TSTP Solution File: SWW533_5 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW533_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:41:16 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 268
% Syntax : Number of formulae : 642 ( 214 unt; 74 typ; 0 def)
% Number of atoms : 1220 ( 345 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1087 ( 435 ~; 397 |; 60 &)
% ( 133 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 87 ( 53 >; 34 *; 0 +; 0 <<)
% Number of predicates : 124 ( 122 usr; 108 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 4 con; 0-5 aty)
% Number of variables : 1062 ( 974 !; 13 ?;1062 :)
% ( 75 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
huffma1450048681e_tree: $tType > $tType ).
tff(type_def_8,type,
list: $tType > $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_11,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
huffma675207370phabet:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).
tff(func_def_6,type,
huffma1516701463abet_F:
!>[X0: $tType] : ( list(huffma1450048681e_tree(X0)) > fun(X0,bool) ) ).
tff(func_def_7,type,
huffma410068972_depth:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_8,type,
huffma1352802255e_freq:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_9,type,
huffma409467474freq_F:
!>[X0: $tType] : ( ( list(huffma1450048681e_tree(X0)) * X0 ) > nat ) ).
tff(func_def_10,type,
huffma945805758height:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_11,type,
huffma632063779ight_F:
!>[X0: $tType] : ( list(huffma1450048681e_tree(X0)) > nat ) ).
tff(func_def_12,type,
huffma1146269203erNode:
!>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_13,type,
huffma2021818691e_Leaf:
!>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_14,type,
huffma107959123e_case:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_15,type,
huffma1280178957ee_rec:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_16,type,
inf_inf:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_17,type,
dropWhile:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).
tff(func_def_18,type,
lexn:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * nat ) > fun(product_prod(list(X0),list(X0)),bool) ) ).
tff(func_def_19,type,
linord467138063of_set:
!>[X0: $tType] : ( fun(X0,bool) > list(X0) ) ).
tff(func_def_20,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_21,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_22,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_23,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_24,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_25,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_26,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_27,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_28,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_29,type,
fFalse: bool ).
tff(func_def_30,type,
fTrue: bool ).
tff(func_def_31,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_32,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_33,type,
a1: a ).
tff(func_def_34,type,
sK0:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_35,type,
sK1:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_36,type,
sK2:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_37,type,
sK3:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_38,type,
sK4:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_39,type,
sK5:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_40,type,
sK6:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_41,type,
sK7:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_42,type,
sK8:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_43,type,
sK9:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_44,type,
sK10:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_45,type,
sK11:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_46,type,
sK12:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_47,type,
sK13:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_48,type,
sK14:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_49,type,
sK15:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_50,type,
sK16:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_51,type,
sK17:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * list(X0) ) > X0 ) ).
tff(pred_def_1,type,
lattice:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
bounded_lattice:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
semilattice_inf:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
bounded_lattice_bot:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
huffma1518433673istent:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_12,type,
huffma594769176tent_F:
!>[X0: $tType] : ( list(huffma1450048681e_tree(X0)) > $o ) ).
tff(pred_def_13,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_14,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(f1227,plain,
$false,
inference(avatar_sat_refutation,[],[f598,f603,f608,f613,f618,f623,f628,f633,f638,f643,f648,f653,f658,f663,f668,f673,f678,f683,f688,f692,f696,f700,f704,f708,f712,f716,f720,f724,f728,f732,f736,f740,f744,f748,f755,f760,f764,f769,f773,f781,f786,f794,f799,f803,f807,f811,f815,f819,f823,f835,f839,f843,f848,f852,f856,f860,f864,f868,f872,f882,f886,f890,f906,f910,f914,f922,f927,f936,f940,f945,f949,f953,f957,f961,f995,f999,f1003,f1007,f1012,f1017,f1022,f1027,f1041,f1048,f1052,f1056,f1064,f1069,f1073,f1078,f1083,f1091,f1095,f1099,f1104,f1109,f1113,f1123,f1127,f1153,f1163,f1169,f1177,f1181,f1185,f1219,f1226]) ).
tff(f1226,plain,
( spl18_1
| ~ spl18_58
| ~ spl18_61
| ~ spl18_65
| ~ spl18_68
| ~ spl18_99
| ~ spl18_103
| ~ spl18_107 ),
inference(avatar_split_clause,[],[f1225,f1216,f1167,f1121,f925,f908,f880,f862,f595]) ).
tff(f595,plain,
( spl18_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
tff(f862,plain,
( spl18_58
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_58])]) ).
tff(f880,plain,
( spl18_61
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_61])]) ).
tff(f908,plain,
( spl18_65
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = huffma1516701463abet_F(X0,nil(huffma1450048681e_tree(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_65])]) ).
tff(f925,plain,
( spl18_68
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_68])]) ).
tff(f1121,plain,
( spl18_99
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK7(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_99])]) ).
tff(f1167,plain,
( spl18_103
<=> ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_103])]) ).
tff(f1216,plain,
( spl18_107
<=> pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),a1),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_107])]) ).
tff(f1225,plain,
( pp(fFalse)
| ~ spl18_58
| ~ spl18_61
| ~ spl18_65
| ~ spl18_68
| ~ spl18_99
| ~ spl18_103
| ~ spl18_107 ),
inference(forward_demodulation,[],[f1224,f863]) ).
tff(f863,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 )
| ~ spl18_58 ),
inference(avatar_component_clause,[],[f862]) ).
tff(f1224,plain,
( pp(aa(a,bool,combk(bool,a,fFalse),a1))
| ~ spl18_61
| ~ spl18_65
| ~ spl18_68
| ~ spl18_99
| ~ spl18_103
| ~ spl18_107 ),
inference(forward_demodulation,[],[f1223,f1170]) ).
tff(f1170,plain,
( ! [X0: $tType] : ( combk(bool,X0,fFalse) = combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)) )
| ~ spl18_99
| ~ spl18_103 ),
inference(resolution,[],[f1168,f1122]) ).
tff(f1122,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,sK7(X0,X1)))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl18_99 ),
inference(avatar_component_clause,[],[f1121]) ).
tff(f1168,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))
| ~ spl18_103 ),
inference(avatar_component_clause,[],[f1167]) ).
tff(f1223,plain,
( pp(aa(a,bool,combc(a,fun(a,bool),bool,member(a),combk(bool,a,fFalse)),a1))
| ~ spl18_61
| ~ spl18_65
| ~ spl18_68
| ~ spl18_107 ),
inference(forward_demodulation,[],[f1222,f928]) ).
tff(f928,plain,
( ! [X0: $tType] : ( set(X0,nil(X0)) = combk(bool,X0,fFalse) )
| ~ spl18_61
| ~ spl18_68 ),
inference(superposition,[],[f926,f881]) ).
tff(f881,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) )
| ~ spl18_61 ),
inference(avatar_component_clause,[],[f880]) ).
tff(f926,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
| ~ spl18_68 ),
inference(avatar_component_clause,[],[f925]) ).
tff(f1222,plain,
( pp(aa(a,bool,combc(a,fun(a,bool),bool,member(a),set(a,nil(a))),a1))
| ~ spl18_61
| ~ spl18_65
| ~ spl18_107 ),
inference(forward_demodulation,[],[f1221,f881]) ).
tff(f1221,plain,
( pp(aa(a,bool,combc(a,fun(a,bool),bool,member(a),bot_bot(fun(a,bool))),a1))
| ~ spl18_65
| ~ spl18_107 ),
inference(forward_demodulation,[],[f1220,f909]) ).
tff(f909,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = huffma1516701463abet_F(X0,nil(huffma1450048681e_tree(X0))) )
| ~ spl18_65 ),
inference(avatar_component_clause,[],[f908]) ).
tff(f1220,plain,
( pp(aa(a,bool,combc(a,fun(a,bool),bool,member(a),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a)))),a1))
| ~ spl18_107 ),
inference(forward_demodulation,[],[f1218,f548]) ).
tff(f548,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f128]) ).
tff(f128,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X60: X0,X61: X1,X62: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X62,X61),X60) = aa(X1,X2,aa(X0,fun(X1,X2),X62,X60),X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f1218,plain,
( pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),a1),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a)))))
| ~ spl18_107 ),
inference(avatar_component_clause,[],[f1216]) ).
tff(f1219,plain,
spl18_107,
inference(avatar_split_clause,[],[f405,f1216]) ).
tff(f405,plain,
pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),a1),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a))))),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(fun(a,bool),bool,aa(a,fun(fun(a,bool),bool),member(a),a1),huffma1516701463abet_F(a,nil(huffma1450048681e_tree(a))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Nil_I3_J) ).
