TSTP Solution File: SWW473+5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW473+5 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:33:47 EDT 2024
% Result : Theorem 2.58s 0.73s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 378
% Syntax : Number of formulae : 1188 ( 360 unt; 0 def)
% Number of atoms : 2794 ( 522 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2650 (1044 ~;1067 |; 98 &)
% ( 260 <=>; 181 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 228 ( 226 usr; 223 prp; 0-2 aty)
% Number of functors : 45 ( 45 usr; 15 con; 0-5 aty)
% Number of variables : 2490 (2443 !; 47 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4304,plain,
$false,
inference(avatar_sat_refutation,[],[f740,f745,f750,f755,f760,f764,f768,f772,f777,f782,f786,f790,f794,f800,f804,f808,f813,f819,f823,f828,f833,f838,f843,f847,f851,f855,f859,f863,f867,f871,f876,f881,f885,f889,f893,f897,f901,f905,f963,f967,f972,f976,f985,f990,f995,f1007,f1011,f1020,f1025,f1029,f1033,f1037,f1041,f1053,f1057,f1061,f1096,f1100,f1104,f1108,f1121,f1129,f1133,f1137,f1209,f1213,f1217,f1232,f1236,f1249,f1253,f1257,f1261,f1265,f1310,f1321,f1328,f1338,f1342,f1347,f1351,f1355,f1409,f1420,f1431,f1435,f1439,f1443,f1467,f1471,f1475,f1479,f1592,f1596,f1600,f1631,f1636,f1641,f1645,f1649,f1673,f1678,f1682,f1703,f1707,f1726,f1732,f1739,f1743,f1747,f1786,f1791,f1798,f1803,f1814,f1818,f1941,f1972,f1976,f1984,f2041,f2108,f2119,f2133,f2138,f2151,f2179,f2183,f2187,f2249,f2253,f2285,f2289,f2315,f2339,f2343,f2482,f2486,f2490,f2494,f2498,f2502,f2507,f2584,f2602,f2606,f2645,f2649,f2727,f2731,f2735,f2758,f2792,f2927,f2931,f2970,f3029,f3070,f3075,f3081,f3085,f3089,f3093,f3112,f3179,f3239,f3267,f3293,f3328,f3347,f3532,f3562,f3568,f3576,f3580,f3586,f3594,f3600,f3609,f3615,f3624,f3628,f3714,f3718,f3769,f3785,f3792,f3823,f3843,f3848,f3869,f3874,f3925,f3929,f3933,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f4016,f4020,f4033,f4084,f4089,f4094,f4098,f4103,f4108,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4212,f4292,f4302,f4303]) ).
fof(f4303,plain,
( ~ spl13_41
| ~ spl13_136
| spl13_221 ),
inference(avatar_split_clause,[],[f4293,f4289,f2341,f969]) ).
fof(f969,plain,
( spl13_41
<=> hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).
fof(f2341,plain,
( spl13_136
<=> ! [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,[spl13_136])]) ).
fof(f4289,plain,
( spl13_221
<=> 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,[spl13_221])]) ).
fof(f4293,plain,
( ~ hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| ~ spl13_136
| spl13_221 ),
inference(resolution,[],[f4291,f2342]) ).
fof(f2342,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)) )
| ~ spl13_136 ),
inference(avatar_component_clause,[],[f2341]) ).
fof(f4291,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)))
| spl13_221 ),
inference(avatar_component_clause,[],[f4289]) ).
fof(f4302,plain,
( spl13_222
| ~ spl13_41
| ~ spl13_85
| ~ spl13_120 ),
inference(avatar_split_clause,[],[f2032,f1982,f1428,f969,f4299]) ).
fof(f4299,plain,
( spl13_222
<=> 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,[spl13_222])]) ).
fof(f1428,plain,
( spl13_85
<=> u = hAPP(fun(pname,bool),fun(pname,bool),collect(pname),u) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_85])]) ).
fof(f1982,plain,
( spl13_120
<=> ! [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,[spl13_120])]) ).
fof(f2032,plain,
( u = hAPP(fun(pname,bool),fun(pname,bool),hAPP(pname,fun(fun(pname,bool),fun(pname,bool)),insert(pname),pn),u)
| ~ spl13_41
| ~ spl13_85
| ~ spl13_120 ),
inference(forward_demodulation,[],[f2027,f1430]) ).
fof(f1430,plain,
( u = hAPP(fun(pname,bool),fun(pname,bool),collect(pname),u)
| ~ spl13_85 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f2027,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)
| ~ spl13_41
| ~ spl13_120 ),
inference(resolution,[],[f1983,f971]) ).
fof(f971,plain,
( hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u))
| ~ spl13_41 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f1983,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) )
| ~ spl13_120 ),
inference(avatar_component_clause,[],[f1982]) ).
fof(f4292,plain,
( ~ spl13_221
| ~ spl13_106
| spl13_39
| ~ spl13_161 ),
inference(avatar_split_clause,[],[f3113,f3083,f960,f1723,f4289]) ).
fof(f1723,plain,
( spl13_106
<=> 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,[spl13_106])]) ).
fof(f960,plain,
( spl13_39
<=> 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,[spl13_39])]) ).
fof(f3083,plain,
( spl13_161
<=> ! [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,[spl13_161])]) ).
fof(f3113,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)))
| spl13_39
| ~ spl13_161 ),
inference(resolution,[],[f3084,f962]) ).
fof(f962,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)))
| spl13_39 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f3084,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)) )
| ~ spl13_161 ),
inference(avatar_component_clause,[],[f3083]) ).
fof(f4212,plain,
( spl13_220
| ~ spl13_63
| ~ spl13_205 ),
inference(avatar_split_clause,[],[f4142,f4031,f1131,f4210]) ).
fof(f4210,plain,
( spl13_220
<=> ! [X0,X1] :
( X0 != X1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_220])]) ).
fof(f1131,plain,
( spl13_63
<=> ! [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,[spl13_63])]) ).
fof(f4031,plain,
( spl13_205
<=> ! [X0] : hAPP(nat,nat,combi(nat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_205])]) ).
fof(f4142,plain,
( ! [X0,X1] :
( X0 != X1
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),X0),X1)) )
| ~ spl13_63
| ~ spl13_205 ),
inference(forward_demodulation,[],[f4120,f4032]) ).
fof(f4032,plain,
( ! [X0] : hAPP(nat,nat,combi(nat),X0) = X0
| ~ spl13_205 ),
inference(avatar_component_clause,[],[f4031]) ).
fof(f4120,plain,
( ! [X0,X1] :
( hAPP(nat,nat,combi(nat),X1) != X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),X0),X1)) )
| ~ spl13_63
| ~ spl13_205 ),
inference(superposition,[],[f1132,f4032]) ).
fof(f1132,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)) )
| ~ spl13_63 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f4200,plain,
( spl13_219
| ~ spl13_61
| ~ spl13_72 ),
inference(avatar_split_clause,[],[f1284,f1255,f1119,f4198]) ).
fof(f4198,plain,
( spl13_219
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| hAPP(nat,nat,suc,sK3(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_219])]) ).
fof(f1119,plain,
( spl13_61
<=> ! [X0,X1] :
( hAPP(nat,nat,suc,sK3(X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_61])]) ).
fof(f1255,plain,
( spl13_72
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).
fof(f1284,plain,
( ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1))
| hAPP(nat,nat,suc,sK3(X0)) = X0 )
| ~ spl13_61
| ~ spl13_72 ),
inference(resolution,[],[f1256,f1120]) ).
fof(f1120,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1))
| hAPP(nat,nat,suc,sK3(X1)) = X1 )
| ~ spl13_61 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f1256,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)) )
| ~ spl13_72 ),
inference(avatar_component_clause,[],[f1255]) ).
fof(f4196,plain,
( spl13_218
| ~ spl13_42
| ~ spl13_70 ),
inference(avatar_split_clause,[],[f1266,f1247,f974,f4194]) ).
fof(f4194,plain,
( spl13_218
<=> ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,X0))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_218])]) ).
fof(f974,plain,
( spl13_42
<=> ! [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,[spl13_42])]) ).
fof(f1247,plain,
( spl13_70
<=> ! [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,[spl13_70])]) ).
fof(f1266,plain,
( ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,X0))),X0))
| ~ spl13_42
| ~ spl13_70 ),
inference(resolution,[],[f1248,f975]) ).
fof(f975,plain,
( ! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X0))
| ~ spl13_42 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f1248,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)) )
| ~ spl13_70 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f4192,plain,
( spl13_217
| ~ spl13_33
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f947,f903,f883,f4190]) ).
fof(f4190,plain,
( spl13_217
<=> ! [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,[spl13_217])]) ).
fof(f883,plain,
( spl13_33
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).
fof(f903,plain,
( spl13_38
<=> ! [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,[spl13_38])]) ).
fof(f947,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1))
| ~ hBOOL(X0) )
| ~ spl13_33
| ~ spl13_38 ),
inference(superposition,[],[f884,f904]) ).
fof(f904,plain,
( ! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,hAPP(X0,X0,combi(X0),X3))
| ~ spl13_38 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f884,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) )
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f4188,plain,
( spl13_216
| ~ spl13_35
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f944,f903,f891,f4186]) ).
fof(f4186,plain,
( spl13_216
<=> ! [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,[spl13_216])]) ).
fof(f891,plain,
( spl13_35
<=> ! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).
fof(f944,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(X0)
| hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl13_35
| ~ spl13_38 ),
inference(superposition,[],[f892,f904]) ).
fof(f892,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(X0)
| hBOOL(X1) )
| ~ spl13_35 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f4184,plain,
( spl13_215
| ~ spl13_34
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f941,f903,f887,f4182]) ).
fof(f4182,plain,
( spl13_215
<=> ! [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,[spl13_215])]) ).
fof(f887,plain,
( spl13_34
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).
fof(f941,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X0)
| hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl13_34
| ~ spl13_38 ),
inference(superposition,[],[f888,f904]) ).
fof(f888,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X0)
| hBOOL(X1) )
| ~ spl13_34 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f4180,plain,
( spl13_214
| ~ spl13_33
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f938,f903,f883,f4178]) ).
fof(f4178,plain,
( spl13_214
<=> ! [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,[spl13_214])]) ).
fof(f938,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl13_33
| ~ spl13_38 ),
inference(superposition,[],[f884,f904]) ).
fof(f4176,plain,
( spl13_213
| ~ spl13_35
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f935,f903,f891,f4174]) ).
fof(f4174,plain,
( spl13_213
<=> ! [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,[spl13_213])]) ).
fof(f935,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0))
| hBOOL(X1) )
| ~ spl13_35
| ~ spl13_38 ),
inference(superposition,[],[f892,f904]) ).
fof(f4172,plain,
( spl13_212
| ~ spl13_34
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f932,f903,f887,f4170]) ).
fof(f4170,plain,
( spl13_212
<=> ! [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,[spl13_212])]) ).
fof(f932,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0))
| hBOOL(X1) )
| ~ spl13_34
| ~ spl13_38 ),
inference(superposition,[],[f888,f904]) ).
fof(f4108,plain,
( spl13_211
| ~ spl13_10
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f1189,f1131,f779,f4106]) ).
fof(f4106,plain,
( spl13_211
<=> ! [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,[spl13_211])]) ).
fof(f779,plain,
( spl13_10
<=> pn = hAPP(pname,pname,combi(pname),pn) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).
fof(f1189,plain,
( ! [X0] :
( pn != hAPP(pname,pname,combi(pname),X0)
| hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),fequal(pname),X0),pn)) )
| ~ spl13_10
| ~ spl13_63 ),
inference(superposition,[],[f1132,f781]) ).
fof(f781,plain,
( pn = hAPP(pname,pname,combi(pname),pn)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f4103,plain,
( spl13_210
| ~ spl13_205
| ~ spl13_209 ),
inference(avatar_split_clause,[],[f4099,f4096,f4031,f4101]) ).
fof(f4101,plain,
( spl13_210
<=> ! [X0] :
( na != X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),X0),na)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_210])]) ).
fof(f4096,plain,
( spl13_209
<=> ! [X0] :
( na != hAPP(nat,nat,combi(nat),X0)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),X0),na)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_209])]) ).
fof(f4099,plain,
( ! [X0] :
( na != X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),X0),na)) )
| ~ spl13_205
| ~ spl13_209 ),
inference(forward_demodulation,[],[f4097,f4032]) ).
fof(f4097,plain,
( ! [X0] :
( na != hAPP(nat,nat,combi(nat),X0)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),X0),na)) )
| ~ spl13_209 ),
inference(avatar_component_clause,[],[f4096]) ).
fof(f4098,plain,
( spl13_209
| ~ spl13_9
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f1188,f1131,f774,f4096]) ).
fof(f774,plain,
( spl13_9
<=> na = hAPP(nat,nat,combi(nat),na) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
fof(f1188,plain,
( ! [X0] :
( na != hAPP(nat,nat,combi(nat),X0)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),X0),na)) )
| ~ spl13_9
| ~ spl13_63 ),
inference(superposition,[],[f1132,f776]) ).
fof(f776,plain,
( na = hAPP(nat,nat,combi(nat),na)
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f4094,plain,
( spl13_208
| ~ spl13_10
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f1170,f1131,f779,f4092]) ).
fof(f4092,plain,
( spl13_208
<=> ! [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,[spl13_208])]) ).
fof(f1170,plain,
( ! [X0] :
( pn != hAPP(pname,pname,combi(pname),X0)
| hBOOL(hAPP(pname,bool,hAPP(pname,fun(pname,bool),fequal(pname),pn),X0)) )
| ~ spl13_10
| ~ spl13_63 ),
inference(superposition,[],[f1132,f781]) ).
fof(f4089,plain,
( spl13_207
| ~ spl13_205
| ~ spl13_206 ),
inference(avatar_split_clause,[],[f4085,f4082,f4031,f4087]) ).
fof(f4087,plain,
( spl13_207
<=> ! [X0] :
( na != X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),na),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_207])]) ).
fof(f4082,plain,
( spl13_206
<=> ! [X0] :
( na != hAPP(nat,nat,combi(nat),X0)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),na),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_206])]) ).
fof(f4085,plain,
( ! [X0] :
( na != X0
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),na),X0)) )
| ~ spl13_205
| ~ spl13_206 ),
inference(forward_demodulation,[],[f4083,f4032]) ).
