TSTP Solution File: COM095_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM095_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 19:12:25 EDT 2024
% Result : Theorem 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 290
% Syntax : Number of formulae : 620 ( 196 unt; 117 typ; 0 def)
% Number of atoms : 1062 ( 369 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 907 ( 348 ~; 301 |; 79 &)
% ( 119 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 128 ( 93 >; 35 *; 0 +; 0 <<)
% Number of predicates : 105 ( 103 usr; 93 prp; 0-3 aty)
% Number of functors : 102 ( 102 usr; 10 con; 0-7 aty)
% Number of variables : 1254 ( 936 !; 62 ?;1254 :)
% ( 256 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
atom: $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,
n_lists:
!>[X0: $tType] : ( ( nat * list(X0) ) > list(list(X0)) ) ).
tff(func_def_1,type,
product:
!>[X0: $tType,X1: $tType] : ( ( list(X0) * list(X1) ) > list(product_prod(X0,X1)) ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
equal_equal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_4,type,
iprod:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > X0 ) ).
tff(func_def_5,type,
zipwith0:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * list(X0) * list(X1) ) > list(X2) ) ).
tff(func_def_6,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
lexord:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > fun(product_prod(list(X0),list(X0)),bool) ) ).
tff(func_def_8,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_9,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_10,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_11,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_12,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_13,type,
member1:
!>[X0: $tType] : fun(list(X0),fun(X0,bool)) ).
tff(func_def_14,type,
remdups:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_15,type,
rotate1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_16,type,
set:
!>[X0: $tType] : fun(list(X0),fun(X0,bool)) ).
tff(func_def_17,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_18,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_19,type,
transpose:
!>[X0: $tType] : ( list(list(X0)) > list(list(X0)) ) ).
tff(func_def_20,type,
divisor: atom > int ).
tff(func_def_21,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(func_def_22,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_23,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(product_prod(X0,X1),X2) * X0 * X1 ) > X2 ) ).
tff(func_def_24,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_25,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_26,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_27,type,
fFalse: bool ).
tff(func_def_28,type,
fTrue: bool ).
tff(func_def_29,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_30,type,
a: atom ).
tff(func_def_31,type,
as: list(atom) ).
tff(func_def_32,type,
li: int ).
tff(func_def_33,type,
lks: list(int) ).
tff(func_def_34,type,
x: int ).
tff(func_def_35,type,
xs: list(int) ).
tff(func_def_36,type,
sK1: int ).
tff(func_def_37,type,
sK2:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_38,type,
sK3:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_39,type,
sK4:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_40,type,
sK5:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_41,type,
sK6:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_42,type,
sK7:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_43,type,
sK8:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_44,type,
sK9:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_45,type,
sK10:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_46,type,
sK11:
!>[X0: $tType] : ( ( list(X0) * X0 ) > X0 ) ).
tff(func_def_47,type,
sK12:
!>[X0: $tType] : ( ( list(X0) * X0 ) > list(X0) ) ).
tff(func_def_48,type,
sK13:
!>[X0: $tType] : ( ( list(X0) * X0 ) > X0 ) ).
tff(func_def_49,type,
sK14:
!>[X0: $tType] : ( ( list(X0) * X0 ) > X0 ) ).
tff(func_def_50,type,
sK15:
!>[X0: $tType] : ( ( list(X0) * X0 ) > list(X0) ) ).
tff(func_def_51,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_52,type,
sK17:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_53,type,
sK18:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_54,type,
sK19:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_55,type,
sK20:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_56,type,
sK21:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_57,type,
sK22:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_58,type,
sK23:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_59,type,
sK24:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_60,type,
sK25:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_61,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_62,type,
sK27:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_63,type,
sK28:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_64,type,
sK29:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_65,type,
sK30:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).
tff(func_def_66,type,
sK31:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).
tff(func_def_67,type,
sK32:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).
tff(func_def_68,type,
sK33:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_69,type,
sK34:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_70,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_71,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_72,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).
tff(func_def_73,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).
tff(func_def_74,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).
tff(func_def_75,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).
tff(func_def_76,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).
tff(func_def_77,type,
sK42:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).
tff(func_def_78,type,
sK43:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).
tff(func_def_79,type,
sK44:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).
tff(func_def_80,type,
sK45:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).
tff(func_def_81,type,
sK46:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X4 ) ).
tff(func_def_82,type,
sK47:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X3 ) ).
tff(func_def_83,type,
sK48:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X2 ) ).
tff(func_def_84,type,
sK49:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X1 ) ).
tff(func_def_85,type,
sK50:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X0 ) ).
tff(func_def_86,type,
sK51:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).
tff(func_def_87,type,
sK52:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).
tff(func_def_88,type,
sK53:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).
tff(func_def_89,type,
sK54:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).
tff(func_def_90,type,
sK55:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).
tff(func_def_91,type,
sK56:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).
tff(func_def_92,type,
sK57:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X5 ) ).
tff(func_def_93,type,
sK58:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X4 ) ).
tff(func_def_94,type,
sK59:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X3 ) ).
tff(func_def_95,type,
sK60:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X2 ) ).
tff(func_def_96,type,
sK61:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X1 ) ).
tff(func_def_97,type,
sK62:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X0 ) ).
tff(func_def_98,type,
sK63: int ).
tff(pred_def_1,type,
enum:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
cl_HOL_Oequal:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
listMem:
!>[X0: $tType] : ( ( X0 * list(X0) ) > $o ) ).
tff(pred_def_6,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_7,type,
null:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_8,type,
i_Z: ( atom * list(int) ) > $o ).
tff(pred_def_9,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_10,type,
pp: bool > $o ).
tff(pred_def_11,type,
sP0:
!>[X0: $tType] : ( ( list(X0) * X0 ) > $o ) ).
tff(f1079,plain,
$false,
inference(avatar_sat_refutation,[],[f578,f583,f588,f593,f598,f603,f608,f613,f618,f623,f628,f632,f636,f640,f644,f648,f652,f656,f660,f664,f668,f672,f676,f680,f684,f688,f692,f696,f700,f705,f709,f713,f717,f721,f725,f729,f733,f737,f746,f750,f754,f758,f762,f776,f780,f784,f788,f792,f797,f810,f814,f822,f826,f830,f834,f838,f842,f846,f860,f864,f868,f872,f876,f880,f886,f890,f894,f898,f902,f906,f910,f914,f968,f972,f976,f980,f984,f989,f993,f1007,f1011,f1015,f1019,f1032,f1037,f1044,f1050,f1055,f1060,f1064,f1069,f1073,f1078]) ).
tff(f1078,plain,
( spl64_1
| ~ spl64_49
| ~ spl64_82 ),
inference(avatar_split_clause,[],[f1025,f1013,f794,f575]) ).
tff(f575,plain,
( spl64_1
<=> i_Z(a,cons(int,x,xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_1])]) ).
tff(f794,plain,
( spl64_49
<=> member(atom,a,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_49])]) ).
tff(f1013,plain,
( spl64_82
<=> ! [X0: atom] :
( i_Z(X0,cons(int,x,xs))
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_82])]) ).
tff(f1025,plain,
( i_Z(a,cons(int,x,xs))
| ~ spl64_49
| ~ spl64_82 ),
inference(resolution,[],[f1014,f796]) ).
tff(f796,plain,
( member(atom,a,aa(list(atom),fun(atom,bool),member1(atom),as))
| ~ spl64_49 ),
inference(avatar_component_clause,[],[f794]) ).
tff(f1014,plain,
( ! [X0: atom] :
( ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as))
| i_Z(X0,cons(int,x,xs)) )
| ~ spl64_82 ),
inference(avatar_component_clause,[],[f1013]) ).
tff(f1073,plain,
( spl64_92
| ~ spl64_12
| ~ spl64_40
| ~ spl64_88 ),
inference(avatar_split_clause,[],[f1056,f1053,f748,f630,f1071]) ).
tff(f1071,plain,
( spl64_92
<=> ! [X0: $tType,X1: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),fequal(list(X0)),X1),nil(X0)))
| ~ null(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_92])]) ).
tff(f630,plain,
( spl64_12
<=> ! [X0: $tType] : cl_HOL_Oequal(list(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_12])]) ).
tff(f748,plain,
( spl64_40
<=> ! [X0: $tType] :
( ( equal_equal(X0) = fequal(X0) )
| ~ cl_HOL_Oequal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_40])]) ).
tff(f1053,plain,
( spl64_88
<=> ! [X0: $tType,X1: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0)))
| ~ null(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_88])]) ).
tff(f1056,plain,
( ! [X0: $tType,X1: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),fequal(list(X0)),X1),nil(X0)))
| ~ null(X0,X1) )
| ~ spl64_12
| ~ spl64_40
| ~ spl64_88 ),
inference(forward_demodulation,[],[f1054,f765]) ).
tff(f765,plain,
( ! [X0: $tType] : ( equal_equal(list(X0)) = fequal(list(X0)) )
| ~ spl64_12
| ~ spl64_40 ),
inference(resolution,[],[f749,f631]) ).
tff(f631,plain,
( ! [X0: $tType] : cl_HOL_Oequal(list(X0))
| ~ spl64_12 ),
inference(avatar_component_clause,[],[f630]) ).
tff(f749,plain,
( ! [X0: $tType] :
( ~ cl_HOL_Oequal(X0)
| ( equal_equal(X0) = fequal(X0) ) )
| ~ spl64_40 ),
inference(avatar_component_clause,[],[f748]) ).