tff(f1185,plain,
spl18_106,
inference(avatar_split_clause,[],[f545,f1183]) ).
tff(f1183,plain,
( spl18_106
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_106])]) ).
tff(f545,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f127]) ).
tff(f127,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X60: X0,X61: fun(X0,X1),X62: fun(X1,X2)] : ( aa(X0,X2,combb(X1,X2,X0,X62,X61),X60) = aa(X1,X2,X62,aa(X0,X1,X61,X60)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1181,plain,
spl18_105,
inference(avatar_split_clause,[],[f491,f1179]) ).
tff(f1179,plain,
( spl18_105
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_105])]) ).
tff(f491,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X1: $tType,X47: fun(X1,bool),X39: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X39,X47) = inf_inf(fun(X1,bool),X39,inf_inf(fun(X1,bool),X39,X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Int__left__absorb) ).
tff(f1177,plain,
spl18_104,
inference(avatar_split_clause,[],[f456,f1175]) ).
tff(f1175,plain,
( spl18_104
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( lexn(X0,X1,zero_zero(nat)) = bot_bot(fun(product_prod(list(X0),list(X0)),bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_104])]) ).
tff(f456,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( lexn(X0,X1,zero_zero(nat)) = bot_bot(fun(product_prod(list(X0),list(X0)),bool)) ),
inference(cnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : ( lexn(X0,X1,zero_zero(nat)) = bot_bot(fun(product_prod(list(X0),list(X0)),bool)) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X1: $tType,X41: fun(product_prod(X1,X1),bool)] : ( lexn(X1,X41,zero_zero(nat)) = bot_bot(fun(product_prod(list(X1),list(X1)),bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_lexn_Osimps_I1_J) ).
tff(f1169,plain,
( spl18_103
| ~ spl18_68
| ~ spl18_102 ),
inference(avatar_split_clause,[],[f1165,f1161,f925,f1167]) ).
tff(f1161,plain,
( spl18_102
<=> ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_102])]) ).
tff(f1165,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))
| ~ spl18_68
| ~ spl18_102 ),
inference(forward_demodulation,[],[f1164,f926]) ).
tff(f1164,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))),X1))
| ~ spl18_102 ),
inference(forward_demodulation,[],[f1162,f548]) ).
tff(f1162,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))
| ~ spl18_102 ),
inference(avatar_component_clause,[],[f1161]) ).
tff(f1163,plain,
spl18_102,
inference(avatar_split_clause,[],[f454,f1161]) ).
tff(f454,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X1: $tType,X38: X1] : ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X38),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_empty__iff) ).
tff(f1153,plain,
spl18_101,
inference(avatar_split_clause,[],[f503,f1151]) ).
tff(f1151,plain,
( spl18_101
<=> ! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
| ~ pp(aa(X0,bool,X2,sK13(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_101])]) ).
tff(f503,plain,
! [X0: $tType,X2: fun(X0,bool),X1: list(X0)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
| ~ pp(aa(X0,bool,X2,sK13(X0,X1,X2))) ),
inference(cnf_transformation,[],[f360]) ).
tff(f360,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = dropWhile(X0,X2,X1) )
| ( ~ pp(aa(X0,bool,X2,sK13(X0,X1,X2)))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1,X2)),set(X0,X1))) ) )
& ( ! [X4: X0] :
( pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1))) )
| ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f358,f359]) ).
tff(f359,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) )
=> ( ~ pp(aa(X0,bool,X2,sK13(X0,X1,X2)))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK13(X0,X1,X2)),set(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f358,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = dropWhile(X0,X2,X1) )
| ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) )
& ( ! [X4: X0] :
( pp(aa(X0,bool,X2,X4))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),set(X0,X1))) )
| ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
inference(rectify,[],[f357]) ).
tff(f357,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( ( nil(X0) = dropWhile(X0,X2,X1) )
| ? [X3: X0] :
( ~ pp(aa(X0,bool,X2,X3))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) )
& ( ! [X3: X0] :
( pp(aa(X0,bool,X2,X3))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) )
| ( nil(X0) != dropWhile(X0,X2,X1) ) ) ),
inference(nnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
<=> ! [X3: X0] :
( pp(aa(X0,bool,X2,X3))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1))) ) ),
inference(ennf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( nil(X0) = dropWhile(X0,X2,X1) )
<=> ! [X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),set(X0,X1)))
=> pp(aa(X0,bool,X2,X3)) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X1: $tType,X19: list(X1),X20: fun(X1,bool)] :
( ( dropWhile(X1,X20,X19) = nil(X1) )
<=> ! [X21: X1] :
( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X21),set(X1,X19)))
=> pp(aa(X1,bool,X20,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dropWhile__eq__Nil__conv) ).
tff(f1127,plain,
( spl18_100
| ~ spl18_68
| ~ spl18_96 ),
inference(avatar_split_clause,[],[f1105,f1102,f925,f1125]) ).
tff(f1125,plain,
( spl18_100
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK8(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_100])]) ).
tff(f1102,plain,
( spl18_96
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK8(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_96])]) ).
tff(f1105,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK8(X0,X1))) )
| ~ spl18_68
| ~ spl18_96 ),
inference(forward_demodulation,[],[f1103,f926]) ).
tff(f1103,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK8(X0,X1))) )
| ~ spl18_96 ),
inference(avatar_component_clause,[],[f1102]) ).
tff(f1123,plain,
( spl18_99
| ~ spl18_68
| ~ spl18_95 ),
inference(avatar_split_clause,[],[f1100,f1097,f925,f1121]) ).
tff(f1097,plain,
( spl18_95
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK7(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_95])]) ).
tff(f1100,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK7(X0,X1))) )
| ~ spl18_68
| ~ spl18_95 ),
inference(forward_demodulation,[],[f1098,f926]) ).
tff(f1098,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK7(X0,X1))) )
| ~ spl18_95 ),
inference(avatar_component_clause,[],[f1097]) ).
tff(f1113,plain,
( spl18_98
| ~ spl18_68
| ~ spl18_90 ),
inference(avatar_split_clause,[],[f1074,f1071,f925,f1111]) ).
tff(f1111,plain,
( spl18_98
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),combk(bool,X0,fFalse),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_98])]) ).
tff(f1071,plain,
( spl18_90
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_90])]) ).
tff(f1074,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),combk(bool,X0,fFalse),X1) )
| ~ spl18_68
| ~ spl18_90 ),
inference(forward_demodulation,[],[f1072,f926]) ).
tff(f1072,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) )
| ~ spl18_90 ),
inference(avatar_component_clause,[],[f1071]) ).
tff(f1109,plain,
( spl18_97
| ~ spl18_68
| ~ spl18_88 ),
inference(avatar_split_clause,[],[f1065,f1062,f925,f1107]) ).
tff(f1107,plain,
( spl18_97
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X1,combk(bool,X0,fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_97])]) ).
tff(f1062,plain,
( spl18_88
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_88])]) ).
tff(f1065,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X1,combk(bool,X0,fFalse)) )
| ~ spl18_68
| ~ spl18_88 ),
inference(forward_demodulation,[],[f1063,f926]) ).
tff(f1063,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) )
| ~ spl18_88 ),
inference(avatar_component_clause,[],[f1062]) ).
tff(f1104,plain,
spl18_96,
inference(avatar_split_clause,[],[f586,f1102]) ).
tff(f586,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK8(X0,X1))) ),
inference(forward_demodulation,[],[f481,f447]) ).
tff(f447,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X1: $tType,X20: fun(X1,bool)] : ( collect(X1,X20) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
tff(f481,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK8(X0,X1))) ),
inference(cnf_transformation,[],[f344]) ).
tff(f344,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK8(X0,X1))) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f342,f343]) ).
tff(f343,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,X1,sK8(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f342,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(rectify,[],[f341]) ).
tff(f341,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(nnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
<=> ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X1: $tType,X20: fun(X1,bool)] :
( ( bot_bot(fun(X1,bool)) = collect(X1,X20) )
<=> ! [X21: X1] : ~ pp(aa(X1,bool,X20,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Collect__empty__eq) ).
tff(f1099,plain,
spl18_95,
inference(avatar_split_clause,[],[f584,f1097]) ).
tff(f584,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK7(X0,X1))) ),
inference(forward_demodulation,[],[f479,f447]) ).
tff(f479,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK7(X0,X1))) ),
inference(cnf_transformation,[],[f340]) ).
tff(f340,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK7(X0,X1))) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f338,f339]) ).
tff(f339,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,X1,sK7(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f338,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(rectify,[],[f337]) ).