fof(f4083,plain,
( ! [X0] :
( na != hAPP(nat,nat,combi(nat),X0)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),na),X0)) )
| ~ spl13_206 ),
inference(avatar_component_clause,[],[f4082]) ).
fof(f4084,plain,
( spl13_206
| ~ spl13_9
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f1169,f1131,f774,f4082]) ).
fof(f1169,plain,
( ! [X0] :
( na != hAPP(nat,nat,combi(nat),X0)
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),fequal(nat),na),X0)) )
| ~ spl13_9
| ~ spl13_63 ),
inference(superposition,[],[f1132,f776]) ).
fof(f4033,plain,
( spl13_205
| ~ spl13_202 ),
inference(avatar_split_clause,[],[f4012,f3972,f4031]) ).
fof(f3972,plain,
( spl13_202
<=> ! [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,[spl13_202])]) ).
fof(f4012,plain,
( ! [X0] : hAPP(nat,nat,combi(nat),X0) = X0
| ~ spl13_202 ),
inference(equality_resolution,[],[f3973]) ).
fof(f3973,plain,
( ! [X0,X1] :
( hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1)
| hAPP(nat,nat,combi(nat),X0) = X1 )
| ~ spl13_202 ),
inference(avatar_component_clause,[],[f3972]) ).
fof(f4020,plain,
( spl13_204
| ~ spl13_52
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f1086,f1059,f1035,f4018]) ).
fof(f4018,plain,
( spl13_204
<=> ! [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,[spl13_204])]) ).
fof(f1035,plain,
( spl13_52
<=> ! [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,[spl13_52])]) ).
fof(f1059,plain,
( spl13_56
<=> ! [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,[spl13_56])]) ).
fof(f1086,plain,
( ! [X2,X0,X1] : hAPP(X0,bool,X1,X2) = hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1),X2)
| ~ spl13_52
| ~ spl13_56 ),
inference(superposition,[],[f1036,f1060]) ).
fof(f1060,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)
| ~ spl13_56 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f1036,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)
| ~ spl13_52 ),
inference(avatar_component_clause,[],[f1035]) ).
fof(f4016,plain,
( spl13_203
| ~ spl13_51
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f1074,f1059,f1031,f4014]) ).
fof(f4014,plain,
( spl13_203
<=> ! [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,[spl13_203])]) ).
fof(f1031,plain,
( spl13_51
<=> ! [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,[spl13_51])]) ).
fof(f1074,plain,
( ! [X0] : finite_finite(X0) = hAPP(fun(fun(X0,bool),bool),fun(fun(X0,bool),bool),collect(fun(X0,bool)),finite_finite(X0))
| ~ spl13_51
| ~ spl13_56 ),
inference(superposition,[],[f1060,f1032]) ).
fof(f1032,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))
| ~ spl13_51 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f3974,plain,
( spl13_202
| ~ spl13_30
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f950,f903,f869,f3972]) ).
fof(f869,plain,
( spl13_30
<=> ! [X0,X1] :
( X0 = X1
| hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).
fof(f950,plain,
( ! [X0,X1] :
( hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1)
| hAPP(nat,nat,combi(nat),X0) = X1 )
| ~ spl13_30
| ~ spl13_38 ),
inference(superposition,[],[f870,f904]) ).
fof(f870,plain,
( ! [X0,X1] :
( hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1)
| X0 = X1 )
| ~ spl13_30 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f3970,plain,
( spl13_201
| ~ spl13_28
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f949,f903,f861,f3968]) ).
fof(f3968,plain,
( spl13_201
<=> ! [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,[spl13_201])]) ).
fof(f861,plain,
( spl13_28
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).
fof(f949,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl13_28
| ~ spl13_38 ),
inference(superposition,[],[f862,f904]) ).
fof(f862,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(X1) )
| ~ spl13_28 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f3966,plain,
( spl13_200
| ~ spl13_25
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f946,f903,f849,f3964]) ).
fof(f3964,plain,
( spl13_200
<=> ! [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,[spl13_200])]) ).
fof(f849,plain,
( spl13_25
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).
fof(f946,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl13_25
| ~ spl13_38 ),
inference(superposition,[],[f850,f904]) ).
fof(f850,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(X1) )
| ~ spl13_25 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f3962,plain,
( spl13_199
| ~ spl13_24
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f943,f903,f845,f3960]) ).
fof(f3960,plain,
( spl13_199
<=> ! [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,[spl13_199])]) ).
fof(f845,plain,
( spl13_24
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).
fof(f943,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X1)) )
| ~ spl13_24
| ~ spl13_38 ),
inference(superposition,[],[f846,f904]) ).
fof(f846,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X1) )
| ~ spl13_24 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f3958,plain,
( spl13_198
| ~ spl13_29
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f939,f903,f865,f3956]) ).
fof(f3956,plain,
( spl13_198
<=> ! [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,[spl13_198])]) ).
fof(f865,plain,
( spl13_29
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).
fof(f939,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl13_29
| ~ spl13_38 ),
inference(superposition,[],[f866,f904]) ).
fof(f866,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1))
| hBOOL(X0) )
| ~ spl13_29 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f3954,plain,
( spl13_197
| ~ spl13_26
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f936,f903,f853,f3952]) ).
fof(f3952,plain,
( spl13_197
<=> ! [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,[spl13_197])]) ).
fof(f853,plain,
( spl13_26
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).
fof(f936,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl13_26
| ~ spl13_38 ),
inference(superposition,[],[f854,f904]) ).
fof(f854,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X0))
| ~ hBOOL(X1) )
| ~ spl13_26 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f3950,plain,
( spl13_196
| ~ spl13_27
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f933,f903,f857,f3948]) ).
fof(f3948,plain,
( spl13_196
<=> ! [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,[spl13_196])]) ).
fof(f857,plain,
( spl13_27
<=> ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).
fof(f933,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl13_27
| ~ spl13_38 ),
inference(superposition,[],[f858,f904]) ).
fof(f858,plain,
( ! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X0))
| hBOOL(X1) )
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f857]) ).
fof(f3933,plain,
( spl13_195
| ~ spl13_47
| ~ spl13_93 ),
inference(avatar_split_clause,[],[f1601,f1590,f1009,f3931]) ).
fof(f3931,plain,
( spl13_195
<=> ! [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,[spl13_195])]) ).
fof(f1009,plain,
( spl13_47
<=> ! [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,[spl13_47])]) ).
fof(f1590,plain,
( spl13_93
<=> ! [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,[spl13_93])]) ).
fof(f1601,plain,
( ! [X0] : hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),p,X0),X0))
| ~ spl13_47
| ~ spl13_93 ),
inference(resolution,[],[f1591,f1010]) ).
fof(f1010,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))
| ~ spl13_47 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f1591,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)) )
| ~ spl13_93 ),
inference(avatar_component_clause,[],[f1590]) ).
fof(f3929,plain,
( spl13_194
| ~ spl13_17
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f1078,f1059,f811,f3927]) ).
fof(f3927,plain,
( spl13_194
<=> ! [X0] : undefined(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),undefined(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_194])]) ).
fof(f811,plain,
( spl13_17
<=> ! [X0] : undefined(X0) = hAPP(X0,X0,combi(X0),undefined(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).
fof(f1078,plain,
( ! [X0] : undefined(fun(X0,bool)) = hAPP(fun(X0,bool),fun(X0,bool),collect(X0),undefined(fun(X0,bool)))
| ~ spl13_17
| ~ spl13_56 ),
inference(superposition,[],[f1060,f812]) ).
fof(f812,plain,
( ! [X0] : undefined(X0) = hAPP(X0,X0,combi(X0),undefined(X0))
| ~ spl13_17 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f3925,plain,
( ~ spl13_14
| spl13_193
| ~ spl13_106
| ~ spl13_140 ),
inference(avatar_split_clause,[],[f2542,f2492,f1723,f3922,f797]) ).
fof(f797,plain,
( spl13_14
<=> hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).
fof(f3922,plain,
( spl13_193
<=> hBOOL(hAPP(fun(x_a,bool),bool,finite_finite(x_a),g)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_193])]) ).
fof(f2492,plain,
( spl13_140
<=> ! [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,[spl13_140])]) ).
fof(f2542,plain,
( hBOOL(hAPP(fun(x_a,bool),bool,finite_finite(x_a),g))
| ~ hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u))
| ~ spl13_106
| ~ spl13_140 ),
inference(resolution,[],[f2493,f1725]) ).
fof(f1725,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)))
| ~ spl13_106 ),
inference(avatar_component_clause,[],[f1723]) ).
fof(f2493,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)) )
| ~ spl13_140 ),
inference(avatar_component_clause,[],[f2492]) ).
fof(f3874,plain,
( spl13_192
| ~ spl13_38
| ~ spl13_56
| ~ spl13_191 ),
inference(avatar_split_clause,[],[f3870,f3867,f1059,f903,f3872]) ).
fof(f3872,plain,
( spl13_192
<=> ! [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,sK6(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,[spl13_192])]) ).
fof(f3867,plain,
( spl13_191
<=> ! [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,sK6(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,[spl13_191])]) ).
fof(f3870,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,sK6(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)) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_191 ),
inference(forward_demodulation,[],[f3868,f1089]) ).
fof(f1089,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))
| ~ spl13_38
| ~ spl13_56 ),
inference(superposition,[],[f904,f1060]) ).
fof(f3868,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,sK6(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)) )
| ~ spl13_191 ),
inference(avatar_component_clause,[],[f3867]) ).
fof(f3869,plain,
spl13_191,
inference(avatar_split_clause,[],[f590,f3867]) ).
fof(f590,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,sK6(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,[],[f417]) ).
fof(f417,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,sK6(X0,X1,X2,X3)))))))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK6(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,[sK6])],[f353,f416]) ).
fof(f416,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,sK6(X0,X1,X2,X3)))))))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK6(X0,X1,X2,X3)),X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f353,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,[],[f352]) ).
fof(f352,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,[],[f260]) ).
fof(f260,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,[],[f79]) ).
fof(f79,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/sandbox2/benchmark/theBenchmark.p',fact_49_pigeonhole__infinite) ).
fof(f3848,plain,
( spl13_190
| ~ spl13_38
| ~ spl13_56
| ~ spl13_189 ),
inference(avatar_split_clause,[],[f3844,f3841,f1059,f903,f3846]) ).
fof(f3846,plain,
( spl13_190
<=> ! [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,[spl13_190])]) ).
fof(f3841,plain,
( spl13_189
<=> ! [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,[spl13_189])]) ).
fof(f3844,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))
| ~ spl13_38
| ~ spl13_56
| ~ spl13_189 ),
inference(forward_demodulation,[],[f3842,f1089]) ).
fof(f3842,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))
| ~ spl13_189 ),
inference(avatar_component_clause,[],[f3841]) ).
fof(f3843,plain,
spl13_189,
inference(avatar_split_clause,[],[f543,f3841]) ).
fof(f543,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,[],[f227]) ).
fof(f227,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,[],[f87]) ).
fof(f87,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/sandbox2/benchmark/theBenchmark.p',fact_57_insert__Collect) ).
fof(f3823,plain,
spl13_188,
inference(avatar_split_clause,[],[f541,f3821]) ).
fof(f3821,plain,
( spl13_188
<=> ! [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,[spl13_188])]) ).
fof(f541,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,[],[f225]) ).
fof(f225,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,[],[f86]) ).
fof(f86,axiom,
! [X0,X10,X12] : 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),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)),X10))),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/sandbox2/benchmark/theBenchmark.p',fact_56_insert__compr) ).
fof(f3792,plain,
( spl13_187
| ~ spl13_38
| ~ spl13_56
| ~ spl13_186 ),
inference(avatar_split_clause,[],[f3788,f3783,f1059,f903,f3790]) ).
fof(f3790,plain,
( spl13_187
<=> ! [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,[spl13_187])]) ).
fof(f3783,plain,
( spl13_186
<=> ! [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,[spl13_186])]) ).
fof(f3788,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))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_186 ),
inference(forward_demodulation,[],[f3787,f1089]) ).
fof(f3787,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))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_186 ),
inference(forward_demodulation,[],[f3786,f1089]) ).
fof(f3786,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))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_186 ),
inference(forward_demodulation,[],[f3784,f1089]) ).
fof(f3784,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))) )
| ~ spl13_186 ),
inference(avatar_component_clause,[],[f3783]) ).
fof(f3785,plain,
spl13_186,
inference(avatar_split_clause,[],[f584,f3783]) ).
fof(f584,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,[],[f415]) ).
fof(f415,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,[],[f414]) ).
fof(f414,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,[],[f255]) ).
fof(f255,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,[],[f56]) ).
fof(f56,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/sandbox2/benchmark/theBenchmark.p',fact_26_finite__Collect__disjI) ).
fof(f3769,plain,
spl13_185,
inference(avatar_split_clause,[],[f734,f3767]) ).
fof(f3767,plain,
( spl13_185
<=> ! [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,[spl13_185])]) ).
fof(f734,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,[],[f700,f666]) ).
fof(f666,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,[],[f494,f493]) ).
fof(f493,plain,
! [X0,X1] : ti(X0,X1) = hAPP(X0,X0,combi(X0),X1),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0,X1] : ti(X0,X1) = hAPP(X0,X0,combi(X0),X1),
inference(rectify,[],[f142]) ).
fof(f142,axiom,
! [X2,X52] : hAPP(X2,X2,combi(X2),X52) = ti(X2,X52),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
fof(f494,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = ti(fun(X0,bool),X1),
inference(cnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0,X1] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X1) = ti(fun(X0,bool),X1),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X0,X15] : hAPP(fun(X0,bool),fun(X0,bool),collect(X0),X15) = ti(fun(X0,bool),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
fof(f700,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,[],[f635,f493]) ).
fof(f635,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,[],[f441]) ).
fof(f441,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),sK12(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)),sK12(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,[sK12])],[f439,f440]) ).
fof(f440,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),sK12(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)),sK12(X0,X1,X2,X3,X4)),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f439,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,[],[f438]) ).
fof(f438,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,[],[f288]) ).
fof(f288,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,[],[f120]) ).
fof(f120,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)))
<=> ? [X43] :
( 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),X43)
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subset__image__iff) ).
fof(f3718,plain,
spl13_184,
inference(avatar_split_clause,[],[f732,f3716]) ).
fof(f3716,plain,
( spl13_184
<=> ! [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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_184])]) ).
fof(f732,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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(forward_demodulation,[],[f731,f666]) ).