tff(f1054,plain,
( ! [X0: $tType,X1: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0)))
| ~ null(X0,X1) )
| ~ spl64_88 ),
inference(avatar_component_clause,[],[f1053]) ).
tff(f1069,plain,
( spl64_91
| ~ spl64_12
| ~ spl64_40
| ~ spl64_87 ),
inference(avatar_split_clause,[],[f1051,f1048,f748,f630,f1067]) ).
tff(f1067,plain,
( spl64_91
<=> ! [X0: $tType,X1: list(X0)] :
( ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),fequal(list(X0)),X1),nil(X0)))
| null(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_91])]) ).
tff(f1048,plain,
( spl64_87
<=> ! [X0: $tType,X1: list(X0)] :
( null(X0,X1)
| ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_87])]) ).
tff(f1051,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),fequal(list(X0)),X1),nil(X0)))
| null(X0,X1) )
| ~ spl64_12
| ~ spl64_40
| ~ spl64_87 ),
inference(forward_demodulation,[],[f1049,f765]) ).
tff(f1049,plain,
( ! [X0: $tType,X1: list(X0)] :
( null(X0,X1)
| ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0))) )
| ~ spl64_87 ),
inference(avatar_component_clause,[],[f1048]) ).
tff(f1064,plain,
spl64_90,
inference(avatar_split_clause,[],[f469,f1062]) ).
tff(f1062,plain,
( spl64_90
<=> ! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( X1 = X2 )
| ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_90])]) ).
tff(f469,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( X1 = X2 )
| ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X2),X1)) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,plain,
! [X0: $tType,X1: list(X0),X2: list(X0)] :
( ( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X2),X1))
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X2),X1)) ) ),
inference(nnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $tType,X1: list(X0),X2: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X2),X1))
<=> ( X1 = X2 ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType,X15: list(X0),X14: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X14),X15))
<=> ( X14 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_equal__list__def) ).
tff(f1060,plain,
spl64_89,
inference(avatar_split_clause,[],[f460,f1058]) ).
tff(f1058,plain,
( spl64_89
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( sP0(X0,X1,X2)
| ( cons(X0,sK14(X0,X1,X2),sK15(X0,X1,X2)) = X1 )
| ~ listMem(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_89])]) ).
tff(f460,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( sP0(X0,X1,X2)
| ( cons(X0,sK14(X0,X1,X2),sK15(X0,X1,X2)) = X1 )
| ~ listMem(X0,X2,X1) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( listMem(X0,X2,X1)
| ( ~ sP0(X0,X1,X2)
& ! [X3: X0,X4: list(X0)] :
( ( cons(X0,X3,X4) != X1 )
| ( X2 != X3 ) ) ) )
& ( sP0(X0,X1,X2)
| ( ( cons(X0,sK14(X0,X1,X2),sK15(X0,X1,X2)) = X1 )
& ( sK14(X0,X1,X2) = X2 ) )
| ~ listMem(X0,X2,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f309,f310]) ).
tff(f310,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ? [X5: X0,X6: list(X0)] :
( ( cons(X0,X5,X6) = X1 )
& ( X2 = X5 ) )
=> ( ( cons(X0,sK14(X0,X1,X2),sK15(X0,X1,X2)) = X1 )
& ( sK14(X0,X1,X2) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f309,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( listMem(X0,X2,X1)
| ( ~ sP0(X0,X1,X2)
& ! [X3: X0,X4: list(X0)] :
( ( cons(X0,X3,X4) != X1 )
| ( X2 != X3 ) ) ) )
& ( sP0(X0,X1,X2)
| ? [X5: X0,X6: list(X0)] :
( ( cons(X0,X5,X6) = X1 )
& ( X2 = X5 ) )
| ~ listMem(X0,X2,X1) ) ),
inference(rectify,[],[f308]) ).
tff(f308,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( listMem(X0,X2,X1)
| ( ~ sP0(X0,X1,X2)
& ! [X6: X0,X7: list(X0)] :
( ( cons(X0,X6,X7) != X1 )
| ( X2 != X6 ) ) ) )
& ( sP0(X0,X1,X2)
| ? [X6: X0,X7: list(X0)] :
( ( cons(X0,X6,X7) = X1 )
& ( X2 = X6 ) )
| ~ listMem(X0,X2,X1) ) ),
inference(flattening,[],[f307]) ).
tff(f307,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( listMem(X0,X2,X1)
| ( ~ sP0(X0,X1,X2)
& ! [X6: X0,X7: list(X0)] :
( ( cons(X0,X6,X7) != X1 )
| ( X2 != X6 ) ) ) )
& ( sP0(X0,X1,X2)
| ? [X6: X0,X7: list(X0)] :
( ( cons(X0,X6,X7) = X1 )
& ( X2 = X6 ) )
| ~ listMem(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( listMem(X0,X2,X1)
<=> ( sP0(X0,X1,X2)
| ? [X6: X0,X7: list(X0)] :
( ( cons(X0,X6,X7) = X1 )
& ( X2 = X6 ) ) ) ),
inference(definition_folding,[],[f179,f276]) ).
tff(f276,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( sP0(X0,X1,X2)
<=> ? [X3: X0,X4: list(X0),X5: X0] :
( listMem(X0,X3,X4)
& ( cons(X0,X5,X4) = X1 )
& ( X2 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f179,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( listMem(X0,X2,X1)
<=> ( ? [X3: X0,X4: list(X0),X5: X0] :
( listMem(X0,X3,X4)
& ( cons(X0,X5,X4) = X1 )
& ( X2 = X3 ) )
| ? [X6: X0,X7: list(X0)] :
( ( cons(X0,X6,X7) = X1 )
& ( X2 = X6 ) ) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType,X22: list(X0),X23: X0] :
( listMem(X0,X23,X22)
<=> ( ? [X24: X0,X25: list(X0),X26: X0] :
( listMem(X0,X24,X25)
& ( cons(X0,X26,X25) = X22 )
& ( X23 = X24 ) )
| ? [X24: X0,X25: list(X0)] :
( ( cons(X0,X24,X25) = X22 )
& ( X23 = X24 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_ListMem_Osimps) ).
tff(f1055,plain,
spl64_88,
inference(avatar_split_clause,[],[f423,f1053]) ).
tff(f423,plain,
! [X0: $tType,X1: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0)))
| ~ null(X0,X1) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: $tType,X1: list(X0)] :
( ( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0)))
| ~ null(X0,X1) )
& ( null(X0,X1)
| ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0))) ) ),
inference(nnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType,X1: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0)))
<=> null(X0,X1) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType,X13: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X13),nil(X0)))
<=> null(X0,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_equal__Nil__null) ).
tff(f1050,plain,
spl64_87,
inference(avatar_split_clause,[],[f422,f1048]) ).
tff(f422,plain,
! [X0: $tType,X1: list(X0)] :
( null(X0,X1)
| ~ pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X1),nil(X0))) ),
inference(cnf_transformation,[],[f295]) ).
tff(f1044,plain,
spl64_86,
inference(avatar_split_clause,[],[f570,f1042]) ).
tff(f1042,plain,
( spl64_86
<=> ! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_86])]) ).
tff(f570,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( insert(X0,X1,nil(X0)) = sublist(X0,insert(X0,X1,nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ),
inference(forward_demodulation,[],[f433,f398]) ).
tff(f398,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType,X11: X0] : ( insert(X0,X11,nil(X0)) = cons(X0,X11,nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_insert__Nil) ).
tff(f433,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType,X1: X0,X2: fun(nat,bool)] :
( ( ( nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) )
& ( ( cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) )
| ~ member(nat,zero_zero(nat),X2) ) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType,X1: X0,X2: fun(nat,bool)] :
( ( ~ member(nat,zero_zero(nat),X2)
=> ( nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) ) )
& ( member(nat,zero_zero(nat),X2)
=> ( cons(X0,X1,nil(X0)) = sublist(X0,cons(X0,X1,nil(X0)),X2) ) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType,X14: X0,X53: fun(nat,bool)] :
( ( ~ member(nat,zero_zero(nat),X53)
=> ( nil(X0) = sublist(X0,cons(X0,X14,nil(X0)),X53) ) )
& ( member(nat,zero_zero(nat),X53)
=> ( cons(X0,X14,nil(X0)) = sublist(X0,cons(X0,X14,nil(X0)),X53) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_sublist__singleton) ).
tff(f1037,plain,
( spl64_85
| ~ spl64_49
| ~ spl64_81 ),
inference(avatar_split_clause,[],[f1023,f1009,f794,f1034]) ).
tff(f1034,plain,
( spl64_85
<=> i_Z(a,cons(int,sK1,xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_85])]) ).
tff(f1009,plain,
( spl64_81
<=> ! [X1: atom] :
( i_Z(X1,cons(int,sK1,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),member1(atom),as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_81])]) ).
tff(f1023,plain,
( i_Z(a,cons(int,sK1,xs))
| ~ spl64_49
| ~ spl64_81 ),
inference(resolution,[],[f1010,f796]) ).
tff(f1010,plain,
( ! [X1: atom] :
( ~ member(atom,X1,aa(list(atom),fun(atom,bool),member1(atom),as))
| i_Z(X1,cons(int,sK1,xs)) )
| ~ spl64_81 ),
inference(avatar_component_clause,[],[f1009]) ).
tff(f1032,plain,
spl64_84,
inference(avatar_split_clause,[],[f526,f1030]) ).