tff(f337,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
<=> ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X1: $tType,X20: fun(X1,bool)] :
( ( bot_bot(fun(X1,bool)) = collect(X1,X20) )
<=> ! [X21: X1] : ~ pp(aa(X1,bool,X20,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_empty__Collect__eq) ).
tff(f1095,plain,
spl18_94,
inference(avatar_split_clause,[],[f554,f1093]) ).
tff(f1093,plain,
( spl18_94
<=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X3: nat,X5: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( ( X1 = X4 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_94])]) ).
tff(f554,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
( ( X1 = X4 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
inference(cnf_transformation,[],[f382]) ).
tff(f382,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
( ( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
| ( X1 != X4 )
| ( X2 != X5 )
| ( X3 != X6 ) )
& ( ( ( X1 = X4 )
& ( X2 = X5 )
& ( X3 = X6 ) )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
inference(flattening,[],[f381]) ).
tff(f381,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
( ( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
| ( X1 != X4 )
| ( X2 != X5 )
| ( X3 != X6 ) )
& ( ( ( X1 = X4 )
& ( X2 = X5 )
& ( X3 = X6 ) )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
inference(nnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
<=> ( ( X1 = X4 )
& ( X2 = X5 )
& ( X3 = X6 ) ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X1: $tType,X22: huffma1450048681e_tree(X1),X23: huffma1450048681e_tree(X1),X5: nat,X24: huffma1450048681e_tree(X1),X25: huffma1450048681e_tree(X1),X7: nat] :
( ( huffma1146269203erNode(X1,X7,X25,X24) = huffma1146269203erNode(X1,X5,X23,X22) )
<=> ( ( X22 = X24 )
& ( X23 = X25 )
& ( X5 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_tree_Osimps_I2_J) ).
tff(f1091,plain,
spl18_93,
inference(avatar_split_clause,[],[f553,f1089]) ).
tff(f1089,plain,
( spl18_93
<=> ! [X0: $tType,X6: nat,X4: huffma1450048681e_tree(X0),X3: nat,X5: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( ( X2 = X5 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_93])]) ).
tff(f553,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
( ( X2 = X5 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
inference(cnf_transformation,[],[f382]) ).
tff(f1083,plain,
( spl18_92
| ~ spl18_91 ),
inference(avatar_split_clause,[],[f1079,f1076,f1081]) ).
tff(f1081,plain,
( spl18_92
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_92])]) ).
tff(f1076,plain,
( spl18_91
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_91])]) ).
tff(f1079,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl18_91 ),
inference(forward_demodulation,[],[f1077,f548]) ).
tff(f1077,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl18_91 ),
inference(avatar_component_clause,[],[f1076]) ).
tff(f1078,plain,
spl18_91,
inference(avatar_split_clause,[],[f457,f1076]) ).
tff(f457,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f131]) ).
tff(f131,axiom,
! [X61: bool,X62: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X62),X61))
| ~ pp(X61)
| ~ pp(X62) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f1073,plain,
spl18_90,
inference(avatar_split_clause,[],[f453,f1071]) ).
tff(f453,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X1: $tType,X47: fun(X1,bool)] : ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),bot_bot(fun(X1,bool)),X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Int__empty__left) ).
tff(f1069,plain,
( ~ spl18_16
| spl18_89
| ~ spl18_36
| ~ spl18_76 ),
inference(avatar_split_clause,[],[f1033,f992,f758,f1067,f670]) ).
tff(f670,plain,
( spl18_16
<=> bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
tff(f1067,plain,
( spl18_89
<=> ! [X0: bool] : ~ ord_less(bool,X0,fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_89])]) ).
tff(f758,plain,
( spl18_36
<=> ! [X0: $tType,X1: X0] :
( ~ ord_less(X0,X1,bot_bot(X0))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_36])]) ).
tff(f992,plain,
( spl18_76
<=> ( fFalse = bot_bot(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_76])]) ).
tff(f1033,plain,
( ! [X0: bool] :
( ~ ord_less(bool,X0,fFalse)
| ~ bot(bool) )
| ~ spl18_36
| ~ spl18_76 ),
inference(superposition,[],[f759,f994]) ).
tff(f994,plain,
( ( fFalse = bot_bot(bool) )
| ~ spl18_76 ),
inference(avatar_component_clause,[],[f992]) ).
tff(f759,plain,
( ! [X0: $tType,X1: X0] :
( ~ ord_less(X0,X1,bot_bot(X0))
| ~ bot(X0) )
| ~ spl18_36 ),
inference(avatar_component_clause,[],[f758]) ).
tff(f1064,plain,
spl18_88,
inference(avatar_split_clause,[],[f452,f1062]) ).
tff(f452,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X1: $tType,X39: fun(X1,bool)] : ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),X39,bot_bot(fun(X1,bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Int__empty__right) ).
tff(f1056,plain,
spl18_87,
inference(avatar_split_clause,[],[f552,f1054]) ).
tff(f1054,plain,
( spl18_87
<=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X6: nat,X3: nat,X1: huffma1450048681e_tree(X0)] :
( ( X3 = X6 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_87])]) ).
tff(f552,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
( ( X3 = X6 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
inference(cnf_transformation,[],[f382]) ).
tff(f1052,plain,
spl18_86,
inference(avatar_split_clause,[],[f490,f1050]) ).
tff(f1050,plain,
( spl18_86
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_86])]) ).
tff(f490,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X1: $tType,X47: fun(X1,bool),X39: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X39,X47) = inf_inf(fun(X1,bool),X47,X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Int__commute) ).
tff(f1048,plain,
spl18_85,
inference(avatar_split_clause,[],[f474,f1046]) ).
tff(f1046,plain,
( spl18_85
<=> ! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_85])]) ).
tff(f474,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( bot_bot(fun(X0,bool)) = set(X0,X1) )
| ( nil(X0) != X1 ) )
& ( ( nil(X0) = X1 )
| ( bot_bot(fun(X0,bool)) != set(X0,X1) ) ) ),
inference(nnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType,X1: list(X0)] :
( ( bot_bot(fun(X0,bool)) = set(X0,X1) )
<=> ( nil(X0) = X1 ) ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X1: $tType,X19: list(X1)] :
( ( set(X1,X19) = bot_bot(fun(X1,bool)) )
<=> ( nil(X1) = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_set__empty2) ).
tff(f1041,plain,
( spl18_84
| ~ spl18_68
| ~ spl18_83 ),
inference(avatar_split_clause,[],[f1028,f1025,f925,f1039]) ).
tff(f1039,plain,
( spl18_84
<=> ! [X0: $tType,X1: fun(X0,bool),X3: X0] :
( ( combk(bool,X0,fFalse) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_84])]) ).
tff(f1025,plain,
( spl18_83
<=> ! [X0: $tType,X1: fun(X0,bool),X3: X0] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_83])]) ).
tff(f1028,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl18_68
| ~ spl18_83 ),
inference(forward_demodulation,[],[f1026,f926]) ).
tff(f1026,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl18_83 ),
inference(avatar_component_clause,[],[f1025]) ).
tff(f1027,plain,
spl18_83,
inference(avatar_split_clause,[],[f585,f1025]) ).
tff(f585,plain,
! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ),
inference(forward_demodulation,[],[f478,f447]) ).
tff(f478,plain,
! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ),
inference(cnf_transformation,[],[f340]) ).
tff(f1022,plain,
( spl18_82
| ~ spl18_81 ),
inference(avatar_split_clause,[],[f1018,f1015,f1020]) ).
tff(f1020,plain,
( spl18_82
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_82])]) ).
tff(f1015,plain,
( spl18_81
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_81])]) ).
tff(f1018,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl18_81 ),
inference(forward_demodulation,[],[f1016,f548]) ).
tff(f1016,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl18_81 ),
inference(avatar_component_clause,[],[f1015]) ).
tff(f1017,plain,
spl18_81,
inference(avatar_split_clause,[],[f459,f1015]) ).
tff(f459,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f132]) ).
tff(f132,axiom,
! [X61: bool,X62: bool] :
( pp(X62)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X62),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f1012,plain,
( spl18_80
| ~ spl18_79 ),
inference(avatar_split_clause,[],[f1008,f1005,f1010]) ).
tff(f1010,plain,
( spl18_80
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_80])]) ).
tff(f1005,plain,
( spl18_79
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_79])]) ).
tff(f1008,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl18_79 ),
inference(forward_demodulation,[],[f1006,f548]) ).
tff(f1006,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl18_79 ),
inference(avatar_component_clause,[],[f1005]) ).
tff(f1007,plain,
spl18_79,
inference(avatar_split_clause,[],[f458,f1005]) ).
