2)
=> ! [X50,X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X21))
=> ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X21),X50))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X50)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_order__less__trans) ).
fof(f9486,plain,
spl86_357,
inference(avatar_split_clause,[],[f2140,f9484]) ).
fof(f9484,plain,
( spl86_357
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_357])]) ).
fof(f2140,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1681]) ).
fof(f1681,plain,
! [X0] :
( ! [X1,X2] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
& ( ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
| ~ preorder(X0) ),
inference(flattening,[],[f1680]) ).
fof(f1680,plain,
! [X0] :
( ! [X1,X2] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
& ( ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
| ~ preorder(X0) ),
inference(nnf_transformation,[],[f1264]) ).
fof(f1264,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
<=> ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f747]) ).
fof(f747,plain,
! [X0] :
( preorder(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
<=> ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) ) ),
inference(rectify,[],[f419]) ).
fof(f419,axiom,
! [X0] :
( preorder(X0)
=> ! [X13,X38] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X13),X38))
<=> ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X38),X13))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X13),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_less__le__not__le) ).
fof(f9479,plain,
( spl86_356
| ~ spl86_108
| ~ spl86_165
| ~ spl86_355 ),
inference(avatar_split_clause,[],[f9388,f9385,f4161,f3698,f9477]) ).
fof(f9477,plain,
( spl86_356
<=> ! [X0] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_356])]) ).
fof(f9385,plain,
( spl86_355
<=> ! [X0] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_355])]) ).
fof(f9388,plain,
( ! [X0] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0)) = X0
| ~ spl86_108
| ~ spl86_165
| ~ spl86_355 ),
inference(forward_demodulation,[],[f9386,f4223]) ).
fof(f9386,plain,
( ! [X0] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0))) = X0
| ~ spl86_355 ),
inference(avatar_component_clause,[],[f9385]) ).
fof(f9387,plain,
spl86_355,
inference(avatar_split_clause,[],[f2026,f9385]) ).
fof(f2026,plain,
! [X0] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0))) = X0,
inference(cnf_transformation,[],[f643]) ).
fof(f643,plain,
! [X0] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0))) = X0,
inference(rectify,[],[f438]) ).
fof(f438,axiom,
! [X19] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X19))) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_card__Collect__less__nat) ).
fof(f8979,plain,
( spl86_354
| ~ spl86_42
| ~ spl86_108
| ~ spl86_339 ),
inference(avatar_split_clause,[],[f8885,f8689,f3698,f3378,f8977]) ).
fof(f8885,plain,
( ! [X0] :
( fTrue = hAPP(bool,bool,fNot,X0)
| hBOOL(X0) )
| ~ spl86_42
| ~ spl86_108
| ~ spl86_339 ),
inference(forward_demodulation,[],[f8817,f3699]) ).
fof(f8817,plain,
( ! [X0] :
( fTrue = hAPP(bool,bool,combi(bool),hAPP(bool,bool,fNot,X0))
| hBOOL(X0) )
| ~ spl86_42
| ~ spl86_339 ),
inference(resolution,[],[f8690,f3379]) ).
fof(f8950,plain,
spl86_353,
inference(avatar_split_clause,[],[f2803,f8948]) ).
fof(f8948,plain,
( spl86_353
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X3)
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_353])]) ).
fof(f2803,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X3)
| ~ cancel_semigroup_add(X0) ),
inference(definition_unfolding,[],[f2066,f2190,f2190]) ).
fof(f2066,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
| ti(X0,X1) != ti(X0,X3)
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f1664]) ).
fof(f1664,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
| ti(X0,X1) != ti(X0,X3) )
& ( ti(X0,X1) = ti(X0,X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2) ) )
| ~ cancel_semigroup_add(X0) ),
inference(nnf_transformation,[],[f1197]) ).
fof(f1197,plain,
! [X0] :
( ! [X1,X2,X3] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
<=> ti(X0,X1) = ti(X0,X3) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f690]) ).
fof(f690,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X1,X2,X3] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
<=> ti(X0,X1) = ti(X0,X3) ) ),
inference(rectify,[],[f300]) ).
fof(f300,axiom,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X33,X10,X34] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X34),X10) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X33),X10)
<=> ti(X0,X33) = ti(X0,X34) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_add__right__cancel) ).
fof(f8946,plain,
spl86_352,
inference(avatar_split_clause,[],[f2801,f8944]) ).
fof(f8944,plain,
( spl86_352
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),X3)
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_352])]) ).
fof(f2801,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),X3)
| ~ cancel_semigroup_add(X0) ),
inference(definition_unfolding,[],[f2064,f2190,f2190]) ).
fof(f2064,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| ti(X0,X2) != ti(X0,X3)
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f1663,plain,
! [X0] :
( ! [X1,X2,X3] :
( ( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| ti(X0,X2) != ti(X0,X3) )
& ( ti(X0,X2) = ti(X0,X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3) ) )
| ~ cancel_semigroup_add(X0) ),
inference(nnf_transformation,[],[f1196]) ).
fof(f1196,plain,
! [X0] :
( ! [X1,X2,X3] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
<=> ti(X0,X2) = ti(X0,X3) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f689]) ).
fof(f689,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X1,X2,X3] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
<=> ti(X0,X2) = ti(X0,X3) ) ),
inference(rectify,[],[f301]) ).
fof(f301,axiom,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X10,X33,X34] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X10),X34) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X10),X33)
<=> ti(X0,X33) = ti(X0,X34) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_add__left__cancel) ).
fof(f8942,plain,
spl86_351,
inference(avatar_split_clause,[],[f2800,f8940]) ).
fof(f8940,plain,
( spl86_351
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X2) = hAPP(X0,X0,combi(X0),X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_351])]) ).
fof(f2800,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X2) = hAPP(X0,X0,combi(X0),X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| ~ cancel_semigroup_add(X0) ),
inference(definition_unfolding,[],[f2062,f2190,f2190]) ).
fof(f2062,plain,
! [X2,X3,X0,X1] :
( ti(X0,X2) = ti(X0,X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f1195]) ).
fof(f1195,plain,
! [X0] :
( ! [X1,X2,X3] :
( ti(X0,X2) = ti(X0,X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f688]) ).
fof(f688,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X1,X2,X3] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
=> ti(X0,X2) = ti(X0,X3) ) ),
inference(rectify,[],[f299]) ).
fof(f299,axiom,
! [X2] :
( cancel_semigroup_add(X2)
=> ! [X48,X52,X51] :
( hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X52)
=> ti(X2,X52) = ti(X2,X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__left__imp__eq) ).
fof(f8938,plain,
spl86_350,
inference(avatar_split_clause,[],[f2799,f8936]) ).
fof(f8936,plain,
( spl86_350
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_350])]) ).
fof(f2799,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
| ~ cancel_semigroup_add(X0) ),
inference(definition_unfolding,[],[f2061,f2190,f2190]) ).
fof(f2061,plain,
! [X2,X3,X0,X1] :
( ti(X0,X1) = ti(X0,X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f1194]) ).
fof(f1194,plain,
! [X0] :
( ! [X1,X2,X3] :
( ti(X0,X1) = ti(X0,X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f687]) ).
fof(f687,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> ! [X1,X2,X3] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X3),X2)
=> ti(X0,X1) = ti(X0,X3) ) ),
inference(rectify,[],[f297]) ).
fof(f297,axiom,
! [X2] :
( cancel_semigroup_add(X2)
=> ! [X52,X48,X51] :
( hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X51),X48) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X52),X48)
=> ti(X2,X52) = ti(X2,X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_add__right__imp__eq) ).
fof(f8934,plain,
spl86_349,
inference(avatar_split_clause,[],[f2782,f8932]) ).
fof(f8932,plain,
( spl86_349
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X2) = hAPP(X0,X0,combi(X0),X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| ~ cancel146912293up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_349])]) ).
fof(f2782,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X2) = hAPP(X0,X0,combi(X0),X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| ~ cancel146912293up_add(X0) ),
inference(definition_unfolding,[],[f2032,f2190,f2190]) ).
fof(f2032,plain,
! [X2,X3,X0,X1] :
( ti(X0,X2) = ti(X0,X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
| ~ cancel146912293up_add(X0) ),
inference(cnf_transformation,[],[f1163]) ).
fof(f1163,plain,
! [X0] :
( ! [X1,X2,X3] :
( ti(X0,X2) = ti(X0,X3)
| hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) != hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3) )
| ~ cancel146912293up_add(X0) ),
inference(ennf_transformation,[],[f664]) ).
fof(f664,plain,
! [X0] :
( cancel146912293up_add(X0)
=> ! [X1,X2,X3] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X2) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),X3)
=> ti(X0,X2) = ti(X0,X3) ) ),
inference(rectify,[],[f298]) ).
fof(f298,axiom,
! [X2] :
( cancel146912293up_add(X2)
=> ! [X48,X52,X51] :
( hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X51) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),X52)
=> ti(X2,X52) = ti(X2,X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__imp__eq) ).
fof(f8930,plain,
spl86_348,
inference(avatar_split_clause,[],[f2602,f8928]) ).
fof(f8928,plain,
( spl86_348
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_348])]) ).
fof(f2602,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(cnf_transformation,[],[f1536]) ).
fof(f1536,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3)) ),
inference(ennf_transformation,[],[f1063]) ).
fof(f1063,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),X3))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X2),X3))) ),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X1,X0,X8,X9] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X9))
=> hBOOL(hAPP(fun(X1,bool),bool,finite_finite(X1),hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X8),X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__imageI) ).
fof(f8926,plain,
spl86_347,
inference(avatar_split_clause,[],[f2507,f8924]) ).
fof(f8924,plain,
( spl86_347
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK64(X0,X2)),X2))
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_347])]) ).
fof(f2507,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK64(X0,X2)),X2))
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1833]) ).
fof(f1833,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X0,X1))
| ( ~ hBOOL(hAPP(nat,bool,X0,sK64(X0,X2)))
& hBOOL(hAPP(nat,bool,X0,hAPP(nat,nat,suc,sK64(X0,X2))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK64(X0,X2)),X2)) )
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64])],[f1490,f1832]) ).
fof(f1832,plain,
! [X0,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(nat,bool,X0,X3))
& hBOOL(hAPP(nat,bool,X0,hAPP(nat,nat,suc,X3)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2)) )
=> ( ~ hBOOL(hAPP(nat,bool,X0,sK64(X0,X2)))
& hBOOL(hAPP(nat,bool,X0,hAPP(nat,nat,suc,sK64(X0,X2))))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK64(X0,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1490,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X0,X1))
| ? [X3] :
( ~ hBOOL(hAPP(nat,bool,X0,X3))
& hBOOL(hAPP(nat,bool,X0,hAPP(nat,nat,suc,X3)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2)) )
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(flattening,[],[f1489]) ).
fof(f1489,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X0,X1))
| ? [X3] :
( ~ hBOOL(hAPP(nat,bool,X0,X3))
& hBOOL(hAPP(nat,bool,X0,hAPP(nat,nat,suc,X3)))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2)) )
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1009]) ).
fof(f1009,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,X0,X2))
=> ( ! [X3] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
=> ( hBOOL(hAPP(nat,bool,X0,hAPP(nat,nat,suc,X3)))
=> hBOOL(hAPP(nat,bool,X0,X3)) ) )
=> hBOOL(hAPP(nat,bool,X0,X1)) ) ) ),
inference(rectify,[],[f459]) ).
fof(f459,axiom,
! [X15,X35,X63] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X35),X63))
=> ( hBOOL(hAPP(nat,bool,X15,X63))
=> ( ! [X68] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X68),X63))
=> ( hBOOL(hAPP(nat,bool,X15,hAPP(nat,nat,suc,X68)))
=> hBOOL(hAPP(nat,bool,X15,X68)) ) )
=> hBOOL(hAPP(nat,bool,X15,X35)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_inc__induct) ).
fof(f8922,plain,
spl86_346,
inference(avatar_split_clause,[],[f2409,f8920]) ).
fof(f2409,plain,
! [X2,X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))),
inference(cnf_transformation,[],[f932]) ).
fof(f932,plain,
! [X0,X1,X2] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X1))),
inference(rectify,[],[f138]) ).
fof(f138,axiom,
! [X0,X12,X10] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X12),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_subset__insertI) ).
fof(f8918,plain,
spl86_345,
inference(avatar_split_clause,[],[f2184,f8916]) ).
fof(f8916,plain,
( spl86_345
<=> ! [X4,X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),sK15(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_345])]) ).
fof(f2184,plain,
! [X0,X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),sK15(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ),
inference(cnf_transformation,[],[f1705]) ).
fof(f1705,plain,
! [X0] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ! [X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK14(X0,X1)),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK14(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),sK15(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f1702,f1704,f1703]) ).
fof(f1703,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) )
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK14(X0,X1)),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK14(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1704,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),sK15(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1702,plain,
! [X0] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ) ),
inference(rectify,[],[f1701]) ).
fof(f1701,plain,
! [X0] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ) ),
inference(nnf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X0] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) ) ),
inference(ennf_transformation,[],[f781]) ).
fof(f781,plain,
! [X0] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ) ),
inference(rectify,[],[f151]) ).
fof(f151,axiom,
! [X47] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X47))
<=> ? [X37] :
! [X32] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X32),X47))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite__nat__set__iff__bounded__le) ).
fof(f8773,plain,
spl86_344,
inference(avatar_split_clause,[],[f2181,f8771]) ).
fof(f8771,plain,
( spl86_344
<=> ! [X4,X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),sK13(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_344])]) ).
fof(f2181,plain,
! [X0,X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),sK13(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0))
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ),
inference(cnf_transformation,[],[f1700]) ).
fof(f1700,plain,
! [X0] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ! [X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK12(X0,X1)),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK12(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),sK13(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f1697,f1699,f1698]) ).
fof(f1698,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) )
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK12(X0,X1)),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK12(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1699,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),sK13(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1697,plain,
! [X0] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ) ),
inference(rectify,[],[f1696]) ).
fof(f1696,plain,
! [X0] :
( ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) )
| ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) ) ),
inference(nnf_transformation,[],[f1319]) ).
fof(f1319,plain,
! [X0] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0)) ) ),
inference(ennf_transformation,[],[f780]) ).
fof(f780,plain,
! [X0] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X0))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ) ),
inference(rectify,[],[f436]) ).
fof(f436,axiom,
! [X47] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X47))
<=> ? [X37] :
! [X32] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X32),X47))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X32),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_finite__nat__set__iff__bounded) ).
fof(f8764,plain,
( spl86_343
| ~ spl86_109
| ~ spl86_165
| ~ spl86_342 ),
inference(avatar_split_clause,[],[f8760,f8757,f4161,f3702,f8762]) ).
fof(f8762,plain,
( spl86_343
<=> ! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_343])]) ).
fof(f8757,plain,
( spl86_342
<=> ! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_342])]) ).
fof(f8760,plain,
( ! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0)))
| ~ spl86_109
| ~ spl86_165
| ~ spl86_342 ),
inference(forward_demodulation,[],[f8758,f4236]) ).
fof(f8758,plain,
( ! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0))))
| ~ spl86_342 ),
inference(avatar_component_clause,[],[f8757]) ).
fof(f8759,plain,
spl86_342,
inference(avatar_split_clause,[],[f2025,f8757]) ).
fof(f2025,plain,
! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0)))),
inference(cnf_transformation,[],[f642]) ).
fof(f642,plain,
! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X0)))),
inference(rectify,[],[f65]) ).
fof(f65,axiom,
! [X18] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X18)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__le__nat) ).
fof(f8750,plain,
( spl86_341
| ~ spl86_109
| ~ spl86_165
| ~ spl86_340 ),
inference(avatar_split_clause,[],[f8746,f8743,f4161,f3702,f8748]) ).
fof(f8748,plain,
( spl86_341
<=> ! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_341])]) ).
fof(f8743,plain,
( spl86_340
<=> ! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_340])]) ).
fof(f8746,plain,
( ! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0)))
| ~ spl86_109
| ~ spl86_165
| ~ spl86_340 ),
inference(forward_demodulation,[],[f8744,f4236]) ).
fof(f8744,plain,
( ! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0))))
| ~ spl86_340 ),
inference(avatar_component_clause,[],[f8743]) ).
fof(f8745,plain,
spl86_340,
inference(avatar_split_clause,[],[f2024,f8743]) ).
fof(f2024,plain,
! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0)))),
inference(cnf_transformation,[],[f641]) ).
fof(f641,plain,
! [X0] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X0)))),
inference(rectify,[],[f345]) ).
fof(f345,axiom,
! [X18] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X18)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_finite__Collect__less__nat) ).
fof(f8691,plain,
( spl86_339
| spl86_1
| ~ spl86_49
| ~ spl86_107 ),
inference(avatar_split_clause,[],[f3726,f3694,f3410,f3181,f8689]) ).
fof(f3410,plain,
( spl86_49
<=> ! [X0] :
( hBOOL(hAPP(bool,bool,combi(bool),X0))
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_49])]) ).
fof(f3726,plain,
( ! [X0] :
( hBOOL(fFalse)
| ~ hBOOL(X0)
| fTrue = hAPP(bool,bool,combi(bool),X0) )
| ~ spl86_49
| ~ spl86_107 ),
inference(superposition,[],[f3411,f3695]) ).
fof(f3411,plain,
( ! [X0] :
( hBOOL(hAPP(bool,bool,combi(bool),X0))
| ~ hBOOL(X0) )
| ~ spl86_49 ),
inference(avatar_component_clause,[],[f3410]) ).
fof(f8586,plain,
spl86_338,
inference(avatar_split_clause,[],[f3057,f8584]) ).
fof(f8584,plain,
( spl86_338
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_338])]) ).
fof(f3057,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ),
inference(forward_demodulation,[],[f2874,f2854]) ).
fof(f2874,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ),
inference(definition_unfolding,[],[f2395,f2190]) ).
fof(f2395,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ),
inference(cnf_transformation,[],[f1806]) ).
fof(f1806,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool))))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) )
& ( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ) ),
inference(nnf_transformation,[],[f922]) ).
fof(f922,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool))))
<=> bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ),
inference(rectify,[],[f177]) ).
fof(f177,axiom,
! [X0,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),bot_bot(fun(X0,bool))))
<=> ti(fun(X0,bool),X7) = bot_bot(fun(X0,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_subset__empty) ).
fof(f8582,plain,
spl86_337,
inference(avatar_split_clause,[],[f3056,f8580]) ).
fof(f8580,plain,
( spl86_337
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_337])]) ).
fof(f3056,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ),
inference(forward_demodulation,[],[f2873,f2854]) ).
fof(f2873,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool))))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(definition_unfolding,[],[f2396,f2190]) ).
fof(f2396,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),bot_bot(fun(X0,bool))))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ),
inference(cnf_transformation,[],[f1806]) ).
fof(f8578,plain,
spl86_336,
inference(avatar_split_clause,[],[f2510,f8576]) ).
fof(f8576,plain,
( spl86_336
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_336])]) ).
fof(f2510,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1492]) ).
fof(f1492,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(flattening,[],[f1491]) ).
fof(f1491,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f1010]) ).
fof(f1010,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X0))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0)) ) ),
inference(rectify,[],[f74]) ).
fof(f74,axiom,
! [X24,X25,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X26))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X24))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_le__trans) ).
fof(f8574,plain,
spl86_335,
inference(avatar_split_clause,[],[f2471,f8572]) ).
fof(f8572,plain,
( spl86_335
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_335])]) ).
fof(f2471,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1448]) ).
fof(f1448,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(flattening,[],[f1447]) ).
fof(f1447,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f975]) ).
fof(f975,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X2))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X0,X7,X12] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X12))
=> ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X12))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rev__finite__subset) ).
fof(f8570,plain,
spl86_334,
inference(avatar_split_clause,[],[f2460,f8568]) ).
fof(f8568,plain,
( spl86_334
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK63(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_334])]) ).
fof(f2460,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK63(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1830]) ).
fof(f8566,plain,
spl86_333,
inference(avatar_split_clause,[],[f2450,f8564]) ).
fof(f8564,plain,
( spl86_333
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK58(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_333])]) ).
fof(f2450,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK58(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f8562,plain,
spl86_332,
inference(avatar_split_clause,[],[f2300,f8560]) ).
fof(f2300,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X0))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),X1)) ),
inference(cnf_transformation,[],[f1383]) ).
fof(f1383,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X0))
| ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),X1)) ),
inference(ennf_transformation,[],[f882]) ).
fof(f882,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X0),X1))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X1),X0)) ),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X5,X6] :
( hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),X5),X6))
=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X6),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
fof(f8168,plain,
spl86_331,
inference(avatar_split_clause,[],[f3004,f8166]) ).
fof(f8166,plain,
( spl86_331
<=> ! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_331])]) ).
fof(f3004,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))),
inference(forward_demodulation,[],[f2860,f2854]) ).
fof(f2860,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1),
inference(definition_unfolding,[],[f2218,f2190]) ).
fof(f2218,plain,
! [X0,X1] : ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))),
inference(cnf_transformation,[],[f808]) ).
fof(f808,plain,
! [X0,X1] : ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),bot_bot(fun(X0,bool))),
inference(rectify,[],[f219]) ).
fof(f219,axiom,
! [X0,X7] : ti(fun(X0,bool),X7) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),bot_bot(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_Diff__empty) ).
fof(f8164,plain,
spl86_330,
inference(avatar_split_clause,[],[f2933,f8162]) ).
fof(f8162,plain,
( spl86_330
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_330])]) ).
fof(f2933,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X3) ),
inference(definition_unfolding,[],[f2652,f2190,f2190]) ).
fof(f2652,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3))
| ti(X0,X1) != ti(X0,X3) ),
inference(cnf_transformation,[],[f1881]) ).
fof(f8160,plain,
spl86_329,
inference(avatar_split_clause,[],[f2737,f8158]) ).
fof(f8158,plain,
( spl86_329
<=> ! [X3,X4,X0,X5,X2,X1] : hAPP(X0,X1,hAPP(fun(X0,X2),fun(X0,X1),hAPP(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5) = hAPP(X2,X1,X3,hAPP(X0,X2,X4,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_329])]) ).
fof(f2737,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(X0,X1,hAPP(fun(X0,X2),fun(X0,X1),hAPP(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5) = hAPP(X2,X1,X3,hAPP(X0,X2,X4,X5)),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(X0,X1,hAPP(fun(X0,X2),fun(X0,X1),hAPP(fun(X2,X1),fun(fun(X0,X2),fun(X0,X1)),combb(X2,X1,X0),X3),X4),X5) = hAPP(X2,X1,X3,hAPP(X0,X2,X4,X5)),
inference(rectify,[],[f585]) ).
fof(f585,axiom,
! [X2,X1,X0,X79,X80,X81] : hAPP(X2,X1,hAPP(fun(X2,X0),fun(X2,X1),hAPP(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1)),combb(X0,X1,X2),X79),X80),X81) = hAPP(X0,X1,X79,hAPP(X2,X0,X80,X81)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
fof(f8156,plain,
spl86_328,
inference(avatar_split_clause,[],[f2736,f8154]) ).
fof(f8154,plain,
( spl86_328
<=> ! [X2,X3,X4,X0,X5,X1] : hAPP(X0,X1,hAPP(X2,fun(X0,X1),hAPP(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_328])]) ).
fof(f2736,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(X0,X1,hAPP(X2,fun(X0,X1),hAPP(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),X4),
inference(cnf_transformation,[],[f1136]) ).
fof(f1136,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(X0,X1,hAPP(X2,fun(X0,X1),hAPP(fun(X0,fun(X2,X1)),fun(X2,fun(X0,X1)),combc(X0,X2,X1),X3),X4),X5) = hAPP(X2,X1,hAPP(X0,fun(X2,X1),X3,X5),X4),
inference(rectify,[],[f586]) ).
fof(f586,axiom,
! [X2,X1,X0,X79,X80,X81] : hAPP(X2,X1,hAPP(X0,fun(X2,X1),hAPP(fun(X2,fun(X0,X1)),fun(X0,fun(X2,X1)),combc(X2,X0,X1),X79),X80),X81) = hAPP(X0,X1,hAPP(X2,fun(X0,X1),X79,X81),X80),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
fof(f8152,plain,
spl86_327,
inference(avatar_split_clause,[],[f2462,f8150]) ).
fof(f8150,plain,
( spl86_327
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| hBOOL(hAPP(fun(X0,bool),bool,X1,sK63(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_327])]) ).
fof(f2462,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| hBOOL(hAPP(fun(X0,bool),bool,X1,sK63(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1830]) ).
fof(f8148,plain,
spl86_326,
inference(avatar_split_clause,[],[f2452,f8146]) ).
fof(f8146,plain,
( spl86_326
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,sK58(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_326])]) ).
fof(f2452,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,bot_bot(fun(X0,bool))))
| hBOOL(hAPP(fun(X0,bool),bool,X1,sK58(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,X1,X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f8144,plain,
spl86_325,
inference(avatar_split_clause,[],[f2283,f8142]) ).
fof(f8142,plain,
( spl86_325
<=> ! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_325])]) ).
fof(f2283,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1363]) ).
fof(f1363,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f867]) ).
fof(f867,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) = X0 ),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X25,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X16))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X16),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X16),X25)) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_diff__diff__cancel) ).
fof(f8140,plain,
spl86_324,
inference(avatar_split_clause,[],[f2282,f8138]) ).
fof(f8138,plain,
( spl86_324
<=> ! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_324])]) ).
fof(f2282,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1362]) ).
fof(f1362,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f866]) ).
fof(f866,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)) = X1 ),
inference(rectify,[],[f329]) ).
fof(f329,axiom,
! [X16,X17] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16)) = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_le__add__diff__inverse) ).
fof(f8136,plain,
spl86_323,
inference(avatar_split_clause,[],[f2264,f8134]) ).
fof(f8134,plain,
( spl86_323
<=> ! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_323])]) ).
fof(f2264,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1343]) ).
fof(f1343,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(ennf_transformation,[],[f850]) ).
fof(f850,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)) = X0 ),
inference(rectify,[],[f453]) ).
fof(f453,axiom,
! [X17,X16] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16)) = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_add__diff__inverse) ).
fof(f8126,plain,
( spl86_322
| ~ spl86_53
| ~ spl86_317 ),
inference(avatar_split_clause,[],[f8095,f7675,f3436,f8124]) ).
fof(f8124,plain,
( spl86_322
<=> ! [X0,X1] :
( ~ sP4(X0,finite_finite(X0),X1)
| ~ finite_finite_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_322])]) ).
fof(f8095,plain,
( ! [X0,X1] :
( ~ sP4(X0,finite_finite(X0),X1)
| ~ finite_finite_1(X0) )
| ~ spl86_53
| ~ spl86_317 ),
inference(resolution,[],[f7676,f3437]) ).
fof(f7839,plain,
( spl86_284
| spl86_171
| ~ spl86_71
| ~ spl86_104 ),
inference(avatar_split_clause,[],[f6818,f3682,f3532,f4256,f7108]) ).
fof(f7108,plain,
( spl86_284
<=> ! [X0] : ~ sP2(X0,bot_bot(fun(fun(X0,bool),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_284])]) ).
fof(f6818,plain,
( ! [X0] :
( hBOOL(bot_bot(bool))
| ~ sP2(X0,bot_bot(fun(fun(X0,bool),bool))) )
| ~ spl86_71
| ~ spl86_104 ),
inference(superposition,[],[f3533,f3683]) ).
fof(f7703,plain,
spl86_321,
inference(avatar_split_clause,[],[f2886,f7701]) ).
fof(f7701,plain,
( spl86_321
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,the(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),sK55(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_321])]) ).
fof(f2886,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,the(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),sK55(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(definition_unfolding,[],[f2436,f2190,f2190,f2190]) ).