tff(f1030,plain,
( spl64_84
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_84])]) ).
tff(f526,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1)) ),
inference(definition_unfolding,[],[f435,f376]) ).
tff(f376,plain,
! [X0: $tType] : ( set(X0) = member1(X0) ),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] : ( set(X0) = member1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_member__set) ).
tff(f435,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1)) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( ( cons(X0,X2,X1) = insert(X0,X2,X1) )
| member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1)) )
& ( ( insert(X0,X2,X1) = X1 )
| ~ member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1)) ) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( ~ member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1))
=> ( cons(X0,X2,X1) = insert(X0,X2,X1) ) )
& ( member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1))
=> ( insert(X0,X2,X1) = X1 ) ) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X0: $tType,X13: list(X0),X14: X0] :
( ( ~ member(X0,X14,aa(list(X0),fun(X0,bool),set(X0),X13))
=> ( cons(X0,X14,X13) = insert(X0,X14,X13) ) )
& ( member(X0,X14,aa(list(X0),fun(X0,bool),set(X0),X13))
=> ( insert(X0,X14,X13) = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_List_Oinsert__def) ).
tff(f1019,plain,
spl64_83,
inference(avatar_split_clause,[],[f546,f1017]) ).
tff(f1017,plain,
( spl64_83
<=> ! [X1: atom] :
( i_Z(X1,cons(int,sK63,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),member1(atom),as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_83])]) ).
tff(f546,plain,
! [X1: atom] :
( i_Z(X1,cons(int,sK63,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
inference(definition_unfolding,[],[f516,f376]) ).
tff(f516,plain,
! [X1: atom] :
( i_Z(X1,cons(int,sK63,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(cnf_transformation,[],[f357]) ).
tff(f357,plain,
! [X1: atom] :
( i_Z(X1,cons(int,sK63,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f275,f356]) ).
tff(f356,plain,
( ? [X0: int] :
! [X1: atom] :
( i_Z(X1,cons(int,X0,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) )
=> ! [X1: atom] :
( i_Z(X1,cons(int,sK63,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) ) ),
introduced(choice_axiom,[]) ).
tff(f275,plain,
? [X0: int] :
! [X1: atom] :
( i_Z(X1,cons(int,X0,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(ennf_transformation,[],[f217]) ).
tff(f217,plain,
? [X0: int] :
! [X1: atom] :
( member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as))
=> i_Z(X1,cons(int,X0,xs)) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
? [X5: int] :
! [X6: atom] :
( member(atom,X6,aa(list(atom),fun(atom,bool),set(atom),as))
=> i_Z(X6,cons(int,X5,xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
tff(f1015,plain,
spl64_82,
inference(avatar_split_clause,[],[f522,f1013]) ).
tff(f522,plain,
! [X0: atom] :
( i_Z(X0,cons(int,x,xs))
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
inference(definition_unfolding,[],[f390,f376]) ).
tff(f390,plain,
! [X0: atom] :
( i_Z(X0,cons(int,x,xs))
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: atom] :
( i_Z(X0,cons(int,x,xs))
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(ennf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: atom] :
( member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as))
=> i_Z(X0,cons(int,x,xs)) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X4: atom] :
( member(atom,X4,aa(list(atom),fun(atom,bool),set(atom),as))
=> i_Z(X4,cons(int,x,xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_x) ).
tff(f1011,plain,
spl64_81,
inference(avatar_split_clause,[],[f519,f1009]) ).
tff(f519,plain,
! [X1: atom] :
( i_Z(X1,cons(int,sK1,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
inference(definition_unfolding,[],[f372,f376]) ).
tff(f372,plain,
! [X1: atom] :
( i_Z(X1,cons(int,sK1,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X1: atom] :
( i_Z(X1,cons(int,sK1,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f219,f278]) ).
tff(f278,plain,
( ? [X0: int] :
! [X1: atom] :
( i_Z(X1,cons(int,X0,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) )
=> ! [X1: atom] :
( i_Z(X1,cons(int,sK1,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) ) ),
introduced(choice_axiom,[]) ).
tff(f219,plain,
? [X0: int] :
! [X1: atom] :
( i_Z(X1,cons(int,X0,xs))
| ~ member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(ennf_transformation,[],[f120]) ).
tff(f120,plain,
~ ! [X0: int] :
~ ! [X1: atom] :
( member(atom,X1,aa(list(atom),fun(atom,bool),set(atom),as))
=> i_Z(X1,cons(int,X0,xs)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
~ ! [X5: int] :
~ ! [X6: atom] :
( member(atom,X6,aa(list(atom),fun(atom,bool),set(atom),as))
=> i_Z(X6,cons(int,X5,xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096_B_Bthesis_O_A_I_B_Bx_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1007,plain,
spl64_80,
inference(avatar_split_clause,[],[f387,f1005]) ).
tff(f1005,plain,
( spl64_80
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X2),X1))
| ~ cl_HOL_Oequal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_80])]) ).
tff(f387,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X2),X1))
| ~ cl_HOL_Oequal(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X2),X1))
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X2),X1)) ) )
| ~ cl_HOL_Oequal(X0) ),
inference(nnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X2),X1))
<=> ( X1 = X2 ) )
| ~ cl_HOL_Oequal(X0) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType] :
( cl_HOL_Oequal(X0)
=> ! [X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X2),X1))
<=> ( X1 = X2 ) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType] :
( cl_HOL_Oequal(X0)
=> ! [X15: X0,X14: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X14),X15))
<=> ( X14 = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_equal__eq) ).
tff(f993,plain,
spl64_79,
inference(avatar_split_clause,[],[f569,f991]) ).
tff(f991,plain,
( spl64_79
<=> ! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_79])]) ).
tff(f569,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( nil(X0) = sublist(X0,insert(X0,X1,nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) ),
inference(forward_demodulation,[],[f434,f398]) ).
tff(f434,plain,
! [X0: $tType,X2: fun(nat,bool),X1: X0] :
( ( nil(X0) = sublist(X0,cons(X0,X1,nil(X0)),X2) )
| member(nat,zero_zero(nat),X2) ),
inference(cnf_transformation,[],[f238]) ).
tff(f989,plain,
spl64_78,
inference(avatar_split_clause,[],[f563,f987]) ).
tff(f987,plain,
( spl64_78
<=> ! [X0: $tType,X2: list(X0),X3: X0] : pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X3,X2)),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_78])]) ).
tff(f563,plain,
! [X0: $tType,X2: list(X0),X3: X0] : pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X3,X2)),X3)),
inference(equality_resolution,[],[f485]) ).
tff(f485,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: X0] :
( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X3,X2)),X1))
| ( X1 != X3 ) ),
inference(cnf_transformation,[],[f333]) ).
tff(f333,plain,
! [X0: $tType,X1: X0,X2: list(X0),X3: X0] :
( ( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X3,X2)),X1))
| ( ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),X2),X1))
& ( X1 != X3 ) ) )
& ( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),X2),X1))
| ( X1 = X3 )
| ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X3,X2)),X1)) ) ),
inference(flattening,[],[f332]) ).
tff(f332,plain,
! [X0: $tType,X1: X0,X2: list(X0),X3: X0] :
( ( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X3,X2)),X1))
| ( ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),X2),X1))
& ( X1 != X3 ) ) )
& ( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),X2),X1))
| ( X1 = X3 )
| ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X3,X2)),X1)) ) ),
inference(nnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: X0,X2: list(X0),X3: X0] :
( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X3,X2)),X1))
<=> ( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),X2),X1))
| ( X1 = X3 ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType,X15: X0,X13: list(X0),X14: X0] :
( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X14,X13)),X15))
<=> ( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),X13),X15))
| ( X14 = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_member__rec_I1_J) ).
tff(f984,plain,
spl64_77,
inference(avatar_split_clause,[],[f562,f982]) ).
tff(f982,plain,
( spl64_77
<=> ! [X0: $tType,X2: list(X0)] : pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_77])]) ).
tff(f562,plain,
! [X0: $tType,X2: list(X0)] : pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X2),X2)),
inference(equality_resolution,[],[f470]) ).
tff(f470,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] :
( pp(aa(list(X0),bool,aa(list(X0),fun(list(X0),bool),equal_equal(list(X0)),X2),X1))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f315]) ).
tff(f980,plain,
spl64_76,
inference(avatar_split_clause,[],[f521,f978]) ).
tff(f978,plain,
( spl64_76
<=> ! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_76])]) ).
tff(f521,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
inference(definition_unfolding,[],[f389,f376]) ).
tff(f389,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(ennf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: atom] :
( member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( zero_zero(int) != divisor(X0) ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X4: atom] :
( member(atom,X4,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( divisor(X4) != zero_zero(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_norm) ).
tff(f976,plain,
spl64_75,
inference(avatar_split_clause,[],[f456,f974]) ).
tff(f974,plain,
( spl64_75
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( cons(X0,sK13(X0,X1,X2),sK12(X0,X1,X2)) = X1 )
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_75])]) ).
tff(f456,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( cons(X0,sK13(X0,X1,X2),sK12(X0,X1,X2)) = X1 )
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( sP0(X0,X1,X2)
| ! [X3: X0,X4: list(X0),X5: X0] :
( ~ listMem(X0,X3,X4)
| ( cons(X0,X5,X4) != X1 )
| ( X2 != X3 ) ) )
& ( ( listMem(X0,sK11(X0,X1,X2),sK12(X0,X1,X2))
& ( cons(X0,sK13(X0,X1,X2),sK12(X0,X1,X2)) = X1 )
& ( sK11(X0,X1,X2) = X2 ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f304,f305]) ).