tff(f458,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f133]) ).
tff(f133,axiom,
! [X61: bool,X62: bool] :
( pp(X61)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X62),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f1003,plain,
spl18_78,
inference(avatar_split_clause,[],[f443,f1001]) ).
tff(f1001,plain,
( spl18_78
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X3,X2)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_78])]) ).
tff(f443,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X3,X2)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X3,X2) )
| ~ preorder(X0) ),
inference(flattening,[],[f280]) ).
tff(f280,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X3,X2) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X2)
=> ( ord_less(X0,X2,X1)
=> ord_less(X0,X3,X1) ) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X50: X0,X30: X0,X49: X0] :
( ord_less(X0,X49,X30)
=> ( ord_less(X0,X30,X50)
=> ord_less(X0,X49,X50) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_order__less__trans) ).
tff(f999,plain,
spl18_77,
inference(avatar_split_clause,[],[f428,f997]) ).
tff(f997,plain,
( spl18_77
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ semilattice_inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_77])]) ).
tff(f428,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ semilattice_inf(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ semilattice_inf(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) ) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X30: X0,X49: X0] : ( inf_inf(X0,X49,X30) = inf_inf(X0,X49,inf_inf(X0,X49,X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_inf__left__idem) ).
tff(f995,plain,
( spl18_76
| ~ spl18_16
| ~ spl18_58
| ~ spl18_68
| ~ spl18_70 ),
inference(avatar_split_clause,[],[f984,f938,f925,f862,f670,f992]) ).
tff(f938,plain,
( spl18_70
<=> ! [X1: $tType,X0: $tType,X2: X0] :
( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_70])]) ).
tff(f984,plain,
( ( fFalse = bot_bot(bool) )
| ~ spl18_16
| ~ spl18_58
| ~ spl18_68
| ~ spl18_70 ),
inference(forward_demodulation,[],[f983,f863]) ).
tff(f983,plain,
( ! [X0: $tType,X1: X0] : ( bot_bot(bool) = aa(X0,bool,combk(bool,X0,fFalse),X1) )
| ~ spl18_16
| ~ spl18_68
| ~ spl18_70 ),
inference(forward_demodulation,[],[f980,f926]) ).
tff(f980,plain,
( ! [X0: $tType,X1: X0] : ( bot_bot(bool) = aa(X0,bool,bot_bot(fun(X0,bool)),X1) )
| ~ spl18_16
| ~ spl18_70 ),
inference(resolution,[],[f939,f672]) ).
tff(f672,plain,
( bot(bool)
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f670]) ).
tff(f939,plain,
( ! [X1: $tType,X0: $tType,X2: X0] :
( ~ bot(X1)
| ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) )
| ~ spl18_70 ),
inference(avatar_component_clause,[],[f938]) ).
tff(f961,plain,
spl18_75,
inference(avatar_split_clause,[],[f541,f959]) ).
tff(f959,plain,
( spl18_75
<=> ! [X0: $tType,X2: nat,X4: nat,X3: X0,X1: X0] :
( ( X1 = X3 )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_75])]) ).
tff(f541,plain,
! [X0: $tType,X2: nat,X3: X0,X1: X0,X4: nat] :
( ( X1 = X3 )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f380]) ).
tff(f380,plain,
! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
( ( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
inference(flattening,[],[f379]) ).
tff(f379,plain,
! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
( ( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
inference(nnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X1: $tType,X4: X1,X5: nat,X6: X1,X7: nat] :
( ( huffma2021818691e_Leaf(X1,X7,X6) = huffma2021818691e_Leaf(X1,X5,X4) )
<=> ( ( X4 = X6 )
& ( X5 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_tree_Osimps_I1_J) ).
tff(f957,plain,
spl18_74,
inference(avatar_split_clause,[],[f540,f955]) ).
tff(f955,plain,
( spl18_74
<=> ! [X0: $tType,X4: nat,X3: X0,X2: nat,X1: X0] :
( ( X2 = X4 )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_74])]) ).
tff(f540,plain,
! [X0: $tType,X2: nat,X3: X0,X1: X0,X4: nat] :
( ( X2 = X4 )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f380]) ).
tff(f953,plain,
spl18_73,
inference(avatar_split_clause,[],[f517,f951]) ).
tff(f951,plain,
( spl18_73
<=> ! [X0: $tType,X3: X0,X2: X0,X1: nat] :
( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_73])]) ).
tff(f517,plain,
! [X0: $tType,X2: X0,X3: X0,X1: nat] :
( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: $tType,X1: nat,X2: X0,X3: X0] :
( ( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
| ( X2 = X3 ) )
& ( ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 )
| ( X2 != X3 ) ) ),
inference(ennf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType,X1: nat,X2: X0,X3: X0] :
( ( ( X2 != X3 )
=> ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) ) )
& ( ( X2 = X3 )
=> ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 ) ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType,X13: nat,X12: X0,X8: X0] :
( ( ( X8 != X12 )
=> ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X13,X12),X8) ) )
& ( ( X8 = X12 )
=> ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X13,X12),X8) = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_freq_Osimps_I1_J) ).
tff(f949,plain,
spl18_72,
inference(avatar_split_clause,[],[f471,f947]) ).
tff(f947,plain,
( spl18_72
<=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK0(X0,X1)) )
| ~ huffma1518433673istent(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_72])]) ).
tff(f471,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK0(X0,X1)) )
| ~ huffma1518433673istent(X0,X1) ),
inference(cnf_transformation,[],[f328]) ).
tff(f328,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK0(X0,X1)) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK0(X0,X1)),huffma675207370phabet(X0,X1))) )
| ~ huffma1518433673istent(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f292,f327]) ).
tff(f327,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ? [X2: X0] :
( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),huffma675207370phabet(X0,X1))) )
=> ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK0(X0,X1)) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK0(X0,X1)),huffma675207370phabet(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f292,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ? [X2: X0] :
( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),huffma675207370phabet(X0,X1))) )
| ~ huffma1518433673istent(X0,X1) ),
inference(ennf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X1)
=> ? [X2: X0] :
( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),huffma675207370phabet(X0,X1))) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X1: $tType,X42: huffma1450048681e_tree(X1)] :
( huffma1518433673istent(X1,X42)
=> ? [X29: X1] :
( ( huffma410068972_depth(X1,X42,X29) = huffma945805758height(X1,X42) )
& pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X29),huffma675207370phabet(X1,X42))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_exists__at__height) ).
tff(f945,plain,
( ~ spl18_71
| spl18_43
| ~ spl18_68 ),
inference(avatar_split_clause,[],[f929,f925,f791,f942]) ).
tff(f942,plain,
( spl18_71
<=> pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),combk(bool,huffma1450048681e_tree(a),fFalse)),huffma2021818691e_Leaf(a,zero_zero(nat),a1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_71])]) ).
tff(f791,plain,
( spl18_43
<=> pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),bot_bot(fun(huffma1450048681e_tree(a),bool))),huffma2021818691e_Leaf(a,zero_zero(nat),a1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_43])]) ).
tff(f929,plain,
( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),combk(bool,huffma1450048681e_tree(a),fFalse)),huffma2021818691e_Leaf(a,zero_zero(nat),a1)))
| spl18_43
| ~ spl18_68 ),
inference(superposition,[],[f793,f926]) ).
tff(f793,plain,
( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),bot_bot(fun(huffma1450048681e_tree(a),bool))),huffma2021818691e_Leaf(a,zero_zero(nat),a1)))
| spl18_43 ),
inference(avatar_component_clause,[],[f791]) ).
tff(f940,plain,
spl18_70,
inference(avatar_split_clause,[],[f467,f938]) ).
tff(f467,plain,
! [X1: $tType,X0: $tType,X2: X0] :
( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: $tType] :
( bot(X1)
=> ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X1: $tType,X2: $tType] :
( bot(X2)
=> ! [X8: X1] : ( aa(X1,X2,bot_bot(fun(X1,X2)),X8) = bot_bot(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).
tff(f936,plain,
spl18_69,
inference(avatar_split_clause,[],[f417,f934]) ).
tff(f934,plain,
( spl18_69
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ( X1 = X2 )
| ord_less(X0,X2,X1)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_69])]) ).
tff(f417,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ( X1 = X2 )
| ord_less(X0,X2,X1)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ( X1 = X2 )
| ord_less(X0,X2,X1) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ( X1 = X2 )
| ord_less(X0,X2,X1) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X30: X0,X49: X0] :
( ord_less(X0,X30,X49)
| ( X30 = X49 )
| ord_less(X0,X49,X30) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_linorder__less__linear) ).