fof(f731,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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(forward_demodulation,[],[f688,f666]) ).
fof(f688,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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(definition_unfolding,[],[f593,f493,f493]) ).
fof(f593,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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(cnf_transformation,[],[f418]) ).
fof(f418,plain,
! [X0,X1,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),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)
| 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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(nnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0,X1,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),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)
<=> 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,[],[f356]) ).
fof(f356,plain,
! [X0,X1,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),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)
<=> 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,[],[f263]) ).
fof(f263,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),X1) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)
<=> ti(fun(X0,bool),X1) = ti(fun(X0,bool),X3) ) ) ),
inference(rectify,[],[f92]) ).
fof(f92,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/sandbox2/benchmark/theBenchmark.p',fact_62_insert__ident) ).
fof(f3714,plain,
spl13_183,
inference(avatar_split_clause,[],[f730,f3712]) ).
fof(f3712,plain,
( spl13_183
<=> ! [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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_183])]) ).
fof(f730,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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(forward_demodulation,[],[f729,f666]) ).
fof(f729,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),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(X0,fun(fun(X0,bool),bool),member(X0),X2),X3)) ),
inference(forward_demodulation,[],[f687,f666]) ).
fof(f687,plain,
! [X2,X3,X0,X1] :
( 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),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)
| 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,[],[f594,f493,f493]) ).
fof(f594,plain,
! [X2,X3,X0,X1] :
( 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),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X2),X3)
| 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,[],[f418]) ).
fof(f3628,plain,
( spl13_182
| ~ spl13_54
| ~ spl13_65 ),
inference(avatar_split_clause,[],[f1218,f1207,f1051,f3626]) ).
fof(f3626,plain,
( spl13_182
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(nat,bool,X0,sK1(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_182])]) ).
fof(f1051,plain,
( spl13_54
<=> ! [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,[spl13_54])]) ).
fof(f1207,plain,
( spl13_65
<=> ! [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),sK1(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_65])]) ).
fof(f1218,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0))
| hBOOL(hAPP(nat,bool,X0,sK1(X0,X1))) )
| ~ spl13_54
| ~ spl13_65 ),
inference(resolution,[],[f1208,f1052]) ).
fof(f1052,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)) )
| ~ spl13_54 ),
inference(avatar_component_clause,[],[f1051]) ).
fof(f1208,plain,
( ! [X0,X1] :
( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK1(X0,X1)),X0))
| hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X0)) )
| ~ spl13_65 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f3624,plain,
spl13_181,
inference(avatar_split_clause,[],[f639,f3622]) ).
fof(f3622,plain,
( spl13_181
<=> ! [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,[spl13_181])]) ).
fof(f639,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,[],[f292]) ).
fof(f292,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,[],[f111]) ).
fof(f111,axiom,
! [X1,X0,X40,X11,X37,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(X40,bool),fun(X1,bool),hAPP(fun(X40,X1),fun(fun(X40,bool),fun(X1,bool)),image(X40,X1),X37),X7)) = hAPP(fun(X40,bool),fun(X0,bool),hAPP(fun(X40,X0),fun(fun(X40,bool),fun(X0,bool)),image(X40,X0),hAPP(fun(X40,X1),fun(X40,X0),hAPP(fun(X1,X0),fun(fun(X40,X1),fun(X40,X0)),combb(X1,X0,X40),X11),X37)),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_image__image) ).
fof(f3615,plain,
( spl13_180
| ~ spl13_38
| ~ spl13_56
| ~ spl13_179 ),
inference(avatar_split_clause,[],[f3611,f3607,f1059,f903,f3613]) ).
fof(f3613,plain,
( spl13_180
<=> ! [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,[spl13_180])]) ).
fof(f3607,plain,
( spl13_179
<=> ! [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,[spl13_179])]) ).
fof(f3611,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)) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_179 ),
inference(forward_demodulation,[],[f3610,f1089]) ).
fof(f3610,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)))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_179 ),
inference(forward_demodulation,[],[f3608,f1089]) ).
fof(f3608,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)))) )
| ~ spl13_179 ),
inference(avatar_component_clause,[],[f3607]) ).
fof(f3609,plain,
spl13_179,
inference(avatar_split_clause,[],[f583,f3607]) ).
fof(f583,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,[],[f415]) ).
fof(f3600,plain,
( spl13_178
| ~ spl13_38
| ~ spl13_56
| ~ spl13_177 ),
inference(avatar_split_clause,[],[f3596,f3592,f1059,f903,f3598]) ).
fof(f3598,plain,
( spl13_178
<=> ! [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,[spl13_178])]) ).
fof(f3592,plain,
( spl13_177
<=> ! [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,[spl13_177])]) ).
fof(f3596,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)) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_177 ),
inference(forward_demodulation,[],[f3595,f1089]) ).
fof(f3595,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)))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_177 ),
inference(forward_demodulation,[],[f3593,f1089]) ).
fof(f3593,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)))) )
| ~ spl13_177 ),
inference(avatar_component_clause,[],[f3592]) ).
fof(f3594,plain,
spl13_177,
inference(avatar_split_clause,[],[f582,f3592]) ).
fof(f582,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,[],[f415]) ).
fof(f3586,plain,
( spl13_176
| ~ spl13_38
| ~ spl13_56
| ~ spl13_175 ),
inference(avatar_split_clause,[],[f3582,f3578,f1059,f903,f3584]) ).
fof(f3584,plain,
( spl13_176
<=> ! [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,[spl13_176])]) ).
fof(f3578,plain,
( spl13_175
<=> ! [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,[spl13_175])]) ).
fof(f3582,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))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_175 ),
inference(forward_demodulation,[],[f3581,f1089]) ).
fof(f3581,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))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_175 ),
inference(forward_demodulation,[],[f3579,f1089]) ).
fof(f3579,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))) )
| ~ spl13_175 ),
inference(avatar_component_clause,[],[f3578]) ).
fof(f3580,plain,
spl13_175,
inference(avatar_split_clause,[],[f572,f3578]) ).
fof(f572,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,[],[f350]) ).
fof(f350,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,[],[f250]) ).
fof(f250,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,[],[f40]) ).
fof(f40,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/sandbox2/benchmark/theBenchmark.p',fact_10_finite__Collect__conjI) ).
fof(f3576,plain,
( spl13_174
| ~ spl13_42
| ~ spl13_62 ),
inference(avatar_split_clause,[],[f1138,f1127,f974,f3574]) ).
fof(f3574,plain,
( spl13_174
<=> ! [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,[spl13_174])]) ).
fof(f1127,plain,
( spl13_62
<=> ! [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,[spl13_62])]) ).
fof(f1138,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),hAPP(nat,nat,suc,X0)))
| ~ spl13_42
| ~ spl13_62 ),
inference(resolution,[],[f1128,f975]) ).
fof(f1128,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)) )
| ~ spl13_62 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f3568,plain,
( spl13_173
| ~ spl13_38
| ~ spl13_56
| ~ spl13_172 ),
inference(avatar_split_clause,[],[f3564,f3560,f1059,f903,f3566]) ).
fof(f3566,plain,
( spl13_173
<=> ! [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,[spl13_173])]) ).
fof(f3560,plain,
( spl13_172
<=> ! [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,[spl13_172])]) ).
fof(f3564,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))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_172 ),
inference(forward_demodulation,[],[f3563,f1089]) ).
fof(f3563,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))) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_172 ),
inference(forward_demodulation,[],[f3561,f1089]) ).
fof(f3561,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))) )
| ~ spl13_172 ),
inference(avatar_component_clause,[],[f3560]) ).
fof(f3562,plain,
spl13_172,
inference(avatar_split_clause,[],[f571,f3560]) ).
fof(f571,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,[],[f350]) ).
fof(f3532,plain,
spl13_171,
inference(avatar_split_clause,[],[f733,f3530]) ).
fof(f3530,plain,
( spl13_171
<=> ! [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),sK8(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,[spl13_171])]) ).
fof(f733,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),sK8(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,[],[f696,f666]) ).
fof(f696,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),sK8(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,[],[f622,f493]) ).
fof(f622,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),sK8(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,[],[f429]) ).
fof(f429,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),sK8(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK8(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)),sK8(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,[sK8])],[f379,f428]) ).
fof(f428,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),sK8(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK8(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)),sK8(X0,X1,X2,X3,X4)),X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f379,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,[],[f378]) ).
fof(f378,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,[],[f281]) ).
fof(f281,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,[],[f77]) ).
fof(f77,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/sandbox2/benchmark/theBenchmark.p',fact_47_finite__subset__image) ).
fof(f3347,plain,
spl13_170,
inference(avatar_split_clause,[],[f618,f3345]) ).
fof(f3345,plain,
( spl13_170
<=> ! [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,[spl13_170])]) ).
fof(f618,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,[],[f279]) ).
fof(f279,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,[],[f118]) ).
fof(f118,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/sandbox2/benchmark/theBenchmark.p',fact_88_image__insert) ).
fof(f3328,plain,
spl13_169,
inference(avatar_split_clause,[],[f624,f3326]) ).
fof(f3326,plain,
( spl13_169
<=> ! [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,[spl13_169])]) ).
fof(f624,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,[],[f381]) ).
fof(f381,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,[],[f283]) ).
fof(f283,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,[],[f119]) ).
fof(f119,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/sandbox2/benchmark/theBenchmark.p',fact_89_insert__image) ).
fof(f3293,plain,
spl13_168,
inference(avatar_split_clause,[],[f625,f3291]) ).
fof(f3291,plain,
( spl13_168
<=> ! [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,[spl13_168])]) ).
fof(f625,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,[],[f382]) ).
fof(f382,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,[],[f284]) ).
fof(f284,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,[],[f121]) ).
fof(f121,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/sandbox2/benchmark/theBenchmark.p',fact_91_image__mono) ).
fof(f3267,plain,
spl13_167,
inference(avatar_split_clause,[],[f735,f3265]) ).
fof(f3265,plain,
( spl13_167
<=> ! [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),sK12(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,[spl13_167])]) ).
fof(f735,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),sK12(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,[],[f701,f666]) ).
fof(f701,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),sK12(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,[],[f634,f493]) ).
fof(f634,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),sK12(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,[],[f441]) ).
fof(f3239,plain,
spl13_166,
inference(avatar_split_clause,[],[f600,f3237]) ).
fof(f3237,plain,
( spl13_166
<=> ! [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,[spl13_166])]) ).
fof(f600,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,[],[f363]) ).
fof(f363,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,[],[f268]) ).
fof(f268,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,[],[f117]) ).
fof(f117,axiom,
! [X0,X10,X36,X42] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X36),X42))
=> 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),X36)),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X10),X42))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_insert__mono) ).
fof(f3179,plain,
spl13_165,
inference(avatar_split_clause,[],[f588,f3177]) ).
fof(f3177,plain,
( spl13_165
<=> ! [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,[spl13_165])]) ).
fof(f588,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,[],[f259]) ).
fof(f259,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,[],[f89]) ).
fof(f89,axiom,
! [X0,X13,X35,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),X35),X7)) = hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X35),hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X13),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_insert__commute) ).
fof(f3112,plain,
( spl13_164
| ~ spl13_8
| ~ spl13_152 ),
inference(avatar_split_clause,[],[f3000,f2756,f770,f3110]) ).
fof(f3110,plain,
( spl13_164
<=> ! [X0] : hAPP(nat,nat,suc,X0) != sK3(hAPP(nat,nat,suc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_164])]) ).
fof(f770,plain,
( spl13_8
<=> ! [X0] : hAPP(nat,nat,suc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
fof(f2756,plain,
( spl13_152
<=> ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK3(hAPP(nat,nat,suc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_152])]) ).
fof(f3000,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) != sK3(hAPP(nat,nat,suc,X0))
| ~ spl13_8
| ~ spl13_152 ),
inference(superposition,[],[f771,f2757]) ).
fof(f2757,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK3(hAPP(nat,nat,suc,X0)))
| ~ spl13_152 ),
inference(avatar_component_clause,[],[f2756]) ).
fof(f771,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) != X0
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f3093,plain,
spl13_163,
inference(avatar_split_clause,[],[f711,f3091]) ).
fof(f3091,plain,
( spl13_163
<=> ! [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,[spl13_163])]) ).
fof(f711,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,[],[f710,f666]) ).
fof(f710,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,[],[f674,f666]) ).
fof(f674,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,[],[f555,f493,f493]) ).
fof(f555,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,[],[f331]) ).
fof(f331,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,[],[f330]) ).
fof(f330,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,[],[f237]) ).
fof(f237,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,[],[f36]) ).
fof(f36,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/sandbox2/benchmark/theBenchmark.p',fact_6_card__seteq) ).
fof(f3089,plain,
spl13_162,
inference(avatar_split_clause,[],[f620,f3087]) ).
fof(f3087,plain,
( spl13_162
<=> ! [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)),sK8(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,[spl13_162])]) ).
fof(f620,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)),sK8(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,[],[f429]) ).
fof(f3085,plain,
spl13_161,
inference(avatar_split_clause,[],[f617,f3083]) ).
fof(f617,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,[],[f427]) ).
fof(f427,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,[],[f426]) ).
fof(f426,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,[],[f278]) ).
fof(f278,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,[],[f114]) ).
fof(f114,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/sandbox2/benchmark/theBenchmark.p',fact_84_insert__subset) ).
fof(f3081,plain,
spl13_160,
inference(avatar_split_clause,[],[f595,f3079]) ).
fof(f3079,plain,
( spl13_160
<=> ! [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,[spl13_160])]) ).
fof(f595,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,[],[f419]) ).
fof(f419,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,[],[f358]) ).
fof(f358,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,[],[f264]) ).
fof(f264,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,[],[f115]) ).
fof(f115,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/sandbox2/benchmark/theBenchmark.p',fact_85_subset__insert) ).
fof(f3075,plain,
( spl13_159
| ~ spl13_38
| ~ spl13_56
| ~ spl13_158 ),
inference(avatar_split_clause,[],[f3071,f3068,f1059,f903,f3073]) ).
fof(f3073,plain,
( spl13_159
<=> ! [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,[spl13_159])]) ).
fof(f3068,plain,
( spl13_158
<=> ! [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,[spl13_158])]) ).
fof(f3071,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)) )
| ~ spl13_38
| ~ spl13_56
| ~ spl13_158 ),
inference(forward_demodulation,[],[f3069,f1089]) ).