tff(f305,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ? [X6: X0,X7: list(X0),X8: X0] :
( listMem(X0,X6,X7)
& ( cons(X0,X8,X7) = X1 )
& ( X2 = X6 ) )
=> ( listMem(X0,sK11(X0,X1,X2),sK12(X0,X1,X2))
& ( cons(X0,sK13(X0,X1,X2),sK12(X0,X1,X2)) = X1 )
& ( sK11(X0,X1,X2) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f304,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( sP0(X0,X1,X2)
| ! [X3: X0,X4: list(X0),X5: X0] :
( ~ listMem(X0,X3,X4)
| ( cons(X0,X5,X4) != X1 )
| ( X2 != X3 ) ) )
& ( ? [X6: X0,X7: list(X0),X8: X0] :
( listMem(X0,X6,X7)
& ( cons(X0,X8,X7) = X1 )
& ( X2 = X6 ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f303]) ).
tff(f303,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( sP0(X0,X1,X2)
| ! [X3: X0,X4: list(X0),X5: X0] :
( ~ listMem(X0,X3,X4)
| ( cons(X0,X5,X4) != X1 )
| ( X2 != X3 ) ) )
& ( ? [X3: X0,X4: list(X0),X5: X0] :
( listMem(X0,X3,X4)
& ( cons(X0,X5,X4) = X1 )
& ( X2 = X3 ) )
| ~ sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f276]) ).
tff(f972,plain,
spl64_74,
inference(avatar_split_clause,[],[f446,f970]) ).
tff(f970,plain,
( spl64_74
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: fun(X1,fun(X0,X2))] :
( ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_74])]) ).
tff(f446,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X1,fun(X0,X2))] :
( ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(flattening,[],[f245]) ).
tff(f245,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) )
| ~ zero(X0)
| ~ zero(X1) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( zero(X0)
& zero(X1) )
=> ! [X3: fun(X1,fun(X0,X2))] : ( nil(X2) = zipwith0(X1,X0,X2,X3,nil(X1),nil(X0)) ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X2: $tType,X1: $tType,X0: $tType] :
( ( zero(X2)
& zero(X1) )
=> ! [X21: fun(X1,fun(X2,X0))] : ( nil(X0) = zipwith0(X1,X2,X0,X21,nil(X1),nil(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_zipwith0_Osimps_I1_J) ).
tff(f968,plain,
( spl64_73
| ~ spl64_49
| ~ spl64_71 ),
inference(avatar_split_clause,[],[f962,f908,f794,f965]) ).
tff(f965,plain,
( spl64_73
<=> listMem(atom,a,as) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_73])]) ).
tff(f908,plain,
( spl64_71
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( listMem(X0,X2,X1)
| ~ member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_71])]) ).
tff(f962,plain,
( listMem(atom,a,as)
| ~ spl64_49
| ~ spl64_71 ),
inference(resolution,[],[f909,f796]) ).
tff(f909,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] :
( ~ member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1))
| listMem(X0,X2,X1) )
| ~ spl64_71 ),
inference(avatar_component_clause,[],[f908]) ).
tff(f914,plain,
spl64_72,
inference(avatar_split_clause,[],[f535,f912]) ).
tff(f912,plain,
( spl64_72
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1))
| ~ listMem(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_72])]) ).
tff(f535,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1))
| ~ listMem(X0,X2,X1) ),
inference(definition_unfolding,[],[f453,f376]) ).
tff(f453,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1))
| ~ listMem(X0,X2,X1) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( ( listMem(X0,X2,X1)
| ~ member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1)) )
& ( member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1))
| ~ listMem(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType,X1: list(X0),X2: X0] :
( listMem(X0,X2,X1)
<=> member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1)) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType,X13: list(X0),X14: X0] :
( listMem(X0,X14,X13)
<=> member(X0,X14,aa(list(X0),fun(X0,bool),set(X0),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_ListMem__iff) ).
tff(f910,plain,
spl64_71,
inference(avatar_split_clause,[],[f534,f908]) ).
tff(f534,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( listMem(X0,X2,X1)
| ~ member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1)) ),
inference(definition_unfolding,[],[f454,f376]) ).
tff(f454,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( listMem(X0,X2,X1)
| ~ member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1)) ),
inference(cnf_transformation,[],[f302]) ).
tff(f906,plain,
spl64_70,
inference(avatar_split_clause,[],[f503,f904]) ).
tff(f904,plain,
( spl64_70
<=> ! [X1: $tType,X0: $tType,X3: X0,X4: X1,X5: X0,X2: X1] :
( ( X2 = X4 )
| ( product_Pair(X0,X1,X3,X2) != product_Pair(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_70])]) ).
tff(f503,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( X2 = X4 )
| ( product_Pair(X0,X1,X3,X2) != product_Pair(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( ( X2 = X4 )
& ( X3 = X5 ) )
| ( product_Pair(X0,X1,X3,X2) != product_Pair(X0,X1,X5,X4) ) ),
inference(ennf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( product_Pair(X0,X1,X3,X2) = product_Pair(X0,X1,X5,X4) )
=> ~ ( ( X3 = X5 )
=> ( X2 != X4 ) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType,X1: $tType,X41: X1,X29: X0,X42: X1,X43: X0] :
( ( product_Pair(X0,X1,X43,X42) = product_Pair(X0,X1,X29,X41) )
=> ~ ( ( X29 = X43 )
=> ( X41 != X42 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Pair__inject) ).
tff(f902,plain,
spl64_69,
inference(avatar_split_clause,[],[f502,f900]) ).
tff(f900,plain,
( spl64_69
<=> ! [X1: $tType,X0: $tType,X2: X1,X4: X1,X5: X0,X3: X0] :
( ( X3 = X5 )
| ( product_Pair(X0,X1,X3,X2) != product_Pair(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_69])]) ).
tff(f502,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X0,X4: X1,X5: X0] :
( ( X3 = X5 )
| ( product_Pair(X0,X1,X3,X2) != product_Pair(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f269]) ).
tff(f898,plain,
spl64_68,
inference(avatar_split_clause,[],[f440,f896]) ).
tff(f896,plain,
( spl64_68
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_68])]) ).
tff(f440,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(cnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType,X1: X0,X2: X0] :
( ( X1 = X2 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1)) ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X0: $tType,X19: X0,X11: X0] :
( ( X11 = X19 )
| ~ pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X11),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
tff(f894,plain,
spl64_67,
inference(avatar_split_clause,[],[f412,f892]) ).
tff(f892,plain,
( spl64_67
<=> ! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK5(X0,X1),sK6(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_67])]) ).
tff(f412,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK5(X0,X1),sK6(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) )
& ( ( cons(X0,sK5(X0,X1),sK6(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f288,f289]) ).
tff(f289,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X4: X0,X5: list(X0)] : ( cons(X0,X4,X5) = X1 )
=> ( cons(X0,sK5(X0,X1),sK6(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f288,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) )
& ( ? [X4: X0,X5: list(X0)] : ( cons(X0,X4,X5) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(rectify,[],[f287]) ).
tff(f287,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) )
& ( ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != X1 )
<=> ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType,X13: list(X0)] :
( ( nil(X0) != X13 )
<=> ? [X26: X0,X32: list(X0)] : ( cons(X0,X26,X32) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_neq__Nil__conv) ).
tff(f890,plain,
spl64_66,
inference(avatar_split_clause,[],[f406,f888]) ).
tff(f888,plain,
( spl64_66
<=> ! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_66])]) ).
tff(f406,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f231,f284]) ).
tff(f284,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 )
=> ( cons(X0,sK3(X0,X1),sK4(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f231,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 )
| ( nil(X0) = X1 ) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != X1 )
=> ~ ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X19: list(X0)] :
( ( nil(X0) != X19 )
=> ~ ! [X33: X0,X34: list(X0)] : ( cons(X0,X33,X34) != X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_list_Oexhaust) ).
tff(f886,plain,
spl64_65,
inference(avatar_split_clause,[],[f401,f884]) ).
tff(f884,plain,
( spl64_65
<=> ! [X0: $tType,X1: list(X0)] : ( cons(list(X0),nil(X0),nil(list(X0))) = n_lists(X0,zero_zero(nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_65])]) ).
tff(f401,plain,
! [X0: $tType,X1: list(X0)] : ( cons(list(X0),nil(X0),nil(list(X0))) = n_lists(X0,zero_zero(nat),X1) ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType,X1: list(X0)] : ( cons(list(X0),nil(X0),nil(list(X0))) = n_lists(X0,zero_zero(nat),X1) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType,X12: list(X0)] : ( cons(list(X0),nil(X0),nil(list(X0))) = n_lists(X0,zero_zero(nat),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_n__lists_Osimps_I1_J) ).
tff(f880,plain,
spl64_64,
inference(avatar_split_clause,[],[f476,f878]) ).
tff(f878,plain,
( spl64_64
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK24(X0,X1,X2),sK25(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_64])]) ).
tff(f476,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK24(X0,X1,X2),sK25(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK24(X0,X1,X2),sK25(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f256,f328]) ).
tff(f328,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) = X2 )
=> ( product_Pair(X0,X1,sK24(X0,X1,X2),sK25(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f256,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) = X2 ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
~ ! [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) != X2 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X1: $tType,X19: product_prod(X0,X1)] :
~ ! [X33: X0,X47: X1] : ( product_Pair(X0,X1,X33,X47) != X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_prod_Oexhaust) ).