fof(f2436,plain,
! [X2,X0,X1] :
( ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),X1)
| ti(X0,X2) != ti(X0,sK55(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1818]) ).
fof(f1818,plain,
! [X0,X1,X2] :
( ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),X1)
| ( ti(X0,X2) != ti(X0,sK55(X0,X1,X2))
& hBOOL(hAPP(X0,bool,X1,sK55(X0,X1,X2))) )
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f1415,f1817]) ).
fof(f1817,plain,
! [X0,X1,X2] :
( ? [X3] :
( ti(X0,X2) != ti(X0,X3)
& hBOOL(hAPP(X0,bool,X1,X3)) )
=> ( ti(X0,X2) != ti(X0,sK55(X0,X1,X2))
& hBOOL(hAPP(X0,bool,X1,sK55(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f1415,plain,
! [X0,X1,X2] :
( ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),X1)
| ? [X3] :
( ti(X0,X2) != ti(X0,X3)
& hBOOL(hAPP(X0,bool,X1,X3)) )
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(flattening,[],[f1414]) ).
fof(f1414,plain,
! [X0,X1,X2] :
( ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),X1)
| ? [X3] :
( ti(X0,X2) != ti(X0,X3)
& hBOOL(hAPP(X0,bool,X1,X3)) )
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(ennf_transformation,[],[f954]) ).
fof(f954,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,bool,X1,X2))
=> ( ! [X3] :
( hBOOL(hAPP(X0,bool,X1,X3))
=> ti(X0,X2) = ti(X0,X3) )
=> ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),X1) ) ),
inference(rectify,[],[f263]) ).
fof(f263,axiom,
! [X0,X15,X10] :
( hBOOL(hAPP(X0,bool,X15,X10))
=> ( ! [X32] :
( hBOOL(hAPP(X0,bool,X15,X32))
=> ti(X0,X10) = ti(X0,X32) )
=> ti(X0,X10) = hAPP(fun(X0,bool),X0,the(X0),X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_the__equality) ).
fof(f7699,plain,
spl86_320,
inference(avatar_split_clause,[],[f2862,f7697]) ).
fof(f7697,plain,
( spl86_320
<=> ! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_320])]) ).
fof(f2862,plain,
! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(definition_unfolding,[],[f2224,f2190]) ).
fof(f2224,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(cnf_transformation,[],[f814]) ).
fof(f814,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X1)),
inference(rectify,[],[f262]) ).
fof(f262,axiom,
! [X0,X10] : ti(X0,X10) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combc(X0,X0,bool),fequal(X0)),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_the__eq__trivial) ).
fof(f7690,plain,
( spl86_319
| ~ spl86_108
| ~ spl86_165
| ~ spl86_318 ),
inference(avatar_split_clause,[],[f7686,f7682,f4161,f3698,f7688]) ).
fof(f7688,plain,
( spl86_319
<=> ! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_319])]) ).
fof(f7682,plain,
( spl86_318
<=> ! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_318])]) ).
fof(f7686,plain,
( ! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1))
| ~ spl86_108
| ~ spl86_165
| ~ spl86_318 ),
inference(forward_demodulation,[],[f7685,f4223]) ).
fof(f7685,plain,
( ! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)))
| ~ spl86_318 ),
inference(forward_demodulation,[],[f7683,f2226]) ).
fof(f7683,plain,
( ! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool))))
| ~ spl86_318 ),
inference(avatar_component_clause,[],[f7682]) ).
fof(f7684,plain,
spl86_318,
inference(avatar_split_clause,[],[f2861,f7682]) ).
fof(f2861,plain,
! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))),
inference(definition_unfolding,[],[f2223,f2190]) ).
fof(f2223,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f813]) ).
fof(f813,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f206]) ).
fof(f206,axiom,
! [X0,X13] : ti(X0,X13) = hAPP(fun(X0,bool),X0,the_elem(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_the__elem__eq) ).
fof(f7677,plain,
spl86_317,
inference(avatar_split_clause,[],[f2612,f7675]) ).
fof(f2612,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2))))
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f1873]) ).
fof(f1873,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,sK74(X0,X1,X2)))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2)))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),X2))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK74(X0,X1,X2))) )
| ~ sP4(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74])],[f1871,f1872]) ).
fof(f1872,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4)) )
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,sK74(X0,X1,X2)))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2)))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),X2))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK74(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f1871,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X3),X4)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X4))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X4))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X4)) )
| ~ sP4(X0,X1,X2) ),
inference(rectify,[],[f1870]) ).
fof(f1870,plain,
! [X0,X1,X2] :
( ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X2))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5)) )
| ~ sP4(X0,X1,X2) ),
inference(nnf_transformation,[],[f1649]) ).
fof(f7673,plain,
spl86_316,
inference(avatar_split_clause,[],[f2572,f7671]) ).
fof(f7671,plain,
( spl86_316
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_316])]) ).
fof(f2572,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))) ),
inference(cnf_transformation,[],[f1862]) ).
fof(f1862,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) )
& ( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))) ) ),
inference(nnf_transformation,[],[f1045]) ).
fof(f1045,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)))
<=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X0,X10,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X7)))
<=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite__insert) ).
fof(f7669,plain,
spl86_315,
inference(avatar_split_clause,[],[f2531,f7667]) ).
fof(f7667,plain,
( spl86_315
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_315])]) ).
fof(f2531,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ),
inference(cnf_transformation,[],[f1514]) ).
fof(f1514,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ),
inference(ennf_transformation,[],[f1026]) ).
fof(f1026,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(rectify,[],[f316]) ).
fof(f316,axiom,
! [X17,X24,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X24)),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X24),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_add__leD2) ).
fof(f7665,plain,
spl86_314,
inference(avatar_split_clause,[],[f2530,f7663]) ).
fof(f7663,plain,
( spl86_314
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_314])]) ).
fof(f2530,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ),
inference(cnf_transformation,[],[f1513]) ).
fof(f1513,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ),
inference(ennf_transformation,[],[f1025]) ).
fof(f1025,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X2)) ),
inference(rectify,[],[f317]) ).
fof(f317,axiom,
! [X17,X24,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X24)),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_add__leD1) ).
fof(f7661,plain,
spl86_313,
inference(avatar_split_clause,[],[f2529,f7659]) ).
fof(f7659,plain,
( spl86_313
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_313])]) ).
fof(f2529,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ),
inference(cnf_transformation,[],[f1512]) ).
fof(f1512,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2)) ),
inference(ennf_transformation,[],[f1024]) ).
fof(f1024,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2)) ),
inference(rectify,[],[f348]) ).
fof(f348,axiom,
! [X25,X26,X24] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X26)),X24))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_add__lessD1) ).
fof(f7657,plain,
spl86_312,
inference(avatar_split_clause,[],[f2508,f7655]) ).
fof(f7655,plain,
( spl86_312
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X1))
| hBOOL(hAPP(nat,bool,X0,hAPP(nat,nat,suc,sK64(X0,X2))))
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_312])]) ).
fof(f2508,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X1))
| hBOOL(hAPP(nat,bool,X0,hAPP(nat,nat,suc,sK64(X0,X2))))
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1833]) ).
fof(f7653,plain,
spl86_311,
inference(avatar_split_clause,[],[f2494,f7651]) ).
fof(f7651,plain,
( spl86_311
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_311])]) ).
fof(f2494,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1476]) ).
fof(f1476,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f996]) ).
fof(f996,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2))) ),
inference(rectify,[],[f340]) ).
fof(f340,axiom,
! [X21,X20,X50] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X20),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),X50))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_termination__basic__simps_I4_J) ).
fof(f7649,plain,
spl86_310,
inference(avatar_split_clause,[],[f2492,f7647]) ).
fof(f7647,plain,
( spl86_310
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_310])]) ).
fof(f2492,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1474]) ).
fof(f1474,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(ennf_transformation,[],[f994]) ).
fof(f994,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0))) ),
inference(rectify,[],[f312]) ).
fof(f312,axiom,
! [X17,X25,X26] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),X26))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X25),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_trans__le__add1) ).
fof(f7645,plain,
spl86_309,
inference(avatar_split_clause,[],[f2487,f7643]) ).
fof(f7643,plain,
( spl86_309
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_309])]) ).
fof(f2487,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1466]) ).
fof(f1466,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(ennf_transformation,[],[f989]) ).
fof(f989,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)),X2)) ),
inference(rectify,[],[f382]) ).
fof(f382,axiom,
! [X16,X26,X24] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X24))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X26),X16)),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_less__imp__diff__less) ).
fof(f7641,plain,
spl86_308,
inference(avatar_split_clause,[],[f2484,f7639]) ).
fof(f7639,plain,
( spl86_308
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_308])]) ).
fof(f2484,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1463]) ).
fof(f1463,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(ennf_transformation,[],[f986]) ).
fof(f986,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2))) ),
inference(rectify,[],[f347]) ).
fof(f347,axiom,
! [X21,X20,X50] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X50))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),X50))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_termination__basic__simps_I2_J) ).
fof(f7637,plain,
spl86_307,
inference(avatar_split_clause,[],[f2483,f7635]) ).
fof(f7635,plain,
( spl86_307
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_307])]) ).
fof(f2483,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1462]) ).
fof(f1462,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
inference(ennf_transformation,[],[f985]) ).
fof(f985,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X0))) ),
inference(rectify,[],[f346]) ).
fof(f346,axiom,
! [X50,X20,X21] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X21))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X21),X50))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_termination__basic__simps_I1_J) ).
fof(f7633,plain,
spl86_306,
inference(avatar_split_clause,[],[f2439,f7631]) ).
fof(f2439,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(cnf_transformation,[],[f1418]) ).
fof(f1418,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2)) ),
inference(ennf_transformation,[],[f956]) ).
fof(f956,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X2))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))) ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X0,X10,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite_OinsertI) ).
fof(f7629,plain,
spl86_305,
inference(avatar_split_clause,[],[f2292,f7627]) ).
fof(f7627,plain,
( spl86_305
<=> ! [X0,X1] :
( hAPP(nat,nat,suc,X1) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_305])]) ).
fof(f2292,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,X1) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1))) ),
inference(cnf_transformation,[],[f1376]) ).
fof(f1376,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,X1) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1))) ),
inference(flattening,[],[f1375]) ).
fof(f1375,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,X1) = X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1))) ),
inference(ennf_transformation,[],[f875]) ).
fof(f875,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hAPP(nat,nat,suc,X1) = X0 ) ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),hAPP(nat,nat,suc,X16)))
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
=> hAPP(nat,nat,suc,X16) = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__SucE) ).
fof(f7625,plain,
spl86_304,
inference(avatar_split_clause,[],[f2275,f7623]) ).
fof(f7623,plain,
( spl86_304
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1))
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_304])]) ).
fof(f2275,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1))
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1355]) ).
fof(f1355,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1))
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(flattening,[],[f1354]) ).
fof(f1354,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1))
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(ennf_transformation,[],[f860]) ).
fof(f860,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> ( hAPP(nat,nat,suc,X0) != X1
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ) ),
inference(rectify,[],[f369]) ).
fof(f369,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16))
=> ( hAPP(nat,nat,suc,X17) != X16
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X17)),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_Suc__lessI) ).
fof(f7476,plain,
spl86_303,
inference(avatar_split_clause,[],[f3027,f7474]) ).
fof(f7474,plain,
( spl86_303
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK46(X0,X1)),sK47(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_303])]) ).
fof(f3027,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK46(X0,X1)),sK47(X0,X1))) ),
inference(forward_demodulation,[],[f2871,f2854]) ).
fof(f2871,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK46(X0,X1)),sK47(X0,X1)))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(definition_unfolding,[],[f2337,f2190]) ).
fof(f2337,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK46(X0,X1)),sK47(X0,X1)))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ),
inference(cnf_transformation,[],[f1763]) ).
fof(f7472,plain,
spl86_302,
inference(avatar_split_clause,[],[f2905,f7470]) ).
fof(f7470,plain,
( spl86_302
<=> ! [X0,X3,X2,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| hBOOL(hAPP(X0,bool,X2,sK71(X0,X2,X3)))
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_302])]) ).
fof(f2905,plain,
! [X2,X3,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| hBOOL(hAPP(X0,bool,X2,sK71(X0,X2,X3)))
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ),
inference(definition_unfolding,[],[f2551,f2190]) ).
fof(f2551,plain,
! [X2,X3,X0,X1] :
( ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),X2)
| ~ hBOOL(hAPP(X0,bool,X2,X1))
| hBOOL(hAPP(X0,bool,X2,sK71(X0,X2,X3)))
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ),
inference(cnf_transformation,[],[f1850]) ).
fof(f7468,plain,
spl86_301,
inference(avatar_split_clause,[],[f2408,f7466]) ).
fof(f7466,plain,
( spl86_301
<=> ! [X2,X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_301])]) ).
fof(f2408,plain,
! [X2,X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))),
inference(cnf_transformation,[],[f931]) ).
fof(f931,plain,
! [X0,X1,X2] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2))),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X0,X10,X12] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X10),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_insertI1) ).
fof(f7464,plain,
( spl86_300
| ~ spl86_53
| ~ spl86_289 ),
inference(avatar_split_clause,[],[f7323,f7141,f3436,f7462]) ).
fof(f7462,plain,
( spl86_300
<=> ! [X0] :
( ~ sP2(X0,finite_finite(X0))
| ~ finite_finite_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_300])]) ).
fof(f7323,plain,
( ! [X0] :
( ~ sP2(X0,finite_finite(X0))
| ~ finite_finite_1(X0) )
| ~ spl86_53
| ~ spl86_289 ),
inference(resolution,[],[f7142,f3437]) ).
fof(f7426,plain,
spl86_299,
inference(avatar_split_clause,[],[f3019,f7424]) ).
fof(f7424,plain,
( spl86_299
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK42(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_299])]) ).
fof(f3019,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK42(X0,X1)))
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(forward_demodulation,[],[f2866,f2854]) ).
fof(f2866,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK42(X0,X1)))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(definition_unfolding,[],[f2331,f2190]) ).
fof(f2331,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK42(X0,X1)))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(cnf_transformation,[],[f1755]) ).
fof(f7422,plain,
spl86_298,
inference(avatar_split_clause,[],[f3003,f7420]) ).
fof(f7420,plain,
( spl86_298
<=> ! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),combi(X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_298])]) ).
fof(f3003,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),combi(X0)),X1),
inference(forward_demodulation,[],[f2859,f2854]) ).
fof(f2859,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),combi(X0)),X1) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1),
inference(definition_unfolding,[],[f2216,f2190]) ).
fof(f2216,plain,
! [X0,X1] : ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),combi(X0)),X1),
inference(cnf_transformation,[],[f806]) ).
fof(f806,plain,
! [X0,X1] : ti(fun(X0,bool),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),combi(X0)),X1),
inference(rectify,[],[f137]) ).
fof(f137,axiom,
! [X0,X44] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),combi(X0)),X44) = ti(fun(X0,bool),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_image__ident) ).
fof(f7418,plain,
spl86_297,
inference(avatar_split_clause,[],[f2888,f7416]) ).
fof(f7416,plain,
( spl86_297
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),sK56(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_297])]) ).
fof(f2888,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),sK56(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(definition_unfolding,[],[f2438,f2190,f2190]) ).
fof(f2438,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| ti(X0,X2) != ti(X0,sK56(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1820]) ).
fof(f1820,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| ( ti(X0,X2) != ti(X0,sK56(X0,X1,X2))
& hBOOL(hAPP(X0,bool,X1,sK56(X0,X1,X2))) )
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f1417,f1819]) ).
fof(f1819,plain,
! [X0,X1,X2] :
( ? [X3] :
( ti(X0,X2) != ti(X0,X3)
& hBOOL(hAPP(X0,bool,X1,X3)) )
=> ( ti(X0,X2) != ti(X0,sK56(X0,X1,X2))
& hBOOL(hAPP(X0,bool,X1,sK56(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f1417,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| ? [X3] :
( ti(X0,X2) != ti(X0,X3)
& hBOOL(hAPP(X0,bool,X1,X3)) )
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(flattening,[],[f1416]) ).
fof(f1416,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| ? [X3] :
( ti(X0,X2) != ti(X0,X3)
& hBOOL(hAPP(X0,bool,X1,X3)) )
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(ennf_transformation,[],[f955]) ).
fof(f955,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,bool,X1,X2))
=> ( ! [X3] :
( hBOOL(hAPP(X0,bool,X1,X3))
=> ti(X0,X2) = ti(X0,X3) )
=> hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1))) ) ),
inference(rectify,[],[f267]) ).
fof(f267,axiom,
! [X0,X15,X10] :
( hBOOL(hAPP(X0,bool,X15,X10))
=> ( ! [X32] :
( hBOOL(hAPP(X0,bool,X15,X32))
=> ti(X0,X10) = ti(X0,X32) )
=> hBOOL(hAPP(X0,bool,X15,hAPP(fun(X0,bool),X0,the(X0),X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_theI) ).
fof(f7414,plain,
spl86_296,
inference(avatar_split_clause,[],[f2863,f7412]) ).
fof(f7412,plain,
( spl86_296
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),sK41(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_296])]) ).
fof(f2863,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| hAPP(X0,X0,combi(X0),X2) != hAPP(X0,X0,combi(X0),sK41(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(definition_unfolding,[],[f2326,f2190,f2190]) ).
fof(f2326,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| ti(X0,X2) != ti(X0,sK41(X0,X1,X2))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1748]) ).
fof(f1748,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| ! [X2] :
( ( ti(X0,X2) != ti(X0,sK41(X0,X1,X2))
& hBOOL(hAPP(X0,bool,X1,sK41(X0,X1,X2))) )
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f1408,f1747]) ).
fof(f1747,plain,
! [X0,X1,X2] :
( ? [X3] :
( ti(X0,X2) != ti(X0,X3)
& hBOOL(hAPP(X0,bool,X1,X3)) )
=> ( ti(X0,X2) != ti(X0,sK41(X0,X1,X2))
& hBOOL(hAPP(X0,bool,X1,sK41(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f1408,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| ! [X2] :
( ? [X3] :
( ti(X0,X2) != ti(X0,X3)
& hBOOL(hAPP(X0,bool,X1,X3)) )
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
inference(ennf_transformation,[],[f897]) ).
fof(f897,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( hBOOL(hAPP(X0,bool,X1,X3))
=> ti(X0,X2) = ti(X0,X3) )
& hBOOL(hAPP(X0,bool,X1,X2)) )
=> hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1))) ),
inference(rectify,[],[f268]) ).
fof(f268,axiom,
! [X0,X15] :
( ? [X32] :
( ! [X60] :
( hBOOL(hAPP(X0,bool,X15,X60))
=> ti(X0,X32) = ti(X0,X60) )
& hBOOL(hAPP(X0,bool,X15,X32)) )
=> hBOOL(hAPP(X0,bool,X15,hAPP(fun(X0,bool),X0,the(X0),X15))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_theI_H) ).
fof(f7410,plain,
spl86_295,
inference(avatar_split_clause,[],[f2276,f7408]) ).
fof(f7408,plain,
( spl86_295
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),sK19(X0,X1)))
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_295])]) ).
fof(f2276,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),sK19(X0,X1)))
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1719]) ).
fof(f1719,plain,
! [X0,X1] :
( ( hAPP(nat,nat,suc,sK19(X0,X1)) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),sK19(X0,X1))) )
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f1357,f1718]) ).
fof(f1718,plain,
! [X0,X1] :
( ? [X2] :
( hAPP(nat,nat,suc,X2) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2)) )
=> ( hAPP(nat,nat,suc,sK19(X0,X1)) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),sK19(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f1357,plain,
! [X0,X1] :
( ? [X2] :
( hAPP(nat,nat,suc,X2) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2)) )
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(flattening,[],[f1356]) ).
fof(f1356,plain,
! [X0,X1] :
( ? [X2] :
( hAPP(nat,nat,suc,X2) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2)) )
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(ennf_transformation,[],[f861]) ).
fof(f861,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> ( hAPP(nat,nat,suc,X0) != X1
=> ~ ! [X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2))
=> hAPP(nat,nat,suc,X2) != X1 ) ) ),
inference(rectify,[],[f482]) ).
fof(f482,axiom,
! [X25,X24] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X24))
=> ( hAPP(nat,nat,suc,X25) != X24
=> ~ ! [X71] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X71))
=> hAPP(nat,nat,suc,X71) != X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_lessE) ).
fof(f7163,plain,
spl86_294,
inference(avatar_split_clause,[],[f3060,f7161]) ).
fof(f7161,plain,
( spl86_294
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK53(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_294])]) ).
fof(f3060,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK53(X0,X1)),X1)) ),
inference(forward_demodulation,[],[f2877,f2854]) ).
fof(f2877,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK53(X0,X1)),X1))
| bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(definition_unfolding,[],[f2400,f2190]) ).
fof(f2400,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK53(X0,X1)),X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ),
inference(cnf_transformation,[],[f1814]) ).
fof(f1814,plain,
! [X0,X1] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK53(X0,X1)),X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) )
& ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
| ! [X3] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f1812,f1813]) ).
fof(f1813,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK53(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
fof(f1812,plain,
! [X0,X1] :
( ( ? [X2] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) )
& ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
| ! [X3] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(rectify,[],[f1811]) ).
fof(f1811,plain,
! [X0,X1] :
( ( ? [X2] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) )
& ( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1)
| ! [X2] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f924]) ).
fof(f924,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ),
inference(rectify,[],[f163]) ).
fof(f163,axiom,
! [X0,X7] :
( ? [X32] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X7))
<=> ti(fun(X0,bool),X7) != bot_bot(fun(X0,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_ex__in__conv) ).
fof(f7159,plain,
spl86_293,
inference(avatar_split_clause,[],[f3059,f7157]) ).
fof(f3059,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK52(X0,X1)),X1)) ),
inference(forward_demodulation,[],[f2876,f2854]) ).
fof(f2876,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK52(X0,X1)),X1)) ),
inference(definition_unfolding,[],[f2397,f2190]) ).
fof(f2397,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK52(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1810]) ).
fof(f1810,plain,
! [X0,X1] :
( ( ! [X2] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) )
& ( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK52(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f1808,f1809]) ).
fof(f1809,plain,
! [X0,X1] :
( ? [X3] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK52(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
fof(f1808,plain,
! [X0,X1] :
( ( ! [X2] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) )
& ( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ? [X3] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(rectify,[],[f1807]) ).
fof(f1807,plain,
! [X0,X1] :
( ( ! [X2] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) )
& ( bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1)
| ? [X2] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f923]) ).
fof(f923,plain,
! [X0,X1] :
( ! [X2] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> bot_bot(fun(X0,bool)) = ti(fun(X0,bool),X1) ),
inference(rectify,[],[f164]) ).
fof(f164,axiom,
! [X0,X7] :
( ! [X32] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X32),X7))
<=> ti(fun(X0,bool),X7) = bot_bot(fun(X0,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_all__not__in__conv) ).
fof(f7155,plain,
spl86_292,
inference(avatar_split_clause,[],[f2778,f7153]) ).
fof(f7153,plain,
( spl86_292
<=> ! [X0] : insert(X0) = hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),combi(fun(X0,fun(fun(X0,bool),fun(X0,bool)))),insert(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_292])]) ).
fof(f2778,plain,
! [X0] : insert(X0) = hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),fun(X0,fun(fun(X0,bool),fun(X0,bool))),combi(fun(X0,fun(fun(X0,bool),fun(X0,bool)))),insert(X0)),
inference(definition_unfolding,[],[f2010,f2190]) ).
fof(f2010,plain,
! [X0] : insert(X0) = ti(fun(X0,fun(fun(X0,bool),fun(X0,bool))),insert(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : insert(X0) = ti(fun(X0,fun(fun(X0,bool),fun(X0,bool))),insert(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
fof(f7151,plain,
spl86_291,
inference(avatar_split_clause,[],[f2777,f7149]) ).
fof(f7149,plain,
( spl86_291
<=> ! [X0] : nat_case(X0) = hAPP(fun(X0,fun(fun(nat,X0),fun(nat,X0))),fun(X0,fun(fun(nat,X0),fun(nat,X0))),combi(fun(X0,fun(fun(nat,X0),fun(nat,X0)))),nat_case(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_291])]) ).
fof(f2777,plain,
! [X0] : nat_case(X0) = hAPP(fun(X0,fun(fun(nat,X0),fun(nat,X0))),fun(X0,fun(fun(nat,X0),fun(nat,X0))),combi(fun(X0,fun(fun(nat,X0),fun(nat,X0)))),nat_case(X0)),
inference(definition_unfolding,[],[f2009,f2190]) ).
fof(f2009,plain,
! [X0] : nat_case(X0) = ti(fun(X0,fun(fun(nat,X0),fun(nat,X0))),nat_case(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : nat_case(X0) = ti(fun(X0,fun(fun(nat,X0),fun(nat,X0))),nat_case(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_Onat_Onat__case_res) ).
fof(f7147,plain,
spl86_290,
inference(avatar_split_clause,[],[f2587,f7145]) ).
fof(f7145,plain,
( spl86_290
<=> ! [X0,X3,X2,X1] : hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X1),X2),hAPP(nat,nat,suc,X3)) = hAPP(nat,X0,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_290])]) ).
fof(f2587,plain,
! [X2,X3,X0,X1] : hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X1),X2),hAPP(nat,nat,suc,X3)) = hAPP(nat,X0,X2,X3),
inference(cnf_transformation,[],[f1054]) ).
fof(f1054,plain,
! [X0,X1,X2,X3] : hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X1),X2),hAPP(nat,nat,suc,X3)) = hAPP(nat,X0,X2,X3),
inference(rectify,[],[f335]) ).
fof(f335,axiom,
! [X0,X64,X65,X22] : hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X64),X65),hAPP(nat,nat,suc,X22)) = hAPP(nat,X0,X65,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_nat__case__Suc) ).
fof(f7143,plain,
spl86_289,
inference(avatar_split_clause,[],[f2458,f7141]) ).
fof(f2458,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK59(X0,X1)),sK60(X0,X1))))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1826]) ).
fof(f1826,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK59(X0,X1)),sK60(X0,X1))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,sK60(X0,X1)))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK59(X0,X1)),sK60(X0,X1)))
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),sK60(X0,X1))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK60(X0,X1))) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60])],[f1824,f1825]) ).
fof(f1825,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X3))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X3)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) )
=> ( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),sK59(X0,X1)),sK60(X0,X1))))
& hBOOL(hAPP(fun(X0,bool),bool,X1,sK60(X0,X1)))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK59(X0,X1)),sK60(X0,X1)))
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),sK60(X0,X1))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK60(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f1824,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X3))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X3))
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X3)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X3)) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f1823]) ).
fof(f1823,plain,
! [X0,X1] :
( ? [X4,X5] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,X1,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X4),X5)))
& hBOOL(hAPP(fun(X0,bool),bool,X1,X5))
& ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X4),X5))
& bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X5)
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X5)) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f1645]) ).
fof(f7139,plain,
spl86_288,
inference(avatar_split_clause,[],[f2433,f7137]) ).
fof(f7137,plain,
( spl86_288
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sK54(X1))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_288])]) ).
fof(f2433,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sK54(X1))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1816]) ).
fof(f1816,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ( ~ hBOOL(hAPP(nat,bool,X1,sK54(X1)))
& hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sK54(X1)))) )
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f1413,f1815]) ).
fof(f1815,plain,
! [X1] :
( ? [X3] :
( ~ hBOOL(hAPP(nat,bool,X1,X3))
& hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,X3))) )
=> ( ~ hBOOL(hAPP(nat,bool,X1,sK54(X1)))
& hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sK54(X1)))) ) ),
introduced(choice_axiom,[]) ).