fof(f3069,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)) )
| ~ spl13_158 ),
inference(avatar_component_clause,[],[f3068]) ).
fof(f3070,plain,
spl13_158,
inference(avatar_split_clause,[],[f513,f3068]) ).
fof(f513,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,[],[f305]) ).
fof(f305,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,[],[f203]) ).
fof(f203,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,[],[f31]) ).
fof(f31,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/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
fof(f3029,plain,
spl13_157,
inference(avatar_split_clause,[],[f566,f3027]) ).
fof(f3027,plain,
( spl13_157
<=> ! [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,[spl13_157])]) ).
fof(f566,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,[],[f407]) ).
fof(f407,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,[],[f344]) ).
fof(f344,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,[],[f343]) ).
fof(f343,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,[],[f246]) ).
fof(f246,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,[],[f69]) ).
fof(f69,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/sandbox2/benchmark/theBenchmark.p',fact_39_le__diff__iff) ).
fof(f2970,plain,
spl13_156,
inference(avatar_split_clause,[],[f563,f2968]) ).
fof(f2968,plain,
( spl13_156
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_156])]) ).
fof(f563,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,[],[f340]) ).
fof(f340,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,[],[f339]) ).
fof(f339,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,[],[f244]) ).
fof(f244,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,[],[f70]) ).
fof(f70,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/sandbox2/benchmark/theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).
fof(f2931,plain,
spl13_155,
inference(avatar_split_clause,[],[f633,f2929]) ).
fof(f2929,plain,
( spl13_155
<=> ! [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)),sK12(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,[spl13_155])]) ).
fof(f633,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)),sK12(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,[],[f441]) ).
fof(f2927,plain,
spl13_154,
inference(avatar_split_clause,[],[f629,f2925]) ).
fof(f2925,plain,
( spl13_154
<=> ! [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,sK10(X0,X1,X2,X3,X4))),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_154])]) ).
fof(f629,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,sK10(X0,X1,X2,X3,X4))),X3)) ),
inference(cnf_transformation,[],[f433]) ).
fof(f433,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,sK10(X0,X1,X2,X3,X4))),X3))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK10(X0,X1,X2,X3,X4)),X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f384,f432]) ).
fof(f432,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,sK10(X0,X1,X2,X3,X4))),X3))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK10(X0,X1,X2,X3,X4)),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f384,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,[],[f286]) ).
fof(f286,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,[],[f126]) ).
fof(f126,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/sandbox2/benchmark/theBenchmark.p',fact_96_image__subsetI) ).
fof(f2792,plain,
spl13_153,
inference(avatar_split_clause,[],[f698,f2790]) ).
fof(f2790,plain,
( spl13_153
<=> ! [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,[spl13_153])]) ).
fof(f698,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,[],[f632,f493]) ).
fof(f632,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,[],[f437]) ).
fof(f437,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,sK11(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK11(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,[sK11])],[f435,f436]) ).
fof(f436,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,sK11(X0,X1,X2,X3,X4))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK11(X0,X1,X2,X3,X4)),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f435,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,[],[f434]) ).
fof(f434,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,[],[f287]) ).
fof(f287,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,[],[f107]) ).
fof(f107,axiom,
! [X0,X1,X38,X11,X7] :
( hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),X38),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,X38) = 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/sandbox2/benchmark/theBenchmark.p',fact_77_image__iff) ).
fof(f2758,plain,
( spl13_152
| ~ spl13_19
| ~ spl13_61 ),
inference(avatar_split_clause,[],[f1122,f1119,f821,f2756]) ).
fof(f821,plain,
( spl13_19
<=> ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).
fof(f1122,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,sK3(hAPP(nat,nat,suc,X0)))
| ~ spl13_19
| ~ spl13_61 ),
inference(resolution,[],[f1120,f822]) ).
fof(f822,plain,
( ! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0))
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f821]) ).
fof(f2735,plain,
spl13_151,
inference(avatar_split_clause,[],[f689,f2733]) ).
fof(f2733,plain,
( spl13_151
<=> ! [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,[spl13_151])]) ).
fof(f689,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,[],[f605,f493,f493]) ).
fof(f605,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,[],[f373]) ).
fof(f373,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,[],[f372]) ).
fof(f372,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,[],[f273]) ).
fof(f273,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,[],[f84]) ).
fof(f84,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/sandbox2/benchmark/theBenchmark.p',fact_54_insertE) ).
fof(f2731,plain,
spl13_150,
inference(avatar_split_clause,[],[f621,f2729]) ).
fof(f2729,plain,
( spl13_150
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK8(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,[spl13_150])]) ).
fof(f621,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),sK8(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,[],[f429]) ).
fof(f2727,plain,
spl13_149,
inference(avatar_split_clause,[],[f551,f2725]) ).
fof(f2725,plain,
( spl13_149
<=> ! [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,[spl13_149])]) ).
fof(f551,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,[],[f323]) ).
fof(f323,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,[],[f233]) ).
fof(f233,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,[],[f38]) ).
fof(f38,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/sandbox2/benchmark/theBenchmark.p',fact_8_card__insert__if) ).
fof(f2649,plain,
spl13_148,
inference(avatar_split_clause,[],[f628,f2647]) ).
fof(f2647,plain,
( spl13_148
<=> ! [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),sK10(X0,X1,X2,X3,X4)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_148])]) ).
fof(f628,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),sK10(X0,X1,X2,X3,X4)),X4)) ),
inference(cnf_transformation,[],[f433]) ).
fof(f2645,plain,
spl13_147,
inference(avatar_split_clause,[],[f486,f2643]) ).
fof(f2643,plain,
( spl13_147
<=> ! [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,sK0(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK0(X0,X3)))))
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_147])]) ).
fof(f486,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,sK0(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK0(X0,X3)))))
| ~ order(X0) ),
inference(cnf_transformation,[],[f391]) ).
fof(f391,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,sK0(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK0(X0,X3))))) )
| ~ order(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f298,f390]) ).
fof(f390,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,sK0(X0,X3))),hAPP(nat,X0,X3,hAPP(nat,nat,suc,sK0(X0,X3))))) ),
introduced(choice_axiom,[]) ).
fof(f298,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,[],[f297]) ).
fof(f297,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,[],[f179]) ).
fof(f179,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,[],[f78]) ).
fof(f78,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/sandbox2/benchmark/theBenchmark.p',fact_48_lift__Suc__mono__le) ).
fof(f2606,plain,
spl13_146,
inference(avatar_split_clause,[],[f722,f2604]) ).
fof(f2604,plain,
( spl13_146
<=> ! [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,[spl13_146])]) ).
fof(f722,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,[],[f721,f666]) ).
fof(f721,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,[],[f680,f666]) ).
fof(f680,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,[],[f570,f493,f493]) ).
fof(f570,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,[],[f349]) ).
fof(f349,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,[],[f348]) ).
fof(f348,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,[],[f249]) ).
fof(f249,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,[],[f81]) ).
fof(f81,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/sandbox2/benchmark/theBenchmark.p',fact_51_equalityI) ).
fof(f2602,plain,
spl13_145,
inference(avatar_split_clause,[],[f604,f2600]) ).
fof(f2600,plain,
( spl13_145
<=> ! [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,[spl13_145])]) ).
fof(f604,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,[],[f371]) ).
fof(f371,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,[],[f370]) ).
fof(f370,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,[],[f272]) ).
fof(f272,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,[],[f102]) ).
fof(f102,axiom,
! [X0,X36,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),X36))
=> hBOOL(hAPP(fun(X0,bool),bool,hAPP(fun(X0,bool),fun(fun(X0,bool),bool),ord_less_eq(fun(X0,bool)),X7),X36)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_subset__trans) ).
fof(f2584,plain,
spl13_144,
inference(avatar_split_clause,[],[f550,f2582]) ).
fof(f2582,plain,
( spl13_144
<=> ! [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,[spl13_144])]) ).
fof(f550,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,[],[f323]) ).
fof(f2507,plain,
( spl13_143
| ~ spl13_36
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f1073,f1059,f895,f2504]) ).
fof(f2504,plain,
( spl13_143
<=> combi(bool) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_143])]) ).
fof(f895,plain,
( spl13_36
<=> ! [X0] : combi(X0) = hAPP(fun(X0,X0),fun(X0,X0),combi(fun(X0,X0)),combi(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).
fof(f1073,plain,
( combi(bool) = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),combi(bool))
| ~ spl13_36
| ~ spl13_56 ),
inference(superposition,[],[f1060,f896]) ).
fof(f896,plain,
( ! [X0] : combi(X0) = hAPP(fun(X0,X0),fun(X0,X0),combi(fun(X0,X0)),combi(X0))
| ~ spl13_36 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f2502,plain,
spl13_142,
inference(avatar_split_clause,[],[f630,f2500]) ).
fof(f2500,plain,
( spl13_142
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK11(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,[spl13_142])]) ).
fof(f630,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK11(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,[],[f437]) ).
fof(f2498,plain,
spl13_141,
inference(avatar_split_clause,[],[f627,f2496]) ).
fof(f2496,plain,
( spl13_141
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK9(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,[spl13_141])]) ).
fof(f627,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK9(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,[],[f431]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK9(X0,X1,X2,X3,X4)),X4))
& ti(X0,X2) = hAPP(X1,X0,X3,sK9(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,[sK9])],[f383,f430]) ).
fof(f430,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),sK9(X0,X1,X2,X3,X4)),X4))
& ti(X0,X2) = hAPP(X1,X0,X3,sK9(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f383,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,[],[f285]) ).
fof(f285,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,[],[f122]) ).
fof(f122,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/sandbox2/benchmark/theBenchmark.p',fact_92_imageE) ).
fof(f2494,plain,
spl13_140,
inference(avatar_split_clause,[],[f619,f2492]) ).
fof(f619,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,[],[f377]) ).
fof(f377,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,[],[f376]) ).
fof(f376,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,[],[f280]) ).
fof(f280,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,[],[f76]) ).
fof(f76,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/sandbox2/benchmark/theBenchmark.p',fact_46_finite__surj) ).
fof(f2490,plain,
spl13_139,
inference(avatar_split_clause,[],[f616,f2488]) ).
fof(f2488,plain,
( spl13_139
<=> ! [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,[spl13_139])]) ).
fof(f616,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,[],[f427]) ).
fof(f2486,plain,
spl13_138,
inference(avatar_split_clause,[],[f599,f2484]) ).
fof(f2484,plain,
( spl13_138
<=> ! [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,[spl13_138])]) ).
fof(f599,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,[],[f362]) ).
fof(f362,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,[],[f267]) ).
fof(f267,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,[],[f116]) ).
fof(f116,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/sandbox2/benchmark/theBenchmark.p',fact_86_subset__insertI2) ).
fof(f2482,plain,
spl13_137,
inference(avatar_split_clause,[],[f589,f2480]) ).
fof(f2480,plain,
( spl13_137
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK6(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,[spl13_137])]) ).
fof(f589,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sK6(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,[],[f417]) ).
fof(f2343,plain,
spl13_136,
inference(avatar_split_clause,[],[f623,f2341]) ).
fof(f623,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,[],[f380]) ).
fof(f380,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,[],[f282]) ).
fof(f282,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,[],[f108]) ).
fof(f108,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/sandbox2/benchmark/theBenchmark.p',fact_78_imageI) ).
fof(f2339,plain,
spl13_135,
inference(avatar_split_clause,[],[f540,f2337]) ).
fof(f2337,plain,
( spl13_135
<=> ! [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,[spl13_135])]) ).
fof(f540,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,[],[f224]) ).
fof(f224,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,[],[f88]) ).
fof(f88,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/sandbox2/benchmark/theBenchmark.p',fact_58_insert__absorb2) ).
fof(f2315,plain,
spl13_134,
inference(avatar_split_clause,[],[f592,f2313]) ).
fof(f2313,plain,
( spl13_134
<=> ! [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,[spl13_134])]) ).
fof(f592,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,[],[f355]) ).
fof(f355,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,[],[f262]) ).
fof(f262,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,[],[f34]) ).
fof(f34,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/sandbox2/benchmark/theBenchmark.p',fact_4_card__image__le) ).
fof(f2289,plain,
spl13_133,
inference(avatar_split_clause,[],[f615,f2287]) ).
fof(f2287,plain,
( spl13_133
<=> ! [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,[spl13_133])]) ).
fof(f615,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,[],[f427]) ).
fof(f2285,plain,
spl13_132,
inference(avatar_split_clause,[],[f554,f2283]) ).
fof(f2283,plain,
( spl13_132
<=> ! [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,[spl13_132])]) ).
fof(f554,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,[],[f329]) ).
fof(f329,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,[],[f328]) ).
fof(f328,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,[],[f236]) ).
fof(f236,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,[],[f35]) ).
fof(f35,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/sandbox2/benchmark/theBenchmark.p',fact_5_card__mono) ).
fof(f2253,plain,
spl13_131,
inference(avatar_split_clause,[],[f699,f2251]) ).
fof(f2251,plain,
( spl13_131
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X1,X0,X3,sK11(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,[spl13_131])]) ).
fof(f699,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X0,X3,sK11(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,[],[f631,f493]) ).
fof(f631,plain,
! [X2,X3,X0,X1,X4] :
( ti(X0,X2) = hAPP(X1,X0,X3,sK11(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,[],[f437]) ).
fof(f2249,plain,
spl13_130,
inference(avatar_split_clause,[],[f697,f2247]) ).
fof(f2247,plain,
( spl13_130
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X1,X0,X3,sK9(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,[spl13_130])]) ).
fof(f697,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X0,X3,sK9(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,[],[f626,f493]) ).
fof(f626,plain,
! [X2,X3,X0,X1,X4] :
( ti(X0,X2) = hAPP(X1,X0,X3,sK9(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,[],[f431]) ).
fof(f2187,plain,
spl13_129,
inference(avatar_split_clause,[],[f598,f2185]) ).
fof(f2185,plain,
( spl13_129
<=> ! [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,[spl13_129])]) ).
fof(f598,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,[],[f361]) ).
fof(f361,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,[],[f360]) ).
fof(f360,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,[],[f266]) ).
fof(f266,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,[],[f100]) ).
fof(f100,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/sandbox2/benchmark/theBenchmark.p',fact_70_set__rev__mp) ).
fof(f2183,plain,
spl13_128,
inference(avatar_split_clause,[],[f549,f2181]) ).
fof(f2181,plain,
( spl13_128
<=> ! [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,[spl13_128])]) ).