tff(f876,plain,
spl64_63,
inference(avatar_split_clause,[],[f475,f874]) ).
tff(f874,plain,
( spl64_63
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK22(X0,X1,X2),sK23(X0,X1,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_63])]) ).
tff(f475,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK22(X0,X1,X2),sK23(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f327]) ).
tff(f327,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( product_Pair(X0,X1,sK22(X0,X1,X2),sK23(X0,X1,X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f255,f326]) ).
tff(f326,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) = X2 )
=> ( product_Pair(X0,X1,sK22(X0,X1,X2),sK23(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
tff(f255,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) = X2 ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
~ ! [X3: X0,X4: X1] : ( product_Pair(X0,X1,X3,X4) != X2 ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType,X1: $tType,X54: product_prod(X0,X1)] :
~ ! [X5: X0,X55: X1] : ( product_Pair(X0,X1,X5,X55) != X54 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_PairE) ).
tff(f872,plain,
spl64_62,
inference(avatar_split_clause,[],[f405,f870]) ).
tff(f870,plain,
( spl64_62
<=> ! [X0: $tType,X1: nat] :
( ( nil(list(X0)) = n_lists(X0,X1,nil(X0)) )
| ( zero_zero(nat) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_62])]) ).
tff(f405,plain,
! [X0: $tType,X1: nat] :
( ( nil(list(X0)) = n_lists(X0,X1,nil(X0)) )
| ( zero_zero(nat) = X1 ) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType,X1: nat] :
( ( ( nil(list(X0)) = n_lists(X0,X1,nil(X0)) )
| ( zero_zero(nat) = X1 ) )
& ( ( cons(list(X0),nil(X0),nil(list(X0))) = n_lists(X0,X1,nil(X0)) )
| ( zero_zero(nat) != X1 ) ) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType,X1: nat] :
( ( ( zero_zero(nat) != X1 )
=> ( nil(list(X0)) = n_lists(X0,X1,nil(X0)) ) )
& ( ( zero_zero(nat) = X1 )
=> ( cons(list(X0),nil(X0),nil(list(X0))) = n_lists(X0,X1,nil(X0)) ) ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType,X61: nat] :
( ( ( zero_zero(nat) != X61 )
=> ( n_lists(X0,X61,nil(X0)) = nil(list(X0)) ) )
& ( ( zero_zero(nat) = X61 )
=> ( n_lists(X0,X61,nil(X0)) = cons(list(X0),nil(X0),nil(list(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_n__lists__Nil) ).
tff(f868,plain,
spl64_61,
inference(avatar_split_clause,[],[f400,f866]) ).
tff(f866,plain,
( spl64_61
<=> ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),nil(X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_61])]) ).
tff(f400,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),nil(X0)),X1)),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),nil(X0)),X1)),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType,X19: X0] : ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),nil(X0)),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_member__rec_I2_J) ).
tff(f864,plain,
spl64_60,
inference(avatar_split_clause,[],[f386,f862]) ).
tff(f862,plain,
( spl64_60
<=> ! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X1),X1))
| ~ cl_HOL_Oequal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_60])]) ).
tff(f386,plain,
! [X0: $tType,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X1),X1))
| ~ cl_HOL_Oequal(X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType] :
( ! [X1: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X1),X1))
| ~ cl_HOL_Oequal(X0) ),
inference(ennf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: $tType] :
( cl_HOL_Oequal(X0)
=> ! [X1: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X1),X1)) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType] :
( cl_HOL_Oequal(X0)
=> ! [X11: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),equal_equal(X0),X11),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_equal__refl) ).
tff(f860,plain,
spl64_59,
inference(avatar_split_clause,[],[f381,f858]) ).
tff(f858,plain,
( spl64_59
<=> ! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( zero_zero(X0) != sK2(X0,X2) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_59])]) ).
tff(f381,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( zero_zero(X0) != sK2(X0,X2) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ( ( zero_zero(X0) != sK2(X0,X2) )
& member(X0,sK2(X0,X2),aa(list(X0),fun(X0,bool),set(X0),X2)) ) )
| ~ ring(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f222,f280]) ).
tff(f280,plain,
! [X0: $tType,X2: list(X0)] :
( ? [X3: X0] :
( ( zero_zero(X0) != X3 )
& member(X0,X3,aa(list(X0),fun(X0,bool),set(X0),X2)) )
=> ( ( zero_zero(X0) != sK2(X0,X2) )
& member(X0,sK2(X0,X2),aa(list(X0),fun(X0,bool),set(X0),X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f222,plain,
! [X0: $tType] :
( ! [X1: list(X0),X2: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X2,X1) )
| ? [X3: X0] :
( ( zero_zero(X0) != X3 )
& member(X0,X3,aa(list(X0),fun(X0,bool),set(X0),X2)) ) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0),X2: list(X0)] :
( ! [X3: X0] :
( member(X0,X3,aa(list(X0),fun(X0,bool),set(X0),X2))
=> ( zero_zero(X0) = X3 ) )
=> ( zero_zero(X0) = iprod(X0,X2,X1) ) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X13: list(X0),X35: list(X0)] :
( ! [X5: X0] :
( member(X0,X5,aa(list(X0),fun(X0,bool),set(X0),X35))
=> ( zero_zero(X0) = X5 ) )
=> ( zero_zero(X0) = iprod(X0,X35,X13) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_iprod0__if__coeffs0) ).
tff(f846,plain,
spl64_58,
inference(avatar_split_clause,[],[f494,f844]) ).
tff(f844,plain,
( spl64_58
<=> ! [X0: $tType,X2: X0,X4: X0,X3: list(X0),X1: list(X0)] :
( ( X1 = X3 )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_58])]) ).
tff(f494,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X1 = X3 )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f339]) ).
tff(f339,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( cons(X0,X2,X1) = cons(X0,X4,X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ) ),
inference(flattening,[],[f338]) ).
tff(f338,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( ( cons(X0,X2,X1) = cons(X0,X4,X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: list(X0),X2: X0,X3: list(X0),X4: X0] :
( ( cons(X0,X2,X1) = cons(X0,X4,X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType,X7: list(X0),X8: X0,X9: list(X0),X10: X0] :
( ( cons(X0,X10,X9) = cons(X0,X8,X7) )
<=> ( ( X7 = X9 )
& ( X8 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_list_Oinject) ).
tff(f842,plain,
spl64_57,
inference(avatar_split_clause,[],[f459,f840]) ).
tff(f840,plain,
( spl64_57
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( sP0(X0,X1,X2)
| ( sK14(X0,X1,X2) = X2 )
| ~ listMem(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_57])]) ).
tff(f459,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( sP0(X0,X1,X2)
| ( sK14(X0,X1,X2) = X2 )
| ~ listMem(X0,X2,X1) ),
inference(cnf_transformation,[],[f311]) ).
tff(f838,plain,
spl64_56,
inference(avatar_split_clause,[],[f457,f836]) ).
tff(f836,plain,
( spl64_56
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( listMem(X0,sK11(X0,X1,X2),sK12(X0,X1,X2))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_56])]) ).
tff(f457,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( listMem(X0,sK11(X0,X1,X2),sK12(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f306]) ).
tff(f834,plain,
spl64_55,
inference(avatar_split_clause,[],[f432,f832]) ).
tff(f832,plain,
( spl64_55
<=> ! [X1: $tType,X0: $tType,X2: list(X0)] : ( product(X1,X0,nil(X1),X2) = nil(product_prod(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_55])]) ).
tff(f432,plain,
! [X1: $tType,X0: $tType,X2: list(X0)] : ( product(X1,X0,nil(X1),X2) = nil(product_prod(X1,X0)) ),
inference(cnf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType,X1: $tType,X2: list(X0)] : ( product(X1,X0,nil(X1),X2) = nil(product_prod(X1,X0)) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X1: $tType,X0: $tType,X60: list(X1)] : ( product(X0,X1,nil(X0),X60) = nil(product_prod(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_product_Osimps_I1_J) ).
tff(f830,plain,
spl64_54,
inference(avatar_split_clause,[],[f431,f828]) ).
tff(f828,plain,
( spl64_54
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( insert(X0,X2,remdups(X0,X1)) = remdups(X0,insert(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_54])]) ).
tff(f431,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( insert(X0,X2,remdups(X0,X1)) = remdups(X0,insert(X0,X2,X1)) ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( insert(X0,X2,remdups(X0,X1)) = remdups(X0,insert(X0,X2,X1)) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType,X12: list(X0),X11: X0] : ( insert(X0,X11,remdups(X0,X12)) = remdups(X0,insert(X0,X11,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_insert__remdups) ).
tff(f826,plain,
spl64_53,
inference(avatar_split_clause,[],[f399,f824]) ).
tff(f824,plain,
( spl64_53
<=> ! [X0: $tType,X1: list(list(X0))] : ( transpose(X0,cons(list(X0),nil(X0),X1)) = transpose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_53])]) ).
tff(f399,plain,
! [X0: $tType,X1: list(list(X0))] : ( transpose(X0,cons(list(X0),nil(X0),X1)) = transpose(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType,X1: list(list(X0))] : ( transpose(X0,cons(list(X0),nil(X0),X1)) = transpose(X0,X1) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType,X62: list(list(X0))] : ( transpose(X0,cons(list(X0),nil(X0),X62)) = transpose(X0,X62) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_transpose_Osimps_I2_J) ).