fof(f1413,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ? [X3] :
( ~ hBOOL(hAPP(nat,bool,X1,X3))
& hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,X3))) )
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(flattening,[],[f1412]) ).
fof(f1412,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ? [X3] :
( ~ hBOOL(hAPP(nat,bool,X1,X3))
& hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,X3))) )
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(ennf_transformation,[],[f953]) ).
fof(f953,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,X1,X2))
=> ( ! [X3] :
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,X3)))
=> hBOOL(hAPP(nat,bool,X1,X3)) )
=> hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0))) ) ),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X35,X15,X18] :
( hBOOL(hAPP(nat,bool,X15,X18))
=> ( ! [X31] :
( hBOOL(hAPP(nat,bool,X15,hAPP(nat,nat,suc,X31)))
=> hBOOL(hAPP(nat,bool,X15,X31)) )
=> hBOOL(hAPP(nat,bool,X15,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X18),X35))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_zero__induct__lemma) ).
fof(f7135,plain,
spl86_287,
inference(avatar_split_clause,[],[f2299,f7133]) ).
fof(f7133,plain,
( spl86_287
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_287])]) ).
fof(f2299,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1))) ),
inference(cnf_transformation,[],[f1382]) ).
fof(f1382,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1))) ),
inference(ennf_transformation,[],[f881]) ).
fof(f881,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(rectify,[],[f365]) ).
fof(f365,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X17)),hAPP(nat,nat,suc,X16)))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_Suc__less__SucD) ).
fof(f7131,plain,
spl86_286,
inference(avatar_split_clause,[],[f2274,f7129]) ).
fof(f7129,plain,
( spl86_286
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_286])]) ).
fof(f2274,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1353]) ).
fof(f1353,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(ennf_transformation,[],[f859]) ).
fof(f859,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1))) ),
inference(rectify,[],[f344]) ).
fof(f344,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X17)),hAPP(nat,nat,suc,X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_Suc__mono) ).
fof(f7127,plain,
spl86_285,
inference(avatar_split_clause,[],[f2180,f7125]) ).
fof(f2180,plain,
! [X0] :
( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0))))
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X0),u)) ),
inference(cnf_transformation,[],[f1318]) ).
fof(f1318,plain,
! [X0] :
( hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0))))
| ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X0),u)) ),
inference(ennf_transformation,[],[f779]) ).
fof(f779,plain,
! [X0] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X0),u))
=> hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X0)))) ),
inference(rectify,[],[f209]) ).
fof(f209,axiom,
! [X55] :
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),X55),u))
=> hBOOL(hAPP(com,bool,wt,hAPP(option(com),com,the_1(com),hAPP(pname,option(com),body,X55)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_assms_I4_J) ).
fof(f7110,plain,
( spl86_284
| spl86_226
| ~ spl86_71
| ~ spl86_104
| ~ spl86_208 ),
inference(avatar_split_clause,[],[f6845,f4881,f3682,f3532,f4978,f7108]) ).
fof(f4881,plain,
( spl86_208
<=> fTrue = bot_bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_208])]) ).
fof(f6845,plain,
( ! [X0] :
( hBOOL(fTrue)
| ~ sP2(X0,bot_bot(fun(fun(X0,bool),bool))) )
| ~ spl86_71
| ~ spl86_104
| ~ spl86_208 ),
inference(forward_demodulation,[],[f6818,f4883]) ).
fof(f4883,plain,
( fTrue = bot_bot(bool)
| ~ spl86_208 ),
inference(avatar_component_clause,[],[f4881]) ).
fof(f6850,plain,
spl86_283,
inference(avatar_split_clause,[],[f2509,f6848]) ).
fof(f2509,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X0,X1))
| ~ hBOOL(hAPP(nat,bool,X0,sK64(X0,X2)))
| ~ hBOOL(hAPP(nat,bool,X0,X2))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
inference(cnf_transformation,[],[f1833]) ).
fof(f6807,plain,
spl86_282,
inference(avatar_split_clause,[],[f2350,f6805]) ).
fof(f2350,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK48(X0,X1))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f1773,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ! [X2] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) != X1 )
& ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK48(X0,X1))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f1771,f1772]) ).
fof(f1772,plain,
! [X0,X1] :
( ? [X3] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3)) = X1
=> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK48(X0,X1))) = X1 ),
introduced(choice_axiom,[]) ).
fof(f1771,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ! [X2] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) != X1 )
& ( ? [X3] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
inference(rectify,[],[f1770]) ).
fof(f1770,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ! [X2] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) != X1 )
& ( ? [X2] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
inference(nnf_transformation,[],[f907]) ).
fof(f907,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
<=> ? [X2] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) = X1 ),
inference(rectify,[],[f444]) ).
fof(f444,axiom,
! [X27,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X27),X19))
<=> ? [X62] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X62)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_less__iff__Suc__add) ).
fof(f6803,plain,
spl86_281,
inference(avatar_split_clause,[],[f2290,f6801]) ).
fof(f2290,plain,
! [X0,X1] :
( X0 = X1
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f1372,plain,
! [X0,X1] :
( X0 = X1
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) ),
inference(flattening,[],[f1371]) ).
fof(f1371,plain,
! [X0,X1] :
( X0 = X1
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) ),
inference(ennf_transformation,[],[f873]) ).
fof(f873,plain,
! [X0,X1] :
( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)
=> ( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X1),X0)
=> X0 = X1 ) ),
inference(rectify,[],[f526]) ).
fof(f526,axiom,
! [X17,X16] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16) = zero_zero(nat)
=> ( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X16),X17)
=> X16 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_diffs0__imp__equal) ).
fof(f6799,plain,
spl86_280,
inference(avatar_split_clause,[],[f2288,f6797]) ).
fof(f6797,plain,
( spl86_280
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_280])]) ).
fof(f2288,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1722]) ).
fof(f1722,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0)))
| X0 != X1 )
& ( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0))) ) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(nnf_transformation,[],[f1370]) ).
fof(f1370,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0)))
<=> X0 = X1 )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f872]) ).
fof(f872,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0)))
<=> X0 = X1 ) ),
inference(rectify,[],[f450]) ).
fof(f450,axiom,
! [X27,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X19))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X19),hAPP(nat,nat,suc,X27)))
<=> X19 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_le__less__Suc__eq) ).
fof(f6795,plain,
spl86_279,
inference(avatar_split_clause,[],[f2278,f6793]) ).
fof(f2278,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK20(X0,X1))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1721]) ).
fof(f1721,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK20(X0,X1))) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f1358,f1720]) ).
fof(f1720,plain,
! [X0,X1] :
( ? [X2] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) = X1
=> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK20(X0,X1))) = X1 ),
introduced(choice_axiom,[]) ).
fof(f1358,plain,
! [X0,X1] :
( ? [X2] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(ennf_transformation,[],[f862]) ).
fof(f862,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> ? [X2] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)) = X1 ),
inference(rectify,[],[f460]) ).
fof(f460,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16))
=> ? [X62] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X62)) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_less__imp__Suc__add) ).
fof(f6791,plain,
spl86_278,
inference(avatar_split_clause,[],[f2265,f6789]) ).
fof(f6789,plain,
( spl86_278
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_278])]) ).
fof(f2265,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1345]) ).
fof(f1345,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(flattening,[],[f1344]) ).
fof(f1344,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(ennf_transformation,[],[f851]) ).
fof(f851,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
=> X0 = X1 ) ),
inference(rectify,[],[f371]) ).
fof(f371,axiom,
! [X16,X17] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X17))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),hAPP(nat,nat,suc,X17)))
=> X16 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_less__antisym) ).
fof(f6787,plain,
spl86_277,
inference(avatar_split_clause,[],[f2221,f6785]) ).
fof(f6785,plain,
( spl86_277
<=> ! [X0,X1] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,suc,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_277])]) ).
fof(f2221,plain,
! [X0,X1] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,suc,X1)),
inference(cnf_transformation,[],[f811]) ).
fof(f811,plain,
! [X0,X1] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),hAPP(nat,nat,suc,X1)),
inference(rectify,[],[f288]) ).
fof(f288,axiom,
! [X17,X16] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),hAPP(nat,nat,suc,X16)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_add__Suc__right) ).
fof(f6783,plain,
spl86_276,
inference(avatar_split_clause,[],[f2220,f6781]) ).
fof(f6781,plain,
( spl86_276
<=> ! [X0,X1] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_276])]) ).
fof(f2220,plain,
! [X0,X1] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X0)),X1),
inference(cnf_transformation,[],[f810]) ).
fof(f810,plain,
! [X0,X1] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X0)),X1),
inference(rectify,[],[f289]) ).
fof(f289,axiom,
! [X17,X16] : hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X16)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X17)),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_add__Suc) ).
fof(f6779,plain,
spl86_275,
inference(avatar_split_clause,[],[f2219,f6777]) ).
fof(f6777,plain,
( spl86_275
<=> ! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_275])]) ).
fof(f2219,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)),
inference(cnf_transformation,[],[f809]) ).
fof(f809,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)),
inference(rectify,[],[f91]) ).
fof(f91,axiom,
! [X17,X16] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X17)),hAPP(nat,nat,suc,X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_diff__Suc__Suc) ).
fof(f6391,plain,
( spl86_274
| ~ spl86_103
| ~ spl86_122 ),
inference(avatar_split_clause,[],[f3906,f3879,f3678,f6389]) ).
fof(f6389,plain,
( spl86_274
<=> ! [X0] : ~ sP3(hAPP(nat,nat,suc,X0),zero_zero(nat),ord_less(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_274])]) ).
fof(f3906,plain,
( ! [X0] : ~ sP3(hAPP(nat,nat,suc,X0),zero_zero(nat),ord_less(nat))
| ~ spl86_103
| ~ spl86_122 ),
inference(resolution,[],[f3880,f3679]) ).
fof(f6387,plain,
spl86_273,
inference(avatar_split_clause,[],[f3058,f6385]) ).
fof(f6385,plain,
( spl86_273
<=> ! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_273])]) ).
fof(f3058,plain,
! [X2,X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(forward_demodulation,[],[f2875,f2854]) ).
fof(f2875,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(definition_unfolding,[],[f2398,f2190]) ).
fof(f2398,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ),
inference(cnf_transformation,[],[f1810]) ).
fof(f6383,plain,
spl86_272,
inference(avatar_split_clause,[],[f2961,f6381]) ).
fof(f6381,plain,
( spl86_272
<=> ! [X2,X4,X0,X3,X1] :
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X0) = hAPP(X1,X1,combi(X1),X4)
| ~ sP8(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_272])]) ).
fof(f2961,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X0) = hAPP(X1,X1,combi(X1),X4)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(definition_unfolding,[],[f2728,f2190,f2190,f2190,f2190]) ).
fof(f2728,plain,
! [X2,X3,X0,X1,X4] :
( ti(X1,X3) = ti(X1,X4)
| ti(X1,X4) = ti(X1,X0)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f1924]) ).
fof(f1924,plain,
! [X0,X1,X2,X3,X4] :
( ( sP8(X0,X1,X2,X3,X4)
| ( ( ti(X1,X2) != ti(X1,X0)
| ti(X1,X3) != ti(X1,X4) )
& ( ti(X1,X2) != ti(X1,X3)
| ti(X1,X4) != ti(X1,X0) ) ) )
& ( ( ti(X1,X2) = ti(X1,X0)
& ti(X1,X3) = ti(X1,X4) )
| ( ti(X1,X2) = ti(X1,X3)
& ti(X1,X4) = ti(X1,X0) )
| ~ sP8(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f1923]) ).
fof(f1923,plain,
! [X3,X0,X2,X4,X1] :
( ( sP8(X3,X0,X2,X4,X1)
| ( ( ti(X0,X2) != ti(X0,X3)
| ti(X0,X1) != ti(X0,X4) )
& ( ti(X0,X2) != ti(X0,X4)
| ti(X0,X1) != ti(X0,X3) ) ) )
& ( ( ti(X0,X2) = ti(X0,X3)
& ti(X0,X1) = ti(X0,X4) )
| ( ti(X0,X2) = ti(X0,X4)
& ti(X0,X1) = ti(X0,X3) )
| ~ sP8(X3,X0,X2,X4,X1) ) ),
inference(flattening,[],[f1922]) ).
fof(f1922,plain,
! [X3,X0,X2,X4,X1] :
( ( sP8(X3,X0,X2,X4,X1)
| ( ( ti(X0,X2) != ti(X0,X3)
| ti(X0,X1) != ti(X0,X4) )
& ( ti(X0,X2) != ti(X0,X4)
| ti(X0,X1) != ti(X0,X3) ) ) )
& ( ( ti(X0,X2) = ti(X0,X3)
& ti(X0,X1) = ti(X0,X4) )
| ( ti(X0,X2) = ti(X0,X4)
& ti(X0,X1) = ti(X0,X3) )
| ~ sP8(X3,X0,X2,X4,X1) ) ),
inference(nnf_transformation,[],[f1656]) ).
fof(f6379,plain,
spl86_271,
inference(avatar_split_clause,[],[f2960,f6377]) ).
fof(f6377,plain,
( spl86_271
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ sP8(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_271])]) ).
fof(f2960,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X1,combi(X1),X3) = hAPP(X1,X1,combi(X1),X4)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(definition_unfolding,[],[f2729,f2190,f2190,f2190,f2190]) ).
fof(f2729,plain,
! [X2,X3,X0,X1,X4] :
( ti(X1,X3) = ti(X1,X4)
| ti(X1,X2) = ti(X1,X3)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f1924]) ).
fof(f6375,plain,
spl86_270,
inference(avatar_split_clause,[],[f2959,f6373]) ).
fof(f6373,plain,
( spl86_270
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X0)
| hAPP(X1,X1,combi(X1),X0) = hAPP(X1,X1,combi(X1),X4)
| ~ sP8(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_270])]) ).
fof(f2959,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X0)
| hAPP(X1,X1,combi(X1),X0) = hAPP(X1,X1,combi(X1),X4)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(definition_unfolding,[],[f2730,f2190,f2190,f2190,f2190]) ).
fof(f2730,plain,
! [X2,X3,X0,X1,X4] :
( ti(X1,X2) = ti(X1,X0)
| ti(X1,X4) = ti(X1,X0)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f1924]) ).
fof(f6371,plain,
spl86_269,
inference(avatar_split_clause,[],[f2958,f6369]) ).
fof(f6369,plain,
( spl86_269
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X0)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ sP8(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_269])]) ).
fof(f2958,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X0)
| hAPP(X1,X1,combi(X1),X2) = hAPP(X1,X1,combi(X1),X3)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(definition_unfolding,[],[f2731,f2190,f2190,f2190,f2190]) ).
fof(f2731,plain,
! [X2,X3,X0,X1,X4] :
( ti(X1,X2) = ti(X1,X0)
| ti(X1,X2) = ti(X1,X3)
| ~ sP8(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f1924]) ).
fof(f6367,plain,
spl86_268,
inference(avatar_split_clause,[],[f2957,f6365]) ).
fof(f2957,plain,
! [X2,X3,X0,X1,X4] :
( sP8(X0,X1,X2,X3,X4)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3)
| hAPP(X1,X1,combi(X1),X0) != hAPP(X1,X1,combi(X1),X4) ),
inference(definition_unfolding,[],[f2732,f2190,f2190,f2190,f2190]) ).
fof(f2732,plain,
! [X2,X3,X0,X1,X4] :
( sP8(X0,X1,X2,X3,X4)
| ti(X1,X2) != ti(X1,X3)
| ti(X1,X4) != ti(X1,X0) ),
inference(cnf_transformation,[],[f1924]) ).
fof(f6363,plain,
spl86_267,
inference(avatar_split_clause,[],[f2956,f6361]) ).
fof(f2956,plain,
! [X2,X3,X0,X1,X4] :
( sP8(X0,X1,X2,X3,X4)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X0)
| hAPP(X1,X1,combi(X1),X3) != hAPP(X1,X1,combi(X1),X4) ),
inference(definition_unfolding,[],[f2733,f2190,f2190,f2190,f2190]) ).
fof(f2733,plain,
! [X2,X3,X0,X1,X4] :
( sP8(X0,X1,X2,X3,X4)
| ti(X1,X2) != ti(X1,X0)
| ti(X1,X3) != ti(X1,X4) ),
inference(cnf_transformation,[],[f1924]) ).
fof(f6359,plain,
spl86_266,
inference(avatar_split_clause,[],[f2882,f6357]) ).
fof(f6357,plain,
( spl86_266
<=> ! [X2,X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X1),X2),zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_266])]) ).
fof(f2882,plain,
! [X2,X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X1),X2),zero_zero(nat)),
inference(definition_unfolding,[],[f2406,f2190]) ).
fof(f2406,plain,
! [X2,X0,X1] : ti(X0,X1) = hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X1),X2),zero_zero(nat)),
inference(cnf_transformation,[],[f929]) ).
fof(f929,plain,
! [X0,X1,X2] : ti(X0,X1) = hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X1),X2),zero_zero(nat)),
inference(rectify,[],[f544]) ).
fof(f544,axiom,
! [X0,X64,X65] : hAPP(nat,X0,hAPP(fun(nat,X0),fun(nat,X0),hAPP(X0,fun(fun(nat,X0),fun(nat,X0)),nat_case(X0),X64),X65),zero_zero(nat)) = ti(X0,X64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_nat__case__0) ).
fof(f6355,plain,
spl86_265,
inference(avatar_split_clause,[],[f2766,f6352]) ).
fof(f6352,plain,
( spl86_265
<=> p = hAPP(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),combi(fun(fun(x_a,bool),fun(fun(x_a,bool),bool))),p) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_265])]) ).
fof(f2766,plain,
p = hAPP(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),combi(fun(fun(x_a,bool),fun(fun(x_a,bool),bool))),p),
inference(definition_unfolding,[],[f1981,f2190]) ).
fof(f1981,plain,
p = ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
p = ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_P_res) ).
fof(f6350,plain,
spl86_264,
inference(avatar_split_clause,[],[f2541,f6348]) ).
fof(f2541,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
| X1 = X2
| sP3(X1,X2,X0) ),
inference(cnf_transformation,[],[f1648]) ).
fof(f1648,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& X1 = X2 )
| sP3(X1,X2,X0) ),
inference(definition_folding,[],[f1522,f1647]) ).
fof(f1647,plain,
! [X1,X2,X0] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
| ~ sP3(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f1522,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& X1 = X2 )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
inference(flattening,[],[f1521]) ).
fof(f1521,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& X1 = X2 )
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ) ),
inference(ennf_transformation,[],[f1032]) ).
fof(f1032,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1)) )
=> ( ( X1 = X2
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1)) ) ) ),
inference(rectify,[],[f412]) ).
fof(f412,axiom,
! [X15,X27,X19] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X27),X19))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X15,X19),X27)) )
=> ( ( X19 = X27
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X15,X19),X27)) )
=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X19),X27))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X15,X19),X27)) )
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X15,X19),X27)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_nat__less__cases) ).
fof(f6346,plain,
spl86_263,
inference(avatar_split_clause,[],[f2294,f6344]) ).
fof(f6344,plain,
( spl86_263
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),sK21(X0,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_263])]) ).
fof(f2294,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),sK21(X0,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(cnf_transformation,[],[f1724]) ).
fof(f1724,plain,
! [X0,X1] :
( ( hAPP(nat,nat,suc,sK21(X0,X1)) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),sK21(X0,X1))) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f1378,f1723]) ).
fof(f1723,plain,
! [X0,X1] :
( ? [X2] :
( hAPP(nat,nat,suc,X2) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2)) )
=> ( hAPP(nat,nat,suc,sK21(X0,X1)) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),sK21(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f1378,plain,
! [X0,X1] :
( ? [X2] :
( hAPP(nat,nat,suc,X2) = X1
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2)) )
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(ennf_transformation,[],[f877]) ).
fof(f877,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1))
=> ~ ! [X2] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X2))
=> hAPP(nat,nat,suc,X2) != X1 ) ),
inference(rectify,[],[f481]) ).
fof(f481,axiom,
! [X25,X24] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X25)),X24))
=> ~ ! [X71] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),X71))
=> hAPP(nat,nat,suc,X71) != X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_Suc__lessE) ).
fof(f6342,plain,
spl86_262,
inference(avatar_split_clause,[],[f2217,f6340]) ).
fof(f2217,plain,
! [X0,X1] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X1),
inference(cnf_transformation,[],[f807]) ).
fof(f807,plain,
! [X0,X1] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X1),
inference(rectify,[],[f220]) ).
fof(f220,axiom,
! [X0,X7] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),bot_bot(fun(X0,bool))),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_empty__Diff) ).
fof(f6307,plain,
spl86_261,
inference(avatar_split_clause,[],[f2675,f6305]) ).
fof(f6305,plain,
( spl86_261
<=> ! [X0,X3,X2,X1] :
( sP6(X0,X1,X2,X3)
| ~ sP5(X3,X2,X1,X0)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_261])]) ).
fof(f2675,plain,
! [X2,X3,X0,X1] :
( sP6(X0,X1,X2,X3)
| ~ sP5(X3,X2,X1,X0)
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
inference(cnf_transformation,[],[f1894]) ).
fof(f6303,plain,
spl86_260,
inference(avatar_split_clause,[],[f2653,f6301]) ).
fof(f6301,plain,
( spl86_260
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3))
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_260])]) ).
fof(f2653,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),X3))
| ~ hBOOL(hAPP(X0,bool,X2,X3)) ),
inference(cnf_transformation,[],[f1881]) ).
fof(f6299,plain,
spl86_259,
inference(avatar_split_clause,[],[f2407,f6297]) ).
fof(f6297,plain,
( spl86_259
<=> ! [X2,X0,X1] : bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_259])]) ).
fof(f2407,plain,
! [X2,X0,X1] : bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),bot_bot(fun(X0,bool))),
inference(cnf_transformation,[],[f930]) ).
fof(f930,plain,
! [X0,X1,X2] : bot_bot(fun(X1,bool)) = hAPP(fun(X0,bool),fun(X1,bool),hAPP(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool)),image(X0,X1),X2),bot_bot(fun(X0,bool))),
inference(rectify,[],[f179]) ).
fof(f179,axiom,
! [X1,X0,X11] : bot_bot(fun(X0,bool)) = hAPP(fun(X1,bool),fun(X0,bool),hAPP(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool)),image(X1,X0),X11),bot_bot(fun(X1,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_image__empty) ).
fof(f6227,plain,
( ~ spl86_258
| spl86_143
| ~ spl86_164 ),
inference(avatar_split_clause,[],[f4208,f4157,f4021,f6224]) ).
fof(f6224,plain,
( spl86_258
<=> hBOOL(hAPP(x_a,bool,g,hAPP(pname,x_a,mgt_call,pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_258])]) ).
fof(f4021,plain,
( spl86_143
<=> hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_143])]) ).
fof(f4208,plain,
( ~ hBOOL(hAPP(x_a,bool,g,hAPP(pname,x_a,mgt_call,pn)))
| spl86_143
| ~ spl86_164 ),
inference(resolution,[],[f4158,f4023]) ).
fof(f4023,plain,
( ~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g))
| spl86_143 ),
inference(avatar_component_clause,[],[f4021]) ).
fof(f6043,plain,
spl86_257,
inference(avatar_split_clause,[],[f2887,f6041]) ).
fof(f6041,plain,
( spl86_257
<=> ! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,the(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| hBOOL(hAPP(X0,bool,X1,sK55(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_257])]) ).
fof(f2887,plain,
! [X2,X0,X1] :
( hAPP(fun(X0,bool),X0,the(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| hBOOL(hAPP(X0,bool,X1,sK55(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(definition_unfolding,[],[f2435,f2190]) ).
fof(f2435,plain,
! [X2,X0,X1] :
( ti(X0,X2) = hAPP(fun(X0,bool),X0,the(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK55(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1818]) ).
fof(f6039,plain,
spl86_256,
inference(avatar_split_clause,[],[f2853,f6037]) ).
fof(f6037,plain,
( spl86_256
<=> ! [X0,X1] : finite_comp_fun_idem(X0,X1) = hAPP(fun(fun(X0,fun(X1,X1)),bool),fun(fun(X0,fun(X1,X1)),bool),combi(fun(fun(X0,fun(X1,X1)),bool)),finite_comp_fun_idem(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_256])]) ).
fof(f2853,plain,
! [X0,X1] : finite_comp_fun_idem(X0,X1) = hAPP(fun(fun(X0,fun(X1,X1)),bool),fun(fun(X0,fun(X1,X1)),bool),combi(fun(fun(X0,fun(X1,X1)),bool)),finite_comp_fun_idem(X0,X1)),
inference(definition_unfolding,[],[f2192,f2190]) ).
fof(f2192,plain,
! [X0,X1] : finite_comp_fun_idem(X0,X1) = ti(fun(fun(X0,fun(X1,X1)),bool),finite_comp_fun_idem(X0,X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] : finite_comp_fun_idem(X0,X1) = ti(fun(fun(X0,fun(X1,X1)),bool),finite_comp_fun_idem(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocomp__fun__idem_res) ).
fof(f6032,plain,
spl86_255,
inference(avatar_split_clause,[],[f2434,f6030]) ).
fof(f6030,plain,
( spl86_255
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,X1,sK54(X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_255])]) ).
fof(f2434,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X2),X0)))
| ~ hBOOL(hAPP(nat,bool,X1,sK54(X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1816]) ).
fof(f6028,plain,
spl86_254,
inference(avatar_split_clause,[],[f2363,f6026]) ).
fof(f6026,plain,
( spl86_254
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_254])]) ).
fof(f2363,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1))) ),
inference(cnf_transformation,[],[f1789]) ).
fof(f1789,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1))) ) ),
inference(nnf_transformation,[],[f913]) ).
fof(f913,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(rectify,[],[f446]) ).
fof(f446,axiom,
! [X27,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X27),hAPP(nat,nat,suc,X19)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_less__Suc__eq__le) ).
fof(f6024,plain,
spl86_253,
inference(avatar_split_clause,[],[f2342,f6022]) ).
fof(f6022,plain,
( spl86_253
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_253])]) ).
fof(f2342,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0))) ),
inference(cnf_transformation,[],[f1765]) ).
fof(f1765,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0))) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
inference(nnf_transformation,[],[f903]) ).
fof(f903,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0))) ),
inference(rectify,[],[f375]) ).
fof(f375,axiom,
! [X27,X19] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X27),X19))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X19),hAPP(nat,nat,suc,X27))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_not__less__eq) ).
fof(f6020,plain,
spl86_252,
inference(avatar_split_clause,[],[f2341,f6018]) ).
fof(f6018,plain,
( spl86_252
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_252])]) ).
fof(f2341,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X0)))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1765]) ).
fof(f6016,plain,
spl86_251,
inference(avatar_split_clause,[],[f2293,f6014]) ).
fof(f6014,plain,
( spl86_251
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_251])]) ).
fof(f2293,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(cnf_transformation,[],[f1377]) ).
fof(f1377,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(ennf_transformation,[],[f876]) ).
fof(f876,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X17)),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_Suc__lessD) ).
fof(f6012,plain,
spl86_250,
inference(avatar_split_clause,[],[f2281,f6010]) ).
fof(f6010,plain,
( spl86_250
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_250])]) ).
fof(f2281,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1361]) ).
fof(f1361,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f865]) ).
fof(f865,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X1))) ),
inference(rectify,[],[f85]) ).
fof(f85,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),hAPP(nat,nat,suc,X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_le__SucI) ).
fof(f6008,plain,
spl86_249,
inference(avatar_split_clause,[],[f2280,f6006]) ).
fof(f6006,plain,
( spl86_249
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_249])]) ).
fof(f2280,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1360]) ).
fof(f1360,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f864]) ).