fof(f549,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,[],[f322]) ).
fof(f322,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,[],[f232]) ).
fof(f232,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,[],[f37]) ).
fof(f37,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/sandbox2/benchmark/theBenchmark.p',fact_7_card__insert__le) ).
fof(f2179,plain,
spl13_127,
inference(avatar_split_clause,[],[f539,f2177]) ).
fof(f2177,plain,
( spl13_127
<=> ! [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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_127])]) ).
fof(f539,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,[],[f223]) ).
fof(f223,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,[],[f67]) ).
fof(f67,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/sandbox2/benchmark/theBenchmark.p',fact_37_Suc__diff__diff) ).
fof(f2151,plain,
spl13_126,
inference(avatar_split_clause,[],[f564,f2149]) ).
fof(f2149,plain,
( spl13_126
<=> ! [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,[spl13_126])]) ).
fof(f564,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,[],[f406]) ).
fof(f406,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,[],[f342]) ).
fof(f342,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,[],[f341]) ).
fof(f341,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,[],[f245]) ).
fof(f245,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,[],[f71]) ).
fof(f71,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/sandbox2/benchmark/theBenchmark.p',fact_41_eq__diff__iff) ).
fof(f2138,plain,
spl13_125,
inference(avatar_split_clause,[],[f455,f2135]) ).
fof(f2135,plain,
( spl13_125
<=> 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,[spl13_125])]) ).
fof(f455,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,[],[f158]) ).
fof(f158,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/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(f2133,plain,
( spl13_124
| ~ spl13_63 ),
inference(avatar_split_clause,[],[f1191,f1131,f2131]) ).
fof(f2131,plain,
( spl13_124
<=> ! [X0,X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_124])]) ).
fof(f1191,plain,
( ! [X0,X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),fequal(X0),X1),X1))
| ~ spl13_63 ),
inference(equality_resolution,[],[f1132]) ).
fof(f2119,plain,
spl13_123,
inference(avatar_split_clause,[],[f597,f2117]) ).
fof(f2117,plain,
( spl13_123
<=> ! [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,[spl13_123])]) ).
fof(f597,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,[],[f359]) ).
fof(f359,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,[],[f265]) ).
fof(f265,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,[],[f93]) ).
fof(f93,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/sandbox2/benchmark/theBenchmark.p',fact_63_insertI2) ).
fof(f2108,plain,
spl13_122,
inference(avatar_split_clause,[],[f671,f2106]) ).
fof(f2106,plain,
( spl13_122
<=> ! [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,[spl13_122])]) ).
fof(f671,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,[],[f535,f493]) ).
fof(f535,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,[],[f219]) ).
fof(f219,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,[],[f4]) ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
fof(f2041,plain,
spl13_121,
inference(avatar_split_clause,[],[f690,f2039]) ).
fof(f2039,plain,
( spl13_121
<=> ! [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,[spl13_121])]) ).
fof(f690,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,[],[f607,f493,f493]) ).
fof(f607,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,[],[f374]) ).
fof(f374,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,[],[f274]) ).
fof(f274,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,[],[f83]) ).
fof(f83,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/sandbox2/benchmark/theBenchmark.p',fact_53_insertCI) ).
fof(f1984,plain,
spl13_120,
inference(avatar_split_clause,[],[f720,f1982]) ).
fof(f720,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,[],[f679,f666]) ).
fof(f679,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,[],[f568,f493]) ).
fof(f568,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,[],[f345]) ).
fof(f345,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,[],[f247]) ).
fof(f247,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,[],[f94]) ).
fof(f94,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/sandbox2/benchmark/theBenchmark.p',fact_64_insert__absorb) ).
fof(f1976,plain,
spl13_119,
inference(avatar_split_clause,[],[f561,f1974]) ).
fof(f1974,plain,
( spl13_119
<=> ! [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,[spl13_119])]) ).
fof(f561,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,[],[f336]) ).
fof(f336,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,[],[f242]) ).
fof(f242,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,[],[f73]) ).
fof(f73,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/sandbox2/benchmark/theBenchmark.p',fact_43_diff__le__mono) ).
fof(f1972,plain,
spl13_118,
inference(avatar_split_clause,[],[f560,f1970]) ).
fof(f1970,plain,
( spl13_118
<=> ! [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,[spl13_118])]) ).
fof(f560,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,[],[f335]) ).
fof(f335,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,[],[f241]) ).
fof(f241,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,[],[f74]) ).
fof(f74,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/sandbox2/benchmark/theBenchmark.p',fact_44_diff__le__mono2) ).
fof(f1941,plain,
spl13_117,
inference(avatar_split_clause,[],[f538,f1939]) ).
fof(f1939,plain,
( spl13_117
<=> ! [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) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_117])]) ).
fof(f538,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,[],[f222]) ).
fof(f222,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,[],[f55]) ).
fof(f55,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/sandbox2/benchmark/theBenchmark.p',fact_25_diff__commute) ).
fof(f1818,plain,
spl13_116,
inference(avatar_split_clause,[],[f638,f1816]) ).
fof(f1816,plain,
( spl13_116
<=> ! [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,[spl13_116])]) ).
fof(f638,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,[],[f291]) ).
fof(f291,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,[],[f143]) ).
fof(f143,axiom,
! [X2,X1,X0,X52,X53,X54] : 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),X52),X53),X54) = hAPP(X0,X1,hAPP(X2,fun(X0,X1),X52,X54),hAPP(X2,X0,X53,X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
fof(f1814,plain,
spl13_115,
inference(avatar_split_clause,[],[f517,f1812]) ).
fof(f1812,plain,
( spl13_115
<=> ! [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,[spl13_115])]) ).
fof(f517,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,[],[f309]) ).
fof(f309,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,[],[f207]) ).
fof(f207,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,[],[f41]) ).
fof(f41,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/sandbox2/benchmark/theBenchmark.p',fact_11_Suc__diff__le) ).
fof(f1803,plain,
spl13_114,
inference(avatar_split_clause,[],[f454,f1800]) ).
fof(f1800,plain,
( spl13_114
<=> 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,[spl13_114])]) ).
fof(f454,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,[],[f157]) ).
fof(f157,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/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(f1798,plain,
( spl13_113
| ~ spl13_11
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f929,f903,f784,f1796]) ).
fof(f1796,plain,
( spl13_113
<=> ! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_113])]) ).
fof(f784,plain,
( spl13_11
<=> ! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).
fof(f929,plain,
( ! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl13_11
| ~ spl13_38 ),
inference(superposition,[],[f785,f904]) ).
fof(f785,plain,
( ! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) )
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f1791,plain,
( spl13_112
| ~ spl13_37
| ~ spl13_56
| ~ spl13_111 ),
inference(avatar_split_clause,[],[f1787,f1784,f1059,f899,f1789]) ).
fof(f1789,plain,
( spl13_112
<=> ! [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,[spl13_112])]) ).
fof(f899,plain,
( spl13_37
<=> ! [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,[spl13_37])]) ).
fof(f1784,plain,
( spl13_111
<=> ! [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,[spl13_111])]) ).
fof(f1787,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))
| ~ spl13_37
| ~ spl13_56
| ~ spl13_111 ),
inference(forward_demodulation,[],[f1785,f1079]) ).
fof(f1079,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))
| ~ spl13_37
| ~ spl13_56 ),
inference(superposition,[],[f1060,f900]) ).
fof(f900,plain,
( ! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = hAPP(X0,X0,combi(X0),hAPP(X1,X0,X2,X3))
| ~ spl13_37 ),
inference(avatar_component_clause,[],[f899]) ).
fof(f1785,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)))
| ~ spl13_111 ),
inference(avatar_component_clause,[],[f1784]) ).
fof(f1786,plain,
spl13_111,
inference(avatar_split_clause,[],[f481,f1784]) ).
fof(f481,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,[],[f174]) ).
fof(f174,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,[],[f43]) ).
fof(f43,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/sandbox2/benchmark/theBenchmark.p',fact_13_card__Collect__le__nat) ).
fof(f1747,plain,
spl13_110,
inference(avatar_split_clause,[],[f693,f1745]) ).
fof(f1745,plain,
( spl13_110
<=> ! [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,[spl13_110])]) ).
fof(f693,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,[],[f609,f493,f493]) ).
fof(f609,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,[],[f423]) ).
fof(f423,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,[],[f422]) ).
fof(f422,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,[],[f276]) ).
fof(f276,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,[],[f91]) ).
fof(f91,axiom,
! [X0,X35,X7,X13] :
( hBOOL(hAPP(X0,bool,hAPP(fun(X0,bool),fun(X0,bool),hAPP(X0,fun(fun(X0,bool),fun(X0,bool)),insert(X0),X35),X7),X13))
<=> ( hBOOL(hAPP(X0,bool,X7,X13))
| ti(X0,X35) = ti(X0,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_insert__code) ).
fof(f1743,plain,
spl13_109,
inference(avatar_split_clause,[],[f691,f1741]) ).
fof(f1741,plain,
( spl13_109
<=> ! [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,sK7(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK7(X0,X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_109])]) ).
fof(f691,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,sK7(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK7(X0,X1,X2,X3)) ),
inference(definition_unfolding,[],[f608,f493,f493]) ).
fof(f608,plain,
! [X2,X3,X0,X1] :
( ti(fun(X0,X1),X2) = ti(fun(X0,X1),X3)
| hAPP(X0,X1,X2,sK7(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK7(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f421]) ).
fof(f421,plain,
! [X0,X1,X2,X3] :
( ti(fun(X0,X1),X2) = ti(fun(X0,X1),X3)
| hAPP(X0,X1,X2,sK7(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK7(X0,X1,X2,X3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f375,f420]) ).
fof(f420,plain,
! [X0,X1,X2,X3] :
( ? [X4] : hAPP(X0,X1,X2,X4) != hAPP(X0,X1,X3,X4)
=> hAPP(X0,X1,X2,sK7(X0,X1,X2,X3)) != hAPP(X0,X1,X3,sK7(X0,X1,X2,X3)) ),
introduced(choice_axiom,[]) ).
fof(f375,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,[],[f275]) ).
fof(f275,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,[],[f104]) ).
fof(f104,axiom,
! [X0,X1,X11,X37] :
( ! [X32] : hAPP(X0,X1,X11,X32) = hAPP(X0,X1,X37,X32)
=> ti(fun(X0,X1),X11) = ti(fun(X0,X1),X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
fof(f1739,plain,
spl13_108,
inference(avatar_split_clause,[],[f670,f1737]) ).
fof(f1737,plain,
( spl13_108
<=> ! [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,[spl13_108])]) ).
fof(f670,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,[],[f534,f493]) ).
fof(f534,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,[],[f218]) ).
fof(f218,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/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
fof(f1732,plain,
spl13_107,
inference(avatar_split_clause,[],[f669,f1730]) ).
fof(f1730,plain,
( spl13_107
<=> ! [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,[spl13_107])]) ).
fof(f669,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,[],[f533,f493]) ).
fof(f533,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/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
fof(f1726,plain,
spl13_106,
inference(avatar_split_clause,[],[f453,f1723]) ).
fof(f453,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,[],[f156]) ).
fof(f156,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/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f1707,plain,
spl13_105,
inference(avatar_split_clause,[],[f713,f1705]) ).
fof(f1705,plain,
( spl13_105
<=> ! [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,[spl13_105])]) ).
fof(f713,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,[],[f712,f666]) ).
fof(f712,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,[],[f675,f666]) ).
fof(f675,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,[],[f556,f493,f493]) ).
fof(f556,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,[],[f332]) ).
fof(f332,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,[],[f238]) ).
fof(f238,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,[],[f97]) ).
fof(f97,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/sandbox2/benchmark/theBenchmark.p',fact_67_equalityD1) ).
fof(f1703,plain,
spl13_104,
inference(avatar_split_clause,[],[f667,f1701]) ).
fof(f1701,plain,
( spl13_104
<=> ! [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,[spl13_104])]) ).
fof(f667,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,[],[f495,f493]) ).
fof(f495,plain,
! [X0,X1] : image(X0,X1) = ti(fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool))),image(X0,X1)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] : image(X0,X1) = ti(fun(fun(X0,X1),fun(fun(X0,bool),fun(X1,bool))),image(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).
fof(f1682,plain,
spl13_103,
inference(avatar_split_clause,[],[f574,f1680]) ).
fof(f1680,plain,
( spl13_103
<=> ! [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),sK5(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_103])]) ).
fof(f574,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),sK5(X0,X1,X2)),X1)) ),
inference(cnf_transformation,[],[f409]) ).
fof(f409,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),sK5(X0,X1,X2)),X1))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1,X2)),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f351,f408]) ).
fof(f408,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),sK5(X0,X1,X2)),X1))
& hBOOL(hAPP(fun(X0,bool),bool,hAPP(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,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,[],[f251]) ).
fof(f251,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,[],[f123]) ).
fof(f123,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/sandbox2/benchmark/theBenchmark.p',fact_93_subsetI) ).
fof(f1678,plain,
( spl13_102
| ~ spl13_31
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f1075,f1059,f873,f1675]) ).
fof(f1675,plain,
( spl13_102
<=> fNot = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),fNot) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_102])]) ).
fof(f873,plain,
( spl13_31
<=> fNot = hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).
fof(f1075,plain,
( fNot = hAPP(fun(bool,bool),fun(bool,bool),collect(bool),fNot)
| ~ spl13_31
| ~ spl13_56 ),
inference(superposition,[],[f1060,f875]) ).
fof(f875,plain,
( fNot = hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot)
| ~ spl13_31 ),
inference(avatar_component_clause,[],[f873]) ).
fof(f1673,plain,
spl13_101,
inference(avatar_split_clause,[],[f573,f1671]) ).
fof(f1671,plain,
( spl13_101
<=> ! [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),sK5(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_101])]) ).
fof(f573,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),sK5(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f409]) ).
fof(f1649,plain,
spl13_100,
inference(avatar_split_clause,[],[f591,f1647]) ).
fof(f1647,plain,
( spl13_100
<=> ! [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,[spl13_100])]) ).
fof(f591,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,[],[f354]) ).
fof(f354,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,[],[f261]) ).
fof(f261,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,[],[f32]) ).
fof(f32,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/sandbox2/benchmark/theBenchmark.p',fact_2_finite__imageI) ).
fof(f1645,plain,
spl13_99,
inference(avatar_split_clause,[],[f537,f1643]) ).