tff(f927,plain,
( spl18_68
| ~ spl18_37
| ~ spl18_67 ),
inference(avatar_split_clause,[],[f923,f920,f762,f925]) ).
tff(f762,plain,
( spl18_37
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_37])]) ).
tff(f920,plain,
( spl18_67
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_67])]) ).
tff(f923,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
| ~ spl18_37
| ~ spl18_67 ),
inference(forward_demodulation,[],[f921,f763]) ).
tff(f763,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 )
| ~ spl18_37 ),
inference(avatar_component_clause,[],[f762]) ).
tff(f921,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) )
| ~ spl18_67 ),
inference(avatar_component_clause,[],[f920]) ).
tff(f922,plain,
spl18_67,
inference(avatar_split_clause,[],[f411,f920]) ).
tff(f411,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X1: $tType] : ( bot_bot(fun(X1,bool)) = collect(X1,combk(bool,X1,fFalse)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_empty__def) ).
tff(f914,plain,
spl18_66,
inference(avatar_split_clause,[],[f416,f912]) ).
tff(f912,plain,
( spl18_66
<=> ! [X0: $tType] :
( ( nil(X0) = linord467138063of_set(X0,bot_bot(fun(X0,bool))) )
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_66])]) ).
tff(f416,plain,
! [X0: $tType] :
( ( nil(X0) = linord467138063of_set(X0,bot_bot(fun(X0,bool))) )
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType] :
( ( nil(X0) = linord467138063of_set(X0,bot_bot(fun(X0,bool))) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType] :
( linorder(X0)
=> ( nil(X0) = linord467138063of_set(X0,bot_bot(fun(X0,bool))) ) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X1: $tType] :
( linorder(X1)
=> ( nil(X1) = linord467138063of_set(X1,bot_bot(fun(X1,bool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_sorted__list__of__set__empty) ).
tff(f910,plain,
spl18_65,
inference(avatar_split_clause,[],[f410,f908]) ).
tff(f410,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = huffma1516701463abet_F(X0,nil(huffma1450048681e_tree(X0))) ),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = huffma1516701463abet_F(X0,nil(huffma1450048681e_tree(X0))) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X1: $tType] : ( huffma1516701463abet_F(X1,nil(huffma1450048681e_tree(X1))) = bot_bot(fun(X1,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_alphabet_092_060_094isub_062F_Osimps_I1_J) ).
tff(f906,plain,
( spl18_64
| ~ spl18_3
| ~ spl18_51 ),
inference(avatar_split_clause,[],[f873,f833,f605,f904]) ).
tff(f904,plain,
( spl18_64
<=> ! [X0: bool] : ( bot_bot(bool) = inf_inf(bool,X0,bot_bot(bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_64])]) ).
tff(f605,plain,
( spl18_3
<=> bounded_lattice_bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
tff(f833,plain,
( spl18_51
<=> ! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
| ~ bounded_lattice_bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_51])]) ).
tff(f873,plain,
( ! [X0: bool] : ( bot_bot(bool) = inf_inf(bool,X0,bot_bot(bool)) )
| ~ spl18_3
| ~ spl18_51 ),
inference(resolution,[],[f834,f607]) ).
tff(f607,plain,
( bounded_lattice_bot(bool)
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f605]) ).
tff(f834,plain,
( ! [X0: $tType,X1: X0] :
( ~ bounded_lattice_bot(X0)
| ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) ) )
| ~ spl18_51 ),
inference(avatar_component_clause,[],[f833]) ).
tff(f890,plain,
spl18_63,
inference(avatar_split_clause,[],[f543,f888]) ).
tff(f888,plain,
( spl18_63
<=> ! [X0: $tType,X2: nat,X4: huffma1450048681e_tree(X0),X5: nat,X3: huffma1450048681e_tree(X0),X1: X0] : ( huffma2021818691e_Leaf(X0,X2,X1) != huffma1146269203erNode(X0,X5,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_63])]) ).
tff(f543,plain,
! [X0: $tType,X2: nat,X3: huffma1450048681e_tree(X0),X1: X0,X4: huffma1450048681e_tree(X0),X5: nat] : ( huffma2021818691e_Leaf(X0,X2,X1) != huffma1146269203erNode(X0,X5,X4,X3) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType,X1: X0,X2: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X5: nat] : ( huffma2021818691e_Leaf(X0,X2,X1) != huffma1146269203erNode(X0,X5,X4,X3) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType,X12: X0,X14: nat,X16: huffma1450048681e_tree(X0),X17: huffma1450048681e_tree(X0),X18: nat] : ( huffma2021818691e_Leaf(X0,X14,X12) != huffma1146269203erNode(X0,X18,X17,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_tree_Osimps_I4_J) ).
tff(f886,plain,
spl18_62,
inference(avatar_split_clause,[],[f435,f884]) ).
tff(f884,plain,
( spl18_62
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,bot_bot(X0),X1)
| ( bot_bot(X0) = X1 )
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_62])]) ).
tff(f435,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,bot_bot(X0),X1)
| ( bot_bot(X0) = X1 )
| ~ bot(X0) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( bot_bot(X0) != X1 )
| ~ ord_less(X0,bot_bot(X0),X1) )
& ( ord_less(X0,bot_bot(X0),X1)
| ( bot_bot(X0) = X1 ) ) )
| ~ bot(X0) ),
inference(nnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( bot_bot(X0) != X1 )
<=> ord_less(X0,bot_bot(X0),X1) )
| ~ bot(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( bot(X0)
=> ! [X1: X0] :
( ( bot_bot(X0) != X1 )
<=> ord_less(X0,bot_bot(X0),X1) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X1: $tType] :
( bot(X1)
=> ! [X6: X1] :
( ( bot_bot(X1) != X6 )
<=> ord_less(X1,bot_bot(X1),X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_bot__less) ).
tff(f882,plain,
spl18_61,
inference(avatar_split_clause,[],[f409,f880]) ).
tff(f409,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = set(X0,nil(X0)) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X1: $tType] : ( bot_bot(fun(X1,bool)) = set(X1,nil(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_List_Oset_Osimps_I1_J) ).
tff(f872,plain,
spl18_60,
inference(avatar_split_clause,[],[f527,f870]) ).
tff(f870,plain,
( spl18_60
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_60])]) ).
tff(f527,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f370]) ).
tff(f370,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) )
& ( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
& huffma1518433673istent(X0,X1)
& huffma1518433673istent(X0,X2) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
inference(flattening,[],[f369]) ).
tff(f369,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) )
& ( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
& huffma1518433673istent(X0,X1)
& huffma1518433673istent(X0,X2) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
inference(nnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
<=> ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
& huffma1518433673istent(X0,X1)
& huffma1518433673istent(X0,X2) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X1: $tType,X43: huffma1450048681e_tree(X1),X44: huffma1450048681e_tree(X1),X45: nat] :
( huffma1518433673istent(X1,huffma1146269203erNode(X1,X45,X44,X43))
<=> ( ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),huffma675207370phabet(X1,X44),huffma675207370phabet(X1,X43)) )
& huffma1518433673istent(X1,X43)
& huffma1518433673istent(X1,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_consistent_Osimps_I2_J) ).
tff(f868,plain,
spl18_59,
inference(avatar_split_clause,[],[f526,f866]) ).
tff(f866,plain,
( spl18_59
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X2)
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_59])]) ).
tff(f526,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X2)
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f370]) ).
tff(f864,plain,
spl18_58,
inference(avatar_split_clause,[],[f513,f862]) ).
tff(f513,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(rectify,[],[f129]) ).
tff(f129,axiom,
! [X1: $tType,X0: $tType,X61: X1,X62: X0] : ( aa(X1,X0,combk(X0,X1,X62),X61) = X62 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f860,plain,
spl18_57,
inference(avatar_split_clause,[],[f512,f858]) ).
tff(f858,plain,
( spl18_57
<=> ! [X0: $tType,X3: nat,X2: X0,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_57])]) ).
tff(f512,plain,
! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType,X1: X0,X2: X0,X3: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType,X12: X0,X15: X0,X13: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X13,X15),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_depth_Osimps_I1_J) ).
tff(f856,plain,
spl18_56,
inference(avatar_split_clause,[],[f489,f854]) ).
tff(f854,plain,
( spl18_56
<=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_56])]) ).
tff(f489,plain,
! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType,X12: X0,X14: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X14,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_tree_Osize_I3_J) ).
tff(f852,plain,
spl18_55,
inference(avatar_split_clause,[],[f451,f850]) ).
tff(f850,plain,
( spl18_55
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_55])]) ).
