TSTP Solution File: COM122_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM122_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:48:29 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 301
% Syntax : Number of formulae : 737 ( 221 unt; 72 typ; 0 def)
% Number of atoms : 1528 ( 585 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1364 ( 501 ~; 459 |; 118 &)
% ( 179 <=>; 107 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 84 ( 43 >; 41 *; 0 +; 0 <<)
% Number of predicates : 144 ( 142 usr; 127 prp; 0-3 aty)
% Number of functors : 52 ( 52 usr; 9 con; 0-6 aty)
% Number of variables : 1286 (1164 !; 63 ?;1286 :)
% ( 59 !>; 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(func_def_0,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
sgn_sgn:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
ring_1_of_int:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_5,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_6,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_8,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_9,type,
member1:
!>[X0: $tType] : fun(list(X0),fun(X0,bool)) ).
tff(func_def_10,type,
set:
!>[X0: $tType] : fun(list(X0),fun(X0,bool)) ).
tff(func_def_11,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_12,type,
semiring_1_Nats:
!>[X0: $tType] : fun(X0,bool) ).
tff(func_def_13,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_14,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(func_def_15,type,
dvd: ( int * int * list(int) ) > atom ).
tff(func_def_16,type,
atom_size: atom > nat ).
tff(func_def_17,type,
decr_Z: atom > atom ).
tff(func_def_18,type,
divisor: atom > int ).
tff(func_def_19,type,
hd_coeff: fun(atom,int) ).
tff(func_def_20,type,
hd_coeff1: int > fun(atom,atom) ).
tff(func_def_21,type,
zlcms: list(int) > int ).
tff(func_def_22,type,
qEpres1907640072oeffs1: list(atom) > list(atom) ).
tff(func_def_23,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_24,type,
fFalse: bool ).
tff(func_def_25,type,
fTrue: bool ).
tff(func_def_26,type,
a: atom ).
tff(func_def_27,type,
as: list(atom) ).
tff(func_def_28,type,
b: atom ).
tff(func_def_29,type,
sK1: atom ).
tff(func_def_30,type,
sK2: atom ).
tff(func_def_31,type,
sK3: list(int) > int ).
tff(func_def_32,type,
sK4:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_33,type,
sK5:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_34,type,
sK6:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_35,type,
sK7:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_36,type,
sK8:
!>[X0: $tType] : ( ( fun(X0,X0) * list(X0) ) > X0 ) ).
tff(func_def_37,type,
sK9:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) * X0 ) > X0 ) ).
tff(func_def_38,type,
sK10:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_39,type,
sK11:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X0) ) > list(X1) ) ).
tff(func_def_40,type,
sK12:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X0) ) > X0 ) ).
tff(func_def_41,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_42,type,
sK14:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * list(X1) ) > X1 ) ).
tff(func_def_43,type,
sK15:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X1) * fun(X1,X0) ) > X1 ) ).
tff(func_def_44,type,
sK16:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * list(X1) ) > X1 ) ).
tff(func_def_45,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_46,type,
sK18:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_47,type,
sK19:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_48,type,
sK20:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_49,type,
sK21: atom ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ring_1:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
sgn_if:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
iszero:
!>[X0: $tType] : ( X0 > $o ) ).
tff(pred_def_11,type,
listMem:
!>[X0: $tType] : ( ( X0 * list(X0) ) > $o ) ).
tff(pred_def_12,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_13,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(pred_def_16,type,
sP0: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).
tff(f1364,plain,
$false,
inference(avatar_sat_refutation,[],[f581,f586,f591,f596,f601,f606,f611,f616,f621,f626,f631,f636,f641,f646,f651,f656,f661,f665,f669,f673,f678,f682,f686,f690,f694,f698,f702,f706,f710,f714,f718,f722,f726,f730,f734,f738,f742,f746,f750,f754,f758,f762,f766,f770,f774,f778,f790,f796,f800,f804,f811,f816,f820,f824,f828,f841,f845,f849,f854,f858,f862,f866,f871,f876,f881,f894,f899,f903,f907,f911,f915,f919,f923,f928,f954,f958,f962,f966,f970,f974,f978,f982,f986,f990,f997,f1001,f1005,f1009,f1086,f1091,f1099,f1103,f1107,f1111,f1115,f1119,f1144,f1148,f1152,f1163,f1167,f1173,f1179,f1183,f1187,f1200,f1204,f1215,f1222,f1228,f1232,f1260,f1264,f1268,f1282,f1286,f1290,f1309,f1313,f1329,f1341,f1353,f1361,f1363]) ).
tff(f1363,plain,
( ~ spl22_63
| ~ spl22_1
| ~ spl22_107 ),
inference(avatar_split_clause,[],[f1206,f1198,f578,f868]) ).
tff(f868,plain,
( spl22_63
<=> member(atom,b,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_63])]) ).
tff(f578,plain,
( spl22_1
<=> ( zero_zero(int) = aa(atom,int,hd_coeff,b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1])]) ).
tff(f1198,plain,
( spl22_107
<=> ! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,hd_coeff,X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_107])]) ).
tff(f1206,plain,
( ~ member(atom,b,aa(list(atom),fun(atom,bool),member1(atom),as))
| ~ spl22_1
| ~ spl22_107 ),
inference(trivial_inequality_removal,[],[f1205]) ).
tff(f1205,plain,
( ( zero_zero(int) != zero_zero(int) )
| ~ member(atom,b,aa(list(atom),fun(atom,bool),member1(atom),as))
| ~ spl22_1
| ~ spl22_107 ),
inference(superposition,[],[f1199,f580]) ).