fof(f1643,plain,
( spl13_99
<=> ! [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,[spl13_99])]) ).
fof(f537,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,[],[f221]) ).
fof(f221,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,[],[f113]) ).
fof(f113,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/sandbox2/benchmark/theBenchmark.p',fact_83_subset__insertI) ).
fof(f1641,plain,
spl13_98,
inference(avatar_split_clause,[],[f489,f1639]) ).
fof(f1639,plain,
( spl13_98
<=> ! [X4,X0] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),sK2(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,[spl13_98])]) ).
fof(f489,plain,
! [X0,X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),sK2(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,[],[f396]) ).
fof(f396,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),sK1(X0,X1)),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK1(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X4),sK2(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,[sK1,sK2])],[f393,f395,f394]) ).
fof(f394,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),sK1(X0,X1)),X1))
& hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sK1(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f395,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),sK2(X0)))
| ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f393,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,[],[f392]) ).
fof(f392,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,[],[f301]) ).
fof(f301,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,[],[f182]) ).
fof(f182,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,[],[f128]) ).
fof(f128,axiom,
! [X47] :
( hBOOL(hAPP(fun(nat,bool),bool,finite_finite(nat),X47))
<=> ? [X46] :
! [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),X46)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_finite__nat__set__iff__bounded__le) ).
fof(f1636,plain,
( spl13_97
| ~ spl13_38
| ~ spl13_56
| ~ spl13_96 ),
inference(avatar_split_clause,[],[f1632,f1629,f1059,f903,f1634]) ).
fof(f1634,plain,
( spl13_97
<=> ! [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,[spl13_97])]) ).
fof(f1629,plain,
( spl13_96
<=> ! [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,[spl13_96])]) ).
fof(f1632,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)))
| ~ spl13_38
| ~ spl13_56
| ~ spl13_96 ),
inference(forward_demodulation,[],[f1630,f1089]) ).
fof(f1630,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))))
| ~ spl13_96 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f1631,plain,
spl13_96,
inference(avatar_split_clause,[],[f480,f1629]) ).
fof(f480,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,[],[f173]) ).
fof(f173,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,[],[f42]) ).
fof(f42,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/sandbox2/benchmark/theBenchmark.p',fact_12_finite__Collect__le__nat) ).
fof(f1600,plain,
spl13_95,
inference(avatar_split_clause,[],[f562,f1598]) ).
fof(f1598,plain,
( spl13_95
<=> ! [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,[spl13_95])]) ).
fof(f562,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,[],[f338]) ).
fof(f338,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,[],[f337]) ).
fof(f337,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,[],[f243]) ).
fof(f243,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,[],[f51]) ).
fof(f51,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/sandbox2/benchmark/theBenchmark.p',fact_21_le__trans) ).
fof(f1596,plain,
spl13_94,
inference(avatar_split_clause,[],[f553,f1594]) ).
fof(f1594,plain,
( spl13_94
<=> ! [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,[spl13_94])]) ).
fof(f553,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,[],[f327]) ).
fof(f327,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,[],[f326]) ).
fof(f326,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,[],[f235]) ).
fof(f235,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,[],[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(fun(X0,bool),bool,finite_finite(X0),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rev__finite__subset) ).
fof(f1592,plain,
spl13_93,
inference(avatar_split_clause,[],[f522,f1590]) ).
fof(f522,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,[],[f316]) ).
fof(f316,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,[],[f212]) ).
fof(f212,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,[],[f30]) ).
fof(f30,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/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
fof(f1479,plain,
spl13_92,
inference(avatar_split_clause,[],[f692,f1477]) ).
fof(f1477,plain,
( spl13_92
<=> ! [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,[spl13_92])]) ).
fof(f692,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,[],[f610,f493,f493]) ).
fof(f610,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,[],[f423]) ).
fof(f1475,plain,
spl13_91,
inference(avatar_split_clause,[],[f637,f1473]) ).
fof(f1473,plain,
( spl13_91
<=> ! [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,[spl13_91])]) ).
fof(f637,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,[],[f290]) ).
fof(f290,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,[],[f140]) ).
fof(f140,axiom,
! [X2,X1,X0,X52,X53,X54] : 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),X52),X53),X54) = hAPP(X0,X1,X52,hAPP(X2,X0,X53,X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
fof(f1471,plain,
spl13_90,
inference(avatar_split_clause,[],[f636,f1469]) ).
fof(f1469,plain,
( spl13_90
<=> ! [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,[spl13_90])]) ).
fof(f636,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,[],[f289]) ).
fof(f289,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,[],[f141]) ).
fof(f141,axiom,
! [X2,X1,X0,X52,X53,X54] : hAPP(X2,X1,hAPP(X0,fun(X2,X1),hAPP(fun(X2,fun(X0,X1)),fun(X0,fun(X2,X1)),combc(X2,X0,X1),X52),X53),X54) = hAPP(X0,X1,hAPP(X2,fun(X0,X1),X52,X54),X53),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
fof(f1467,plain,
spl13_89,
inference(avatar_split_clause,[],[f516,f1465]) ).
fof(f1465,plain,
( spl13_89
<=> ! [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,[spl13_89])]) ).
fof(f516,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,[],[f308]) ).
fof(f308,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,[],[f206]) ).
fof(f206,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,[],[f72]) ).
fof(f72,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/sandbox2/benchmark/theBenchmark.p',fact_42_diff__diff__cancel) ).
fof(f1443,plain,
spl13_88,
inference(avatar_split_clause,[],[f580,f1441]) ).
fof(f1441,plain,
( spl13_88
<=> ! [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,[spl13_88])]) ).
fof(f580,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,[],[f413]) ).
fof(f413,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,[],[f254]) ).
fof(f254,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,[],[f57]) ).
fof(f57,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/sandbox2/benchmark/theBenchmark.p',fact_27_finite__insert) ).
fof(f1439,plain,
spl13_87,
inference(avatar_split_clause,[],[f548,f1437]) ).
fof(f1437,plain,
( spl13_87
<=> ! [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,[spl13_87])]) ).
fof(f548,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,[],[f321]) ).
fof(f321,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,[],[f231]) ).
fof(f231,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,[],[f33]) ).
fof(f33,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/sandbox2/benchmark/theBenchmark.p',fact_3_finite_OinsertI) ).
fof(f1435,plain,
spl13_86,
inference(avatar_split_clause,[],[f519,f1433]) ).
fof(f1433,plain,
( spl13_86
<=> ! [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,[spl13_86])]) ).
fof(f519,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,[],[f313]) ).
fof(f313,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,[],[f312]) ).
fof(f312,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,[],[f209]) ).
fof(f209,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,[],[f61]) ).
fof(f61,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/sandbox2/benchmark/theBenchmark.p',fact_31_le__SucE) ).
fof(f1431,plain,
( spl13_85
| ~ spl13_22
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f1077,f1059,f835,f1428]) ).
fof(f835,plain,
( spl13_22
<=> u = hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).
fof(f1077,plain,
( u = hAPP(fun(pname,bool),fun(pname,bool),collect(pname),u)
| ~ spl13_22
| ~ spl13_56 ),
inference(superposition,[],[f1060,f837]) ).
fof(f837,plain,
( u = hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u)
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f1420,plain,
spl13_84,
inference(avatar_split_clause,[],[f536,f1418]) ).
fof(f1418,plain,
( spl13_84
<=> ! [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,[spl13_84])]) ).
fof(f536,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,[],[f220]) ).
fof(f220,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,[],[f85]) ).
fof(f85,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/sandbox2/benchmark/theBenchmark.p',fact_55_insertI1) ).
fof(f1409,plain,
spl13_83,
inference(avatar_split_clause,[],[f709,f1407]) ).
fof(f1407,plain,
( spl13_83
<=> ! [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,[spl13_83])]) ).
fof(f709,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,[],[f668,f666]) ).
fof(f668,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,[],[f498,f493]) ).
fof(f498,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,[],[f188]) ).
fof(f188,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,[],[f112]) ).
fof(f112,axiom,
! [X0,X41] : hAPP(fun(X0,bool),fun(X0,bool),hAPP(fun(X0,X0),fun(fun(X0,bool),fun(X0,bool)),image(X0,X0),combi(X0)),X41) = ti(fun(X0,bool),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_image__ident) ).
fof(f1355,plain,
spl13_82,
inference(avatar_split_clause,[],[f663,f1353]) ).
fof(f1353,plain,
( spl13_82
<=> ! [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,[spl13_82])]) ).
fof(f663,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,[],[f478,f493]) ).
fof(f478,plain,
! [X0] : insert(X0) = ti(fun(X0,fun(fun(X0,bool),fun(X0,bool))),insert(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] : insert(X0) = ti(fun(X0,fun(fun(X0,bool),fun(X0,bool))),insert(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
fof(f1351,plain,
spl13_81,
inference(avatar_split_clause,[],[f546,f1349]) ).
fof(f1349,plain,
( spl13_81
<=> ! [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,sK4(X1))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_81])]) ).
fof(f546,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,sK4(X1))))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(cnf_transformation,[],[f405]) ).
fof(f405,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,sK4(X1)))
& hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sK4(X1)))) )
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f320,f404]) ).
fof(f404,plain,
! [X1] :
( ? [X3] :
( ~ hBOOL(hAPP(nat,bool,X1,X3))
& hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,X3))) )
=> ( ~ hBOOL(hAPP(nat,bool,X1,sK4(X1)))
& hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sK4(X1)))) ) ),
introduced(choice_axiom,[]) ).
fof(f320,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,[],[f319]) ).
fof(f319,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,[],[f230]) ).
fof(f230,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,[],[f124]) ).
fof(f124,axiom,
! [X44,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),X44))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zero__induct__lemma) ).
fof(f1347,plain,
( spl13_80
| ~ spl13_20
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f1076,f1059,f825,f1344]) ).
fof(f1344,plain,
( spl13_80
<=> g = hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),g) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_80])]) ).
fof(f825,plain,
( spl13_20
<=> g = hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).
fof(f1076,plain,
( g = hAPP(fun(x_a,bool),fun(x_a,bool),collect(x_a),g)
| ~ spl13_20
| ~ spl13_56 ),
inference(superposition,[],[f1060,f827]) ).
fof(f827,plain,
( g = hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g)
| ~ spl13_20 ),
inference(avatar_component_clause,[],[f825]) ).
fof(f1342,plain,
spl13_79,
inference(avatar_split_clause,[],[f532,f1340]) ).
fof(f1340,plain,
( spl13_79
<=> ! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,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,[spl13_79])]) ).
fof(f532,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)))
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(cnf_transformation,[],[f403]) ).
fof(f403,plain,
! [X0,X1] :
( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,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_eq(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1))) ) ),
inference(nnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0,X1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),hAPP(nat,nat,suc,X1)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(rectify,[],[f63]) ).
fof(f63,axiom,
! [X19,X27] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X19)),hAPP(nat,nat,suc,X27)))
<=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X19),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Suc__le__mono) ).
fof(f1338,plain,
spl13_78,
inference(avatar_split_clause,[],[f531,f1336]) ).
fof(f1336,plain,
( spl13_78
<=> ! [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,X0)),hAPP(nat,nat,suc,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_78])]) ).
fof(f531,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,X0)),hAPP(nat,nat,suc,X1))) ),
inference(cnf_transformation,[],[f403]) ).
fof(f1328,plain,
spl13_77,
inference(avatar_split_clause,[],[f499,f1326]) ).
fof(f1326,plain,
( spl13_77
<=> ! [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,[spl13_77])]) ).
fof(f499,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,[],[f189]) ).
fof(f189,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,[],[f68]) ).
fof(f68,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/sandbox2/benchmark/theBenchmark.p',fact_38_diff__Suc__Suc) ).
fof(f1321,plain,
spl13_76,
inference(avatar_split_clause,[],[f655,f1318]) ).
fof(f1318,plain,
( spl13_76
<=> 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,[spl13_76])]) ).
fof(f655,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,[],[f467,f493]) ).
fof(f467,plain,
p = ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p),
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
p = ti(fun(fun(x_a,bool),fun(fun(x_a,bool),bool)),p),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_P_res) ).
fof(f1310,plain,
spl13_75,
inference(avatar_split_clause,[],[f611,f1308]) ).
fof(f1308,plain,
( spl13_75
<=> ! [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,[spl13_75])]) ).
fof(f611,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,[],[f423]) ).
fof(f1265,plain,
spl13_74,
inference(avatar_split_clause,[],[f547,f1263]) ).
fof(f1263,plain,
( spl13_74
<=> ! [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,sK4(X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_74])]) ).
fof(f547,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,sK4(X1)))
| ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
inference(cnf_transformation,[],[f405]) ).
fof(f1261,plain,
spl13_73,
inference(avatar_split_clause,[],[f527,f1259]) ).
fof(f1259,plain,
( spl13_73
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).
fof(f527,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,[],[f400]) ).
fof(f400,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,[],[f215]) ).
fof(f215,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,[],[f65]) ).
fof(f65,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/sandbox2/benchmark/theBenchmark.p',fact_35_not__less__eq__eq) ).
fof(f1257,plain,
spl13_72,
inference(avatar_split_clause,[],[f526,f1255]) ).
fof(f526,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,[],[f400]) ).
fof(f1253,plain,
spl13_71,
inference(avatar_split_clause,[],[f520,f1251]) ).
fof(f1251,plain,
( spl13_71
<=> ! [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,X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).
fof(f520,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,X0)),X1)) ),
inference(cnf_transformation,[],[f314]) ).
fof(f314,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,X0)),X1)) ),
inference(ennf_transformation,[],[f210]) ).
fof(f210,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(nat,fun(nat,bool),ord_less_eq(nat),X0),X1)) ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X17,X16] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X17)),X16))
=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X17),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Suc__leD) ).
fof(f1249,plain,
spl13_70,
inference(avatar_split_clause,[],[f515,f1247]) ).
fof(f515,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,[],[f307]) ).
fof(f307,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,[],[f205]) ).
fof(f205,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,[],[f62]) ).
fof(f62,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/sandbox2/benchmark/theBenchmark.p',fact_32_le__SucI) ).
fof(f1236,plain,
spl13_69,
inference(avatar_split_clause,[],[f518,f1234]) ).
fof(f1234,plain,
( spl13_69
<=> ! [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,[spl13_69])]) ).
fof(f518,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,[],[f311]) ).
fof(f311,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,[],[f310]) ).
fof(f310,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,[],[f208]) ).