fof(f864,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1))) ),
inference(rectify,[],[f448]) ).
fof(f448,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),hAPP(nat,nat,suc,X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_le__imp__less__Suc) ).
fof(f6004,plain,
spl86_248,
inference(avatar_split_clause,[],[f2272,f6002]) ).
fof(f6002,plain,
( spl86_248
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_248])]) ).
fof(f2272,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1351]) ).
fof(f1351,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(ennf_transformation,[],[f857]) ).
fof(f857,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X1))) ),
inference(rectify,[],[f370]) ).
fof(f370,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),hAPP(nat,nat,suc,X16))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_less__SucI) ).
fof(f5819,plain,
spl86_247,
inference(avatar_split_clause,[],[f2355,f5817]) ).
fof(f2355,plain,
! [X0,X1] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK49(X0,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1779]) ).
fof(f1779,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ! [X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2) != X1 )
& ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK49(X0,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f1777,f1778]) ).
fof(f1778,plain,
! [X0,X1] :
( ? [X3] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3) = X1
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),sK49(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f1777,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ! [X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2) != X1 )
& ( ? [X3] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X3) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
inference(rectify,[],[f1776]) ).
fof(f1776,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ! [X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2) != X1 )
& ( ? [X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
inference(nnf_transformation,[],[f909]) ).
fof(f909,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
<=> ? [X2] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2) = X1 ),
inference(rectify,[],[f310]) ).
fof(f310,axiom,
! [X27,X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X19))
<=> ? [X62] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X62) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_le__iff__add) ).
fof(f5815,plain,
spl86_246,
inference(avatar_split_clause,[],[f2287,f5813]) ).
fof(f5813,plain,
( spl86_246
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_246])]) ).
fof(f2287,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1369]) ).
fof(f1369,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(flattening,[],[f1368]) ).
fof(f1368,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f871]) ).
fof(f871,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
=> X0 = X1 ) ),
inference(rectify,[],[f73]) ).
fof(f73,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17))
=> X16 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_le__antisym) ).
fof(f5811,plain,
spl86_245,
inference(avatar_split_clause,[],[f2286,f5809]) ).
fof(f2286,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(flattening,[],[f1366]) ).
fof(f1366,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f870]) ).
fof(f870,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> ( X0 != X1
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
inference(rectify,[],[f377]) ).
fof(f377,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
=> ( X16 != X17
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_le__neq__implies__less) ).
fof(f5807,plain,
spl86_244,
inference(avatar_split_clause,[],[f2277,f5805]) ).
fof(f5805,plain,
( spl86_244
<=> ! [X0,X1] :
( hAPP(nat,nat,suc,sK19(X0,X1)) = X1
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_244])]) ).
fof(f2277,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,sK19(X0,X1)) = X1
| hAPP(nat,nat,suc,X0) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1719]) ).
fof(f5803,plain,
spl86_243,
inference(avatar_split_clause,[],[f2257,f5801]) ).
fof(f5801,plain,
( spl86_243
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_243])]) ).
fof(f2257,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f1336]) ).
fof(f1336,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1 ),
inference(flattening,[],[f1335]) ).
fof(f1335,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| X0 = X1 ),
inference(ennf_transformation,[],[f844]) ).
fof(f844,plain,
! [X0,X1] :
( X0 != X1
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0)) ) ),
inference(rectify,[],[f408]) ).
fof(f408,axiom,
! [X20,X21] :
( X20 != X21
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X20),X21))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X21),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_linorder__neqE__nat) ).
fof(f5799,plain,
spl86_242,
inference(avatar_split_clause,[],[f2215,f5797]) ).
fof(f5797,plain,
( spl86_242
<=> ! [X0,X1] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_242])]) ).
fof(f2215,plain,
! [X0,X1] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1),
inference(cnf_transformation,[],[f805]) ).
fof(f805,plain,
! [X0,X1] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X1),X1),
inference(rectify,[],[f218]) ).
fof(f218,axiom,
! [X0,X7] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,bool),fun(fun(X0,bool),fun(X0,bool)),minus_minus(fun(X0,bool)),X7),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_Diff__cancel) ).
fof(f5795,plain,
( ~ spl86_241
| ~ spl86_13
| ~ spl86_103
| ~ spl86_118 ),
inference(avatar_split_clause,[],[f3875,f3853,f3678,f3241,f5792]) ).
fof(f5792,plain,
( spl86_241
<=> sP3(one_one(nat),zero_zero(nat),ord_less(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_241])]) ).
fof(f3875,plain,
( ~ linordered_semidom(nat)
| ~ sP3(one_one(nat),zero_zero(nat),ord_less(nat))
| ~ spl86_103
| ~ spl86_118 ),
inference(resolution,[],[f3854,f3679]) ).
fof(f5408,plain,
( spl86_240
| ~ spl86_103
| ~ spl86_115 ),
inference(avatar_split_clause,[],[f3869,f3841,f3678,f5406]) ).
fof(f5406,plain,
( spl86_240
<=> ! [X0] : ~ sP3(hAPP(nat,nat,suc,X0),X0,ord_less(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_240])]) ).
fof(f3869,plain,
( ! [X0] : ~ sP3(hAPP(nat,nat,suc,X0),X0,ord_less(nat))
| ~ spl86_103
| ~ spl86_115 ),
inference(resolution,[],[f3842,f3679]) ).
fof(f5033,plain,
spl86_239,
inference(avatar_split_clause,[],[f2841,f5031]) ).
fof(f2841,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ order(X0) ),
inference(definition_unfolding,[],[f2160,f2190,f2190]) ).
fof(f2160,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ti(X0,X1) != ti(X0,X2)
| ~ order(X0) ),
inference(cnf_transformation,[],[f1684]) ).
fof(f1684,plain,
! [X0] :
( ! [X1,X2] :
( ( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
& ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ti(X0,X1) != ti(X0,X2) ) )
| ~ order(X0) ),
inference(flattening,[],[f1683]) ).
fof(f1683,plain,
! [X0] :
( ! [X1,X2] :
( ( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
& ( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ti(X0,X1) != ti(X0,X2) ) )
| ~ order(X0) ),
inference(nnf_transformation,[],[f1294]) ).
fof(f1294,plain,
! [X0] :
( ! [X1,X2] :
( ti(X0,X1) = ti(X0,X2)
<=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f765]) ).
fof(f765,plain,
! [X0] :
( order(X0)
=> ! [X1,X2] :
( ti(X0,X1) = ti(X0,X2)
<=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) ) ),
inference(rectify,[],[f199]) ).
fof(f199,axiom,
! [X0] :
( order(X0)
=> ! [X13,X38] :
( ti(X0,X38) = ti(X0,X13)
<=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X38),X13))
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X13),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_order__eq__iff) ).
fof(f5029,plain,
spl86_238,
inference(avatar_split_clause,[],[f2830,f5027]) ).
fof(f2830,plain,
! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ order(X0) ),
inference(definition_unfolding,[],[f2148,f2190,f2190]) ).
fof(f2148,plain,
! [X2,X0,X1] :
( ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1279]) ).
fof(f1279,plain,
! [X0] :
( ! [X1,X2] :
( ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f755]) ).
fof(f755,plain,
! [X0] :
( order(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> ti(X0,X1) != ti(X0,X2) ) ),
inference(rectify,[],[f389]) ).
fof(f389,axiom,
! [X2] :
( order(X2)
=> ! [X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X21))
=> ti(X2,X20) != ti(X2,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_less__imp__neq) ).
fof(f5025,plain,
spl86_237,
inference(avatar_split_clause,[],[f2814,f5023]) ).
fof(f2814,plain,
! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ linorder(X0) ),
inference(definition_unfolding,[],[f2105,f2190,f2190]) ).
fof(f2105,plain,
! [X2,X0,X1] :
( ti(X0,X1) != ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f1673]) ).
fof(f1673,plain,
! [X0] :
( ! [X1,X2] :
( ( ti(X0,X1) != ti(X0,X2)
| ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
& ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
& ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ti(X0,X1) = ti(X0,X2) ) )
| ~ linorder(X0) ),
inference(flattening,[],[f1672]) ).
fof(f1672,plain,
! [X0] :
( ! [X1,X2] :
( ( ti(X0,X1) != ti(X0,X2)
| ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
& ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
& ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ti(X0,X1) = ti(X0,X2) ) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f1233]) ).
fof(f1233,plain,
! [X0] :
( ! [X1,X2] :
( ti(X0,X1) != ti(X0,X2)
<=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f720]) ).
fof(f720,plain,
! [X0] :
( linorder(X0)
=> ! [X1,X2] :
( ti(X0,X1) != ti(X0,X2)
<=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) ) ),
inference(rectify,[],[f384]) ).
fof(f384,axiom,
! [X0] :
( linorder(X0)
=> ! [X13,X38] :
( ti(X0,X38) != ti(X0,X13)
<=> ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X38),X13))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X13),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_linorder__neq__iff) ).
fof(f5021,plain,
spl86_236,
inference(avatar_split_clause,[],[f2776,f5019]) ).
fof(f5019,plain,
( spl86_236
<=> ! [X0] : member(X0) = hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(X0,fun(fun(X0,bool),bool)),combi(fun(X0,fun(fun(X0,bool),bool))),member(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_236])]) ).
fof(f2776,plain,
! [X0] : member(X0) = hAPP(fun(X0,fun(fun(X0,bool),bool)),fun(X0,fun(fun(X0,bool),bool)),combi(fun(X0,fun(fun(X0,bool),bool))),member(X0)),
inference(definition_unfolding,[],[f2002,f2190]) ).
fof(f2002,plain,
! [X0] : member(X0) = ti(fun(X0,fun(fun(X0,bool),bool)),member(X0)),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] : member(X0) = ti(fun(X0,fun(fun(X0,bool),bool)),member(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
fof(f5017,plain,
spl86_235,
inference(avatar_split_clause,[],[f2775,f5015]) ).
fof(f5015,plain,
( spl86_235
<=> ! [X0] : collect(X0) = hAPP(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),combi(fun(fun(X0,bool),fun(X0,bool))),collect(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_235])]) ).
fof(f2775,plain,
! [X0] : collect(X0) = hAPP(fun(fun(X0,bool),fun(X0,bool)),fun(fun(X0,bool),fun(X0,bool)),combi(fun(fun(X0,bool),fun(X0,bool))),collect(X0)),
inference(definition_unfolding,[],[f2001,f2190]) ).
fof(f2001,plain,
! [X0] : collect(X0) = ti(fun(fun(X0,bool),fun(X0,bool)),collect(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] : collect(X0) = ti(fun(fun(X0,bool),fun(X0,bool)),collect(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
fof(f5013,plain,
spl86_234,
inference(avatar_split_clause,[],[f2774,f5011]) ).
fof(f5011,plain,
( spl86_234
<=> ! [X0] : partial_flat_lub(X0) = hAPP(fun(X0,fun(fun(X0,bool),X0)),fun(X0,fun(fun(X0,bool),X0)),combi(fun(X0,fun(fun(X0,bool),X0))),partial_flat_lub(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_234])]) ).
fof(f2774,plain,
! [X0] : partial_flat_lub(X0) = hAPP(fun(X0,fun(fun(X0,bool),X0)),fun(X0,fun(fun(X0,bool),X0)),combi(fun(X0,fun(fun(X0,bool),X0))),partial_flat_lub(X0)),
inference(definition_unfolding,[],[f2000,f2190]) ).
fof(f2000,plain,
! [X0] : partial_flat_lub(X0) = ti(fun(X0,fun(fun(X0,bool),X0)),partial_flat_lub(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] : partial_flat_lub(X0) = ti(fun(X0,fun(fun(X0,bool),X0)),partial_flat_lub(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Partial__Function_Oflat__lub_res) ).
fof(f5009,plain,
spl86_233,
inference(avatar_split_clause,[],[f2570,f5007]) ).
fof(f5007,plain,
( spl86_233
<=> ! [X2,X0,X1] :
( X0 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_233])]) ).
fof(f2570,plain,
! [X2,X0,X1] :
( X0 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) ),
inference(cnf_transformation,[],[f1861]) ).
fof(f1861,plain,
! [X0,X1,X2] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)
| X0 != X2 )
& ( X0 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) ) ),
inference(nnf_transformation,[],[f1044]) ).
fof(f1044,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)
<=> X0 = X2 ),
inference(rectify,[],[f292]) ).
fof(f292,axiom,
! [X27,X18,X19] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X18) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X19),X18)
<=> X19 = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_nat__add__right__cancel) ).
fof(f5005,plain,
spl86_232,
inference(avatar_split_clause,[],[f2568,f5003]) ).
fof(f5003,plain,
( spl86_232
<=> ! [X2,X0,X1] :
( X1 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_232])]) ).
fof(f2568,plain,
! [X2,X0,X1] :
( X1 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2) ),
inference(cnf_transformation,[],[f1860]) ).
fof(f1860,plain,
! [X0,X1,X2] :
( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)
| X1 != X2 )
& ( X1 = X2
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2) ) ),
inference(nnf_transformation,[],[f1043]) ).
fof(f1043,plain,
! [X0,X1,X2] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X2)
<=> X1 = X2 ),
inference(rectify,[],[f293]) ).
fof(f293,axiom,
! [X18,X27,X19] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X27) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X18),X19)
<=> X19 = X27 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_nat__add__left__cancel) ).
fof(f5001,plain,
spl86_231,
inference(avatar_split_clause,[],[f2437,f4999]) ).
fof(f4999,plain,
( spl86_231
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| hBOOL(hAPP(X0,bool,X1,sK56(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_231])]) ).
fof(f2437,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| hBOOL(hAPP(X0,bool,X1,sK56(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1820]) ).
fof(f4997,plain,
spl86_230,
inference(avatar_split_clause,[],[f2357,f4995]) ).
fof(f2357,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) ),
inference(cnf_transformation,[],[f1780]) ).
fof(f1780,plain,
! [X0,X1] :
( ( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) ) ),
inference(nnf_transformation,[],[f910]) ).
fof(f910,plain,
! [X0,X1] :
( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(rectify,[],[f524]) ).
fof(f524,axiom,
! [X27,X19] :
( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X27),X19)
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_diff__is__0__eq) ).
fof(f4993,plain,
spl86_229,
inference(avatar_split_clause,[],[f2325,f4991]) ).
fof(f4991,plain,
( spl86_229
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| hBOOL(hAPP(X0,bool,X1,sK41(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_229])]) ).
fof(f2325,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X1,hAPP(fun(X0,bool),X0,the(X0),X1)))
| hBOOL(hAPP(X0,bool,X1,sK41(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f1748]) ).
fof(f4989,plain,
spl86_228,
inference(avatar_split_clause,[],[f2323,f4987]) ).
fof(f2323,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK40(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1746]) ).
fof(f1746,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK40(X0,X1)),X0))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK40(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1407,f1745]) ).
fof(f1745,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X1)) )
=> ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK40(X0,X1)),X0))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK40(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1407,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ? [X2] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X1)) ) ),
inference(ennf_transformation,[],[f896]) ).
fof(f896,plain,
! [X0,X1] :
( ! [X2] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X2),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X0)) )
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1)) ),
inference(rectify,[],[f478]) ).
fof(f478,axiom,
! [X19,X47] :
( ! [X32] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X32),X47))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X32),X19)) )
=> hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_bounded__nat__set__is__finite) ).
fof(f4985,plain,
spl86_227,
inference(avatar_split_clause,[],[f2279,f4983]) ).
fof(f4983,plain,
( spl86_227
<=> ! [X0,X1] :
( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_227])]) ).
fof(f2279,plain,
! [X0,X1] :
( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1359]) ).
fof(f1359,plain,
! [X0,X1] :
( zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(ennf_transformation,[],[f863]) ).
fof(f863,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
=> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1) ),
inference(rectify,[],[f523]) ).
fof(f523,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16))
=> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16) = zero_zero(nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_diff__is__0__eq_H) ).
fof(f4981,plain,
( ~ spl86_226
| spl86_171
| ~ spl86_208 ),
inference(avatar_split_clause,[],[f4931,f4881,f4256,f4978]) ).
fof(f4931,plain,
( ~ hBOOL(fTrue)
| spl86_171
| ~ spl86_208 ),
inference(superposition,[],[f4258,f4883]) ).
fof(f4976,plain,
spl86_225,
inference(avatar_split_clause,[],[f2214,f4974]) ).
fof(f2214,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),hAPP(nat,nat,suc,X0))),
inference(cnf_transformation,[],[f804]) ).
fof(f804,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),hAPP(nat,nat,suc,X0))),
inference(rectify,[],[f452]) ).
fof(f452,axiom,
! [X17,X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16)),hAPP(nat,nat,suc,X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_diff__less__Suc) ).
fof(f4972,plain,
spl86_224,
inference(avatar_split_clause,[],[f2213,f4970]) ).
fof(f2213,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)))),
inference(cnf_transformation,[],[f803]) ).
fof(f803,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0)))),
inference(rectify,[],[f443]) ).
fof(f443,axiom,
! [X25,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X25)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_less__add__Suc2) ).
fof(f4968,plain,
spl86_223,
inference(avatar_split_clause,[],[f2212,f4966]) ).
fof(f2212,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)))),
inference(cnf_transformation,[],[f802]) ).
fof(f802,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)))),
inference(rectify,[],[f442]) ).
fof(f442,axiom,
! [X25,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X25),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X17)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_less__add__Suc1) ).
fof(f4964,plain,
spl86_222,
inference(avatar_split_clause,[],[f2185,f4962]) ).
fof(f2185,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK14(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1705]) ).
fof(f4960,plain,
spl86_221,
inference(avatar_split_clause,[],[f2182,f4958]) ).
fof(f2182,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK12(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1700]) ).
fof(f4956,plain,
spl86_220,
inference(avatar_split_clause,[],[f2162,f4954]) ).
fof(f4954,plain,
( spl86_220
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_220])]) ).
fof(f2162,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1686]) ).
fof(f1686,plain,
! [X0] :
( ! [X1,X2] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
& ( ( ti(X0,X1) != ti(X0,X2)
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
| ~ order(X0) ),
inference(flattening,[],[f1685]) ).
fof(f1685,plain,
! [X0] :
( ! [X1,X2] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
& ( ( ti(X0,X1) != ti(X0,X2)
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
| ~ order(X0) ),
inference(nnf_transformation,[],[f1295]) ).
fof(f1295,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
<=> ( ti(X0,X1) != ti(X0,X2)
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f766]) ).
fof(f766,plain,
! [X0] :
( order(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
<=> ( ti(X0,X1) != ti(X0,X2)
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) ) ),
inference(rectify,[],[f418]) ).
fof(f418,axiom,
! [X0] :
( order(X0)
=> ! [X13,X38] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X13),X38))
<=> ( ti(X0,X38) != ti(X0,X13)
& hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X13),X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_order__less__le) ).
fof(f4952,plain,
spl86_219,
inference(avatar_split_clause,[],[f2151,f4950]) ).
fof(f4950,plain,
( spl86_219
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_219])]) ).
fof(f2151,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ order(X0) ),
inference(cnf_transformation,[],[f1282]) ).
fof(f1282,plain,
! [X0] :
( ! [X1,X2] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f758]) ).
fof(f758,plain,
! [X0] :
( order(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ),
inference(rectify,[],[f396]) ).
fof(f396,axiom,
! [X2] :
( order(X2)
=> ! [X52,X48] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X52),X48))
=> ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_xt1_I9_J) ).
fof(f4948,plain,
spl86_218,
inference(avatar_split_clause,[],[f2139,f4946]) ).
fof(f4946,plain,
( spl86_218
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_218])]) ).
fof(f2139,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1681]) ).
fof(f4944,plain,
spl86_217,
inference(avatar_split_clause,[],[f2137,f4942]) ).
fof(f4942,plain,
( spl86_217
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_217])]) ).
fof(f2137,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1263]) ).
fof(f1263,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f746]) ).
fof(f746,plain,
! [X0] :
( preorder(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) ),
inference(rectify,[],[f427]) ).
fof(f427,axiom,
! [X2] :
( preorder(X2)
=> ! [X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X21))
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_order__less__imp__le) ).
fof(f4940,plain,
spl86_216,
inference(avatar_split_clause,[],[f2133,f4938]) ).
fof(f4938,plain,
( spl86_216
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_216])]) ).
fof(f2133,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1259]) ).
fof(f1259,plain,
! [X0] :
( ! [X1,X2] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f742]) ).
fof(f742,plain,
! [X0] :
( preorder(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ),
inference(rectify,[],[f403]) ).
fof(f403,axiom,
! [X2] :
( preorder(X2)
=> ! [X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X21))
=> ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X21),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_order__less__asym) ).
fof(f4930,plain,
spl86_215,
inference(avatar_split_clause,[],[f2109,f4928]) ).
fof(f4928,plain,
( spl86_215
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_215])]) ).
fof(f2109,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f1676]) ).
fof(f1676,plain,
! [X0] :
( ! [X1,X2] :
( ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ( ti(X0,X1) != ti(X0,X2)
& ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) )
& ( ti(X0,X1) = ti(X0,X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
| ~ linorder(X0) ),
inference(flattening,[],[f1675]) ).
fof(f1675,plain,
! [X0] :
( ! [X1,X2] :
( ( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ( ti(X0,X1) != ti(X0,X2)
& ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) )
& ( ti(X0,X1) = ti(X0,X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2)) ) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f1235]) ).
fof(f1235,plain,
! [X0] :
( ! [X1,X2] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
<=> ( ti(X0,X1) = ti(X0,X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f722]) ).
fof(f722,plain,
! [X0] :
( linorder(X0)
=> ! [X1,X2] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
<=> ( ti(X0,X1) = ti(X0,X2)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ) ),
inference(rectify,[],[f385]) ).
fof(f385,axiom,
! [X0] :
( linorder(X0)
=> ! [X13,X38] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X13),X38))
<=> ( ti(X0,X38) = ti(X0,X13)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X38),X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_not__less__iff__gr__or__eq) ).
fof(f4926,plain,
spl86_214,
inference(avatar_split_clause,[],[f2100,f4924]) ).
fof(f4924,plain,
( spl86_214
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_214])]) ).
fof(f2100,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f1231]) ).
fof(f1231,plain,
! [X0] :
( ! [X1,X2] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f718]) ).
fof(f718,plain,
! [X0] :
( linorder(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1)) ) ),
inference(rectify,[],[f426]) ).
fof(f426,axiom,
! [X2] :
( linorder(X2)
=> ! [X21,X20] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X21),X20))
=> ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_leD) ).
fof(f4922,plain,
spl86_213,
inference(avatar_split_clause,[],[f2090,f4920]) ).
fof(f2090,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f1221]) ).
fof(f1221,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f710]) ).
fof(f710,plain,
! [X0] :
( linorder(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) ),
inference(rectify,[],[f200]) ).
fof(f200,axiom,
! [X2] :
( linorder(X2)
=> ! [X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X21),X20))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_linorder__linear) ).
fof(f4918,plain,
spl86_212,
inference(avatar_split_clause,[],[f2089,f4916]) ).
fof(f2089,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2))
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f1220]) ).
fof(f1220,plain,
! [X0] :
( ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f709]) ).
fof(f709,plain,
! [X0] :
( linorder(X0)
=> ! [X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X2)) ) ),
inference(rectify,[],[f417]) ).
fof(f417,axiom,
! [X2] :
( linorder(X2)
=> ! [X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X21),X20))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_linorder__le__less__linear) ).
fof(f4896,plain,
spl86_211,
inference(avatar_split_clause,[],[f2674,f4894]) ).
fof(f4894,plain,
( spl86_211
<=> ! [X0,X3,X2,X1] :
( sP6(X0,X1,X2,X3)
| ~ sP5(X3,X2,X1,X0)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_211])]) ).
fof(f2674,plain,
! [X2,X3,X0,X1] :
( sP6(X0,X1,X2,X3)
| ~ sP5(X3,X2,X1,X0)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3)) ),
inference(cnf_transformation,[],[f1894]) ).
fof(f4892,plain,
spl86_210,
inference(avatar_split_clause,[],[f2671,f4890]) ).
fof(f4890,plain,
( spl86_210
<=> ! [X0,X3,X2,X1] :
( sP5(X3,X2,X1,X0)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3))
| ~ sP6(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_210])]) ).
fof(f2671,plain,
! [X2,X3,X0,X1] :
( sP5(X3,X2,X1,X0)
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X0),X3))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1894]) ).
fof(f4888,plain,
( spl86_208
| spl86_209
| ~ spl86_82
| ~ spl86_107 ),
inference(avatar_split_clause,[],[f3722,f3694,f3585,f4885,f4881]) ).
fof(f3585,plain,
( spl86_82
<=> bot_bot(bool) = hAPP(bool,bool,combi(bool),bot_bot(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_82])]) ).
fof(f3722,plain,
( fFalse = bot_bot(bool)
| fTrue = bot_bot(bool)
| ~ spl86_82
| ~ spl86_107 ),
inference(superposition,[],[f3695,f3587]) ).
fof(f3587,plain,
( bot_bot(bool) = hAPP(bool,bool,combi(bool),bot_bot(bool))
| ~ spl86_82 ),
inference(avatar_component_clause,[],[f3585]) ).
fof(f4879,plain,
spl86_207,
inference(avatar_split_clause,[],[f2610,f4877]) ).
fof(f2610,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f1873]) ).
fof(f4875,plain,
spl86_206,
inference(avatar_split_clause,[],[f2074,f4873]) ).
fof(f4873,plain,
( spl86_206
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_206])]) ).
fof(f2074,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f1208]) ).
fof(f1208,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0))))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f698]) ).
fof(f698,plain,
! [X0] :
( linordered_semidom(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),one_one(X0)))) ),
inference(rectify,[],[f476]) ).
fof(f476,axiom,
! [X2] :
( linordered_semidom(X2)
=> ! [X48] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),one_one(X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_less__add__one) ).
fof(f4682,plain,
spl86_205,
inference(avatar_split_clause,[],[f3031,f4680]) ).
fof(f3031,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(forward_demodulation,[],[f2343,f2022]) ).
fof(f2343,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1766]) ).
fof(f1766,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X0)) )
& ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
inference(nnf_transformation,[],[f904]) ).
fof(f904,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X0)) ),
inference(rectify,[],[f88]) ).
fof(f88,axiom,
! [X27,X19] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X27),X19))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X19)),X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_not__less__eq__eq) ).
fof(f4678,plain,
spl86_204,
inference(avatar_split_clause,[],[f3030,f4676]) ).
fof(f4676,plain,
( spl86_204
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_204])]) ).
fof(f3030,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(forward_demodulation,[],[f2344,f2022]) ).
fof(f2344,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X0)) ),
inference(cnf_transformation,[],[f1766]) ).
fof(f4674,plain,
spl86_203,
inference(avatar_split_clause,[],[f2885,f4672]) ).
fof(f4672,plain,
( spl86_203
<=> ! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_203])]) ).
fof(f2885,plain,
! [X2,X0,X1] :
( hAPP(X0,X0,combi(X0),X1) = hAPP(X0,X0,combi(X0),X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2)) ),
inference(definition_unfolding,[],[f2432,f2190,f2190]) ).
fof(f2432,plain,
! [X2,X0,X1] :
( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2)) ),
inference(cnf_transformation,[],[f952]) ).
fof(f952,plain,
! [X0,X1,X2] :
( ti(X0,X1) = ti(X0,X2)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2)) ),
inference(rectify,[],[f598]) ).
fof(f598,axiom,
! [X2,X20,X21] :
( ti(X2,X20) = ti(X2,X21)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),fequal(X2),X20),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
fof(f4670,plain,
spl86_202,
inference(avatar_split_clause,[],[f2884,f4668]) ).