tff(f822,plain,
( spl64_52
| ~ spl64_16
| ~ spl64_45 ),
inference(avatar_split_clause,[],[f803,f778,f646,f820]) ).
tff(f820,plain,
( spl64_52
<=> ! [X0: $tType,X1: X0] : ~ null(X0,insert(X0,X1,nil(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_52])]) ).
tff(f646,plain,
( spl64_16
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ~ null(X0,cons(X0,X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_16])]) ).
tff(f778,plain,
( spl64_45
<=> ! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_45])]) ).
tff(f803,plain,
( ! [X0: $tType,X1: X0] : ~ null(X0,insert(X0,X1,nil(X0)))
| ~ spl64_16
| ~ spl64_45 ),
inference(superposition,[],[f647,f779]) ).
tff(f779,plain,
( ! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) )
| ~ spl64_45 ),
inference(avatar_component_clause,[],[f778]) ).
tff(f647,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] : ~ null(X0,cons(X0,X2,X1))
| ~ spl64_16 ),
inference(avatar_component_clause,[],[f646]) ).
tff(f814,plain,
spl64_51,
inference(avatar_split_clause,[],[f557,f812]) ).
tff(f812,plain,
( spl64_51
<=> ! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_51])]) ).
tff(f557,plain,
! [X0: $tType,X2: X0] : pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X2)),
inference(equality_resolution,[],[f439]) ).
tff(f439,plain,
! [X0: $tType,X2: X0,X1: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType,X1: X0,X2: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X2),X1))
| ( X1 != X2 ) ),
inference(rectify,[],[f116]) ).
tff(f116,axiom,
! [X0: $tType,X19: X0,X11: X0] :
( pp(aa(X0,bool,aa(X0,fun(X0,bool),fequal(X0),X11),X19))
| ( X11 != X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
tff(f810,plain,
spl64_50,
inference(avatar_split_clause,[],[f493,f808]) ).
tff(f808,plain,
( spl64_50
<=> ! [X0: $tType,X4: X0,X3: list(X0),X2: X0,X1: list(X0)] :
( ( X2 = X4 )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_50])]) ).
tff(f493,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0),X4: X0] :
( ( X2 = X4 )
| ( cons(X0,X2,X1) != cons(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f339]) ).
tff(f797,plain,
spl64_49,
inference(avatar_split_clause,[],[f517,f794]) ).
tff(f517,plain,
member(atom,a,aa(list(atom),fun(atom,bool),member1(atom),as)),
inference(definition_unfolding,[],[f370,f376]) ).
tff(f370,plain,
member(atom,a,aa(list(atom),fun(atom,bool),set(atom),as)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
member(atom,a,aa(list(atom),fun(atom,bool),set(atom),as)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096a_A_058_Aset_Aas_096) ).
tff(f792,plain,
( spl64_48
| ~ spl64_3
| ~ spl64_34 ),
inference(avatar_split_clause,[],[f739,f719,f585,f790]) ).
tff(f790,plain,
( spl64_48
<=> ! [X0: list(int)] : ( zero_zero(int) = iprod(int,nil(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_48])]) ).
tff(f585,plain,
( spl64_3
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_3])]) ).
tff(f719,plain,
( spl64_34
<=> ! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_34])]) ).
tff(f739,plain,
( ! [X0: list(int)] : ( zero_zero(int) = iprod(int,nil(int),X0) )
| ~ spl64_3
| ~ spl64_34 ),
inference(resolution,[],[f720,f587]) ).
tff(f587,plain,
( ring(int)
| ~ spl64_3 ),
inference(avatar_component_clause,[],[f585]) ).
tff(f720,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ ring(X0)
| ( zero_zero(X0) = iprod(X0,nil(X0),X1) ) )
| ~ spl64_34 ),
inference(avatar_component_clause,[],[f719]) ).
tff(f788,plain,
spl64_47,
inference(avatar_split_clause,[],[f420,f786]) ).
tff(f786,plain,
( spl64_47
<=> ! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( nil(X0) != rotate1(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_47])]) ).
tff(f420,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( nil(X0) != rotate1(X0,X1) ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) = rotate1(X0,X1) )
| ( nil(X0) != X1 ) )
& ( ( nil(X0) = X1 )
| ( nil(X0) != rotate1(X0,X1) ) ) ),
inference(nnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = rotate1(X0,X1) )
<=> ( nil(X0) = X1 ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X13: list(X0)] :
( ( rotate1(X0,X13) = nil(X0) )
<=> ( nil(X0) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rotate1__is__Nil__conv) ).
tff(f784,plain,
spl64_46,
inference(avatar_split_clause,[],[f416,f782]) ).
tff(f782,plain,
( spl64_46
<=> ! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( nil(X0) != remdups(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_46])]) ).
tff(f416,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ( nil(X0) != remdups(X0,X1) ) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) = remdups(X0,X1) )
| ( nil(X0) != X1 ) )
& ( ( nil(X0) = X1 )
| ( nil(X0) != remdups(X0,X1) ) ) ),
inference(nnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = remdups(X0,X1) )
<=> ( nil(X0) = X1 ) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType,X14: list(X0)] :
( ( nil(X0) = remdups(X0,X14) )
<=> ( nil(X0) = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_remdups__eq__nil__iff) ).
tff(f780,plain,
spl64_45,
inference(avatar_split_clause,[],[f398,f778]) ).
tff(f776,plain,
~ spl64_44,
inference(avatar_split_clause,[],[f369,f773]) ).
tff(f773,plain,
( spl64_44
<=> ( lbounds(as) = nil(product_prod(int,list(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_44])]) ).
tff(f369,plain,
lbounds(as) != nil(product_prod(int,list(int))),
inference(cnf_transformation,[],[f21]) ).
tff(f21,axiom,
lbounds(as) != nil(product_prod(int,list(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20__096lbounds_Aas_A_126_061_A_091_093_096) ).
tff(f762,plain,
spl64_43,
inference(avatar_split_clause,[],[f559,f760]) ).
tff(f760,plain,
( spl64_43
<=> ! [X0: $tType,X4: list(X0),X5: X0,X3: X0] :
( sP0(X0,cons(X0,X5,X4),X3)
| ~ listMem(X0,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_43])]) ).
tff(f559,plain,
! [X0: $tType,X3: X0,X4: list(X0),X5: X0] :
( sP0(X0,cons(X0,X5,X4),X3)
| ~ listMem(X0,X3,X4) ),
inference(equality_resolution,[],[f558]) ).
tff(f558,plain,
! [X0: $tType,X2: X0,X3: X0,X4: list(X0),X5: X0] :
( sP0(X0,cons(X0,X5,X4),X2)
| ~ listMem(X0,X3,X4)
| ( X2 != X3 ) ),
inference(equality_resolution,[],[f458]) ).
tff(f458,plain,
! [X0: $tType,X2: X0,X3: X0,X1: list(X0),X4: list(X0),X5: X0] :
( sP0(X0,X1,X2)
| ~ listMem(X0,X3,X4)
| ( cons(X0,X5,X4) != X1 )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f306]) ).
tff(f758,plain,
spl64_42,
inference(avatar_split_clause,[],[f479,f756]) ).
tff(f756,plain,
( spl64_42
<=> ! [X0: $tType,X3: X0,X2: list(X0),X1: X0] :
( listMem(X0,X3,cons(X0,X1,X2))
| ~ listMem(X0,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_42])]) ).
tff(f479,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: X0] :
( listMem(X0,X3,cons(X0,X1,X2))
| ~ listMem(X0,X3,X2) ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: $tType,X1: X0,X2: list(X0),X3: X0] :
( listMem(X0,X3,cons(X0,X1,X2))
| ~ listMem(X0,X3,X2) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType,X1: X0,X2: list(X0),X3: X0] :
( listMem(X0,X3,X2)
=> listMem(X0,X3,cons(X0,X1,X2)) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X19: X0,X12: list(X0),X11: X0] :
( listMem(X0,X11,X12)
=> listMem(X0,X11,cons(X0,X19,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_insert) ).
tff(f754,plain,
( spl64_41
| ~ spl64_3
| ~ spl64_33 ),
inference(avatar_split_clause,[],[f738,f715,f585,f752]) ).
tff(f752,plain,
( spl64_41
<=> ! [X0: list(int)] : ( zero_zero(int) = iprod(int,X0,nil(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_41])]) ).
tff(f715,plain,
( spl64_33
<=> ! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_33])]) ).
tff(f738,plain,
( ! [X0: list(int)] : ( zero_zero(int) = iprod(int,X0,nil(int)) )
| ~ spl64_3
| ~ spl64_33 ),
inference(resolution,[],[f716,f587]) ).
tff(f716,plain,
( ! [X0: $tType,X1: list(X0)] :
( ~ ring(X0)
| ( zero_zero(X0) = iprod(X0,X1,nil(X0)) ) )
| ~ spl64_33 ),
inference(avatar_component_clause,[],[f715]) ).
tff(f750,plain,
spl64_40,
inference(avatar_split_clause,[],[f384,f748]) ).
tff(f384,plain,
! [X0: $tType] :
( ( equal_equal(X0) = fequal(X0) )
| ~ cl_HOL_Oequal(X0) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType] :
( ( equal_equal(X0) = fequal(X0) )
| ~ cl_HOL_Oequal(X0) ),
inference(ennf_transformation,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( cl_HOL_Oequal(X0)
=> ( equal_equal(X0) = fequal(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_equal) ).