tff(f451,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X1: $tType,X39: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X39,X39) = X39 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Int__absorb) ).
tff(f848,plain,
( ~ spl18_15
| spl18_54
| ~ spl18_36
| ~ spl18_44 ),
inference(avatar_split_clause,[],[f829,f797,f758,f845,f665]) ).
tff(f665,plain,
( spl18_15
<=> bot(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).
tff(f845,plain,
( spl18_54
<=> ( zero_zero(nat) = bot_bot(nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_54])]) ).
tff(f797,plain,
( spl18_44
<=> ! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_44])]) ).
tff(f829,plain,
( ( zero_zero(nat) = bot_bot(nat) )
| ~ bot(nat)
| ~ spl18_36
| ~ spl18_44 ),
inference(resolution,[],[f798,f759]) ).
tff(f798,plain,
( ! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) )
| ~ spl18_44 ),
inference(avatar_component_clause,[],[f797]) ).
tff(f843,plain,
spl18_53,
inference(avatar_split_clause,[],[f438,f841]) ).
tff(f841,plain,
( spl18_53
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less(X0,X2,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_53])]) ).
tff(f438,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less(X0,X2,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X1,X2)
| ~ ord_less(X0,X2,X1) )
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
=> ~ ord_less(X0,X1,X2) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X30: X0,X49: X0] :
( ord_less(X0,X49,X30)
=> ~ ord_less(X0,X30,X49) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_order__less__imp__not__less) ).
tff(f839,plain,
spl18_52,
inference(avatar_split_clause,[],[f426,f837]) ).
tff(f837,plain,
( spl18_52
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X1,X2)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_52])]) ).
tff(f426,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X1,X2)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ~ ord_less(X0,X2,X1)
| ( ( X1 != X2 )
& ~ ord_less(X0,X1,X2) ) )
& ( ( X1 = X2 )
| ord_less(X0,X1,X2)
| ord_less(X0,X2,X1) ) )
| ~ linorder(X0) ),
inference(flattening,[],[f323]) ).
tff(f323,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ~ ord_less(X0,X2,X1)
| ( ( X1 != X2 )
& ~ ord_less(X0,X1,X2) ) )
& ( ( X1 = X2 )
| ord_less(X0,X1,X2)
| ord_less(X0,X2,X1) ) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X2,X1)
<=> ( ( X1 = X2 )
| ord_less(X0,X1,X2) ) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X2,X1)
<=> ( ( X1 = X2 )
| ord_less(X0,X1,X2) ) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X1: $tType] :
( linorder(X1)
=> ! [X52: X1,X37: X1] :
( ~ ord_less(X1,X37,X52)
<=> ( ( X37 = X52 )
| ord_less(X1,X52,X37) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_not__less__iff__gr__or__eq) ).
tff(f835,plain,
spl18_51,
inference(avatar_split_clause,[],[f415,f833]) ).
tff(f415,plain,
! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
| ~ bounded_lattice_bot(X0) ),
inference(cnf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: $tType] :
( ! [X1: X0] : ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
| ~ bounded_lattice_bot(X0) ),
inference(ennf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: $tType] :
( bounded_lattice_bot(X0)
=> ! [X1: X0] : ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType] :
( bounded_lattice_bot(X0)
=> ! [X49: X0] : ( bot_bot(X0) = inf_inf(X0,X49,bot_bot(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_inf__bot__right) ).
tff(f823,plain,
spl18_50,
inference(avatar_split_clause,[],[f575,f821]) ).
tff(f821,plain,
( spl18_50
<=> ! [X0: $tType,X1: nat,X3: X0] : ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3),X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_50])]) ).
tff(f575,plain,
! [X0: $tType,X3: X0,X1: nat] : ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3),X3) = X1 ),
inference(equality_resolution,[],[f516]) ).
tff(f516,plain,
! [X0: $tType,X2: X0,X3: X0,X1: nat] :
( ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f304]) ).
tff(f819,plain,
spl18_49,
inference(avatar_split_clause,[],[f511,f817]) ).
tff(f817,plain,
( spl18_49
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_49])]) ).
tff(f511,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X2: $tType,X1: $tType,X9: fun(X2,fun(list(X2),X1)),X10: X1] : ( list_case(X1,X2,X10,X9,nil(X2)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_list_Osimps_I4_J) ).
tff(f815,plain,
spl18_48,
inference(avatar_split_clause,[],[f510,f813]) ).
tff(f813,plain,
( spl18_48
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_48])]) ).
tff(f510,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(list(X0),fun(X1,X1))),X3: X1] : ( list_rec(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X2: $tType,X1: $tType,X9: fun(X2,fun(list(X2),fun(X1,X1))),X10: X1] : ( list_rec(X1,X2,X10,X9,nil(X2)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_list_Orecs_I1_J) ).
tff(f811,plain,
spl18_47,
inference(avatar_split_clause,[],[f488,f809]) ).
tff(f809,plain,
( spl18_47
<=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_47])]) ).
tff(f488,plain,
! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType,X12: X0,X13: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X13,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_height_Osimps_I1_J) ).
tff(f807,plain,
spl18_46,
inference(avatar_split_clause,[],[f450,f805]) ).
tff(f805,plain,
( spl18_46
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_46])]) ).
tff(f450,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( nil(X0) = dropWhile(X0,X1,nil(X0)) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X1: $tType,X20: fun(X1,bool)] : ( nil(X1) = dropWhile(X1,X20,nil(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_dropWhile_Osimps_I1_J) ).
tff(f803,plain,
spl18_45,
inference(avatar_split_clause,[],[f449,f801]) ).
tff(f801,plain,
( spl18_45
<=> ! [X0: $tType,X1: X0] : ( zero_zero(nat) = huffma409467474freq_F(X0,nil(huffma1450048681e_tree(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_45])]) ).
tff(f449,plain,
! [X0: $tType,X1: X0] : ( zero_zero(nat) = huffma409467474freq_F(X0,nil(huffma1450048681e_tree(X0)),X1) ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType,X1: X0] : ( zero_zero(nat) = huffma409467474freq_F(X0,nil(huffma1450048681e_tree(X0)),X1) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType,X8: X0] : ( zero_zero(nat) = huffma409467474freq_F(X0,nil(huffma1450048681e_tree(X0)),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_freq_092_060_094isub_062F_Osimps_I1_J) ).
tff(f799,plain,
spl18_44,
inference(avatar_split_clause,[],[f444,f797]) ).
tff(f444,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f326,plain,
! [X0: nat] :
( ( ( zero_zero(nat) != X0 )
| ~ ord_less(nat,zero_zero(nat),X0) )
& ( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ) ),
inference(nnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
<=> ord_less(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X57: nat] :
( ( zero_zero(nat) != X57 )
<=> ord_less(nat,zero_zero(nat),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_neq0__conv) ).
tff(f794,plain,
( ~ spl18_43
| spl18_42 ),
inference(avatar_split_clause,[],[f789,f783,f791]) ).
tff(f783,plain,
( spl18_42
<=> pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_42])]) ).
tff(f789,plain,
( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),bot_bot(fun(huffma1450048681e_tree(a),bool))),huffma2021818691e_Leaf(a,zero_zero(nat),a1)))
| spl18_42 ),
inference(forward_demodulation,[],[f788,f409]) ).
tff(f788,plain,
( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a)))),huffma2021818691e_Leaf(a,zero_zero(nat),a1)))
| spl18_42 ),
inference(forward_demodulation,[],[f787,f449]) ).
tff(f787,plain,
( ~ pp(aa(huffma1450048681e_tree(a),bool,combc(huffma1450048681e_tree(a),fun(huffma1450048681e_tree(a),bool),bool,member(huffma1450048681e_tree(a)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a)))),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)))
| spl18_42 ),
inference(forward_demodulation,[],[f785,f548]) ).
tff(f785,plain,
( ~ pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a)))))
| spl18_42 ),
inference(avatar_component_clause,[],[f783]) ).
tff(f786,plain,
~ spl18_42,
inference(avatar_split_clause,[],[f383,f783]) ).
tff(f383,plain,
~ pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
~ pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))),
inference(flattening,[],[f137]) ).
tff(f137,negated_conjecture,
~ pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))),
inference(negated_conjecture,[],[f136]) ).
tff(f136,conjecture,
pp(aa(fun(huffma1450048681e_tree(a),bool),bool,aa(huffma1450048681e_tree(a),fun(fun(huffma1450048681e_tree(a),bool),bool),member(huffma1450048681e_tree(a)),huffma2021818691e_Leaf(a,huffma409467474freq_F(a,nil(huffma1450048681e_tree(a)),a1),a1)),set(huffma1450048681e_tree(a),nil(huffma1450048681e_tree(a))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f781,plain,
( spl18_40
| ~ spl18_41
| ~ spl18_22 ),
inference(avatar_split_clause,[],[f751,f698,f778,f775]) ).