fof(f2884,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2))
| hAPP(X0,X0,combi(X0),X1) != hAPP(X0,X0,combi(X0),X2) ),
inference(definition_unfolding,[],[f2431,f2190,f2190]) ).
fof(f2431,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2))
| ti(X0,X1) != ti(X0,X2) ),
inference(cnf_transformation,[],[f951]) ).
fof(f951,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X2))
| ti(X0,X1) != ti(X0,X2) ),
inference(rectify,[],[f599]) ).
fof(f599,axiom,
! [X2,X20,X21] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),fequal(X2),X20),X21))
| ti(X2,X20) != ti(X2,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
fof(f4666,plain,
spl86_201,
inference(avatar_split_clause,[],[f2295,f4664]) ).
fof(f4664,plain,
( spl86_201
<=> ! [X0,X1] :
( hAPP(nat,nat,suc,sK21(X0,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_201])]) ).
fof(f2295,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,sK21(X0,X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(cnf_transformation,[],[f1724]) ).
fof(f4662,plain,
spl86_200,
inference(avatar_split_clause,[],[f2270,f4660]) ).
fof(f4660,plain,
( spl86_200
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_200])]) ).
fof(f2270,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(cnf_transformation,[],[f1349]) ).
fof(f1349,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) ),
inference(ennf_transformation,[],[f855]) ).
fof(f855,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(rectify,[],[f378]) ).
fof(f378,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X17),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_less__imp__le__nat) ).
fof(f4658,plain,
spl86_199,
inference(avatar_split_clause,[],[f2239,f4656]) ).
fof(f2239,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f829]) ).
fof(f829,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X0))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X17))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nat__le__linear) ).
fof(f4654,plain,
spl86_198,
inference(avatar_split_clause,[],[f2210,f4652]) ).
fof(f2210,plain,
! [X0,X1] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),
inference(cnf_transformation,[],[f801]) ).
fof(f801,plain,
! [X0,X1] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),
inference(rectify,[],[f522]) ).
fof(f522,axiom,
! [X16,X17] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X16),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_diff__add__0) ).
fof(f4442,plain,
spl86_197,
inference(avatar_split_clause,[],[f2824,f4440]) ).
fof(f4440,plain,
( spl86_197
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| bot_bot(X0) != hAPP(X0,X0,combi(X0),X1)
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_197])]) ).
fof(f2824,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| bot_bot(X0) != hAPP(X0,X0,combi(X0),X1)
| ~ bot(X0) ),
inference(definition_unfolding,[],[f2123,f2190]) ).
fof(f2123,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| bot_bot(X0) != ti(X0,X1)
| ~ bot(X0) ),
inference(cnf_transformation,[],[f1679]) ).
fof(f1679,plain,
! [X0] :
( ! [X1] :
( ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| bot_bot(X0) != ti(X0,X1) )
& ( bot_bot(X0) = ti(X0,X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0))) ) )
| ~ bot(X0) ),
inference(nnf_transformation,[],[f1245]) ).
fof(f1245,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
<=> bot_bot(X0) = ti(X0,X1) )
| ~ bot(X0) ),
inference(ennf_transformation,[],[f732]) ).
fof(f732,plain,
! [X0] :
( bot(X0)
=> ! [X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
<=> bot_bot(X0) = ti(X0,X1) ) ),
inference(rectify,[],[f169]) ).
fof(f169,axiom,
! [X0] :
( bot(X0)
=> ! [X10] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X10),bot_bot(X0)))
<=> ti(X0,X10) = bot_bot(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_bot__unique) ).
fof(f4438,plain,
spl86_196,
inference(avatar_split_clause,[],[f2823,f4436]) ).
fof(f2823,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| bot_bot(X0) = hAPP(X0,X0,combi(X0),X1)
| ~ bot(X0) ),
inference(definition_unfolding,[],[f2120,f2190]) ).
fof(f2120,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| bot_bot(X0) = ti(X0,X1)
| ~ bot(X0) ),
inference(cnf_transformation,[],[f1678]) ).
fof(f1678,plain,
! [X0] :
( ! [X1] :
( ( bot_bot(X0) != ti(X0,X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1)) )
& ( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| bot_bot(X0) = ti(X0,X1) ) )
| ~ bot(X0) ),
inference(nnf_transformation,[],[f1244]) ).
fof(f1244,plain,
! [X0] :
( ! [X1] :
( bot_bot(X0) != ti(X0,X1)
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1)) )
| ~ bot(X0) ),
inference(ennf_transformation,[],[f731]) ).
fof(f731,plain,
! [X0] :
( bot(X0)
=> ! [X1] :
( bot_bot(X0) != ti(X0,X1)
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1)) ) ),
inference(rectify,[],[f414]) ).
fof(f414,axiom,
! [X0] :
( bot(X0)
=> ! [X10] :
( ti(X0,X10) != bot_bot(X0)
<=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_bot__less) ).
fof(f4434,plain,
spl86_195,
inference(avatar_split_clause,[],[f2822,f4432]) ).
fof(f2822,plain,
! [X0,X1] :
( bot_bot(X0) != hAPP(X0,X0,combi(X0),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| ~ bot(X0) ),
inference(definition_unfolding,[],[f2121,f2190]) ).
fof(f2121,plain,
! [X0,X1] :
( bot_bot(X0) != ti(X0,X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),bot_bot(X0)),X1))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f1678]) ).
fof(f4430,plain,
spl86_194,
inference(avatar_split_clause,[],[f2821,f4428]) ).
fof(f4428,plain,
( spl86_194
<=> ! [X0,X1] :
( bot_bot(X0) = hAPP(X0,X0,combi(X0),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_194])]) ).
fof(f2821,plain,
! [X0,X1] :
( bot_bot(X0) = hAPP(X0,X0,combi(X0),X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| ~ bot(X0) ),
inference(definition_unfolding,[],[f2119,f2190]) ).
fof(f2119,plain,
! [X0,X1] :
( bot_bot(X0) = ti(X0,X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f1243]) ).
fof(f1243,plain,
! [X0] :
( ! [X1] :
( bot_bot(X0) = ti(X0,X1)
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0))) )
| ~ bot(X0) ),
inference(ennf_transformation,[],[f730]) ).
fof(f730,plain,
! [X0] :
( bot(X0)
=> ! [X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),bot_bot(X0)))
=> bot_bot(X0) = ti(X0,X1) ) ),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X2] :
( bot(X2)
=> ! [X48] :
( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X48),bot_bot(X2)))
=> bot_bot(X2) = ti(X2,X48) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_le__bot) ).
fof(f4426,plain,
( spl86_193
| ~ spl86_134
| ~ spl86_179 ),
inference(avatar_split_clause,[],[f4386,f4289,f3966,f4424]) ).
fof(f4424,plain,
( spl86_193
<=> ! [X0,X1] : ~ sP4(X0,X1,bot_bot(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_193])]) ).
fof(f4386,plain,
( ! [X0,X1] : ~ sP4(X0,X1,bot_bot(fun(X0,bool)))
| ~ spl86_134
| ~ spl86_179 ),
inference(resolution,[],[f4290,f3967]) ).
fof(f4422,plain,
spl86_192,
inference(avatar_split_clause,[],[f2404,f4420]) ).
fof(f2404,plain,
! [X2,X0,X1] : bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),
inference(cnf_transformation,[],[f927]) ).
fof(f927,plain,
! [X0,X1,X2] : bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X1),X2),
inference(rectify,[],[f175]) ).
fof(f175,axiom,
! [X0,X10,X7] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X7) != bot_bot(fun(X0,bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_insert__not__empty) ).
fof(f4418,plain,
spl86_191,
inference(avatar_split_clause,[],[f2209,f4416]) ).
fof(f4416,plain,
( spl86_191
<=> ! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl86_191])]) ).
fof(f2209,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0,
inference(cnf_transformation,[],[f800]) ).
fof(f800,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0,
inference(rectify,[],[f303]) ).
fof(f303,axiom,
! [X17,X16] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X16)),X16) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_diff__add__inverse2) ).
fof(f4414,plain,
spl86_190,
inference(avatar_split_clause,[],[f2208,f4412]) ).
fof(f2208,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1,
inference(cnf_transformation,[],[f799]) ).
fof(f799,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1,
inference(rectify,[],[f304]) ).
fof(f304,axiom,
! [X16,X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X17)),X16) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_diff__add__inverse) ).
fof(f4410,plain,
spl86_189,
inference(avatar_split_clause,[],[f2207,f4408]) ).
fof(f2207,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0),
inference(cnf_transformation,[],[f798]) ).
fof(f798,plain,
! [X0,X1] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0),
inference(rectify,[],[f296]) ).
fof(f296,axiom,
! [X17,X16] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X16) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_nat__add__commute) ).
fof(f4346,plain,
( spl86_188
| ~ spl86_112
| ~ spl86_163 ),
inference(avatar_split_clause,[],[f4197,f4153,f3827,f4343]) ).
fof(f4197,plain,
( hBOOL(hAPP(pname,bool,u,pn))
| ~ spl86_112
| ~ spl86_163 ),
inference(resolution,[],[f4154,f3829]) ).
fof(f4323,plain,
spl86_187,
inference(avatar_split_clause,[],[f3018,f4321]) ).
fof(f3018,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(forward_demodulation,[],[f2865,f2854]) ).
fof(f2865,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),X1) ),
inference(definition_unfolding,[],[f2332,f2190]) ).
fof(f2332,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| bot_bot(fun(X0,bool)) != ti(fun(X0,bool),X1) ),
inference(cnf_transformation,[],[f1755]) ).
fof(f4319,plain,
spl86_186,
inference(avatar_split_clause,[],[f2852,f4317]) ).
fof(f4317,plain,
( spl86_186
<=> ! [X0,X1] : combk(X0,X1) = hAPP(fun(X0,fun(X1,X0)),fun(X0,fun(X1,X0)),combi(fun(X0,fun(X1,X0))),combk(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_186])]) ).
fof(f2852,plain,
! [X0,X1] : combk(X0,X1) = hAPP(fun(X0,fun(X1,X0)),fun(X0,fun(X1,X0)),combi(fun(X0,fun(X1,X0))),combk(X0,X1)),
inference(definition_unfolding,[],[f2191,f2190]) ).
fof(f2191,plain,
! [X0,X1] : combk(X0,X1) = ti(fun(X0,fun(X1,X0)),combk(X0,X1)),
inference(cnf_transformation,[],[f785]) ).
fof(f785,plain,
! [X0,X1] : combk(X0,X1) = ti(fun(X0,fun(X1,X0)),combk(X0,X1)),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0] : combk(X2,X0) = ti(fun(X2,fun(X0,X2)),combk(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBK_res) ).
fof(f4315,plain,
spl86_185,
inference(avatar_split_clause,[],[f2827,f4313]) ).
fof(f4313,plain,
( spl86_185
<=> ! [X0] :
( ord_less_eq(X0) = hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combi(fun(X0,fun(X0,bool))),ord_less_eq(X0))
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_185])]) ).
fof(f2827,plain,
! [X0] :
( ord_less_eq(X0) = hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combi(fun(X0,fun(X0,bool))),ord_less_eq(X0))
| ~ ord(X0) ),
inference(definition_unfolding,[],[f2125,f2190]) ).
fof(f2125,plain,
! [X0] :
( ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0))
| ~ ord(X0) ),
inference(cnf_transformation,[],[f1247]) ).
fof(f1247,plain,
! [X0] :
( ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0))
| ~ ord(X0) ),
inference(ennf_transformation,[],[f734]) ).
fof(f734,plain,
! [X0] :
( ord(X0)
=> ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0)) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1] :
( ord(X1)
=> ord_less_eq(X1) = ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(f4311,plain,
spl86_184,
inference(avatar_split_clause,[],[f2826,f4309]) ).
fof(f4309,plain,
( spl86_184
<=> ! [X0] :
( ord_less(X0) = hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combi(fun(X0,fun(X0,bool))),ord_less(X0))
| ~ ord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_184])]) ).
fof(f2826,plain,
! [X0] :
( ord_less(X0) = hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combi(fun(X0,fun(X0,bool))),ord_less(X0))
| ~ ord(X0) ),
inference(definition_unfolding,[],[f2124,f2190]) ).
fof(f2124,plain,
! [X0] :
( ord_less(X0) = ti(fun(X0,fun(X0,bool)),ord_less(X0))
| ~ ord(X0) ),
inference(cnf_transformation,[],[f1246]) ).
fof(f1246,plain,
! [X0] :
( ord_less(X0) = ti(fun(X0,fun(X0,bool)),ord_less(X0))
| ~ ord(X0) ),
inference(ennf_transformation,[],[f733]) ).
fof(f733,plain,
! [X0] :
( ord(X0)
=> ord_less(X0) = ti(fun(X0,fun(X0,bool)),ord_less(X0)) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X2] :
( ord(X2)
=> ord_less(X2) = ti(fun(X2,fun(X2,bool)),ord_less(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_res) ).
fof(f4307,plain,
spl86_183,
inference(avatar_split_clause,[],[f2819,f4305]) ).
fof(f4305,plain,
( spl86_183
<=> ! [X0] :
( minus_minus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),minus_minus(X0))
| ~ minus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_183])]) ).
fof(f2819,plain,
! [X0] :
( minus_minus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),minus_minus(X0))
| ~ minus(X0) ),
inference(definition_unfolding,[],[f2113,f2190]) ).
fof(f2113,plain,
! [X0] :
( minus_minus(X0) = ti(fun(X0,fun(X0,X0)),minus_minus(X0))
| ~ minus(X0) ),
inference(cnf_transformation,[],[f1237]) ).
fof(f1237,plain,
! [X0] :
( minus_minus(X0) = ti(fun(X0,fun(X0,X0)),minus_minus(X0))
| ~ minus(X0) ),
inference(ennf_transformation,[],[f724]) ).
fof(f724,plain,
! [X0] :
( minus(X0)
=> minus_minus(X0) = ti(fun(X0,fun(X0,X0)),minus_minus(X0)) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X1] :
( minus(X1)
=> minus_minus(X1) = ti(fun(X1,fun(X1,X1)),minus_minus(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).
fof(f4303,plain,
spl86_182,
inference(avatar_split_clause,[],[f2795,f4301]) ).
fof(f4301,plain,
( spl86_182
<=> ! [X0] :
( plus_plus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),plus_plus(X0))
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_182])]) ).
fof(f2795,plain,
! [X0] :
( plus_plus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),plus_plus(X0))
| ~ cancel_semigroup_add(X0) ),
inference(definition_unfolding,[],[f2051,f2190]) ).
fof(f2051,plain,
! [X0] :
( plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0))
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f1181]) ).
fof(f1181,plain,
! [X0] :
( plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0))
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f679]) ).
fof(f679,plain,
! [X0] :
( cancel_semigroup_add(X0)
=> plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0)) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X2] :
( cancel_semigroup_add(X2)
=> plus_plus(X2) = ti(fun(X2,fun(X2,X2)),plus_plus(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).
fof(f4299,plain,
spl86_181,
inference(avatar_split_clause,[],[f2792,f4297]) ).
fof(f4297,plain,
( spl86_181
<=> ! [X0] :
( plus_plus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),plus_plus(X0))
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_181])]) ).
fof(f2792,plain,
! [X0] :
( plus_plus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),plus_plus(X0))
| ~ monoid_add(X0) ),
inference(definition_unfolding,[],[f2045,f2190]) ).
fof(f2045,plain,
! [X0] :
( plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0))
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f1174]) ).
fof(f1174,plain,
! [X0] :
( plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0))
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f673]) ).
fof(f673,plain,
! [X0] :
( monoid_add(X0)
=> plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0)) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X2] :
( monoid_add(X2)
=> plus_plus(X2) = ti(fun(X2,fun(X2,X2)),plus_plus(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
fof(f4295,plain,
spl86_180,
inference(avatar_split_clause,[],[f2785,f4293]) ).
fof(f2785,plain,
! [X0] :
( plus_plus(X0) = hAPP(fun(X0,fun(X0,X0)),fun(X0,fun(X0,X0)),combi(fun(X0,fun(X0,X0))),plus_plus(X0))
| ~ ab_semigroup_add(X0) ),
inference(definition_unfolding,[],[f2037,f2190]) ).
fof(f2037,plain,
! [X0] :
( plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0))
| ~ ab_semigroup_add(X0) ),
inference(cnf_transformation,[],[f1168]) ).
fof(f1168,plain,
! [X0] :
( plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0))
| ~ ab_semigroup_add(X0) ),
inference(ennf_transformation,[],[f667]) ).
fof(f667,plain,
! [X0] :
( ab_semigroup_add(X0)
=> plus_plus(X0) = ti(fun(X0,fun(X0,X0)),plus_plus(X0)) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X2] :
( ab_semigroup_add(X2)
=> plus_plus(X2) = ti(fun(X2,fun(X2,X2)),plus_plus(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
fof(f4291,plain,
spl86_179,
inference(avatar_split_clause,[],[f2609,f4289]) ).
fof(f2609,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK73(X0,X1,X2)),X2))
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f1873]) ).
fof(f4287,plain,
spl86_178,
inference(avatar_split_clause,[],[f2456,f4285]) ).
fof(f2456,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK59(X0,X1)),sK60(X0,X1)))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1826]) ).
fof(f4283,plain,
spl86_177,
inference(avatar_split_clause,[],[f2324,f4281]) ).
fof(f4281,plain,
( spl86_177
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK40(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_177])]) ).
fof(f2324,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X1))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK40(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f1746]) ).
fof(f4279,plain,
spl86_176,
inference(avatar_split_clause,[],[f2206,f4277]) ).
fof(f2206,plain,
! [X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1)),
inference(cnf_transformation,[],[f797]) ).
fof(f797,plain,
! [X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X1)),
inference(rectify,[],[f158]) ).
fof(f158,axiom,
! [X0,X7] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),bot_bot(fun(X0,bool))),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_empty__subsetI) ).
fof(f4275,plain,
spl86_175,
inference(avatar_split_clause,[],[f2205,f4273]) ).
fof(f2205,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X0)),
inference(cnf_transformation,[],[f796]) ).
fof(f796,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X1)),X0)),
inference(rectify,[],[f98]) ).
fof(f98,axiom,
! [X17,X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X16)),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_diff__le__self) ).
fof(f4271,plain,
spl86_174,
inference(avatar_split_clause,[],[f2204,f4269]) ).
fof(f2204,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))),
inference(cnf_transformation,[],[f795]) ).
fof(f795,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1))),
inference(rectify,[],[f309]) ).
fof(f309,axiom,
! [X16,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),X17))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_le__add1) ).
fof(f4267,plain,
spl86_173,
inference(avatar_split_clause,[],[f2203,f4265]) ).
fof(f2203,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0))),
inference(cnf_transformation,[],[f794]) ).
fof(f794,plain,
! [X0,X1] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X0))),
inference(rectify,[],[f308]) ).
fof(f308,axiom,
! [X16,X17] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X17),X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_le__add2) ).
fof(f4263,plain,
spl86_172,
inference(avatar_split_clause,[],[f2202,f4261]) ).
fof(f4261,plain,
( spl86_172
<=> ! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_172])]) ).
fof(f2202,plain,
! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f793]) ).
fof(f793,plain,
! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X1),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f466]) ).
fof(f466,axiom,
! [X0,X7] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less(fun(X0,bool)),X7),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_not__psubset__empty) ).
fof(f4259,plain,
( ~ spl86_171
| ~ spl86_104
| ~ spl86_134
| ~ spl86_164 ),
inference(avatar_split_clause,[],[f4211,f4157,f3966,f3682,f4256]) ).
fof(f4211,plain,
( ~ hBOOL(bot_bot(bool))
| ~ spl86_104
| ~ spl86_134
| ~ spl86_164 ),
inference(forward_demodulation,[],[f4207,f3683]) ).
fof(f4207,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(X0,bool,bot_bot(fun(X0,bool)),X1))
| ~ spl86_134
| ~ spl86_164 ),
inference(resolution,[],[f4158,f3967]) ).
fof(f4254,plain,
spl86_170,
inference(avatar_split_clause,[],[f2201,f4252]) ).
fof(f4252,plain,
( spl86_170
<=> ! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_170])]) ).
fof(f2201,plain,
! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0)),
inference(cnf_transformation,[],[f792]) ).
fof(f792,plain,
! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X0)),
inference(rectify,[],[f356]) ).
fof(f356,axiom,
! [X25,X26] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X25),X26)),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_not__add__less1) ).
fof(f4250,plain,
spl86_169,
inference(avatar_split_clause,[],[f2200,f4248]) ).
fof(f2200,plain,
! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1)),
inference(cnf_transformation,[],[f791]) ).
fof(f791,plain,
! [X0,X1] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)),X1)),
inference(rectify,[],[f355]) ).
fof(f355,axiom,
! [X26,X25] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X26),X25)),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_not__add__less2) ).
fof(f4246,plain,
spl86_168,
inference(avatar_split_clause,[],[f2186,f4244]) ).
fof(f4244,plain,
( spl86_168
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK14(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_168])]) ).
fof(f2186,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sK14(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1705]) ).
fof(f4242,plain,
spl86_167,
inference(avatar_split_clause,[],[f2183,f4240]) ).
fof(f4240,plain,
( spl86_167
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK12(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_167])]) ).
fof(f2183,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sK12(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f1700]) ).
fof(f4167,plain,
( spl86_166
| ~ spl86_93
| ~ spl86_108 ),
inference(avatar_split_clause,[],[f3752,f3698,f3636,f4165]) ).
fof(f4163,plain,
spl86_165,
inference(avatar_split_clause,[],[f2854,f4161]) ).
fof(f4159,plain,
spl86_164,
inference(avatar_split_clause,[],[f2557,f4157]) ).
fof(f2557,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,X2,X1)) ),
inference(cnf_transformation,[],[f1853]) ).
fof(f1853,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,X2,X1)) )
& ( hBOOL(hAPP(X0,bool,X2,X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ) ),
inference(nnf_transformation,[],[f1038]) ).
fof(f1038,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2))
<=> hBOOL(hAPP(X0,bool,X2,X1)) ),
inference(rectify,[],[f128]) ).
fof(f128,axiom,
! [X0,X13,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X13),X7))
<=> hBOOL(hAPP(X0,bool,X7,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
fof(f4155,plain,
spl86_163,
inference(avatar_split_clause,[],[f2556,f4153]) ).
fof(f2556,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,bool,X2,X1))
| ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),X2)) ),
inference(cnf_transformation,[],[f1853]) ).
fof(f4151,plain,
spl86_162,
inference(avatar_split_clause,[],[f2362,f4149]) ).
fof(f2362,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK51(X0,X1))) ),
inference(cnf_transformation,[],[f1788]) ).
fof(f1788,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK51(X0,X1))) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f1786,f1787]) ).
fof(f1787,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X0,bool,X1,X2))
=> hBOOL(hAPP(X0,bool,X1,sK51(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f1786,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ? [X2] : hBOOL(hAPP(X0,bool,X1,X2)) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(rectify,[],[f1785]) ).
fof(f1785,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ? [X2] : hBOOL(hAPP(X0,bool,X1,X2)) )
& ( ! [X2] : ~ hBOOL(hAPP(X0,bool,X1,X2))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(nnf_transformation,[],[f912]) ).
fof(f912,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
<=> ! [X2] : ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(rectify,[],[f160]) ).
fof(f160,axiom,
! [X0,X15] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15) = bot_bot(fun(X0,bool))
<=> ! [X32] : ~ hBOOL(hAPP(X0,bool,X15,X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Collect__empty__eq) ).
fof(f4147,plain,
spl86_161,
inference(avatar_split_clause,[],[f2360,f4145]) ).
fof(f2360,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK50(X0,X1))) ),
inference(cnf_transformation,[],[f1784]) ).
fof(f1784,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| hBOOL(hAPP(X0,bool,X1,sK50(X0,X1))) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f1782,f1783]) ).
fof(f1783,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X0,bool,X1,X2))
=> hBOOL(hAPP(X0,bool,X1,sK50(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f1782,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ? [X2] : hBOOL(hAPP(X0,bool,X1,X2)) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(rectify,[],[f1781]) ).
fof(f1781,plain,
! [X0,X1] :
( ( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
| ? [X2] : hBOOL(hAPP(X0,bool,X1,X2)) )
& ( ! [X2] : ~ hBOOL(hAPP(X0,bool,X1,X2))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ) ),
inference(nnf_transformation,[],[f911]) ).
fof(f911,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1)
<=> ! [X2] : ~ hBOOL(hAPP(X0,bool,X1,X2)) ),
inference(rectify,[],[f162]) ).
fof(f162,axiom,
! [X0,X15] :
( hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15) = bot_bot(fun(X0,bool))
<=> ! [X32] : ~ hBOOL(hAPP(X0,bool,X15,X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_empty__Collect__eq) ).
fof(f4143,plain,
spl86_160,
inference(avatar_split_clause,[],[f2023,f4141]) ).
fof(f2023,plain,
! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse)),
inference(cnf_transformation,[],[f165]) ).
fof(f165,axiom,
! [X0] : bot_bot(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),hAPP(bool,fun(X0,bool),combk(bool,X0),fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_empty__def) ).
fof(f4111,plain,
spl86_159,
inference(avatar_split_clause,[],[f2917,f4109]) ).
fof(f2917,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,hAPP(fun(X0,X1),fun(X0,X1),combi(fun(X0,X1)),X2),X3),
inference(definition_unfolding,[],[f2585,f2190]) ).
fof(f2585,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,ti(fun(X0,X1),X2),X3),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,ti(fun(X0,X1),X2),X3),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X2,X1,X3,X4] : hAPP(X2,X1,ti(fun(X2,X1),X3),X4) = hAPP(X2,X1,X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(f4107,plain,
spl86_158,
inference(avatar_split_clause,[],[f2856,f4105]) ).
fof(f4105,plain,
( spl86_158
<=> ! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_158])]) ).
fof(f2856,plain,
! [X0,X1] : hAPP(X0,X0,combi(X0),X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(definition_unfolding,[],[f2195,f2190]) ).
fof(f2195,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(cnf_transformation,[],[f787]) ).
fof(f787,plain,
! [X0,X1] : ti(X0,X1) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X1)),
inference(rectify,[],[f251]) ).
fof(f251,axiom,
! [X0,X13] : ti(X0,X13) = hAPP(fun(X0,bool),X0,the(X0),hAPP(X0,fun(X0,bool),fequal(X0),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_the__sym__eq__trivial) ).
fof(f4103,plain,
spl86_157,
inference(avatar_split_clause,[],[f2794,f4101]) ).
fof(f4101,plain,
( spl86_157
<=> ! [X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = hAPP(X0,X0,combi(X0),X1)
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_157])]) ).
fof(f2794,plain,
! [X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = hAPP(X0,X0,combi(X0),X1)
| ~ monoid_add(X0) ),
inference(definition_unfolding,[],[f2047,f2190]) ).
fof(f2047,plain,
! [X0,X1] :
( ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1)
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f1176]) ).
fof(f1176,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1)
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f675]) ).
fof(f675,plain,
! [X0] :
( monoid_add(X0)
=> ! [X1] : ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) ),
inference(rectify,[],[f545]) ).
fof(f545,axiom,
! [X2] :
( monoid_add(X2)
=> ! [X48] : ti(X2,X48) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),zero_zero(X2)),X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_add__0__left) ).
fof(f4099,plain,
( ~ spl86_156
| spl86_136
| ~ spl86_137 ),
inference(avatar_split_clause,[],[f4053,f3978,f3974,f4096]) ).
fof(f4096,plain,
( spl86_156
<=> fFalse = fTrue ),
introduced(avatar_definition,[new_symbols(naming,[spl86_156])]) ).
fof(f3974,plain,
( spl86_136
<=> fTrue = undefined(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_136])]) ).