tff(f746,plain,
spl64_39,
inference(avatar_split_clause,[],[f377,f744]) ).
tff(f744,plain,
( spl64_39
<=> ! [X0: $tType] : ( nil(list(X0)) = transpose(X0,nil(list(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_39])]) ).
tff(f377,plain,
! [X0: $tType] : ( nil(list(X0)) = transpose(X0,nil(list(X0))) ),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
! [X0: $tType] : ( nil(list(X0)) = transpose(X0,nil(list(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_transpose_Osimps_I1_J) ).
tff(f737,plain,
spl64_38,
inference(avatar_split_clause,[],[f464,f735]) ).
tff(f735,plain,
( spl64_38
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_38])]) ).
tff(f464,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( member(X0,X2,X1)
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X53: fun(X0,bool),X14: X0] :
( member(X0,X14,X53)
<=> pp(aa(X0,bool,X53,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f733,plain,
spl64_37,
inference(avatar_split_clause,[],[f463,f731]) ).
tff(f731,plain,
( spl64_37
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_37])]) ).
tff(f463,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f312]) ).
tff(f729,plain,
spl64_36,
inference(avatar_split_clause,[],[f455,f727]) ).
tff(f727,plain,
( spl64_36
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( sK11(X0,X1,X2) = X2 )
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_36])]) ).
tff(f455,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( sK11(X0,X1,X2) = X2 )
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f306]) ).
tff(f725,plain,
spl64_35,
inference(avatar_split_clause,[],[f397,f723]) ).
tff(f723,plain,
( spl64_35
<=> ! [X0: $tType,X1: list(X0)] : ( remdups(X0,X1) = remdups(X0,remdups(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_35])]) ).
tff(f397,plain,
! [X0: $tType,X1: list(X0)] : ( remdups(X0,X1) = remdups(X0,remdups(X0,X1)) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType,X1: list(X0)] : ( remdups(X0,X1) = remdups(X0,remdups(X0,X1)) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType,X12: list(X0)] : ( remdups(X0,X12) = remdups(X0,remdups(X0,X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_remdups__remdups) ).
tff(f721,plain,
spl64_34,
inference(avatar_split_clause,[],[f379,f719]) ).
tff(f379,plain,
! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,nil(X0),X1) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,nil(X0),X1) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X18: list(X0)] : ( iprod(X0,nil(X0),X18) = zero_zero(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_iprod__Nil) ).
tff(f717,plain,
spl64_33,
inference(avatar_split_clause,[],[f378,f715]) ).
tff(f378,plain,
! [X0: $tType,X1: list(X0)] :
( ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType] :
( ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,X1,nil(X0)) )
| ~ ring(X0) ),
inference(ennf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: $tType] :
( ring(X0)
=> ! [X1: list(X0)] : ( zero_zero(X0) = iprod(X0,X1,nil(X0)) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType] :
( ring(X0)
=> ! [X12: list(X0)] : ( zero_zero(X0) = iprod(X0,X12,nil(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_iprod__Nil2) ).
tff(f713,plain,
spl64_32,
inference(avatar_split_clause,[],[f478,f711]) ).
tff(f711,plain,
( spl64_32
<=> ! [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,[spl64_32])]) ).
tff(f478,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,[],[f189]) ).
tff(f189,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,[],[f50]) ).
tff(f50,axiom,
! [X1: $tType,X0: $tType,X16: fun(X1,fun(list(X1),fun(X0,X0))),X17: X0] : ( list_rec(X0,X1,X17,X16,nil(X1)) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_list_Orecs_I1_J) ).
tff(f709,plain,
spl64_31,
inference(avatar_split_clause,[],[f477,f707]) ).
tff(f707,plain,
( spl64_31
<=> ! [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,[spl64_31])]) ).
tff(f477,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,[],[f188]) ).
tff(f188,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,[],[f43]) ).
tff(f43,axiom,
! [X1: $tType,X0: $tType,X16: fun(X1,fun(list(X1),X0)),X17: X0] : ( list_case(X0,X1,X17,X16,nil(X1)) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_list_Osimps_I4_J) ).
tff(f705,plain,
spl64_30,
inference(avatar_split_clause,[],[f396,f703]) ).
tff(f703,plain,
( spl64_30
<=> ! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_30])]) ).
tff(f396,plain,
! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X0: $tType,X53: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_sublist__nil) ).
tff(f700,plain,
spl64_29,
inference(avatar_split_clause,[],[f556,f698]) ).
tff(f698,plain,
( spl64_29
<=> ! [X0: $tType] : ( nil(X0) = rotate1(X0,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_29])]) ).
tff(f556,plain,
! [X0: $tType] : ( nil(X0) = rotate1(X0,nil(X0)) ),
inference(equality_resolution,[],[f421]) ).
tff(f421,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = rotate1(X0,X1) )
| ( nil(X0) != X1 ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f696,plain,
spl64_28,
inference(avatar_split_clause,[],[f552,f694]) ).
tff(f694,plain,
( spl64_28
<=> ! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != cons(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_28])]) ).
tff(f552,plain,
! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != cons(X0,X2,X3) ),
inference(equality_resolution,[],[f413]) ).
tff(f413,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( nil(X0) != X1 )
| ( cons(X0,X2,X3) != X1 ) ),
inference(cnf_transformation,[],[f290]) ).
tff(f692,plain,
spl64_27,
inference(avatar_split_clause,[],[f462,f690]) ).
tff(f690,plain,
( spl64_27
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( listMem(X0,X2,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_27])]) ).
tff(f462,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( listMem(X0,X2,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f311]) ).
tff(f688,plain,
spl64_26,
inference(avatar_split_clause,[],[f410,f686]) ).
tff(f686,plain,
( spl64_26
<=> ! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ~ null(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_26])]) ).
tff(f410,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) = X1 )
| ~ null(X0,X1) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $tType,X1: list(X0)] :
( ( null(X0,X1)
| ( nil(X0) != X1 ) )
& ( ( nil(X0) = X1 )
| ~ null(X0,X1) ) ),
inference(nnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType,X1: list(X0)] :
( null(X0,X1)
<=> ( nil(X0) = X1 ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType,X13: list(X0)] :
( null(X0,X13)
<=> ( nil(X0) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_List_Onull__def) ).
tff(f684,plain,
spl64_25,
inference(avatar_split_clause,[],[f409,f682]) ).
tff(f682,plain,
( spl64_25
<=> ! [X1: $tType,X0: $tType] :
( cl_HOL_Oequal(fun(X0,X1))
| ~ enum(X0)
| ~ cl_HOL_Oequal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_25])]) ).
tff(f409,plain,
! [X1: $tType,X0: $tType] :
( cl_HOL_Oequal(fun(X0,X1))
| ~ enum(X0)
| ~ cl_HOL_Oequal(X1) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType,X1: $tType] :
( cl_HOL_Oequal(fun(X0,X1))
| ~ enum(X0)
| ~ cl_HOL_Oequal(X1) ),
inference(flattening,[],[f236]) ).
tff(f236,plain,
! [X0: $tType,X1: $tType] :
( cl_HOL_Oequal(fun(X0,X1))
| ~ enum(X0)
| ~ cl_HOL_Oequal(X1) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType,X1: $tType] :
( ( enum(X0)
& cl_HOL_Oequal(X1) )
=> cl_HOL_Oequal(fun(X0,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X64: $tType,X65: $tType] :
( ( enum(X64)
& cl_HOL_Oequal(X65) )
=> cl_HOL_Oequal(fun(X64,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
tff(f680,plain,
spl64_24,
inference(avatar_split_clause,[],[f408,f678]) ).
tff(f678,plain,
( spl64_24
<=> ! [X1: $tType,X0: $tType] :
( enum(product_prod(X0,X1))
| ~ enum(X0)
| ~ enum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_24])]) ).
tff(f408,plain,
! [X1: $tType,X0: $tType] :
( enum(product_prod(X0,X1))
| ~ enum(X0)
| ~ enum(X1) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType,X1: $tType] :
( enum(product_prod(X0,X1))
| ~ enum(X0)
| ~ enum(X1) ),
inference(flattening,[],[f234]) ).
tff(f234,plain,
! [X0: $tType,X1: $tType] :
( enum(product_prod(X0,X1))
| ~ enum(X0)
| ~ enum(X1) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType,X1: $tType] :
( ( enum(X0)
& enum(X1) )
=> enum(product_prod(X0,X1)) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X64: $tType,X65: $tType] :
( ( enum(X64)
& enum(X65) )
=> enum(product_prod(X64,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod___Enum_Oenum) ).
tff(f676,plain,
spl64_23,
inference(avatar_split_clause,[],[f407,f674]) ).
tff(f674,plain,
( spl64_23
<=> ! [X1: $tType,X0: $tType] :
( enum(fun(X0,X1))
| ~ enum(X0)
| ~ enum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_23])]) ).
tff(f407,plain,
! [X1: $tType,X0: $tType] :
( enum(fun(X0,X1))
| ~ enum(X0)
| ~ enum(X1) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType,X1: $tType] :
( enum(fun(X0,X1))
| ~ enum(X0)
| ~ enum(X1) ),
inference(flattening,[],[f232]) ).