tff(f775,plain,
( spl18_40
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_40])]) ).
tff(f778,plain,
( spl18_41
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_41])]) ).
tff(f698,plain,
( spl18_22
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).
tff(f751,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl18_22 ),
inference(equality_factoring,[],[f699]) ).
tff(f699,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl18_22 ),
inference(avatar_component_clause,[],[f698]) ).
tff(f773,plain,
spl18_39,
inference(avatar_split_clause,[],[f448,f771]) ).
tff(f771,plain,
( spl18_39
<=> ! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_39])]) ).
tff(f448,plain,
! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X1: $tType,X35: fun(X1,nat)] : ( zero_zero(nat) = list_size(X1,X35,nil(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_list_Osize_I1_J) ).
tff(f769,plain,
spl18_38,
inference(avatar_split_clause,[],[f408,f767]) ).
tff(f767,plain,
( spl18_38
<=> ! [X0: $tType] : ( zero_zero(nat) = huffma632063779ight_F(X0,nil(huffma1450048681e_tree(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_38])]) ).
tff(f408,plain,
! [X0: $tType] : ( zero_zero(nat) = huffma632063779ight_F(X0,nil(huffma1450048681e_tree(X0))) ),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] : ( zero_zero(nat) = huffma632063779ight_F(X0,nil(huffma1450048681e_tree(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_height_092_060_094isub_062F_Osimps_I1_J) ).
tff(f764,plain,
spl18_37,
inference(avatar_split_clause,[],[f447,f762]) ).
tff(f760,plain,
spl18_36,
inference(avatar_split_clause,[],[f434,f758]) ).
tff(f434,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,X1,bot_bot(X0))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( ! [X1: X0] : ~ ord_less(X0,X1,bot_bot(X0))
| ~ bot(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( bot(X0)
=> ! [X1: X0] : ~ ord_less(X0,X1,bot_bot(X0)) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( bot(X0)
=> ! [X12: X0] : ~ ord_less(X0,X12,bot_bot(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_not__less__bot) ).
tff(f755,plain,
( spl18_35
| spl18_1
| ~ spl18_22 ),
inference(avatar_split_clause,[],[f750,f698,f595,f753]) ).
tff(f753,plain,
( spl18_35
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_35])]) ).
tff(f750,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl18_1
| ~ spl18_22 ),
inference(superposition,[],[f597,f699]) ).
tff(f597,plain,
( ~ pp(fFalse)
| spl18_1 ),
inference(avatar_component_clause,[],[f595]) ).
tff(f748,plain,
spl18_34,
inference(avatar_split_clause,[],[f564,f746]) ).
tff(f746,plain,
( spl18_34
<=> ! [X0: $tType,X2: X0] :
( ~ ord_less(X0,X2,X2)
| ~ order(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_34])]) ).
tff(f564,plain,
! [X0: $tType,X2: X0] :
( ~ ord_less(X0,X2,X2)
| ~ order(X0) ),
inference(equality_resolution,[],[f431]) ).
tff(f431,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 != X2 )
| ~ ord_less(X0,X2,X1)
| ~ order(X0) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 != X2 )
| ~ ord_less(X0,X2,X1) )
| ~ order(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X2,X1)
=> ( X1 != X2 ) ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X30: X0,X49: X0] :
( ord_less(X0,X49,X30)
=> ( X30 != X49 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_less__imp__neq) ).
tff(f744,plain,
spl18_33,
inference(avatar_split_clause,[],[f559,f742]) ).
tff(f742,plain,
( spl18_33
<=> ! [X0: $tType,X2: X0] :
( ~ ord_less(X0,X2,X2)
| ~ linorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_33])]) ).
tff(f559,plain,
! [X0: $tType,X2: X0] :
( ~ ord_less(X0,X2,X2)
| ~ linorder(X0) ),
inference(equality_resolution,[],[f424]) ).
tff(f424,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 != X2 )
| ~ ord_less(X0,X1,X2)
| ~ linorder(X0) ),
inference(cnf_transformation,[],[f322]) ).
tff(f322,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 != X2 )
| ( ~ ord_less(X0,X1,X2)
& ~ ord_less(X0,X2,X1) ) )
& ( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) ) )
| ~ linorder(X0) ),
inference(flattening,[],[f321]) ).
tff(f321,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( X1 != X2 )
| ( ~ ord_less(X0,X1,X2)
& ~ ord_less(X0,X2,X1) ) )
& ( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) ) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X1 != X2 )
<=> ( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1) ) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 != X2 )
<=> ( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1) ) ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X1: $tType] :
( linorder(X1)
=> ! [X52: X1,X37: X1] :
( ( X37 != X52 )
<=> ( ord_less(X1,X52,X37)
| ord_less(X1,X37,X52) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_linorder__neq__iff) ).
tff(f740,plain,
spl18_32,
inference(avatar_split_clause,[],[f487,f738]) ).
tff(f738,plain,
( spl18_32
<=> ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_32])]) ).
tff(f487,plain,
! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType,X1: X0,X2: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType,X12: X0,X13: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X13,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_consistent_Osimps_I1_J) ).
tff(f736,plain,
spl18_31,
inference(avatar_split_clause,[],[f469,f734]) ).
tff(f734,plain,
( spl18_31
<=> ! [X1: $tType,X0: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_31])]) ).
tff(f469,plain,
! [X1: $tType,X0: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: $tType,X1: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: $tType] :
( preorder(X1)
=> preorder(fun(X0,X1)) ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X58: $tType,X59: $tType] :
( preorder(X59)
=> preorder(fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
tff(f732,plain,
spl18_30,
inference(avatar_split_clause,[],[f466,f730]) ).
tff(f730,plain,
( spl18_30
<=> ! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_30])]) ).
tff(f466,plain,
! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: $tType,X1: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType,X1: $tType] :
( bot(X1)
=> bot(fun(X0,X1)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X58: $tType,X59: $tType] :
( bot(X59)
=> bot(fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
tff(f728,plain,
spl18_29,
inference(avatar_split_clause,[],[f465,f726]) ).
tff(f726,plain,
( spl18_29
<=> ! [X1: $tType,X0: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_29])]) ).
tff(f465,plain,
! [X1: $tType,X0: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: $tType,X1: $tType] :
( order(fun(X0,X1))
| ~ order(X1) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType,X1: $tType] :
( order(X1)
=> order(fun(X0,X1)) ),
inference(rectify,[],[f108]) ).
tff(f108,axiom,
! [X58: $tType,X59: $tType] :
( order(X59)
=> order(fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
tff(f724,plain,
spl18_28,
inference(avatar_split_clause,[],[f464,f722]) ).
tff(f722,plain,
( spl18_28
<=> ! [X1: $tType,X0: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_28])]) ).
tff(f464,plain,
! [X1: $tType,X0: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $tType,X1: $tType] :
( ord(fun(X0,X1))
| ~ ord(X1) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: $tType] :
( ord(X1)
=> ord(fun(X0,X1)) ),
inference(rectify,[],[f109]) ).
tff(f109,axiom,
! [X58: $tType,X59: $tType] :
( ord(X59)
=> ord(fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
tff(f720,plain,
spl18_27,
inference(avatar_split_clause,[],[f463,f718]) ).
tff(f718,plain,
( spl18_27
<=> ! [X1: $tType,X0: $tType] :
( lattice(fun(X0,X1))
| ~ lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_27])]) ).
tff(f463,plain,
! [X1: $tType,X0: $tType] :
( lattice(fun(X0,X1))
| ~ lattice(X1) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType,X1: $tType] :
( lattice(fun(X0,X1))
| ~ lattice(X1) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: $tType,X1: $tType] :
( lattice(X1)
=> lattice(fun(X0,X1)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X58: $tType,X59: $tType] :
( lattice(X59)
=> lattice(fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).
tff(f716,plain,
spl18_26,
inference(avatar_split_clause,[],[f462,f714]) ).
tff(f714,plain,
( spl18_26
<=> ! [X1: $tType,X0: $tType] :
( semilattice_inf(fun(X0,X1))
| ~ lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).
tff(f462,plain,
! [X1: $tType,X0: $tType] :
( semilattice_inf(fun(X0,X1))
| ~ lattice(X1) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: $tType,X1: $tType] :
( semilattice_inf(fun(X0,X1))
| ~ lattice(X1) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType,X1: $tType] :
( lattice(X1)
=> semilattice_inf(fun(X0,X1)) ),
inference(rectify,[],[f106]) ).