fof(f3978,plain,
( spl86_137
<=> fFalse = undefined(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_137])]) ).
fof(f4053,plain,
( fFalse != fTrue
| spl86_136
| ~ spl86_137 ),
inference(superposition,[],[f3975,f3980]) ).
fof(f3980,plain,
( fFalse = undefined(bool)
| ~ spl86_137 ),
inference(avatar_component_clause,[],[f3978]) ).
fof(f3975,plain,
( fTrue != undefined(bool)
| spl86_136 ),
inference(avatar_component_clause,[],[f3974]) ).
fof(f4094,plain,
spl86_155,
inference(avatar_split_clause,[],[f2793,f4092]) ).
fof(f4092,plain,
( spl86_155
<=> ! [X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = hAPP(X0,X0,combi(X0),X1)
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_155])]) ).
fof(f2793,plain,
! [X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = hAPP(X0,X0,combi(X0),X1)
| ~ monoid_add(X0) ),
inference(definition_unfolding,[],[f2046,f2190]) ).
fof(f2046,plain,
! [X0,X1] :
( ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0))
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f1175]) ).
fof(f1175,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0))
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f674]) ).
fof(f674,plain,
! [X0] :
( monoid_add(X0)
=> ! [X1] : ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) ),
inference(rectify,[],[f548]) ).
fof(f548,axiom,
! [X2] :
( monoid_add(X2)
=> ! [X48] : ti(X2,X48) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),zero_zero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_add__0__right) ).
fof(f4090,plain,
spl86_154,
inference(avatar_split_clause,[],[f2787,f4088]) ).
fof(f2787,plain,
! [X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = hAPP(X0,X0,combi(X0),X1)
| ~ comm_monoid_add(X0) ),
inference(definition_unfolding,[],[f2039,f2190]) ).
fof(f2039,plain,
! [X0,X1] :
( ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1)
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f1170]) ).
fof(f1170,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1)
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f669]) ).
fof(f669,plain,
! [X0] :
( comm_monoid_add(X0)
=> ! [X1] : ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) ),
inference(rectify,[],[f546]) ).
fof(f546,axiom,
! [X2] :
( comm_monoid_add(X2)
=> ! [X48] : ti(X2,X48) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),zero_zero(X2)),X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_add__0) ).
fof(f4086,plain,
spl86_153,
inference(avatar_split_clause,[],[f2786,f4084]) ).
fof(f2786,plain,
! [X0,X1] :
( hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = hAPP(X0,X0,combi(X0),X1)
| ~ comm_monoid_add(X0) ),
inference(definition_unfolding,[],[f2038,f2190]) ).
fof(f2038,plain,
! [X0,X1] :
( ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0))
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f1169]) ).
fof(f1169,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0))
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f668]) ).
fof(f668,plain,
! [X0] :
( comm_monoid_add(X0)
=> ! [X1] : ti(X0,X1) = hAPP(X0,X0,hAPP(X0,fun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) ),
inference(rectify,[],[f549]) ).
fof(f549,axiom,
! [X2] :
( comm_monoid_add(X2)
=> ! [X48] : ti(X2,X48) = hAPP(X2,X2,hAPP(X2,fun(X2,X2),plus_plus(X2),X48),zero_zero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_add_Ocomm__neutral) ).
fof(f4082,plain,
spl86_152,
inference(avatar_split_clause,[],[f2773,f4080]) ).
fof(f2773,plain,
! [X0] : finite_finite(X0) = hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),combi(fun(fun(X0,bool),bool)),finite_finite(X0)),
inference(definition_unfolding,[],[f1996,f2190]) ).
fof(f1996,plain,
! [X0] : finite_finite(X0) = ti(fun(fun(X0,bool),bool),finite_finite(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] : finite_finite(X0) = ti(fun(fun(X0,bool),bool),finite_finite(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
fof(f4078,plain,
spl86_151,
inference(avatar_split_clause,[],[f2772,f4076]) ).
fof(f4076,plain,
( spl86_151
<=> ! [X0] : finite_card(X0) = hAPP(fun(fun(X0,bool),nat),fun(fun(X0,bool),nat),combi(fun(fun(X0,bool),nat)),finite_card(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_151])]) ).
fof(f2772,plain,
! [X0] : finite_card(X0) = hAPP(fun(fun(X0,bool),nat),fun(fun(X0,bool),nat),combi(fun(fun(X0,bool),nat)),finite_card(X0)),
inference(definition_unfolding,[],[f1995,f2190]) ).
fof(f1995,plain,
! [X0] : finite_card(X0) = ti(fun(fun(X0,bool),nat),finite_card(X0)),
inference(cnf_transformation,[],[f624]) ).
fof(f624,plain,
! [X0] : finite_card(X0) = ti(fun(fun(X0,bool),nat),finite_card(X0)),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1] : finite_card(X1) = ti(fun(fun(X1,bool),nat),finite_card(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).
fof(f4074,plain,
spl86_150,
inference(avatar_split_clause,[],[f2771,f4072]) ).
fof(f4072,plain,
( spl86_150
<=> ! [X0] : fequal(X0) = hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combi(fun(X0,fun(X0,bool))),fequal(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_150])]) ).
fof(f2771,plain,
! [X0] : fequal(X0) = hAPP(fun(X0,fun(X0,bool)),fun(X0,fun(X0,bool)),combi(fun(X0,fun(X0,bool))),fequal(X0)),
inference(definition_unfolding,[],[f1994,f2190]) ).
fof(f1994,plain,
! [X0] : fequal(X0) = ti(fun(X0,fun(X0,bool)),fequal(X0)),
inference(cnf_transformation,[],[f623]) ).
fof(f623,plain,
! [X0] : fequal(X0) = ti(fun(X0,fun(X0,bool)),fequal(X0)),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X2] : fequal(X2) = ti(fun(X2,fun(X2,bool)),fequal(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
fof(f4070,plain,
spl86_149,
inference(avatar_split_clause,[],[f2770,f4068]) ).
fof(f2770,plain,
! [X0] : the(X0) = hAPP(fun(fun(X0,bool),X0),fun(fun(X0,bool),X0),combi(fun(fun(X0,bool),X0)),the(X0)),
inference(definition_unfolding,[],[f1993,f2190]) ).
fof(f1993,plain,
! [X0] : the(X0) = ti(fun(fun(X0,bool),X0),the(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : the(X0) = ti(fun(fun(X0,bool),X0),the(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_OThe_res) ).
fof(f4066,plain,
spl86_148,
inference(avatar_split_clause,[],[f2769,f4064]) ).
fof(f2769,plain,
! [X0] : the_elem(X0) = hAPP(fun(fun(X0,bool),X0),fun(fun(X0,bool),X0),combi(fun(fun(X0,bool),X0)),the_elem(X0)),
inference(definition_unfolding,[],[f1992,f2190]) ).
fof(f1992,plain,
! [X0] : the_elem(X0) = ti(fun(fun(X0,bool),X0),the_elem(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] : the_elem(X0) = ti(fun(fun(X0,bool),X0),the_elem(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Othe__elem_res) ).
fof(f4040,plain,
spl86_147,
inference(avatar_split_clause,[],[f3014,f4038]) ).
fof(f3014,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| hAPP(nat,nat,suc,sK22(X1)) = X1 ),
inference(forward_demodulation,[],[f2298,f2022]) ).
fof(f2298,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,sK22(X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(cnf_transformation,[],[f1726]) ).
fof(f1726,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,sK22(X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f1381,f1725]) ).
fof(f1725,plain,
! [X1] :
( ? [X2] : hAPP(nat,nat,suc,X2) = X1
=> hAPP(nat,nat,suc,sK22(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f1381,plain,
! [X0,X1] :
( ? [X2] : hAPP(nat,nat,suc,X2) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(ennf_transformation,[],[f880]) ).
fof(f880,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1))
=> ? [X2] : hAPP(nat,nat,suc,X2) = X1 ),
inference(rectify,[],[f109]) ).
fof(f109,axiom,
! [X16,X36] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X16)),X36))
=> ? [X37] : hAPP(nat,nat,suc,X37) = X36 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Suc__le__D) ).
fof(f4036,plain,
spl86_146,
inference(avatar_split_clause,[],[f2359,f4034]) ).
fof(f2359,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP(X0,bool,X1,X3))
| bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) ),
inference(cnf_transformation,[],[f1784]) ).
fof(f4032,plain,
spl86_145,
inference(avatar_split_clause,[],[f2199,f4030]) ).
fof(f2199,plain,
! [X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1)),
inference(cnf_transformation,[],[f790]) ).
fof(f790,plain,
! [X0,X1] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X1),X1)),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X0,X7] : hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_subset__refl) ).
fof(f4028,plain,
spl86_144,
inference(avatar_split_clause,[],[f2022,f4026]) ).
fof(f4024,plain,
~ spl86_143,
inference(avatar_split_clause,[],[f1937,f4021]) ).
fof(f1937,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
inference(cnf_transformation,[],[f608]) ).
fof(f608,axiom,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
fof(f4004,plain,
spl86_142,
inference(avatar_split_clause,[],[f3077,f4002]) ).
fof(f4002,plain,
( spl86_142
<=> ! [X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),sK60(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_142])]) ).
fof(f3077,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),collect(X0),sK60(X0,X1))
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f2889,f2854]) ).
fof(f2889,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) != hAPP(fun(X0,bool),fun(X0,bool),combi(fun(X0,bool)),sK60(X0,X1))
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f2455,f2190]) ).
fof(f2455,plain,
! [X0,X1] :
( bot_bot(fun(X0,bool)) != ti(fun(X0,bool),sK60(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1826]) ).
fof(f4000,plain,
spl86_141,
inference(avatar_split_clause,[],[f2918,f3998]) ).
fof(f2918,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3) = hAPP(X1,X1,combi(X1),X2),
inference(definition_unfolding,[],[f2586,f2190]) ).
fof(f2586,plain,
! [X2,X3,X0,X1] : ti(X1,X2) = hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3),
inference(cnf_transformation,[],[f1053]) ).
fof(f1053,plain,
! [X0,X1,X2,X3] : ti(X1,X2) = hAPP(X0,X1,hAPP(X1,fun(X0,X1),combk(X1,X0),X2),X3),
inference(rectify,[],[f588]) ).
fof(f588,axiom,
! [X0,X2,X79,X80] : ti(X2,X79) = hAPP(X0,X2,hAPP(X2,fun(X0,X2),combk(X2,X0),X79),X80),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(f3996,plain,
spl86_140,
inference(avatar_split_clause,[],[f2764,f3993]) ).
fof(f3993,plain,
( spl86_140
<=> fconj = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fconj) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_140])]) ).
fof(f2764,plain,
fconj = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fconj),
inference(definition_unfolding,[],[f1978,f2190]) ).
fof(f1978,plain,
fconj = ti(fun(bool,fun(bool,bool)),fconj),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
fconj = ti(fun(bool,fun(bool,bool)),fconj),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
fof(f3991,plain,
spl86_139,
inference(avatar_split_clause,[],[f2763,f3988]) ).
fof(f3988,plain,
( spl86_139
<=> fimplies = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fimplies) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_139])]) ).
fof(f2763,plain,
fimplies = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fimplies),
inference(definition_unfolding,[],[f1977,f2190]) ).
fof(f1977,plain,
fimplies = ti(fun(bool,fun(bool,bool)),fimplies),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
fimplies = ti(fun(bool,fun(bool,bool)),fimplies),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
fof(f3986,plain,
spl86_138,
inference(avatar_split_clause,[],[f2762,f3983]) ).
fof(f3983,plain,
( spl86_138
<=> fdisj = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fdisj) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_138])]) ).
fof(f2762,plain,
fdisj = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fdisj),
inference(definition_unfolding,[],[f1976,f2190]) ).
fof(f1976,plain,
fdisj = ti(fun(bool,fun(bool,bool)),fdisj),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
fdisj = ti(fun(bool,fun(bool,bool)),fdisj),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
fof(f3981,plain,
( spl86_136
| spl86_137
| ~ spl86_52
| ~ spl86_107 ),
inference(avatar_split_clause,[],[f3724,f3694,f3430,f3978,f3974]) ).
fof(f3724,plain,
( fFalse = undefined(bool)
| fTrue = undefined(bool)
| ~ spl86_52
| ~ spl86_107 ),
inference(superposition,[],[f3695,f3431]) ).
fof(f3972,plain,
spl86_135,
inference(avatar_split_clause,[],[f2261,f3970]) ).
fof(f3970,plain,
( spl86_135
<=> ! [X0,X1] :
( zero_zero(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_135])]) ).
fof(f2261,plain,
! [X0,X1] :
( zero_zero(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(cnf_transformation,[],[f1340]) ).
fof(f1340,plain,
! [X0,X1] :
( zero_zero(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),X1)
| hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(ennf_transformation,[],[f847]) ).
fof(f847,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
=> zero_zero(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),X1) ),
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X0,X7] :
( ~ hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7))
=> hAPP(fun(X0,bool),nat,finite_card(X0),X7) = zero_zero(nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_card__infinite) ).
fof(f3968,plain,
spl86_134,
inference(avatar_split_clause,[],[f2196,f3966]) ).
fof(f2196,plain,
! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f788]) ).
fof(f788,plain,
! [X0,X1] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f161]) ).
fof(f161,axiom,
! [X0,X34] : ~ hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X34),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_empty__iff) ).
fof(f3947,plain,
spl86_133,
inference(avatar_split_clause,[],[f2765,f3944]) ).
fof(f3944,plain,
( spl86_133
<=> the_1(com) = hAPP(fun(option(com),com),fun(option(com),com),combi(fun(option(com),com)),the_1(com)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_133])]) ).
fof(f2765,plain,
the_1(com) = hAPP(fun(option(com),com),fun(option(com),com),combi(fun(option(com),com)),the_1(com)),
inference(definition_unfolding,[],[f1980,f2190]) ).
fof(f1980,plain,
the_1(com) = ti(fun(option(com),com),the_1(com)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
the_1(com) = ti(fun(option(com),com),the_1(com)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Option_Othe_res) ).
fof(f3942,plain,
spl86_132,
inference(avatar_split_clause,[],[f2021,f3940]) ).
fof(f3940,plain,
( spl86_132
<=> ! [X0] : hBOOL(hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),bool,finite_comp_fun_idem(X0,fun(X0,bool)),insert(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_132])]) ).
fof(f2021,plain,
! [X0] : hBOOL(hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),bool,finite_comp_fun_idem(X0,fun(X0,bool)),insert(X0))),
inference(cnf_transformation,[],[f321]) ).
fof(f321,axiom,
! [X0] : hBOOL(hAPP(fun(X0,fun(fun(X0,bool),fun(X0,bool))),bool,finite_comp_fun_idem(X0,fun(X0,bool)),insert(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_comp__fun__idem__insert) ).
fof(f3938,plain,
spl86_131,
inference(avatar_split_clause,[],[f2020,f3936]) ).
fof(f2020,plain,
! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),one_one(nat)) = X0,
inference(cnf_transformation,[],[f639]) ).
fof(f639,plain,
! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X0)),one_one(nat)) = X0,
inference(rectify,[],[f275]) ).
fof(f275,axiom,
! [X16] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,X16)),one_one(nat)) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_diff__Suc__1) ).
fof(f3934,plain,
spl86_130,
inference(avatar_split_clause,[],[f2019,f3932]) ).
fof(f2019,plain,
! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X0),
inference(cnf_transformation,[],[f638]) ).
fof(f638,plain,
! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X0),
inference(rectify,[],[f334]) ).
fof(f334,axiom,
! [X16] : hAPP(nat,nat,suc,X16) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_Suc__eq__plus1__left) ).
fof(f3930,plain,
spl86_129,
inference(avatar_split_clause,[],[f2018,f3928]) ).
fof(f2018,plain,
! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),one_one(nat)),
inference(cnf_transformation,[],[f637]) ).
fof(f637,plain,
! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),one_one(nat)),
inference(rectify,[],[f333]) ).
fof(f333,axiom,
! [X16] : hAPP(nat,nat,suc,X16) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X16),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_Suc__eq__plus1) ).
fof(f3905,plain,
spl86_128,
inference(avatar_split_clause,[],[f3053,f3903]) ).
fof(f3053,plain,
! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| sP1(X1,X0) ),
inference(forward_demodulation,[],[f2389,f1979]) ).
fof(f1979,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(cnf_transformation,[],[f525]) ).
fof(f525,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_One__nat__def) ).
fof(f2389,plain,
! [X0,X1] :
( sP1(X1,X0)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) ),
inference(cnf_transformation,[],[f1803]) ).
fof(f1803,plain,
! [X0,X1] :
( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) ) ),
inference(nnf_transformation,[],[f1644]) ).
fof(f1644,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
<=> sP1(X1,X0) ),
inference(definition_folding,[],[f919,f1643]) ).
fof(f1643,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X1
& zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1
& hAPP(nat,nat,suc,zero_zero(nat)) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f919,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
<=> ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X1
& zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1
& hAPP(nat,nat,suc,zero_zero(nat)) = X0 ) ) ),
inference(rectify,[],[f520]) ).
fof(f520,axiom,
! [X27,X19] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X19) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X19
& zero_zero(nat) = X27 )
| ( zero_zero(nat) = X19
& hAPP(nat,nat,suc,zero_zero(nat)) = X27 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_add__is__1) ).
fof(f3901,plain,
spl86_127,
inference(avatar_split_clause,[],[f3052,f3899]) ).
fof(f3899,plain,
( spl86_127
<=> ! [X0,X1] :
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| ~ sP1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_127])]) ).
fof(f3052,plain,
! [X0,X1] :
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| ~ sP1(X1,X0) ),
inference(forward_demodulation,[],[f2390,f1979]) ).
fof(f2390,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| ~ sP1(X1,X0) ),
inference(cnf_transformation,[],[f1803]) ).
fof(f3897,plain,
( spl86_126
| ~ spl86_79
| ~ spl86_103 ),
inference(avatar_split_clause,[],[f3718,f3678,f3573,f3895]) ).
fof(f3895,plain,
( spl86_126
<=> ! [X0] : ~ sP3(X0,zero_zero(nat),ord_less_eq(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_126])]) ).
fof(f3718,plain,
( ! [X0] : ~ sP3(X0,zero_zero(nat),ord_less_eq(nat))
| ~ spl86_79
| ~ spl86_103 ),
inference(resolution,[],[f3679,f3574]) ).
fof(f3893,plain,
spl86_125,
inference(avatar_split_clause,[],[f3045,f3891]) ).
fof(f3045,plain,
! [X0,X1] :
( one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| sP0(X1,X0) ),
inference(forward_demodulation,[],[f2381,f1979]) ).
fof(f2381,plain,
! [X0,X1] :
( sP0(X1,X0)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) ),
inference(cnf_transformation,[],[f1799]) ).
fof(f1799,plain,
! [X0,X1] :
( ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1) ) ),
inference(nnf_transformation,[],[f1642]) ).
fof(f1642,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
<=> sP0(X1,X0) ),
inference(definition_folding,[],[f918,f1641]) ).
fof(f1641,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X1
& zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1
& hAPP(nat,nat,suc,zero_zero(nat)) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f918,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
<=> ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X1
& zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1
& hAPP(nat,nat,suc,zero_zero(nat)) = X0 ) ) ),
inference(rectify,[],[f521]) ).
fof(f521,axiom,
! [X27,X19] :
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X27),X19) = hAPP(nat,nat,suc,zero_zero(nat))
<=> ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X19
& zero_zero(nat) = X27 )
| ( zero_zero(nat) = X19
& hAPP(nat,nat,suc,zero_zero(nat)) = X27 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_one__is__add) ).
fof(f3889,plain,
spl86_124,
inference(avatar_split_clause,[],[f3044,f3887]) ).
fof(f3887,plain,
( spl86_124
<=> ! [X0,X1] :
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| ~ sP0(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_124])]) ).
fof(f3044,plain,
! [X0,X1] :
( one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| ~ sP0(X1,X0) ),
inference(forward_demodulation,[],[f2382,f1979]) ).
fof(f2382,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X0),X1)
| ~ sP0(X1,X0) ),
inference(cnf_transformation,[],[f1799]) ).
fof(f3885,plain,
spl86_123,
inference(avatar_split_clause,[],[f2187,f3883]) ).
fof(f2187,plain,
! [X0] :
( zero_zero(nat) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat))) ),
inference(cnf_transformation,[],[f1706]) ).
fof(f1706,plain,
! [X0] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat)))
| zero_zero(nat) != X0 )
& ( zero_zero(nat) = X0
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat))) ) ),
inference(nnf_transformation,[],[f782]) ).
fof(f782,plain,
! [X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),zero_zero(nat)))
<=> zero_zero(nat) = X0 ),
inference(rectify,[],[f542]) ).
fof(f542,axiom,
! [X19] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),zero_zero(nat)))
<=> zero_zero(nat) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_le__0__eq) ).
fof(f3881,plain,
spl86_122,
inference(avatar_split_clause,[],[f2015,f3879]) ).
fof(f2015,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X0))),
inference(cnf_transformation,[],[f636]) ).
fof(f636,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X0))),
inference(rectify,[],[f502]) ).
fof(f502,axiom,
! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_zero__less__Suc) ).
fof(f3868,plain,
spl86_121,
inference(avatar_split_clause,[],[f2761,f3865]) ).
fof(f3865,plain,
( spl86_121
<=> body = hAPP(fun(pname,option(com)),fun(pname,option(com)),combi(fun(pname,option(com))),body) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_121])]) ).
fof(f2761,plain,
body = hAPP(fun(pname,option(com)),fun(pname,option(com)),combi(fun(pname,option(com))),body),
inference(definition_unfolding,[],[f1975,f2190]) ).
fof(f1975,plain,
body = ti(fun(pname,option(com)),body),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
body = ti(fun(pname,option(com)),body),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Com_Obody_res) ).
fof(f3863,plain,
spl86_120,
inference(avatar_split_clause,[],[f2539,f3861]) ).
fof(f3861,plain,
( spl86_120
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_120])]) ).
fof(f2539,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f1842]) ).
fof(f1842,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2,X1),X0))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X1)) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f1841]) ).
fof(f1841,plain,
! [X1,X2,X0] :
( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X0,X2),X1))
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) )
| ~ sP3(X1,X2,X0) ),
inference(nnf_transformation,[],[f1647]) ).
fof(f3859,plain,
spl86_119,
inference(avatar_split_clause,[],[f2073,f3857]) ).
fof(f3857,plain,
( spl86_119
<=> ! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_119])]) ).
fof(f2073,plain,
! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f1207]) ).
fof(f1207,plain,
! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f697]) ).
fof(f697,plain,
! [X0] :
( linordered_semidom(X0)
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),zero_zero(X0)),one_one(X0))) ),
inference(rectify,[],[f509]) ).
fof(f509,axiom,
! [X2] :
( linordered_semidom(X2)
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),zero_zero(X2)),one_one(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_zero__le__one) ).
fof(f3855,plain,
spl86_118,
inference(avatar_split_clause,[],[f2072,f3853]) ).
fof(f2072,plain,
! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f1206]) ).
fof(f1206,plain,
! [X0] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f696]) ).
fof(f696,plain,
! [X0] :
( linordered_semidom(X0)
=> hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),one_one(X0))) ),
inference(rectify,[],[f505]) ).
fof(f505,axiom,
! [X2] :
( linordered_semidom(X2)
=> hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),zero_zero(X2)),one_one(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_zero__less__one) ).
fof(f3851,plain,
spl86_117,
inference(avatar_split_clause,[],[f2071,f3849]) ).
fof(f3849,plain,
( spl86_117
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_117])]) ).
fof(f2071,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f1205]) ).
fof(f1205,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f695]) ).
fof(f695,plain,
! [X0] :
( linordered_semidom(X0)
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),one_one(X0)),zero_zero(X0))) ),
inference(rectify,[],[f508]) ).
fof(f508,axiom,
! [X2] :
( linordered_semidom(X2)
=> ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),one_one(X2)),zero_zero(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_not__one__le__zero) ).
fof(f3847,plain,
spl86_116,
inference(avatar_split_clause,[],[f2070,f3845]) ).
fof(f3845,plain,
( spl86_116
<=> ! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_116])]) ).
fof(f2070,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f694]) ).
fof(f694,plain,
! [X0] :
( linordered_semidom(X0)
=> ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),one_one(X0)),zero_zero(X0))) ),
inference(rectify,[],[f506]) ).
fof(f506,axiom,
! [X2] :
( linordered_semidom(X2)
=> ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),one_one(X2)),zero_zero(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_not__one__less__zero) ).
fof(f3843,plain,
spl86_115,
inference(avatar_split_clause,[],[f2014,f3841]) ).
fof(f2014,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X0))),
inference(cnf_transformation,[],[f635]) ).
fof(f635,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),hAPP(nat,nat,suc,X0))),
inference(rectify,[],[f343]) ).
fof(f343,axiom,
! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),hAPP(nat,nat,suc,X16))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_lessI) ).
fof(f3838,plain,
spl86_114,
inference(avatar_split_clause,[],[f2013,f3836]) ).
fof(f3836,plain,
( spl86_114
<=> ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_114])]) ).
fof(f2013,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X0)),
inference(cnf_transformation,[],[f634]) ).
fof(f634,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X0)),
inference(rectify,[],[f89]) ).
fof(f89,axiom,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X16)),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Suc__n__not__le__n) ).
fof(f3834,plain,
( spl86_113
| ~ spl86_69
| ~ spl86_103 ),
inference(avatar_split_clause,[],[f3717,f3678,f3524,f3832]) ).
fof(f3832,plain,
( spl86_113
<=> ! [X0] : ~ sP3(X0,X0,ord_less_eq(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_113])]) ).
fof(f3717,plain,
( ! [X0] : ~ sP3(X0,X0,ord_less_eq(nat))
| ~ spl86_69
| ~ spl86_103 ),
inference(resolution,[],[f3679,f3525]) ).
fof(f3830,plain,
spl86_112,
inference(avatar_split_clause,[],[f1936,f3827]) ).
fof(f1936,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(cnf_transformation,[],[f607]) ).
fof(f607,axiom,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(f3825,plain,
~ spl86_111,
inference(avatar_split_clause,[],[f1928,f3822]) ).
fof(f1928,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cnf_transformation,[],[f611]) ).
fof(f611,plain,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(flattening,[],[f610]) ).
fof(f610,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(negated_conjecture,[],[f609]) ).
fof(f609,conjecture,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
fof(f3714,plain,
( spl86_110
| ~ spl86_19
| ~ spl86_27
| ~ spl86_70 ),
inference(avatar_split_clause,[],[f3538,f3528,f3311,f3271,f3712]) ).
fof(f3712,plain,
( spl86_110
<=> ! [X0,X1] : zero_zero(nat) = hAPP(X0,nat,bot_bot(fun(X0,nat)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_110])]) ).
fof(f3538,plain,
( ! [X0,X1] : zero_zero(nat) = hAPP(X0,nat,bot_bot(fun(X0,nat)),X1)
| ~ spl86_19
| ~ spl86_27
| ~ spl86_70 ),
inference(forward_demodulation,[],[f3535,f3313]) ).
fof(f3535,plain,
( ! [X0,X1] : bot_bot(nat) = hAPP(X0,nat,bot_bot(fun(X0,nat)),X1)
| ~ spl86_19
| ~ spl86_70 ),
inference(resolution,[],[f3529,f3273]) ).
fof(f3273,plain,
( bot(nat)
| ~ spl86_19 ),
inference(avatar_component_clause,[],[f3271]) ).
fof(f3704,plain,
spl86_109,
inference(avatar_split_clause,[],[f2916,f3702]) ).