fof(f208,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,[],[f50]) ).
fof(f50,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/sandbox2/benchmark/theBenchmark.p',fact_20_le__antisym) ).
fof(f1232,plain,
( ~ spl13_68
| spl13_46
| ~ spl13_55 ),
inference(avatar_split_clause,[],[f1067,f1055,f1004,f1229]) ).
fof(f1229,plain,
( spl13_68
<=> hBOOL(hAPP(x_a,bool,g,hAPP(pname,x_a,mgt_call,pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_68])]) ).
fof(f1004,plain,
( spl13_46
<=> 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,[spl13_46])]) ).
fof(f1055,plain,
( spl13_55
<=> ! [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,[spl13_55])]) ).
fof(f1067,plain,
( ~ hBOOL(hAPP(x_a,bool,g,hAPP(pname,x_a,mgt_call,pn)))
| spl13_46
| ~ spl13_55 ),
inference(resolution,[],[f1056,f1006]) ).
fof(f1006,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))
| spl13_46 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f1056,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)) )
| ~ spl13_55 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1217,plain,
spl13_67,
inference(avatar_split_clause,[],[f662,f1215]) ).
fof(f1215,plain,
( spl13_67
<=> ! [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,[spl13_67])]) ).
fof(f662,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,[],[f476,f493]) ).
fof(f476,plain,
! [X0] : member(X0) = ti(fun(X0,fun(fun(X0,bool),bool)),member(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] : member(X0) = ti(fun(X0,fun(fun(X0,bool),bool)),member(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).
fof(f1213,plain,
spl13_66,
inference(avatar_split_clause,[],[f661,f1211]) ).
fof(f1211,plain,
( spl13_66
<=> ! [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,[spl13_66])]) ).
fof(f661,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,[],[f475,f493]) ).
fof(f475,plain,
! [X0] : collect(X0) = ti(fun(fun(X0,bool),fun(X0,bool)),collect(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : collect(X0) = ti(fun(fun(X0,bool),fun(X0,bool)),collect(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
fof(f1209,plain,
spl13_65,
inference(avatar_split_clause,[],[f490,f1207]) ).
fof(f490,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),sK1(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f396]) ).
fof(f1137,plain,
spl13_64,
inference(avatar_split_clause,[],[f673,f1135]) ).
fof(f1135,plain,
( spl13_64
<=> ! [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,[spl13_64])]) ).
fof(f673,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,[],[f545,f493,f493]) ).
fof(f545,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,[],[f229]) ).
fof(f229,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,[],[f150]) ).
fof(f150,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/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
fof(f1133,plain,
spl13_63,
inference(avatar_split_clause,[],[f672,f1131]) ).
fof(f672,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,[],[f544,f493,f493]) ).
fof(f544,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,[],[f228]) ).
fof(f228,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,[],[f151]) ).
fof(f151,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/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
fof(f1129,plain,
spl13_62,
inference(avatar_split_clause,[],[f509,f1127]) ).
fof(f509,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,[],[f199]) ).
fof(f199,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,[],[f53]) ).
fof(f53,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/sandbox2/benchmark/theBenchmark.p',fact_23_nat__le__linear) ).
fof(f1121,plain,
spl13_61,
inference(avatar_split_clause,[],[f521,f1119]) ).
fof(f521,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,sK3(X1)) = X1
| ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X1)) ),
inference(cnf_transformation,[],[f398]) ).
fof(f398,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,sK3(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,[sK3])],[f315,f397]) ).
fof(f397,plain,
! [X1] :
( ? [X2] : hAPP(nat,nat,suc,X2) = X1
=> hAPP(nat,nat,suc,sK3(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f315,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,[],[f211]) ).
fof(f211,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,[],[f125]) ).
fof(f125,axiom,
! [X16,X45] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X16)),X45))
=> ? [X46] : hAPP(nat,nat,suc,X46) = X45 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Suc__le__D) ).
fof(f1108,plain,
spl13_60,
inference(avatar_split_clause,[],[f664,f1106]) ).
fof(f1106,plain,
( spl13_60
<=> ! [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))
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_60])]) ).
fof(f664,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))
| ~ preorder(X0) ),
inference(definition_unfolding,[],[f487,f493]) ).
fof(f487,plain,
! [X0] :
( ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f299,plain,
! [X0] :
( ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0))
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( preorder(X0)
=> ord_less_eq(X0) = ti(fun(X0,fun(X0,bool)),ord_less_eq(X0)) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X2] :
( preorder(X2)
=> ord_less_eq(X2) = ti(fun(X2,fun(X2,bool)),ord_less_eq(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
fof(f1104,plain,
spl13_59,
inference(avatar_split_clause,[],[f497,f1102]) ).
fof(f1102,plain,
( spl13_59
<=> ! [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,[spl13_59])]) ).
fof(f497,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,[],[f187]) ).
fof(f187,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,[],[f75]) ).
fof(f75,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/sandbox2/benchmark/theBenchmark.p',fact_45_diff__le__self) ).
fof(f1100,plain,
spl13_58,
inference(avatar_split_clause,[],[f491,f1098]) ).
fof(f1098,plain,
( spl13_58
<=> ! [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),sK1(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_58])]) ).
fof(f491,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),sK1(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f396]) ).
fof(f1096,plain,
( spl13_57
| ~ spl13_41
| ~ spl13_54 ),
inference(avatar_split_clause,[],[f1062,f1051,f969,f1093]) ).
fof(f1093,plain,
( spl13_57
<=> hBOOL(hAPP(pname,bool,u,pn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_57])]) ).
fof(f1062,plain,
( hBOOL(hAPP(pname,bool,u,pn))
| ~ spl13_41
| ~ spl13_54 ),
inference(resolution,[],[f1052,f971]) ).
fof(f1061,plain,
spl13_56,
inference(avatar_split_clause,[],[f666,f1059]) ).
fof(f1057,plain,
spl13_55,
inference(avatar_split_clause,[],[f579,f1055]) ).
fof(f579,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,[],[f412]) ).
fof(f412,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,[],[f253]) ).
fof(f253,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,[],[f105]) ).
fof(f105,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/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
fof(f1053,plain,
spl13_54,
inference(avatar_split_clause,[],[f578,f1051]) ).
fof(f578,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,[],[f412]) ).
fof(f1041,plain,
( spl13_53
| ~ spl13_12
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f928,f903,f788,f1039]) ).
fof(f1039,plain,
( spl13_53
<=> ! [X0] :
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).
fof(f788,plain,
( spl13_12
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).
fof(f928,plain,
( ! [X0] :
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) )
| ~ spl13_12
| ~ spl13_38 ),
inference(superposition,[],[f789,f904]) ).
fof(f789,plain,
( ! [X0] :
( ~ hBOOL(hAPP(bool,bool,fNot,X0))
| ~ hBOOL(X0) )
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f1037,plain,
spl13_52,
inference(avatar_split_clause,[],[f686,f1035]) ).
fof(f686,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,[],[f587,f493]) ).
fof(f587,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,ti(fun(X0,X1),X2),X3),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,ti(fun(X0,X1),X2),X3),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X2,X1,X3,X4] : hAPP(X2,X1,ti(fun(X2,X1),X3),X4) = hAPP(X2,X1,X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(f1033,plain,
spl13_51,
inference(avatar_split_clause,[],[f660,f1031]) ).
fof(f660,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,[],[f474,f493]) ).
fof(f474,plain,
! [X0] : finite_finite(X0) = ti(fun(fun(X0,bool),bool),finite_finite(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : finite_finite(X0) = ti(fun(fun(X0,bool),bool),finite_finite(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
fof(f1029,plain,
spl13_50,
inference(avatar_split_clause,[],[f659,f1027]) ).
fof(f1027,plain,
( spl13_50
<=> ! [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,[spl13_50])]) ).
fof(f659,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,[],[f473,f493]) ).
fof(f473,plain,
! [X0] : finite_card(X0) = ti(fun(fun(X0,bool),nat),finite_card(X0)),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0] : finite_card(X0) = ti(fun(fun(X0,bool),nat),finite_card(X0)),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1] : finite_card(X1) = ti(fun(fun(X1,bool),nat),finite_card(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).
fof(f1025,plain,
spl13_49,
inference(avatar_split_clause,[],[f658,f1023]) ).
fof(f1023,plain,
( spl13_49
<=> ! [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,[spl13_49])]) ).
fof(f658,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,[],[f472,f493]) ).
fof(f472,plain,
! [X0] : fequal(X0) = ti(fun(X0,fun(X0,bool)),fequal(X0)),
inference(cnf_transformation,[],[f169]) ).
fof(f169,plain,
! [X0] : fequal(X0) = ti(fun(X0,fun(X0,bool)),fequal(X0)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X2] : fequal(X2) = ti(fun(X2,fun(X2,bool)),fequal(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
fof(f1020,plain,
spl13_48,
inference(avatar_split_clause,[],[f648,f1017]) ).
fof(f1017,plain,
( spl13_48
<=> minus_minus(nat) = hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combi(fun(nat,fun(nat,nat))),minus_minus(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).
fof(f648,plain,
minus_minus(nat) = hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combi(fun(nat,fun(nat,nat))),minus_minus(nat)),
inference(definition_unfolding,[],[f450,f493]) ).
fof(f450,plain,
minus_minus(nat) = ti(fun(nat,fun(nat,nat)),minus_minus(nat)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
minus_minus(nat) = ti(fun(nat,fun(nat,nat)),minus_minus(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).
fof(f1011,plain,
spl13_47,
inference(avatar_split_clause,[],[f496,f1009]) ).
fof(f496,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,[],[f186]) ).
fof(f186,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,[],[f95]) ).
fof(f95,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/sandbox2/benchmark/theBenchmark.p',fact_65_subset__refl) ).
fof(f1007,plain,
~ spl13_46,
inference(avatar_split_clause,[],[f452,f1004]) ).
fof(f452,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,[],[f160]) ).
fof(f160,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/sandbox2/benchmark/theBenchmark.p',conj_5) ).
fof(f995,plain,
spl13_45,
inference(avatar_split_clause,[],[f654,f992]) ).
fof(f992,plain,
( spl13_45
<=> 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,[spl13_45])]) ).
fof(f654,plain,
fdisj = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fdisj),
inference(definition_unfolding,[],[f466,f493]) ).
fof(f466,plain,
fdisj = ti(fun(bool,fun(bool,bool)),fdisj),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
fdisj = ti(fun(bool,fun(bool,bool)),fdisj),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
fof(f990,plain,
spl13_44,
inference(avatar_split_clause,[],[f653,f987]) ).
fof(f987,plain,
( spl13_44
<=> 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,[spl13_44])]) ).
fof(f653,plain,
fconj = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fconj),
inference(definition_unfolding,[],[f465,f493]) ).
fof(f465,plain,
fconj = ti(fun(bool,fun(bool,bool)),fconj),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
fconj = ti(fun(bool,fun(bool,bool)),fconj),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
fof(f985,plain,
spl13_43,
inference(avatar_split_clause,[],[f652,f982]) ).
fof(f982,plain,
( spl13_43
<=> 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,[spl13_43])]) ).
fof(f652,plain,
fimplies = hAPP(fun(bool,fun(bool,bool)),fun(bool,fun(bool,bool)),combi(fun(bool,fun(bool,bool))),fimplies),
inference(definition_unfolding,[],[f464,f493]) ).
fof(f464,plain,
fimplies = ti(fun(bool,fun(bool,bool)),fimplies),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
fimplies = ti(fun(bool,fun(bool,bool)),fimplies),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
fof(f976,plain,
spl13_42,
inference(avatar_split_clause,[],[f479,f974]) ).
fof(f479,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X0)),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X0)),X0)),
inference(rectify,[],[f66]) ).
fof(f66,axiom,
! [X16] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X16)),X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Suc__n__not__le__n) ).
fof(f972,plain,
spl13_41,
inference(avatar_split_clause,[],[f451,f969]) ).
fof(f451,plain,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(cnf_transformation,[],[f159]) ).
fof(f159,axiom,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(f967,plain,
( spl13_40
| ~ spl13_8
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f952,f903,f770,f965]) ).
fof(f965,plain,
( spl13_40
<=> ! [X0] : hAPP(nat,nat,suc,X0) != hAPP(nat,nat,combi(nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).
fof(f952,plain,
( ! [X0] : hAPP(nat,nat,suc,X0) != hAPP(nat,nat,combi(nat),X0)
| ~ spl13_8
| ~ spl13_38 ),
inference(superposition,[],[f771,f904]) ).
fof(f963,plain,
~ spl13_39,
inference(avatar_split_clause,[],[f442,f960]) ).
fof(f442,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,[],[f163]) ).
fof(f163,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,[],[f162]) ).
fof(f162,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,[],[f161]) ).
fof(f161,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/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(f905,plain,
spl13_38,
inference(avatar_split_clause,[],[f685,f903]) ).
fof(f685,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,hAPP(X0,X0,combi(X0),X3)),
inference(definition_unfolding,[],[f586,f493]) ).
fof(f586,plain,
! [X2,X3,X0,X1] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0,X1,X2,X3] : hAPP(X0,X1,X2,X3) = hAPP(X0,X1,X2,ti(X0,X3)),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X2,X1,X3,X4] : hAPP(X2,X1,X3,X4) = hAPP(X2,X1,X3,ti(X2,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(f901,plain,
spl13_37,
inference(avatar_split_clause,[],[f684,f899]) ).
fof(f684,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = hAPP(X0,X0,combi(X0),hAPP(X1,X0,X2,X3)),
inference(definition_unfolding,[],[f585,f493]) ).
fof(f585,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0,X2,X3) = ti(X0,hAPP(X1,X0,X2,X3)),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X1,X2,X3,X4] : hAPP(X2,X1,X3,X4) = ti(X1,hAPP(X2,X1,X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(f897,plain,
spl13_36,
inference(avatar_split_clause,[],[f657,f895]) ).
fof(f657,plain,
! [X0] : combi(X0) = hAPP(fun(X0,X0),fun(X0,X0),combi(fun(X0,X0)),combi(X0)),
inference(definition_unfolding,[],[f471,f493]) ).
fof(f471,plain,
! [X0] : combi(X0) = ti(fun(X0,X0),combi(X0)),
inference(cnf_transformation,[],[f168]) ).
fof(f168,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/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
fof(f893,plain,
spl13_35,
inference(avatar_split_clause,[],[f508,f891]) ).