tff(f106,axiom,
! [X58: $tType,X59: $tType] :
( lattice(X59)
=> semilattice_inf(fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).
tff(f712,plain,
spl18_25,
inference(avatar_split_clause,[],[f461,f710]) ).
tff(f710,plain,
( spl18_25
<=> ! [X1: $tType,X0: $tType] :
( bounded_lattice(fun(X0,X1))
| ~ bounded_lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).
tff(f461,plain,
! [X1: $tType,X0: $tType] :
( bounded_lattice(fun(X0,X1))
| ~ bounded_lattice(X1) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType,X1: $tType] :
( bounded_lattice(fun(X0,X1))
| ~ bounded_lattice(X1) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: $tType,X1: $tType] :
( bounded_lattice(X1)
=> bounded_lattice(fun(X0,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X58: $tType,X59: $tType] :
( bounded_lattice(X59)
=> bounded_lattice(fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).
tff(f708,plain,
spl18_24,
inference(avatar_split_clause,[],[f460,f706]) ).
tff(f706,plain,
( spl18_24
<=> ! [X1: $tType,X0: $tType] :
( bounded_lattice_bot(fun(X0,X1))
| ~ bounded_lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).
tff(f460,plain,
! [X1: $tType,X0: $tType] :
( bounded_lattice_bot(fun(X0,X1))
| ~ bounded_lattice(X1) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: $tType,X1: $tType] :
( bounded_lattice_bot(fun(X0,X1))
| ~ bounded_lattice(X1) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType,X1: $tType] :
( bounded_lattice(X1)
=> bounded_lattice_bot(fun(X0,X1)) ),
inference(rectify,[],[f105]) ).
tff(f105,axiom,
! [X58: $tType,X59: $tType] :
( bounded_lattice(X59)
=> bounded_lattice_bot(fun(X58,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__bot) ).
tff(f704,plain,
spl18_23,
inference(avatar_split_clause,[],[f437,f702]) ).
tff(f702,plain,
( spl18_23
<=> ! [X0: $tType,X1: X0] :
( ~ ord_less(X0,X1,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).
tff(f437,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,X1,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: X0] : ~ ord_less(X0,X1,X1)
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0] : ~ ord_less(X0,X1,X1) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X49: X0] : ~ ord_less(X0,X49,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_order__less__irrefl) ).
tff(f700,plain,
spl18_22,
inference(avatar_split_clause,[],[f412,f698]) ).
tff(f412,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f135]) ).
tff(f135,axiom,
! [X62: bool] :
( ( fFalse = X62 )
| ( fTrue = X62 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
tff(f696,plain,
spl18_21,
inference(avatar_split_clause,[],[f446,f694]) ).
tff(f694,plain,
( spl18_21
<=> ! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).
tff(f446,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X1: $tType,X20: fun(X1,bool)] : ~ list_ex1(X1,X20,nil(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_list__ex1__simps_I1_J) ).
tff(f692,plain,
spl18_20,
inference(avatar_split_clause,[],[f406,f690]) ).
tff(f690,plain,
( spl18_20
<=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).
tff(f406,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X56: nat] : ~ ord_less(nat,X56,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_less__nat__zero__code) ).
tff(f688,plain,
spl18_19,
inference(avatar_split_clause,[],[f403,f685]) ).
tff(f685,plain,
( spl18_19
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).
tff(f403,plain,
pp(fTrue),
inference(cnf_transformation,[],[f126]) ).
tff(f126,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f683,plain,
spl18_18,
inference(avatar_split_clause,[],[f402,f680]) ).
tff(f680,plain,
( spl18_18
<=> preorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).
tff(f402,plain,
preorder(bool),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
preorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
tff(f678,plain,
spl18_17,
inference(avatar_split_clause,[],[f401,f675]) ).
tff(f675,plain,
( spl18_17
<=> preorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_17])]) ).
tff(f401,plain,
preorder(nat),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
preorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
tff(f673,plain,
spl18_16,
inference(avatar_split_clause,[],[f400,f670]) ).
tff(f400,plain,
bot(bool),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
tff(f668,plain,
spl18_15,
inference(avatar_split_clause,[],[f399,f665]) ).
tff(f399,plain,
bot(nat),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
bot(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
tff(f663,plain,
spl18_14,
inference(avatar_split_clause,[],[f398,f660]) ).
tff(f660,plain,
( spl18_14
<=> order(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
tff(f398,plain,
order(bool),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
order(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
tff(f658,plain,
spl18_13,
inference(avatar_split_clause,[],[f397,f655]) ).
tff(f655,plain,
( spl18_13
<=> order(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
tff(f397,plain,
order(nat),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
order(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
tff(f653,plain,
spl18_12,
inference(avatar_split_clause,[],[f396,f650]) ).
tff(f650,plain,
( spl18_12
<=> ord(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
tff(f396,plain,
ord(bool),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
ord(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
tff(f648,plain,
spl18_11,
inference(avatar_split_clause,[],[f395,f645]) ).
tff(f645,plain,
( spl18_11
<=> ord(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).
tff(f395,plain,
ord(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
ord(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
tff(f643,plain,
spl18_10,
inference(avatar_split_clause,[],[f394,f640]) ).
tff(f640,plain,
( spl18_10
<=> lattice(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).
tff(f394,plain,
lattice(bool),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
lattice(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).
tff(f638,plain,
spl18_9,
inference(avatar_split_clause,[],[f393,f635]) ).
tff(f635,plain,
( spl18_9
<=> lattice(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).
tff(f393,plain,
lattice(nat),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
lattice(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).
tff(f633,plain,
spl18_8,
inference(avatar_split_clause,[],[f392,f630]) ).
tff(f630,plain,
( spl18_8
<=> semilattice_inf(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).
tff(f392,plain,
semilattice_inf(bool),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
semilattice_inf(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).
tff(f628,plain,
spl18_7,
inference(avatar_split_clause,[],[f391,f625]) ).
tff(f625,plain,
( spl18_7
<=> semilattice_inf(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
tff(f391,plain,
semilattice_inf(nat),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
semilattice_inf(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).
tff(f623,plain,
spl18_6,
inference(avatar_split_clause,[],[f390,f620]) ).
tff(f620,plain,
( spl18_6
<=> linorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
tff(f390,plain,
linorder(bool),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
linorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
tff(f618,plain,
spl18_5,
inference(avatar_split_clause,[],[f389,f615]) ).
tff(f615,plain,
( spl18_5
<=> linorder(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
tff(f389,plain,
linorder(nat),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
linorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
tff(f613,plain,
spl18_4,
inference(avatar_split_clause,[],[f388,f610]) ).
tff(f610,plain,
( spl18_4
<=> bounded_lattice(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
tff(f388,plain,
bounded_lattice(bool),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
bounded_lattice(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).
tff(f608,plain,
spl18_3,
inference(avatar_split_clause,[],[f387,f605]) ).
tff(f387,plain,
bounded_lattice_bot(bool),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
bounded_lattice_bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__bot) ).
tff(f603,plain,
spl18_2,
inference(avatar_split_clause,[],[f386,f600]) ).
tff(f600,plain,
( spl18_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
tff(f386,plain,
zero(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f598,plain,
~ spl18_1,
inference(avatar_split_clause,[],[f384,f595]) ).
tff(f384,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f134]) ).
tff(f134,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWW533_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 19:25:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (18066)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (18073)WARNING: value z3 for option sas not known
% 0.15/0.39 % (18074)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (18071)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (18075)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)
% 0.15/0.39 % (18072)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (18073)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)
% 0.15/0.39 % (18076)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)
% 0.15/0.39 % (18077)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)
% 0.15/0.39 % (18077)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level% Exception at run slice level
% 0.15/0.39
% 0.15/0.39 % Exception at run slice levelUser error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.41 % (18088)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.41 % (18089)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.41 % (18087)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.41 % (18075)First to succeed.
% 0.22/0.42 % (18088)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % (18087)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % Exception at run slice level
% 0.22/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42 % (18075)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18066"
% 0.22/0.43 % (18075)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43 % (18075)------------------------------
% 0.22/0.43 % (18075)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.43 % (18075)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (18075)Memory used [KB]: 1373
% 0.22/0.43 % (18075)Time elapsed: 0.037 s
% 0.22/0.43 % (18075)Instructions burned: 56 (million)
% 0.22/0.43 % (18066)Success in time 0.061 s
%------------------------------------------------------------------------------