fof(f2916,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,hAPP(X0,X0,combi(X0),X3)),
inference(definition_unfolding,[],[f2584,f2190]) ).
fof(f2584,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X2,X1,X3,X4] : hAPP(X2,X1,X3,X4) = hAPP(X2,X1,X3,ti(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(f3700,plain,
spl86_108,
inference(avatar_split_clause,[],[f2915,f3698]) ).
fof(f2915,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = hAPP(X0,X0,combi(X0),hAPP(X1,X0,X2,X3)),
inference(definition_unfolding,[],[f2583,f2190]) ).
fof(f2583,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(cnf_transformation,[],[f1050]) ).
fof(f1050,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X1,X2,X3,X4] : hAPP(X2,X1,X3,X4) = ti(X1,hAPP(X2,X1,X3,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(f3696,plain,
spl86_107,
inference(avatar_split_clause,[],[f2781,f3694]) ).
fof(f2781,plain,
! [X0] :
( fFalse = hAPP(bool,bool,combi(bool),X0)
| fTrue = hAPP(bool,bool,combi(bool),X0) ),
inference(definition_unfolding,[],[f2030,f2190,f2190]) ).
fof(f2030,plain,
! [X0] :
( fFalse = ti(bool,X0)
| fTrue = ti(bool,X0) ),
inference(cnf_transformation,[],[f646]) ).
fof(f646,plain,
! [X0] :
( fFalse = ti(bool,X0)
| fTrue = ti(bool,X0) ),
inference(rectify,[],[f597]) ).
fof(f597,axiom,
! [X79] :
( fFalse = ti(bool,X79)
| fTrue = ti(bool,X79) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(f3692,plain,
spl86_106,
inference(avatar_split_clause,[],[f2768,f3690]) ).
fof(f2768,plain,
! [X0] : combi(X0) = hAPP(fun(X0,X0),fun(X0,X0),combi(fun(X0,X0)),combi(X0)),
inference(definition_unfolding,[],[f1991,f2190]) ).
fof(f1991,plain,
! [X0] : combi(X0) = ti(fun(X0,X0),combi(X0)),
inference(cnf_transformation,[],[f622]) ).
fof(f622,plain,
! [X0] : combi(X0) = ti(fun(X0,X0),combi(X0)),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2] : combi(X2) = ti(fun(X2,X2),combi(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
fof(f3688,plain,
spl86_105,
inference(avatar_split_clause,[],[f2608,f3686]) ).
fof(f2608,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f1873]) ).
fof(f3684,plain,
( spl86_104
| ~ spl86_20
| ~ spl86_70 ),
inference(avatar_split_clause,[],[f3536,f3528,f3276,f3682]) ).
fof(f3276,plain,
( spl86_20
<=> bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_20])]) ).
fof(f3536,plain,
( ! [X0,X1] : bot_bot(bool) = hAPP(X0,bool,bot_bot(fun(X0,bool)),X1)
| ~ spl86_20
| ~ spl86_70 ),
inference(resolution,[],[f3529,f3278]) ).
fof(f3278,plain,
( bot(bool)
| ~ spl86_20 ),
inference(avatar_component_clause,[],[f3276]) ).
fof(f3680,plain,
spl86_103,
inference(avatar_split_clause,[],[f2540,f3678]) ).
fof(f2540,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X2,X1),X0))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f1842]) ).
fof(f3676,plain,
spl86_102,
inference(avatar_split_clause,[],[f2236,f3674]) ).
fof(f2236,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1)) ),
inference(cnf_transformation,[],[f826]) ).
fof(f826,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1)) ),
inference(rectify,[],[f602]) ).
fof(f602,axiom,
! [X79,X80] :
( hBOOL(X80)
| ~ hBOOL(X79)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X79),X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(f3672,plain,
spl86_101,
inference(avatar_split_clause,[],[f2235,f3670]) ).
fof(f2235,plain,
! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1)) ),
inference(cnf_transformation,[],[f825]) ).
fof(f825,plain,
! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1)) ),
inference(rectify,[],[f595]) ).
fof(f595,axiom,
! [X79,X80] :
( hBOOL(X80)
| hBOOL(X79)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X79),X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
fof(f3668,plain,
spl86_100,
inference(avatar_split_clause,[],[f2230,f3666]) ).
fof(f2230,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f820]) ).
fof(f820,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f590]) ).
fof(f590,axiom,
! [X80,X79] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X79),X80))
| ~ hBOOL(X80)
| ~ hBOOL(X79) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
fof(f3664,plain,
spl86_99,
inference(avatar_split_clause,[],[f2118,f3662]) ).
fof(f3662,plain,
( spl86_99
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_99])]) ).
fof(f2118,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f1242]) ).
fof(f1242,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1))
| ~ bot(X0) ),
inference(ennf_transformation,[],[f729]) ).
fof(f729,plain,
! [X0] :
( bot(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),bot_bot(X0)),X1)) ),
inference(rectify,[],[f170]) ).
fof(f170,axiom,
! [X2] :
( bot(X2)
=> ! [X48] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),bot_bot(X2)),X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_bot__least) ).
fof(f3660,plain,
spl86_98,
inference(avatar_split_clause,[],[f2117,f3658]) ).
fof(f3658,plain,
( spl86_98
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),bot_bot(X0)))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_98])]) ).
fof(f2117,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),bot_bot(X0)))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f1241]) ).
fof(f1241,plain,
! [X0] :
( ! [X1] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),bot_bot(X0)))
| ~ bot(X0) ),
inference(ennf_transformation,[],[f728]) ).
fof(f728,plain,
! [X0] :
( bot(X0)
=> ! [X1] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),bot_bot(X0))) ),
inference(rectify,[],[f413]) ).
fof(f413,axiom,
! [X2] :
( bot(X2)
=> ! [X48] : ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X48),bot_bot(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_not__less__bot) ).
fof(f3656,plain,
spl86_97,
inference(avatar_split_clause,[],[f2012,f3654]) ).
fof(f2012,plain,
! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X0),
inference(cnf_transformation,[],[f633]) ).
fof(f633,plain,
! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X0),
inference(rectify,[],[f529]) ).
fof(f529,axiom,
! [X16] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_diff__0__eq__0) ).
fof(f3650,plain,
spl86_96,
inference(avatar_split_clause,[],[f2611,f3648]) ).
fof(f2611,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,sK74(X0,X1,X2)))
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f1873]) ).
fof(f3646,plain,
spl86_95,
inference(avatar_split_clause,[],[f2131,f3644]) ).
fof(f3644,plain,
( spl86_95
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_95])]) ).
fof(f2131,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1257]) ).
fof(f1257,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f740]) ).
fof(f740,plain,
! [X0] :
( preorder(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1)) ),
inference(rectify,[],[f150]) ).
fof(f150,axiom,
! [X2] :
( preorder(X2)
=> ! [X20] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_order__refl) ).
fof(f3642,plain,
spl86_94,
inference(avatar_split_clause,[],[f2130,f3640]) ).
fof(f3640,plain,
( spl86_94
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_94])]) ).
fof(f2130,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f1256]) ).
fof(f1256,plain,
! [X0] :
( ! [X1] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X1))
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f739]) ).
fof(f739,plain,
! [X0] :
( preorder(X0)
=> ! [X1] : ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X1)) ),
inference(rectify,[],[f383]) ).
fof(f383,axiom,
! [X2] :
( preorder(X2)
=> ! [X20] : ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X20),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_order__less__irrefl) ).
fof(f3638,plain,
spl86_93,
inference(avatar_split_clause,[],[f2011,f3636]) ).
fof(f2011,plain,
! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) = X0,
inference(cnf_transformation,[],[f632]) ).
fof(f632,plain,
! [X0] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),zero_zero(nat)) = X0,
inference(rectify,[],[f528]) ).
fof(f528,axiom,
! [X17] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),zero_zero(nat)) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_minus__nat_Odiff__0) ).
fof(f3634,plain,
spl86_92,
inference(avatar_split_clause,[],[f2008,f3632]) ).
fof(f2008,plain,
! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X0),
inference(cnf_transformation,[],[f631]) ).
fof(f631,plain,
! [X0] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X0),X0),
inference(rectify,[],[f527]) ).
fof(f527,axiom,
! [X17] : zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X17),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_diff__self__eq__0) ).
fof(f3627,plain,
spl86_91,
inference(avatar_split_clause,[],[f2760,f3624]) ).
fof(f2760,plain,
fNot = hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot),
inference(definition_unfolding,[],[f1974,f2190]) ).
fof(f1974,plain,
fNot = ti(fun(bool,bool),fNot),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
fNot = ti(fun(bool,bool),fNot),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
fof(f3622,plain,
spl86_90,
inference(avatar_split_clause,[],[f2759,f3619]) ).
fof(f2759,plain,
wt = hAPP(fun(com,bool),fun(com,bool),combi(fun(com,bool)),wt),
inference(definition_unfolding,[],[f1973,f2190]) ).
fof(f1973,plain,
wt = ti(fun(com,bool),wt),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
wt = ti(fun(com,bool),wt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_wt_res) ).
fof(f3617,plain,
spl86_89,
inference(avatar_split_clause,[],[f2758,f3614]) ).
fof(f3614,plain,
( spl86_89
<=> mgt = hAPP(fun(com,x_a),fun(com,x_a),combi(fun(com,x_a)),mgt) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_89])]) ).
fof(f2758,plain,
mgt = hAPP(fun(com,x_a),fun(com,x_a),combi(fun(com,x_a)),mgt),
inference(definition_unfolding,[],[f1972,f2190]) ).
fof(f1972,plain,
mgt = ti(fun(com,x_a),mgt),
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
mgt = ti(fun(com,x_a),mgt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_mgt_res) ).
fof(f3612,plain,
spl86_88,
inference(avatar_split_clause,[],[f2454,f3610]) ).
fof(f2454,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK60(X0,X1)))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1826]) ).
fof(f3608,plain,
spl86_87,
inference(avatar_split_clause,[],[f2263,f3606]) ).
fof(f2263,plain,
! [X0,X1] :
( X0 = X1
| hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1) ),
inference(cnf_transformation,[],[f1342]) ).
fof(f1342,plain,
! [X0,X1] :
( X0 = X1
| hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1) ),
inference(ennf_transformation,[],[f849]) ).
fof(f849,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,X1)
=> X0 = X1 ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X20,X21] :
( hAPP(nat,nat,suc,X20) = hAPP(nat,nat,suc,X21)
=> X20 = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Suc__inject) ).
fof(f3604,plain,
spl86_86,
inference(avatar_split_clause,[],[f2238,f3602]) ).
fof(f2238,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(cnf_transformation,[],[f828]) ).
fof(f828,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(rectify,[],[f591]) ).
fof(f591,axiom,
! [X79,X80] :
( hBOOL(X79)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X79),X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(f3600,plain,
spl86_85,
inference(avatar_split_clause,[],[f2237,f3598]) ).
fof(f2237,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(cnf_transformation,[],[f827]) ).
fof(f827,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(rectify,[],[f592]) ).
fof(f592,axiom,
! [X79,X80] :
( hBOOL(X80)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X79),X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
fof(f3596,plain,
spl86_84,
inference(avatar_split_clause,[],[f2234,f3594]) ).
fof(f2234,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f824]) ).
fof(f824,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f600]) ).
fof(f600,axiom,
! [X80,X79] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X79),X80))
| hBOOL(X79) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(f3592,plain,
spl86_83,
inference(avatar_split_clause,[],[f2233,f3590]) ).
fof(f2233,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f823]) ).
fof(f823,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f601]) ).
fof(f601,axiom,
! [X79,X80] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X79),X80))
| ~ hBOOL(X80) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
fof(f3588,plain,
( spl86_82
| ~ spl86_20
| ~ spl86_66 ),
inference(avatar_split_clause,[],[f3511,f3505,f3276,f3585]) ).
fof(f3511,plain,
( bot_bot(bool) = hAPP(bool,bool,combi(bool),bot_bot(bool))
| ~ spl86_20
| ~ spl86_66 ),
inference(resolution,[],[f3506,f3278]) ).
fof(f3583,plain,
spl86_81,
inference(avatar_split_clause,[],[f2232,f3581]) ).
fof(f2232,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f822]) ).
fof(f822,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f594]) ).
fof(f594,axiom,
! [X79,X80] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X79),X80))
| ~ hBOOL(X80) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
fof(f3579,plain,
spl86_80,
inference(avatar_split_clause,[],[f2231,f3577]) ).
fof(f2231,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f821]) ).
fof(f821,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f593]) ).
fof(f593,axiom,
! [X80,X79] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X79),X80))
| ~ hBOOL(X79) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
fof(f3575,plain,
spl86_79,
inference(avatar_split_clause,[],[f2006,f3573]) ).
fof(f2006,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X0)),
inference(cnf_transformation,[],[f629]) ).
fof(f629,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X0)),
inference(rectify,[],[f501]) ).
fof(f501,axiom,
! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_le0) ).
fof(f3571,plain,
spl86_78,
inference(avatar_split_clause,[],[f2005,f3569]) ).
fof(f2005,plain,
! [X0] : zero_zero(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),bot_bot(fun(X0,bool))),
inference(cnf_transformation,[],[f504]) ).
fof(f504,axiom,
! [X0] : zero_zero(nat) = hAPP(fun(X0,bool),nat,finite_card(X0),bot_bot(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_card_Oempty) ).
fof(f3567,plain,
spl86_77,
inference(avatar_split_clause,[],[f2004,f3565]) ).
fof(f3565,plain,
( spl86_77
<=> ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_77])]) ).
fof(f2004,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),zero_zero(nat))),
inference(cnf_transformation,[],[f628]) ).
fof(f628,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),zero_zero(nat))),
inference(rectify,[],[f500]) ).
fof(f500,axiom,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),zero_zero(nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_less__zeroE) ).
fof(f3563,plain,
spl86_76,
inference(avatar_split_clause,[],[f2753,f3560]) ).
fof(f3560,plain,
( spl86_76
<=> suc = hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_76])]) ).
fof(f2753,plain,
suc = hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc),
inference(definition_unfolding,[],[f1934,f2190]) ).
fof(f1934,plain,
suc = ti(fun(nat,nat),suc),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
suc = ti(fun(nat,nat),suc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_OSuc_res) ).
fof(f3558,plain,
( spl86_75
| ~ spl86_6
| ~ spl86_65 ),
inference(avatar_split_clause,[],[f3509,f3501,f3206,f3555]) ).
fof(f3555,plain,
( spl86_75
<=> zero_zero(nat) = hAPP(nat,nat,combi(nat),zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_75])]) ).
fof(f3206,plain,
( spl86_6
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_6])]) ).
fof(f3501,plain,
( spl86_65
<=> ! [X0] :
( zero_zero(X0) = hAPP(X0,X0,combi(X0),zero_zero(X0))
| ~ zero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_65])]) ).
fof(f3509,plain,
( zero_zero(nat) = hAPP(nat,nat,combi(nat),zero_zero(nat))
| ~ spl86_6
| ~ spl86_65 ),
inference(resolution,[],[f3502,f3208]) ).
fof(f3208,plain,
( zero(nat)
| ~ spl86_6 ),
inference(avatar_component_clause,[],[f3206]) ).
fof(f3502,plain,
( ! [X0] :
( ~ zero(X0)
| zero_zero(X0) = hAPP(X0,X0,combi(X0),zero_zero(X0)) )
| ~ spl86_65 ),
inference(avatar_component_clause,[],[f3501]) ).
fof(f3553,plain,
spl86_74,
inference(avatar_split_clause,[],[f2752,f3550]) ).
fof(f3550,plain,
( spl86_74
<=> mgt_call = hAPP(fun(pname,x_a),fun(pname,x_a),combi(fun(pname,x_a)),mgt_call) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_74])]) ).
fof(f2752,plain,
mgt_call = hAPP(fun(pname,x_a),fun(pname,x_a),combi(fun(pname,x_a)),mgt_call),
inference(definition_unfolding,[],[f1933,f2190]) ).
fof(f1933,plain,
mgt_call = ti(fun(pname,x_a),mgt_call),
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
mgt_call = ti(fun(pname,x_a),mgt_call),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_mgt__call_res) ).
fof(f3548,plain,
spl86_73,
inference(avatar_split_clause,[],[f2751,f3545]) ).
fof(f2751,plain,
u = hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u),
inference(definition_unfolding,[],[f1932,f2190]) ).
fof(f1932,plain,
u = ti(fun(pname,bool),u),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
u = ti(fun(pname,bool),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_U_res) ).
fof(f3543,plain,
spl86_72,
inference(avatar_split_clause,[],[f2750,f3540]) ).
fof(f2750,plain,
g = hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g),
inference(definition_unfolding,[],[f1931,f2190]) ).
fof(f1931,plain,
g = ti(fun(x_a,bool),g),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
g = ti(fun(x_a,bool),g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_G_res) ).
fof(f3534,plain,
spl86_71,
inference(avatar_split_clause,[],[f2457,f3532]) ).
fof(f2457,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,X1,sK60(X0,X1)))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1826]) ).
fof(f3530,plain,
spl86_70,
inference(avatar_split_clause,[],[f2244,f3528]) ).
fof(f2244,plain,
! [X2,X0,X1] :
( bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2)
| ~ bot(X1) ),
inference(cnf_transformation,[],[f1325]) ).
fof(f1325,plain,
! [X0,X1] :
( ! [X2] : bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2)
| ~ bot(X1) ),
inference(ennf_transformation,[],[f834]) ).
fof(f834,plain,
! [X0,X1] :
( bot(X1)
=> ! [X2] : bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X2) ),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X0,X1] :
( bot(X1)
=> ! [X32] : bot_bot(X1) = hAPP(X0,X1,bot_bot(fun(X0,X1)),X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_bot__fun__def) ).
fof(f3526,plain,
spl86_69,
inference(avatar_split_clause,[],[f2003,f3524]) ).
fof(f2003,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)),
inference(cnf_transformation,[],[f627]) ).
fof(f627,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)),
inference(rectify,[],[f77]) ).
fof(f77,axiom,
! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_le__refl) ).
fof(f3522,plain,
( spl86_68
| ~ spl86_5
| ~ spl86_64 ),
inference(avatar_split_clause,[],[f3508,f3497,f3201,f3519]) ).
fof(f3519,plain,
( spl86_68
<=> one_one(nat) = hAPP(nat,nat,combi(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_68])]) ).
fof(f3201,plain,
( spl86_5
<=> one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_5])]) ).
fof(f3497,plain,
( spl86_64
<=> ! [X0] :
( one_one(X0) = hAPP(X0,X0,combi(X0),one_one(X0))
| ~ one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_64])]) ).
fof(f3508,plain,
( one_one(nat) = hAPP(nat,nat,combi(nat),one_one(nat))
| ~ spl86_5
| ~ spl86_64 ),
inference(resolution,[],[f3498,f3203]) ).
fof(f3203,plain,
( one(nat)
| ~ spl86_5 ),
inference(avatar_component_clause,[],[f3201]) ).
fof(f3498,plain,
( ! [X0] :
( ~ one(X0)
| one_one(X0) = hAPP(X0,X0,combi(X0),one_one(X0)) )
| ~ spl86_64 ),
inference(avatar_component_clause,[],[f3497]) ).
fof(f3517,plain,
spl86_67,
inference(avatar_split_clause,[],[f1998,f3515]) ).
fof(f3515,plain,
( spl86_67
<=> ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_67])]) ).
fof(f1998,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X0)),
inference(cnf_transformation,[],[f625]) ).
fof(f625,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X0),X0)),
inference(rectify,[],[f409]) ).
fof(f409,axiom,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_less__irrefl__nat) ).
fof(f3507,plain,
spl86_66,
inference(avatar_split_clause,[],[f2820,f3505]) ).
fof(f2820,plain,
! [X0] :
( bot_bot(X0) = hAPP(X0,X0,combi(X0),bot_bot(X0))
| ~ bot(X0) ),
inference(definition_unfolding,[],[f2116,f2190]) ).
fof(f2116,plain,
! [X0] :
( bot_bot(X0) = ti(X0,bot_bot(X0))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f1240]) ).
fof(f1240,plain,
! [X0] :
( bot_bot(X0) = ti(X0,bot_bot(X0))
| ~ bot(X0) ),
inference(ennf_transformation,[],[f727]) ).
fof(f727,plain,
! [X0] :
( bot(X0)
=> bot_bot(X0) = ti(X0,bot_bot(X0)) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X1] :
( bot(X1)
=> bot_bot(X1) = ti(X1,bot_bot(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
fof(f3503,plain,
spl86_65,
inference(avatar_split_clause,[],[f2784,f3501]) ).
fof(f2784,plain,
! [X0] :
( zero_zero(X0) = hAPP(X0,X0,combi(X0),zero_zero(X0))
| ~ zero(X0) ),
inference(definition_unfolding,[],[f2036,f2190]) ).
fof(f2036,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero(X0) ),
inference(cnf_transformation,[],[f1167]) ).
fof(f1167,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( zero(X0)
=> zero_zero(X0) = ti(X0,zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_res) ).
fof(f3499,plain,
spl86_64,
inference(avatar_split_clause,[],[f2783,f3497]) ).
fof(f2783,plain,
! [X0] :
( one_one(X0) = hAPP(X0,X0,combi(X0),one_one(X0))
| ~ one(X0) ),
inference(definition_unfolding,[],[f2035,f2190]) ).
fof(f2035,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ one(X0) ),
inference(cnf_transformation,[],[f1166]) ).
fof(f1166,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ one(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( one(X0)
=> one_one(X0) = ti(X0,one_one(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
fof(f3495,plain,
spl86_63,
inference(avatar_split_clause,[],[f1997,f3493]) ).
fof(f1997,plain,
! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f157]) ).
fof(f157,axiom,
! [X0] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_finite_OemptyI) ).
fof(f3475,plain,
spl86_62,
inference(avatar_split_clause,[],[f3051,f3473]) ).
fof(f3473,plain,
( spl86_62
<=> ! [X0,X1] :
( one_one(nat) = X1
| zero_zero(nat) = X1
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_62])]) ).
fof(f3051,plain,
! [X0,X1] :
( one_one(nat) = X1
| zero_zero(nat) = X1
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f2383,f1979]) ).
fof(f2383,plain,
! [X0,X1] :
( zero_zero(nat) = X1
| hAPP(nat,nat,suc,zero_zero(nat)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1802]) ).
fof(f1802,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( hAPP(nat,nat,suc,zero_zero(nat)) != X0
| zero_zero(nat) != X1 )
& ( zero_zero(nat) != X0
| hAPP(nat,nat,suc,zero_zero(nat)) != X1 ) ) )
& ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X0
& zero_zero(nat) = X1 )
| ( zero_zero(nat) = X0
& hAPP(nat,nat,suc,zero_zero(nat)) = X1 )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f1801]) ).
fof(f1801,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( hAPP(nat,nat,suc,zero_zero(nat)) != X1
| zero_zero(nat) != X0 )
& ( zero_zero(nat) != X1
| hAPP(nat,nat,suc,zero_zero(nat)) != X0 ) ) )
& ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X1
& zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1
& hAPP(nat,nat,suc,zero_zero(nat)) = X0 )
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f1800]) ).
fof(f1800,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( hAPP(nat,nat,suc,zero_zero(nat)) != X1
| zero_zero(nat) != X0 )
& ( zero_zero(nat) != X1
| hAPP(nat,nat,suc,zero_zero(nat)) != X0 ) ) )
& ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X1
& zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1
& hAPP(nat,nat,suc,zero_zero(nat)) = X0 )
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f1643]) ).
fof(f3471,plain,
spl86_61,
inference(avatar_split_clause,[],[f3050,f3469]) ).
fof(f3469,plain,
( spl86_61
<=> ! [X0,X1] :
( one_one(nat) = X1
| one_one(nat) = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_61])]) ).
fof(f3050,plain,
! [X0,X1] :
( one_one(nat) = X1
| one_one(nat) = X0
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f3049,f1979]) ).
fof(f3049,plain,
! [X0,X1] :
( one_one(nat) = X0
| hAPP(nat,nat,suc,zero_zero(nat)) = X1
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f2385,f1979]) ).
fof(f2385,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = X0
| hAPP(nat,nat,suc,zero_zero(nat)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1802]) ).
fof(f3467,plain,
( ~ spl86_60
| ~ spl86_41
| ~ spl86_51 ),
inference(avatar_split_clause,[],[f3427,f3423,f3374,f3464]) ).
fof(f3464,plain,
( spl86_60
<=> one_one(nat) = zero_zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_60])]) ).
fof(f3374,plain,
( spl86_41
<=> ! [X0] : zero_zero(nat) != hAPP(nat,nat,suc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_41])]) ).
fof(f3427,plain,
( one_one(nat) != zero_zero(nat)
| ~ spl86_41
| ~ spl86_51 ),
inference(superposition,[],[f3375,f3425]) ).
fof(f3375,plain,
( ! [X0] : zero_zero(nat) != hAPP(nat,nat,suc,X0)
| ~ spl86_41 ),
inference(avatar_component_clause,[],[f3374]) ).
fof(f3462,plain,
spl86_59,
inference(avatar_split_clause,[],[f3048,f3460]) ).
fof(f3460,plain,
( spl86_59
<=> ! [X0,X1] :
( one_one(nat) = X0
| zero_zero(nat) = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_59])]) ).
fof(f3048,plain,
! [X0,X1] :
( one_one(nat) = X0
| zero_zero(nat) = X0
| ~ sP1(X0,X1) ),
inference(forward_demodulation,[],[f2386,f1979]) ).
fof(f2386,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = X0
| zero_zero(nat) = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1802]) ).
fof(f3458,plain,
spl86_58,
inference(avatar_split_clause,[],[f3043,f3456]) ).
fof(f3456,plain,
( spl86_58
<=> ! [X0,X1] :
( one_one(nat) = X1
| zero_zero(nat) = X1
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_58])]) ).
fof(f3043,plain,
! [X0,X1] :
( one_one(nat) = X1
| zero_zero(nat) = X1
| ~ sP0(X0,X1) ),
inference(forward_demodulation,[],[f2375,f1979]) ).
fof(f2375,plain,
! [X0,X1] :
( zero_zero(nat) = X1
| hAPP(nat,nat,suc,zero_zero(nat)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1798]) ).
fof(f1798,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( hAPP(nat,nat,suc,zero_zero(nat)) != X0
| zero_zero(nat) != X1 )
& ( zero_zero(nat) != X0
| hAPP(nat,nat,suc,zero_zero(nat)) != X1 ) ) )
& ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X0
& zero_zero(nat) = X1 )
| ( zero_zero(nat) = X0
& hAPP(nat,nat,suc,zero_zero(nat)) = X1 )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f1797]) ).
fof(f1797,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( hAPP(nat,nat,suc,zero_zero(nat)) != X1
| zero_zero(nat) != X0 )
& ( zero_zero(nat) != X1
| hAPP(nat,nat,suc,zero_zero(nat)) != X0 ) ) )
& ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X1
& zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1
& hAPP(nat,nat,suc,zero_zero(nat)) = X0 )
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f1796]) ).
fof(f1796,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( hAPP(nat,nat,suc,zero_zero(nat)) != X1
| zero_zero(nat) != X0 )
& ( zero_zero(nat) != X1
| hAPP(nat,nat,suc,zero_zero(nat)) != X0 ) ) )
& ( ( hAPP(nat,nat,suc,zero_zero(nat)) = X1
& zero_zero(nat) = X0 )
| ( zero_zero(nat) = X1
& hAPP(nat,nat,suc,zero_zero(nat)) = X0 )
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f1641]) ).
fof(f3454,plain,
spl86_57,
inference(avatar_split_clause,[],[f3042,f3452]) ).