fof(f508,plain,
! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1)) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0,X1] :
( hBOOL(X1)
| hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1)) ),
inference(rectify,[],[f149]) ).
fof(f149,axiom,
! [X52,X53] :
( hBOOL(X53)
| hBOOL(X52)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X52),X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
fof(f889,plain,
spl13_34,
inference(avatar_split_clause,[],[f505,f887]) ).
fof(f505,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1)) ),
inference(cnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1)) ),
inference(rectify,[],[f154]) ).
fof(f154,axiom,
! [X52,X53] :
( hBOOL(X53)
| ~ hBOOL(X52)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X52),X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(f885,plain,
spl13_33,
inference(avatar_split_clause,[],[f500,f883]) ).
fof(f500,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f144]) ).
fof(f144,axiom,
! [X53,X52] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X52),X53))
| ~ hBOOL(X53)
| ~ hBOOL(X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
fof(f881,plain,
spl13_32,
inference(avatar_split_clause,[],[f488,f879]) ).
fof(f879,plain,
( spl13_32
<=> ! [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,[spl13_32])]) ).
fof(f488,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f300,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1))
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( preorder(X0)
=> ! [X1] : hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less_eq(X0),X1),X1)) ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X2] :
( preorder(X2)
=> ! [X20] : hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X20),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_order__refl) ).
fof(f876,plain,
spl13_31,
inference(avatar_split_clause,[],[f651,f873]) ).
fof(f651,plain,
fNot = hAPP(fun(bool,bool),fun(bool,bool),combi(fun(bool,bool)),fNot),
inference(definition_unfolding,[],[f463,f493]) ).
fof(f463,plain,
fNot = ti(fun(bool,bool),fNot),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
fNot = ti(fun(bool,bool),fNot),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
fof(f871,plain,
spl13_30,
inference(avatar_split_clause,[],[f514,f869]) ).
fof(f514,plain,
! [X0,X1] :
( X0 = X1
| hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1) ),
inference(cnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0,X1] :
( X0 = X1
| hAPP(nat,nat,suc,X0) != hAPP(nat,nat,suc,X1) ),
inference(ennf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0,X1] :
( hAPP(nat,nat,suc,X0) = hAPP(nat,nat,suc,X1)
=> X0 = X1 ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X20,X21] :
( hAPP(nat,nat,suc,X20) = hAPP(nat,nat,suc,X21)
=> X20 = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Suc__inject) ).
fof(f867,plain,
spl13_29,
inference(avatar_split_clause,[],[f507,f865]) ).
fof(f507,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(rectify,[],[f145]) ).
fof(f145,axiom,
! [X52,X53] :
( hBOOL(X52)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X52),X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(f863,plain,
spl13_28,
inference(avatar_split_clause,[],[f506,f861]) ).
fof(f506,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X0),X1)) ),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X52,X53] :
( hBOOL(X53)
| ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X52),X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
fof(f859,plain,
spl13_27,
inference(avatar_split_clause,[],[f504,f857]) ).
fof(f504,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X53,X52] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X52),X53))
| hBOOL(X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(f855,plain,
spl13_26,
inference(avatar_split_clause,[],[f503,f853]) ).
fof(f503,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f147]) ).
fof(f147,axiom,
! [X53,X52] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X52),X53))
| ~ hBOOL(X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
fof(f851,plain,
spl13_25,
inference(avatar_split_clause,[],[f502,f849]) ).
fof(f502,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f148]) ).
fof(f148,axiom,
! [X52,X53] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X52),X53))
| ~ hBOOL(X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
fof(f847,plain,
spl13_24,
inference(avatar_split_clause,[],[f501,f845]) ).
fof(f501,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f191]) ).
fof(f191,plain,
! [X0,X1] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f153]) ).
fof(f153,axiom,
! [X52,X53] :
( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,X52),X53))
| ~ hBOOL(X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
fof(f843,plain,
spl13_23,
inference(avatar_split_clause,[],[f647,f840]) ).
fof(f840,plain,
( spl13_23
<=> suc = hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).
fof(f647,plain,
suc = hAPP(fun(nat,nat),fun(nat,nat),combi(fun(nat,nat)),suc),
inference(definition_unfolding,[],[f448,f493]) ).
fof(f448,plain,
suc = ti(fun(nat,nat),suc),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
suc = ti(fun(nat,nat),suc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_OSuc_res) ).
fof(f838,plain,
spl13_22,
inference(avatar_split_clause,[],[f646,f835]) ).
fof(f646,plain,
u = hAPP(fun(pname,bool),fun(pname,bool),combi(fun(pname,bool)),u),
inference(definition_unfolding,[],[f447,f493]) ).
fof(f447,plain,
u = ti(fun(pname,bool),u),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
u = ti(fun(pname,bool),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_U_res) ).
fof(f833,plain,
spl13_21,
inference(avatar_split_clause,[],[f645,f830]) ).
fof(f830,plain,
( spl13_21
<=> mgt_call = hAPP(fun(pname,x_a),fun(pname,x_a),combi(fun(pname,x_a)),mgt_call) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).
fof(f645,plain,
mgt_call = hAPP(fun(pname,x_a),fun(pname,x_a),combi(fun(pname,x_a)),mgt_call),
inference(definition_unfolding,[],[f446,f493]) ).
fof(f446,plain,
mgt_call = ti(fun(pname,x_a),mgt_call),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
mgt_call = ti(fun(pname,x_a),mgt_call),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_mgt__call_res) ).
fof(f828,plain,
spl13_20,
inference(avatar_split_clause,[],[f644,f825]) ).
fof(f644,plain,
g = hAPP(fun(x_a,bool),fun(x_a,bool),combi(fun(x_a,bool)),g),
inference(definition_unfolding,[],[f445,f493]) ).
fof(f445,plain,
g = ti(fun(x_a,bool),g),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
g = ti(fun(x_a,bool),g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_G_res) ).
fof(f823,plain,
spl13_19,
inference(avatar_split_clause,[],[f477,f821]) ).
fof(f477,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)),
inference(cnf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X0),X0)),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X16] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_le__refl) ).
fof(f819,plain,
spl13_18,
inference(avatar_split_clause,[],[f484,f817]) ).
fof(f817,plain,
( spl13_18
<=> ! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).
fof(f484,plain,
! [X0,X1] :
( hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1))
| ~ finite_finite_1(X0) ),
inference(ennf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( finite_finite_1(X0)
=> ! [X1] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X1)) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( finite_finite_1(X0)
=> ! [X7] : hBOOL(hAPP(fun(X0,bool),bool,finite_finite(X0),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__code) ).
fof(f813,plain,
spl13_17,
inference(avatar_split_clause,[],[f656,f811]) ).
fof(f656,plain,
! [X0] : undefined(X0) = hAPP(X0,X0,combi(X0),undefined(X0)),
inference(definition_unfolding,[],[f470,f493]) ).
fof(f470,plain,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
inference(cnf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2] : undefined(X2) = ti(X2,undefined(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
fof(f808,plain,
spl13_16,
inference(avatar_split_clause,[],[f650,f806]) ).
fof(f806,plain,
( spl13_16
<=> ! [X0] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).
fof(f650,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,combi(bool),X0)) ),
inference(definition_unfolding,[],[f456,f493]) ).
fof(f456,plain,
! [X0] :
( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ),
inference(cnf_transformation,[],[f389]) ).
fof(f389,plain,
! [X0] :
( ( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) )
& ( hBOOL(X0)
| ~ hBOOL(ti(bool,X0)) ) ),
inference(nnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0] :
( hBOOL(ti(bool,X0))
<=> hBOOL(X0) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X3] :
( hBOOL(ti(bool,X3))
<=> hBOOL(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(f804,plain,
spl13_15,
inference(avatar_split_clause,[],[f649,f802]) ).
fof(f802,plain,
( spl13_15
<=> ! [X0] :
( hBOOL(hAPP(bool,bool,combi(bool),X0))
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).
fof(f649,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,combi(bool),X0))
| ~ hBOOL(X0) ),
inference(definition_unfolding,[],[f457,f493]) ).
fof(f457,plain,
! [X0] :
( hBOOL(ti(bool,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f800,plain,
spl13_14,
inference(avatar_split_clause,[],[f449,f797]) ).
fof(f449,plain,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
inference(cnf_transformation,[],[f155]) ).
fof(f155,axiom,
hBOOL(hAPP(fun(pname,bool),bool,finite_finite(pname),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f794,plain,
spl13_13,
inference(avatar_split_clause,[],[f523,f792]) ).
fof(f792,plain,
( spl13_13
<=> ! [X0,X1] :
( finite_finite_1(fun(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).
fof(f523,plain,
! [X0,X1] :
( finite_finite_1(fun(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0,X1] :
( finite_finite_1(fun(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(flattening,[],[f317]) ).
fof(f317,plain,
! [X0,X1] :
( finite_finite_1(fun(X0,X1))
| ~ finite_finite_1(X0)
| ~ finite_finite_1(X1) ),
inference(ennf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0,X1] :
( ( finite_finite_1(X0)
& finite_finite_1(X1) )
=> finite_finite_1(fun(X0,X1)) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X48,X49] :
( ( finite_finite_1(X48)
& finite_finite_1(X49) )
=> finite_finite_1(fun(X48,X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
fof(f790,plain,
spl13_12,
inference(avatar_split_clause,[],[f483,f788]) ).
fof(f483,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(bool,bool,fNot,X0)) ),
inference(rectify,[],[f138]) ).
fof(f138,axiom,
! [X52] :
( ~ hBOOL(X52)
| ~ hBOOL(hAPP(bool,bool,fNot,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(f786,plain,
spl13_11,
inference(avatar_split_clause,[],[f482,f784]) ).
fof(f482,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0] :
( hBOOL(hAPP(bool,bool,fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f139]) ).
fof(f139,axiom,
! [X52] :
( hBOOL(hAPP(bool,bool,fNot,X52))
| hBOOL(X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(f782,plain,
spl13_10,
inference(avatar_split_clause,[],[f643,f779]) ).
fof(f643,plain,
pn = hAPP(pname,pname,combi(pname),pn),
inference(definition_unfolding,[],[f444,f493]) ).
fof(f444,plain,
pn = ti(pname,pn),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
pn = ti(pname,pn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_pn_res) ).
fof(f777,plain,
spl13_9,
inference(avatar_split_clause,[],[f642,f774]) ).
fof(f642,plain,
na = hAPP(nat,nat,combi(nat),na),
inference(definition_unfolding,[],[f443,f493]) ).
fof(f443,plain,
na = ti(nat,na),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
na = ti(nat,na),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_na_res) ).
fof(f772,plain,
spl13_8,
inference(avatar_split_clause,[],[f468,f770]) ).
fof(f468,plain,
! [X0] : hAPP(nat,nat,suc,X0) != X0,
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0] : hAPP(nat,nat,suc,X0) != X0,
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X16] : hAPP(nat,nat,suc,X16) != X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Suc__n__not__n) ).
fof(f768,plain,
spl13_7,
inference(avatar_split_clause,[],[f511,f766]) ).
fof(f766,plain,
( spl13_7
<=> ! [X0,X1] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).
fof(f511,plain,
! [X0,X1] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(cnf_transformation,[],[f303]) ).
fof(f303,plain,
! [X0,X1] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(ennf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0,X1] :
( preorder(X1)
=> preorder(fun(X0,X1)) ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X48,X49] :
( preorder(X49)
=> preorder(fun(X48,X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
fof(f764,plain,
spl13_6,
inference(avatar_split_clause,[],[f510,f762]) ).
fof(f762,plain,
( spl13_6
<=> ! [X0,X1] :
( order(fun(X0,X1))
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f510,plain,
! [X0,X1] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0,X1] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(ennf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0,X1] :
( order(X1)
=> order(fun(X0,X1)) ),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X48,X49] :
( order(X49)
=> order(fun(X48,X49)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
fof(f760,plain,
spl13_5,
inference(avatar_split_clause,[],[f462,f757]) ).
fof(f757,plain,
( spl13_5
<=> preorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f462,plain,
preorder(bool),
inference(cnf_transformation,[],[f134]) ).
fof(f134,axiom,
preorder(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
fof(f755,plain,
spl13_4,
inference(avatar_split_clause,[],[f461,f752]) ).
fof(f752,plain,
( spl13_4
<=> preorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f461,plain,
preorder(nat),
inference(cnf_transformation,[],[f132]) ).
fof(f132,axiom,
preorder(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
fof(f750,plain,
spl13_3,
inference(avatar_split_clause,[],[f460,f747]) ).
fof(f747,plain,
( spl13_3
<=> order(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f460,plain,
order(bool),
inference(cnf_transformation,[],[f136]) ).
fof(f136,axiom,
order(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
fof(f745,plain,
spl13_2,
inference(avatar_split_clause,[],[f459,f742]) ).
fof(f742,plain,
( spl13_2
<=> order(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f459,plain,
order(nat),
inference(cnf_transformation,[],[f133]) ).
fof(f133,axiom,
order(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
fof(f740,plain,
spl13_1,
inference(avatar_split_clause,[],[f458,f737]) ).
fof(f737,plain,
( spl13_1
<=> finite_finite_1(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f458,plain,
finite_finite_1(bool),
inference(cnf_transformation,[],[f135]) ).
fof(f135,axiom,
finite_finite_1(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 30 03:29:04 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % (9209)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.38 % (9212)WARNING: value z3 for option sas not known
% 0.19/0.38 % (9212)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)
% 0.19/0.38 % (9213)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.38 % (9215)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)
% 0.19/0.38 % (9214)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)
% 0.19/0.38 % (9211)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.38 % (9216)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.19/0.38 % (9210)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 2.07/0.69 % (9214)First to succeed.
% 2.58/0.73 % (9214)Refutation found. Thanks to Tanya!
% 2.58/0.73 % SZS status Theorem for theBenchmark
% 2.58/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/0.74 % (9214)------------------------------
% 2.58/0.74 % (9214)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.58/0.74 % (9214)Termination reason: Refutation
% 2.58/0.74
% 2.58/0.74 % (9214)Memory used [KB]: 3811
% 2.58/0.74 % (9214)Time elapsed: 0.348 s
% 2.58/0.74 % (9214)Instructions burned: 705 (million)
% 2.58/0.74 % (9214)------------------------------
% 2.58/0.74 % (9214)------------------------------
% 2.58/0.74 % (9209)Success in time 0.384 s
%------------------------------------------------------------------------------