tff(f232,plain,
! [X0: $tType,X1: $tType] :
( enum(fun(X0,X1))
| ~ enum(X0)
| ~ enum(X1) ),
inference(ennf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: $tType,X1: $tType] :
( ( enum(X0)
& enum(X1) )
=> enum(fun(X0,X1)) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X64: $tType,X65: $tType] :
( ( enum(X64)
& enum(X65) )
=> enum(fun(X64,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
tff(f672,plain,
spl64_22,
inference(avatar_split_clause,[],[f395,f670]) ).
tff(f670,plain,
( spl64_22
<=> ! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_22])]) ).
tff(f395,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,nil(X0),X1) = X1 ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType,X18: list(X0)] : ( splice(X0,nil(X0),X18) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_splice_Osimps_I1_J) ).
tff(f668,plain,
spl64_21,
inference(avatar_split_clause,[],[f394,f666]) ).
tff(f666,plain,
( spl64_21
<=> ! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_21])]) ).
tff(f394,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType,X1: list(X0)] : ( splice(X0,X1,nil(X0)) = X1 ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType,X12: list(X0)] : ( splice(X0,X12,nil(X0)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_splice__Nil2) ).
tff(f664,plain,
spl64_20,
inference(avatar_split_clause,[],[f393,f662]) ).
tff(f662,plain,
( spl64_20
<=> ! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_20])]) ).
tff(f393,plain,
! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType,X1: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X1,nil(X0)) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType,X58: fun(X0,nat)] : ( zero_zero(nat) = list_size(X0,X58,nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_list_Osize_I1_J) ).
tff(f660,plain,
spl64_19,
inference(avatar_split_clause,[],[f375,f658]) ).
tff(f658,plain,
( spl64_19
<=> ! [X0: $tType] : ( nil(X0) = remdups(X0,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_19])]) ).
tff(f375,plain,
! [X0: $tType] : ( nil(X0) = remdups(X0,nil(X0)) ),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType] : ( nil(X0) = remdups(X0,nil(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_remdups_Osimps_I1_J) ).
tff(f656,plain,
spl64_18,
inference(avatar_split_clause,[],[f427,f654]) ).
tff(f654,plain,
( spl64_18
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : listMem(X0,X2,cons(X0,X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_18])]) ).
tff(f427,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : listMem(X0,X2,cons(X0,X2,X1)),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType,X1: list(X0),X2: X0] : listMem(X0,X2,cons(X0,X2,X1)),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType,X12: list(X0),X11: X0] : listMem(X0,X11,cons(X0,X11,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_elem) ).
tff(f652,plain,
spl64_17,
inference(avatar_split_clause,[],[f425,f650]) ).
tff(f650,plain,
( spl64_17
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_17])]) ).
tff(f425,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( cons(X0,X2,X1) != X1 ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X12: list(X0),X11: X0] : ( cons(X0,X11,X12) != X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_not__Cons__self2) ).
tff(f648,plain,
spl64_16,
inference(avatar_split_clause,[],[f424,f646]) ).
tff(f424,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ~ null(X0,cons(X0,X2,X1)),
inference(cnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ~ null(X0,cons(X0,X2,X1)),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType,X12: list(X0),X11: X0] : ~ null(X0,cons(X0,X11,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_null__rec_I1_J) ).
tff(f644,plain,
spl64_15,
inference(avatar_split_clause,[],[f392,f642]) ).
tff(f642,plain,
( spl64_15
<=> ! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_15])]) ).
tff(f392,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X0: $tType,X27: fun(X0,bool)] : ~ list_ex1(X0,X27,nil(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_list__ex1__simps_I1_J) ).
tff(f640,plain,
spl64_14,
inference(avatar_split_clause,[],[f391,f638]) ).
tff(f638,plain,
( spl64_14
<=> ! [X1: $tType,X0: $tType] : cl_HOL_Oequal(product_prod(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_14])]) ).
tff(f391,plain,
! [X1: $tType,X0: $tType] : cl_HOL_Oequal(product_prod(X0,X1)),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType,X1: $tType] : cl_HOL_Oequal(product_prod(X0,X1)),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X64: $tType,X65: $tType] : cl_HOL_Oequal(product_prod(X64,X65)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod___HOL_Oequal) ).
tff(f636,plain,
spl64_13,
inference(avatar_split_clause,[],[f374,f634]) ).
tff(f634,plain,
( spl64_13
<=> ! [X0: $tType] : null(X0,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_13])]) ).
tff(f374,plain,
! [X0: $tType] : null(X0,nil(X0)),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: $tType] : null(X0,nil(X0)),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X1: $tType] : null(X1,nil(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_null__rec_I2_J) ).
tff(f632,plain,
spl64_12,
inference(avatar_split_clause,[],[f373,f630]) ).
tff(f373,plain,
! [X0: $tType] : cl_HOL_Oequal(list(X0)),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: $tType] : cl_HOL_Oequal(list(X0)),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X64: $tType] : cl_HOL_Oequal(list(X64)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List_Olist___HOL_Oequal) ).
tff(f628,plain,
spl64_11,
inference(avatar_split_clause,[],[f368,f625]) ).
tff(f625,plain,
( spl64_11
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_11])]) ).
tff(f368,plain,
pp(fTrue),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f623,plain,
spl64_10,
inference(avatar_split_clause,[],[f367,f620]) ).
tff(f620,plain,
( spl64_10
<=> cl_HOL_Oequal(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_10])]) ).
tff(f367,plain,
cl_HOL_Oequal(bool),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
cl_HOL_Oequal(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
tff(f618,plain,
spl64_9,
inference(avatar_split_clause,[],[f366,f615]) ).
tff(f615,plain,
( spl64_9
<=> cl_HOL_Oequal(atom) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_9])]) ).
tff(f366,plain,
cl_HOL_Oequal(atom),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
cl_HOL_Oequal(atom),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_PresArith_Oatom___HOL_Oequal) ).
tff(f613,plain,
spl64_8,
inference(avatar_split_clause,[],[f365,f610]) ).
tff(f610,plain,
( spl64_8
<=> cl_HOL_Oequal(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_8])]) ).
tff(f365,plain,
cl_HOL_Oequal(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
cl_HOL_Oequal(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___HOL_Oequal) ).
tff(f608,plain,
spl64_7,
inference(avatar_split_clause,[],[f364,f605]) ).
tff(f605,plain,
( spl64_7
<=> cl_HOL_Oequal(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_7])]) ).
tff(f364,plain,
cl_HOL_Oequal(nat),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
cl_HOL_Oequal(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___HOL_Oequal) ).
tff(f603,plain,
spl64_6,
inference(avatar_split_clause,[],[f363,f600]) ).
tff(f600,plain,
( spl64_6
<=> enum(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_6])]) ).
tff(f363,plain,
enum(bool),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
enum(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
tff(f598,plain,
spl64_5,
inference(avatar_split_clause,[],[f362,f595]) ).
tff(f595,plain,
( spl64_5
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_5])]) ).
tff(f362,plain,
zero(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f593,plain,
spl64_4,
inference(avatar_split_clause,[],[f361,f590]) ).
tff(f590,plain,
( spl64_4
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_4])]) ).
tff(f361,plain,
zero(nat),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
zero(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f588,plain,
spl64_3,
inference(avatar_split_clause,[],[f360,f585]) ).
tff(f360,plain,
ring(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f583,plain,
~ spl64_2,
inference(avatar_split_clause,[],[f359,f580]) ).
tff(f580,plain,
( spl64_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl64_2])]) ).
tff(f359,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
tff(f578,plain,
~ spl64_1,
inference(avatar_split_clause,[],[f358,f575]) ).
tff(f358,plain,
~ i_Z(a,cons(int,x,xs)),
inference(cnf_transformation,[],[f119]) ).
tff(f119,plain,
~ i_Z(a,cons(int,x,xs)),
inference(flattening,[],[f118]) ).
tff(f118,negated_conjecture,
~ i_Z(a,cons(int,x,xs)),
inference(negated_conjecture,[],[f117]) ).
tff(f117,conjecture,
i_Z(a,cons(int,x,xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COM095_5 : TPTP v8.2.0. Released v6.0.0.
% 0.08/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 10:19:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (25443)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (25446)WARNING: value z3 for option sas not known
% 0.13/0.37 % (25447)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (25449)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)
% 0.13/0.37 % (25448)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)
% 0.13/0.37 % (25446)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)
% 0.13/0.37 % (25445)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (25450)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)
% 0.13/0.37 % (25444)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (25450)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.38 % Exception at run slice level
% 0.19/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.38 % Exception at run slice level
% 0.19/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.38 % Exception at run slice level
% 0.19/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.39 % (25453)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)
% 0.19/0.39 % (25451)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.39 % (25452)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)
% 0.19/0.39 % (25448)First to succeed.
% 0.19/0.40 % (25451)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.40 % (25452)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.40 % Exception at run slice level
% 0.19/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.40 % (25448)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25443"
% 0.19/0.40 % (25448)Refutation found. Thanks to Tanya!
% 0.19/0.40 % SZS status Theorem for theBenchmark
% 0.19/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.41 % (25448)------------------------------
% 0.19/0.41 % (25448)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.41 % (25448)Termination reason: Refutation
% 0.19/0.41
% 0.19/0.41 % (25448)Memory used [KB]: 1358
% 0.19/0.41 % (25448)Time elapsed: 0.034 s
% 0.19/0.41 % (25448)Instructions burned: 55 (million)
% 0.19/0.41 % (25443)Success in time 0.045 s
%------------------------------------------------------------------------------