fof(f3452,plain,
( spl86_57
<=> ! [X0,X1] :
( one_one(nat) = X1
| one_one(nat) = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_57])]) ).
fof(f3042,plain,
! [X0,X1] :
( one_one(nat) = X1
| one_one(nat) = X0
| ~ sP0(X0,X1) ),
inference(forward_demodulation,[],[f3041,f1979]) ).
fof(f3041,plain,
! [X0,X1] :
( one_one(nat) = X0
| hAPP(nat,nat,suc,zero_zero(nat)) = X1
| ~ sP0(X0,X1) ),
inference(forward_demodulation,[],[f2377,f1979]) ).
fof(f2377,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = X0
| hAPP(nat,nat,suc,zero_zero(nat)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1798]) ).
fof(f3450,plain,
spl86_56,
inference(avatar_split_clause,[],[f3040,f3448]) ).
fof(f3448,plain,
( spl86_56
<=> ! [X0,X1] :
( one_one(nat) = X0
| zero_zero(nat) = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_56])]) ).
fof(f3040,plain,
! [X0,X1] :
( one_one(nat) = X0
| zero_zero(nat) = X0
| ~ sP0(X0,X1) ),
inference(forward_demodulation,[],[f2378,f1979]) ).
fof(f2378,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,zero_zero(nat)) = X0
| zero_zero(nat) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1798]) ).
fof(f3446,plain,
spl86_55,
inference(avatar_split_clause,[],[f2384,f3444]) ).
fof(f3444,plain,
( spl86_55
<=> ! [X0,X1] :
( zero_zero(nat) = X1
| zero_zero(nat) = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_55])]) ).
fof(f2384,plain,
! [X0,X1] :
( zero_zero(nat) = X1
| zero_zero(nat) = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1802]) ).
fof(f3442,plain,
spl86_54,
inference(avatar_split_clause,[],[f2376,f3440]) ).
fof(f3440,plain,
( spl86_54
<=> ! [X0,X1] :
( zero_zero(nat) = X1
| zero_zero(nat) = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_54])]) ).
fof(f2376,plain,
! [X0,X1] :
( zero_zero(nat) = X1
| zero_zero(nat) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1798]) ).
fof(f3438,plain,
spl86_53,
inference(avatar_split_clause,[],[f2114,f3436]) ).
fof(f2114,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(X0) ),
inference(cnf_transformation,[],[f1238]) ).
fof(f1238,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(X0) ),
inference(ennf_transformation,[],[f725]) ).
fof(f725,plain,
! [X0] :
( finite_finite_1(X0)
=> ! [X1] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( finite_finite_1(X0)
=> ! [X7] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite) ).
fof(f3432,plain,
spl86_52,
inference(avatar_split_clause,[],[f2767,f3430]) ).
fof(f2767,plain,
! [X0] : undefined(X0) = hAPP(X0,X0,combi(X0),undefined(X0)),
inference(definition_unfolding,[],[f1984,f2190]) ).
fof(f1984,plain,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
inference(cnf_transformation,[],[f615]) ).
fof(f615,plain,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X2] : undefined(X2) = ti(X2,undefined(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(f3426,plain,
spl86_51,
inference(avatar_split_clause,[],[f1979,f3423]) ).
fof(f3416,plain,
spl86_50,
inference(avatar_split_clause,[],[f2755,f3414]) ).
fof(f2755,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) ),
inference(definition_unfolding,[],[f1941,f2190]) ).
fof(f1941,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ),
inference(cnf_transformation,[],[f1658]) ).
fof(f1658,plain,
! [X0] :
( ( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) )
& ( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ) ),
inference(nnf_transformation,[],[f612]) ).
fof(f612,plain,
! [X0] :
( hBOOL(ti(bool,X0))
<=> hBOOL(X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X3] :
( hBOOL(ti(bool,X3))
<=> hBOOL(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(f3412,plain,
spl86_49,
inference(avatar_split_clause,[],[f2754,f3410]) ).
fof(f2754,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,combi(bool),X0))
| ~ hBOOL(X0) ),
inference(definition_unfolding,[],[f1942,f2190]) ).
fof(f1942,plain,
! [X0] :
( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f1658]) ).
fof(f3408,plain,
spl86_48,
inference(avatar_split_clause,[],[f1935,f3405]) ).
fof(f1935,plain,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
inference(cnf_transformation,[],[f603]) ).
fof(f603,axiom,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f3402,plain,
spl86_47,
inference(avatar_split_clause,[],[f2757,f3399]) ).
fof(f2757,plain,
fFalse = hAPP(bool,bool,combi(bool),fFalse),
inference(definition_unfolding,[],[f1970,f2190]) ).
fof(f1970,plain,
fFalse = ti(bool,fFalse),
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
fFalse = ti(bool,fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
fof(f3397,plain,
spl86_46,
inference(avatar_split_clause,[],[f2756,f3394]) ).
fof(f2756,plain,
fTrue = hAPP(bool,bool,combi(bool),fTrue),
inference(definition_unfolding,[],[f1969,f2190]) ).
fof(f1969,plain,
fTrue = ti(bool,fTrue),
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
fTrue = ti(bool,fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
fof(f3392,plain,
spl86_45,
inference(avatar_split_clause,[],[f2303,f3390]) ).
fof(f3390,plain,
( spl86_45
<=> ! [X0,X1] :
( finite_finite_1(fun(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_45])]) ).
fof(f2303,plain,
! [X0,X1] :
( finite_finite_1(fun(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(cnf_transformation,[],[f1388]) ).
fof(f1388,plain,
! [X0,X1] :
( finite_finite_1(fun(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(flattening,[],[f1387]) ).
fof(f1387,plain,
! [X0,X1] :
( finite_finite_1(fun(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(ennf_transformation,[],[f885]) ).
fof(f885,plain,
! [X0,X1] :
( ( finite_finite_1(X0)
& finite_finite_1(X1) )
=> finite_finite_1(fun(X0,X1)) ),
inference(rectify,[],[f551]) ).
fof(f551,axiom,
! [X75,X76] :
( ( finite_finite_1(X75)
& finite_finite_1(X76) )
=> finite_finite_1(fun(X75,X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
fof(f3388,plain,
spl86_44,
inference(avatar_split_clause,[],[f2302,f3386]) ).
fof(f3386,plain,
( spl86_44
<=> ! [X0,X1] :
( finite_finite_1(sum_sum(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_44])]) ).
fof(f2302,plain,
! [X0,X1] :
( finite_finite_1(sum_sum(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(cnf_transformation,[],[f1386]) ).
fof(f1386,plain,
! [X0,X1] :
( finite_finite_1(sum_sum(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(flattening,[],[f1385]) ).
fof(f1385,plain,
! [X0,X1] :
( finite_finite_1(sum_sum(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(ennf_transformation,[],[f884]) ).
fof(f884,plain,
! [X0,X1] :
( ( finite_finite_1(X0)
& finite_finite_1(X1) )
=> finite_finite_1(sum_sum(X0,X1)) ),
inference(rectify,[],[f581]) ).
fof(f581,axiom,
! [X75,X76] :
( ( finite_finite_1(X75)
& finite_finite_1(X76) )
=> finite_finite_1(sum_sum(X75,X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___Finite__Set_Ofinite) ).
fof(f3384,plain,
spl86_43,
inference(avatar_split_clause,[],[f2031,f3382]) ).
fof(f2031,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(cnf_transformation,[],[f647]) ).
fof(f647,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(rectify,[],[f583]) ).
fof(f583,axiom,
! [X79] :
( ~ hBOOL(X79)
| ~ hBOOL(hAPP(bool,bool,fNot,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(f3380,plain,
spl86_42,
inference(avatar_split_clause,[],[f2029,f3378]) ).
fof(f2029,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f645]) ).
fof(f645,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f584]) ).
fof(f584,axiom,
! [X79] :
( hBOOL(hAPP(bool,bool,fNot,X79))
| hBOOL(X79) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(f3376,plain,
spl86_41,
inference(avatar_split_clause,[],[f1985,f3374]) ).
fof(f1985,plain,
! [X0] : zero_zero(nat) != hAPP(nat,nat,suc,X0),
inference(cnf_transformation,[],[f616]) ).
fof(f616,plain,
! [X0] : zero_zero(nat) != hAPP(nat,nat,suc,X0),
inference(rectify,[],[f536]) ).
fof(f536,axiom,
! [X73] : zero_zero(nat) != hAPP(nat,nat,suc,X73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_nat_Osimps_I3_J) ).
fof(f3372,plain,
spl86_40,
inference(avatar_split_clause,[],[f2749,f3369]) ).
fof(f2749,plain,
pn = hAPP(pname,pname,combi(pname),pn),
inference(definition_unfolding,[],[f1930,f2190]) ).
fof(f1930,plain,
pn = ti(pname,pn),
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
pn = ti(pname,pn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_pn_res) ).
fof(f3367,plain,
spl86_39,
inference(avatar_split_clause,[],[f2748,f3364]) ).
fof(f3364,plain,
( spl86_39
<=> na = hAPP(nat,nat,combi(nat),na) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_39])]) ).
fof(f2748,plain,
na = hAPP(nat,nat,combi(nat),na),
inference(definition_unfolding,[],[f1929,f2190]) ).
fof(f1929,plain,
na = ti(nat,na),
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
na = ti(nat,na),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_na_res) ).
fof(f3362,plain,
spl86_38,
inference(avatar_split_clause,[],[f2033,f3360]) ).
fof(f3360,plain,
( spl86_38
<=> ! [X0] :
( one_one(X0) != zero_zero(X0)
| ~ zero_neq_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_38])]) ).
fof(f2033,plain,
! [X0] :
( one_one(X0) != zero_zero(X0)
| ~ zero_neq_one(X0) ),
inference(cnf_transformation,[],[f1164]) ).
fof(f1164,plain,
! [X0] :
( one_one(X0) != zero_zero(X0)
| ~ zero_neq_one(X0) ),
inference(ennf_transformation,[],[f665]) ).
fof(f665,plain,
! [X0] :
( zero_neq_one(X0)
=> one_one(X0) != zero_zero(X0) ),
inference(rectify,[],[f510]) ).
fof(f510,axiom,
! [X2] :
( zero_neq_one(X2)
=> one_one(X2) != zero_zero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_one__neq__zero) ).
fof(f3358,plain,
spl86_37,
inference(avatar_split_clause,[],[f1982,f3356]) ).
fof(f1982,plain,
! [X0] : hAPP(nat,nat,suc,X0) != X0,
inference(cnf_transformation,[],[f613]) ).
fof(f613,plain,
! [X0] : hAPP(nat,nat,suc,X0) != X0,
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X16] : hAPP(nat,nat,suc,X16) != X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Suc__n__not__n) ).
fof(f3354,plain,
spl86_36,
inference(avatar_split_clause,[],[f2256,f3352]) ).
fof(f3352,plain,
( spl86_36
<=> ! [X0,X1] :
( order(fun(X0,X1))
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_36])]) ).
fof(f2256,plain,
! [X0,X1] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(cnf_transformation,[],[f1334]) ).
fof(f1334,plain,
! [X0,X1] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(ennf_transformation,[],[f843]) ).
fof(f843,plain,
! [X0,X1] :
( order(X1)
=> order(fun(X0,X1)) ),
inference(rectify,[],[f552]) ).
fof(f552,axiom,
! [X75,X76] :
( order(X76)
=> order(fun(X75,X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
fof(f3350,plain,
spl86_35,
inference(avatar_split_clause,[],[f2255,f3348]) ).
fof(f3348,plain,
( spl86_35
<=> ! [X0,X1] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_35])]) ).
fof(f2255,plain,
! [X0,X1] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(cnf_transformation,[],[f1333]) ).
fof(f1333,plain,
! [X0,X1] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(ennf_transformation,[],[f842]) ).
fof(f842,plain,
! [X0,X1] :
( preorder(X1)
=> preorder(fun(X0,X1)) ),
inference(rectify,[],[f550]) ).
fof(f550,axiom,
! [X75,X76] :
( preorder(X76)
=> preorder(fun(X75,X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
fof(f3346,plain,
spl86_34,
inference(avatar_split_clause,[],[f2246,f3344]) ).
fof(f3344,plain,
( spl86_34
<=> ! [X0,X1] :
( ord(fun(X0,X1))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_34])]) ).
fof(f2246,plain,
! [X0,X1] :
( ord(fun(X0,X1))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f1327]) ).
fof(f1327,plain,
! [X0,X1] :
( ord(fun(X0,X1))
| ~ ord(X1) ),
inference(ennf_transformation,[],[f836]) ).
fof(f836,plain,
! [X0,X1] :
( ord(X1)
=> ord(fun(X0,X1)) ),
inference(rectify,[],[f553]) ).
fof(f553,axiom,
! [X75,X76] :
( ord(X76)
=> ord(fun(X75,X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
fof(f3342,plain,
spl86_33,
inference(avatar_split_clause,[],[f2243,f3340]) ).
fof(f2243,plain,
! [X0,X1] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(cnf_transformation,[],[f1324]) ).
fof(f1324,plain,
! [X0,X1] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(ennf_transformation,[],[f833]) ).
fof(f833,plain,
! [X0,X1] :
( bot(X1)
=> bot(fun(X0,X1)) ),
inference(rectify,[],[f554]) ).
fof(f554,axiom,
! [X75,X76] :
( bot(X76)
=> bot(fun(X75,X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
fof(f3338,plain,
spl86_32,
inference(avatar_split_clause,[],[f2240,f3336]) ).
fof(f3336,plain,
( spl86_32
<=> ! [X0,X1] :
( minus(fun(X0,X1))
| ~ minus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_32])]) ).
fof(f2240,plain,
! [X0,X1] :
( minus(fun(X0,X1))
| ~ minus(X1) ),
inference(cnf_transformation,[],[f1321]) ).
fof(f1321,plain,
! [X0,X1] :
( minus(fun(X0,X1))
| ~ minus(X1) ),
inference(ennf_transformation,[],[f830]) ).
fof(f830,plain,
! [X0,X1] :
( minus(X1)
=> minus(fun(X0,X1)) ),
inference(rectify,[],[f555]) ).
fof(f555,axiom,
! [X75,X76] :
( minus(X76)
=> minus(fun(X75,X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
fof(f3334,plain,
spl86_31,
inference(avatar_split_clause,[],[f3047,f3331]) ).
fof(f3331,plain,
( spl86_31
<=> sP1(zero_zero(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_31])]) ).
fof(f3047,plain,
sP1(zero_zero(nat),one_one(nat)),
inference(forward_demodulation,[],[f2995,f1979]) ).
fof(f2995,plain,
sP1(zero_zero(nat),hAPP(nat,nat,suc,zero_zero(nat))),
inference(equality_resolution,[],[f2994]) ).
fof(f2994,plain,
! [X1] :
( sP1(zero_zero(nat),X1)
| hAPP(nat,nat,suc,zero_zero(nat)) != X1 ),
inference(equality_resolution,[],[f2387]) ).
fof(f2387,plain,
! [X0,X1] :
( sP1(X0,X1)
| zero_zero(nat) != X0
| hAPP(nat,nat,suc,zero_zero(nat)) != X1 ),
inference(cnf_transformation,[],[f1802]) ).
fof(f3329,plain,
spl86_30,
inference(avatar_split_clause,[],[f3046,f3326]) ).
fof(f3326,plain,
( spl86_30
<=> sP1(one_one(nat),zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_30])]) ).
fof(f3046,plain,
sP1(one_one(nat),zero_zero(nat)),
inference(forward_demodulation,[],[f2993,f1979]) ).
fof(f2993,plain,
sP1(hAPP(nat,nat,suc,zero_zero(nat)),zero_zero(nat)),
inference(equality_resolution,[],[f2992]) ).
fof(f2992,plain,
! [X1] :
( sP1(hAPP(nat,nat,suc,zero_zero(nat)),X1)
| zero_zero(nat) != X1 ),
inference(equality_resolution,[],[f2388]) ).
fof(f2388,plain,
! [X0,X1] :
( sP1(X0,X1)
| hAPP(nat,nat,suc,zero_zero(nat)) != X0
| zero_zero(nat) != X1 ),
inference(cnf_transformation,[],[f1802]) ).
fof(f3324,plain,
spl86_29,
inference(avatar_split_clause,[],[f3039,f3321]) ).
fof(f3321,plain,
( spl86_29
<=> sP0(zero_zero(nat),one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_29])]) ).
fof(f3039,plain,
sP0(zero_zero(nat),one_one(nat)),
inference(forward_demodulation,[],[f2991,f1979]) ).
fof(f2991,plain,
sP0(zero_zero(nat),hAPP(nat,nat,suc,zero_zero(nat))),
inference(equality_resolution,[],[f2990]) ).
fof(f2990,plain,
! [X1] :
( sP0(zero_zero(nat),X1)
| hAPP(nat,nat,suc,zero_zero(nat)) != X1 ),
inference(equality_resolution,[],[f2379]) ).
fof(f2379,plain,
! [X0,X1] :
( sP0(X0,X1)
| zero_zero(nat) != X0
| hAPP(nat,nat,suc,zero_zero(nat)) != X1 ),
inference(cnf_transformation,[],[f1798]) ).
fof(f3319,plain,
spl86_28,
inference(avatar_split_clause,[],[f3038,f3316]) ).
fof(f3316,plain,
( spl86_28
<=> sP0(one_one(nat),zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_28])]) ).
fof(f3038,plain,
sP0(one_one(nat),zero_zero(nat)),
inference(forward_demodulation,[],[f2989,f1979]) ).
fof(f2989,plain,
sP0(hAPP(nat,nat,suc,zero_zero(nat)),zero_zero(nat)),
inference(equality_resolution,[],[f2988]) ).
fof(f2988,plain,
! [X1] :
( sP0(hAPP(nat,nat,suc,zero_zero(nat)),X1)
| zero_zero(nat) != X1 ),
inference(equality_resolution,[],[f2380]) ).
fof(f2380,plain,
! [X0,X1] :
( sP0(X0,X1)
| hAPP(nat,nat,suc,zero_zero(nat)) != X0
| zero_zero(nat) != X1 ),
inference(cnf_transformation,[],[f1798]) ).
fof(f3314,plain,
spl86_27,
inference(avatar_split_clause,[],[f1971,f3311]) ).
fof(f1971,plain,
zero_zero(nat) = bot_bot(nat),
inference(cnf_transformation,[],[f541]) ).
fof(f541,axiom,
zero_zero(nat) = bot_bot(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_bot__nat__def) ).
fof(f3309,plain,
spl86_26,
inference(avatar_split_clause,[],[f1968,f3306]) ).
fof(f3306,plain,
( spl86_26
<=> order(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_26])]) ).
fof(f1968,plain,
order(bool),
inference(cnf_transformation,[],[f577]) ).
fof(f577,axiom,
order(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
fof(f3304,plain,
spl86_25,
inference(avatar_split_clause,[],[f1967,f3301]) ).
fof(f3301,plain,
( spl86_25
<=> order(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_25])]) ).
fof(f1967,plain,
order(nat),
inference(cnf_transformation,[],[f569]) ).
fof(f569,axiom,
order(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
fof(f3299,plain,
spl86_24,
inference(avatar_split_clause,[],[f1966,f3296]) ).
fof(f3296,plain,
( spl86_24
<=> preorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_24])]) ).
fof(f1966,plain,
preorder(bool),
inference(cnf_transformation,[],[f575]) ).
fof(f575,axiom,
preorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
fof(f3294,plain,
spl86_23,
inference(avatar_split_clause,[],[f1965,f3291]) ).
fof(f3291,plain,
( spl86_23
<=> preorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_23])]) ).
fof(f1965,plain,
preorder(nat),
inference(cnf_transformation,[],[f566]) ).
fof(f566,axiom,
preorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
fof(f3289,plain,
spl86_22,
inference(avatar_split_clause,[],[f1964,f3286]) ).
fof(f1964,plain,
ord(bool),
inference(cnf_transformation,[],[f578]) ).
fof(f578,axiom,
ord(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
fof(f3284,plain,
spl86_21,
inference(avatar_split_clause,[],[f1963,f3281]) ).
fof(f3281,plain,
( spl86_21
<=> ord(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_21])]) ).
fof(f1963,plain,
ord(nat),
inference(cnf_transformation,[],[f570]) ).
fof(f570,axiom,
ord(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
fof(f3279,plain,
spl86_20,
inference(avatar_split_clause,[],[f1962,f3276]) ).
fof(f1962,plain,
bot(bool),
inference(cnf_transformation,[],[f579]) ).
fof(f579,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
fof(f3274,plain,
spl86_19,
inference(avatar_split_clause,[],[f1961,f3271]) ).
fof(f1961,plain,
bot(nat),
inference(cnf_transformation,[],[f571]) ).
fof(f571,axiom,
bot(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
fof(f3269,plain,
spl86_18,
inference(avatar_split_clause,[],[f1960,f3266]) ).
fof(f1960,plain,
finite_finite_1(bool),
inference(cnf_transformation,[],[f576]) ).
fof(f576,axiom,
finite_finite_1(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
fof(f3264,plain,
spl86_17,
inference(avatar_split_clause,[],[f1959,f3261]) ).
fof(f3261,plain,
( spl86_17
<=> minus(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_17])]) ).
fof(f1959,plain,
minus(bool),
inference(cnf_transformation,[],[f580]) ).
fof(f580,axiom,
minus(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
fof(f3259,plain,
spl86_16,
inference(avatar_split_clause,[],[f1958,f3256]) ).
fof(f3256,plain,
( spl86_16
<=> minus(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_16])]) ).
fof(f1958,plain,
minus(nat),
inference(cnf_transformation,[],[f572]) ).
fof(f572,axiom,
minus(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ominus) ).
fof(f3254,plain,
spl86_15,
inference(avatar_split_clause,[],[f1957,f3251]) ).
fof(f3251,plain,
( spl86_15
<=> linorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_15])]) ).
fof(f1957,plain,
linorder(nat),
inference(cnf_transformation,[],[f567]) ).
fof(f567,axiom,
linorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
fof(f3249,plain,
spl86_14,
inference(avatar_split_clause,[],[f1956,f3246]) ).
fof(f3246,plain,
( spl86_14
<=> ordere236663937imp_le(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_14])]) ).
fof(f1956,plain,
ordere236663937imp_le(nat),
inference(cnf_transformation,[],[f557]) ).
fof(f557,axiom,
ordere236663937imp_le(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f3244,plain,
spl86_13,
inference(avatar_split_clause,[],[f1955,f3241]) ).
fof(f1955,plain,
linordered_semidom(nat),
inference(cnf_transformation,[],[f562]) ).
fof(f562,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
fof(f3239,plain,
spl86_12,
inference(avatar_split_clause,[],[f1954,f3236]) ).
fof(f3236,plain,
( spl86_12
<=> ordere223160158up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_12])]) ).
fof(f1954,plain,
ordere223160158up_add(nat),
inference(cnf_transformation,[],[f556]) ).
fof(f556,axiom,
ordere223160158up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f3234,plain,
spl86_11,
inference(avatar_split_clause,[],[f1953,f3231]) ).
fof(f3231,plain,
( spl86_11
<=> ordere216010020id_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_11])]) ).
fof(f1953,plain,
ordere216010020id_add(nat),
inference(cnf_transformation,[],[f559]) ).
fof(f559,axiom,
ordere216010020id_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
fof(f3229,plain,
spl86_10,
inference(avatar_split_clause,[],[f1952,f3226]) ).
fof(f3226,plain,
( spl86_10
<=> cancel_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_10])]) ).
fof(f1952,plain,
cancel_semigroup_add(nat),
inference(cnf_transformation,[],[f561]) ).
fof(f561,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
fof(f3224,plain,
spl86_9,
inference(avatar_split_clause,[],[f1951,f3221]) ).
fof(f3221,plain,
( spl86_9
<=> ordere779506340up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_9])]) ).
fof(f1951,plain,
ordere779506340up_add(nat),
inference(cnf_transformation,[],[f558]) ).
fof(f558,axiom,
ordere779506340up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
fof(f3219,plain,
spl86_8,
inference(avatar_split_clause,[],[f1950,f3216]) ).
fof(f3216,plain,
( spl86_8
<=> monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_8])]) ).
fof(f1950,plain,
monoid_add(nat),
inference(cnf_transformation,[],[f568]) ).
fof(f568,axiom,
monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
fof(f3214,plain,
spl86_7,
inference(avatar_split_clause,[],[f1949,f3211]) ).
fof(f1949,plain,
comm_monoid_add(nat),
inference(cnf_transformation,[],[f564]) ).
fof(f564,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
fof(f3209,plain,
spl86_6,
inference(avatar_split_clause,[],[f1948,f3206]) ).
fof(f1948,plain,
zero(nat),
inference(cnf_transformation,[],[f573]) ).
fof(f573,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
fof(f3204,plain,
spl86_5,
inference(avatar_split_clause,[],[f1947,f3201]) ).
fof(f1947,plain,
one(nat),
inference(cnf_transformation,[],[f574]) ).
fof(f574,axiom,
one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
fof(f3199,plain,
spl86_4,
inference(avatar_split_clause,[],[f1946,f3196]) ).
fof(f1946,plain,
ab_semigroup_add(nat),
inference(cnf_transformation,[],[f563]) ).
fof(f563,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
fof(f3194,plain,
spl86_3,
inference(avatar_split_clause,[],[f1945,f3191]) ).
fof(f3191,plain,
( spl86_3
<=> zero_neq_one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_3])]) ).
fof(f1945,plain,
zero_neq_one(nat),
inference(cnf_transformation,[],[f565]) ).
fof(f565,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
fof(f3189,plain,
spl86_2,
inference(avatar_split_clause,[],[f1944,f3186]) ).
fof(f3186,plain,
( spl86_2
<=> cancel146912293up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl86_2])]) ).
fof(f1944,plain,
cancel146912293up_add(nat),
inference(cnf_transformation,[],[f560]) ).
fof(f560,axiom,
cancel146912293up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
fof(f3184,plain,
~ spl86_1,
inference(avatar_split_clause,[],[f1943,f3181]) ).
fof(f1943,plain,
~ hBOOL(fFalse),
inference(cnf_transformation,[],[f596]) ).
fof(f596,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW473+6 : TPTP v8.1.2. Released v5.3.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n027.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 19:26:08 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % (25544)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.46 % (25547)WARNING: value z3 for option sas not known
% 0.22/0.47 % (25545)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.47 % (25546)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.47 % (25548)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.47 % (25547)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)
% 0.22/0.47 % (25549)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)
% 0.22/0.47 % (25550)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)
% 0.22/0.47 % (25551)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)
% 7.85/1.54 TRYING [1]
% 7.85/1.63 TRYING [2]
% 14.46/2.49 TRYING [1]
% 14.70/2.58 TRYING [2]
% 19.04/3.14 TRYING [3]
% 21.29/3.47 % (25549)First to succeed.
% 21.88/3.56 % (25549)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25544"
% 21.88/3.57 % (25549)Refutation found. Thanks to Tanya!
% 21.88/3.57 % SZS status Theorem for theBenchmark
% 21.88/3.57 % SZS output start Proof for theBenchmark
% See solution above
% 22.16/3.59 % (25549)------------------------------
% 22.16/3.59 % (25549)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 22.16/3.59 % (25549)Termination reason: Refutation
% 22.16/3.59
% 22.16/3.59 % (25549)Memory used [KB]: 26258
% 22.16/3.59 % (25549)Time elapsed: 3.098 s
% 22.16/3.59 % (25549)Instructions burned: 10246 (million)
% 22.16/3.59 % (25544)Success in time 3.14 s
%------------------------------------------------------------------------------