tff(f580,plain,
( ( zero_zero(int) = aa(atom,int,hd_coeff,b) )
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f578]) ).
tff(f1199,plain,
( ! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,hd_coeff,X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as)) )
| ~ spl22_107 ),
inference(avatar_component_clause,[],[f1198]) ).
tff(f1361,plain,
( spl22_126
| ~ spl22_60
| ~ spl22_124 ),
inference(avatar_split_clause,[],[f1354,f1346,f856,f1358]) ).
tff(f1358,plain,
( spl22_126
<=> ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),insert(int,one_one(int),nil(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_126])]) ).
tff(f856,plain,
( spl22_60
<=> ! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_60])]) ).
tff(f1346,plain,
( spl22_124
<=> ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),cons(int,one_one(int),nil(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_124])]) ).
tff(f1354,plain,
( ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),insert(int,one_one(int),nil(int))) )
| ~ spl22_60
| ~ spl22_124 ),
inference(forward_demodulation,[],[f1348,f857]) ).
tff(f857,plain,
( ! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) )
| ~ spl22_60 ),
inference(avatar_component_clause,[],[f856]) ).
tff(f1348,plain,
( ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),cons(int,one_one(int),nil(int))) )
| ~ spl22_124 ),
inference(avatar_component_clause,[],[f1346]) ).
tff(f1353,plain,
( spl22_124
| spl22_125 ),
inference(avatar_split_clause,[],[f512,f1350,f1346]) ).
tff(f1350,plain,
( spl22_125
<=> member(atom,sK1,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_125])]) ).
tff(f512,plain,
( member(atom,sK1,aa(list(atom),fun(atom,bool),member1(atom),as))
| ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),cons(int,one_one(int),nil(int))) ) ),
inference(definition_unfolding,[],[f358,f367]) ).
tff(f367,plain,
! [X0: $tType] : ( set(X0) = member1(X0) ),
inference(cnf_transformation,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType] : ( set(X0) = member1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_member__set) ).
tff(f358,plain,
( member(atom,sK1,aa(list(atom),fun(atom,bool),set(atom),as))
| ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),cons(int,one_one(int),nil(int))) ) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
( ( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK1) )
& member(atom,sK1,aa(list(atom),fun(atom,bool),set(atom),as)) )
| ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),cons(int,one_one(int),nil(int))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f119,f264]) ).
tff(f264,plain,
( ? [X0: atom] :
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X0) )
& member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) )
=> ( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK1) )
& member(atom,sK1,aa(list(atom),fun(atom,bool),set(atom),as)) ) ),
introduced(choice_axiom,[]) ).
tff(f119,plain,
( ? [X0: atom] :
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X0) )
& member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) )
| ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),cons(int,one_one(int),nil(int))) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
( ? [X3: atom] :
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X3) )
& member(atom,X3,aa(list(atom),fun(atom,bool),set(atom),as)) )
| ( a = dvd(zlcms(map(atom,int,hd_coeff,as)),zero_zero(int),cons(int,one_one(int),nil(int))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__096a_A_061_ADvd_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_A0_A_0911_093_A_124_IEX_Ab_058set_Aas_O_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_J_096) ).
tff(f1341,plain,
spl22_123,
inference(avatar_split_clause,[],[f534,f1339]) ).
tff(f1339,plain,
( spl22_123
<=> ! [X1: $tType,X0: $tType,X3: list(X0),X2: fun(X1,X0)] :
( ( map(X1,X0,X2,sK11(X0,X1,X2,X3)) = X3 )
| member(X0,sK12(X0,X1,X2,X3),aa(list(X0),fun(X0,bool),member1(X0),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_123])]) ).
tff(f534,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( map(X1,X0,X2,sK11(X0,X1,X2,X3)) = X3 )
| member(X0,sK12(X0,X1,X2,X3),aa(list(X0),fun(X0,bool),member1(X0),X3)) ),
inference(definition_unfolding,[],[f483,f367]) ).
tff(f483,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( map(X1,X0,X2,sK11(X0,X1,X2,X3)) = X3 )
| member(X0,sK12(X0,X1,X2,X3),aa(list(X0),fun(X0,bool),set(X0),X3)) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( ( map(X1,X0,X2,sK11(X0,X1,X2,X3)) = X3 )
| ( ! [X6: X1] : ( aa(X1,X0,X2,X6) != sK12(X0,X1,X2,X3) )
& member(X0,sK12(X0,X1,X2,X3),aa(list(X0),fun(X0,bool),set(X0),X3)) ) )
& ( ! [X7: X0] :
( ( aa(X1,X0,X2,sK13(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,aa(list(X0),fun(X0,bool),set(X0),X3)) )
| ! [X9: list(X1)] : ( map(X1,X0,X2,X9) != X3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f310,f313,f312,f311]) ).
tff(f311,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ? [X4: list(X1)] : ( map(X1,X0,X2,X4) = X3 )
=> ( map(X1,X0,X2,sK11(X0,X1,X2,X3)) = X3 ) ),
introduced(choice_axiom,[]) ).
tff(f312,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ? [X5: X0] :
( ! [X6: X1] : ( aa(X1,X0,X2,X6) != X5 )
& member(X0,X5,aa(list(X0),fun(X0,bool),set(X0),X3)) )
=> ( ! [X6: X1] : ( aa(X1,X0,X2,X6) != sK12(X0,X1,X2,X3) )
& member(X0,sK12(X0,X1,X2,X3),aa(list(X0),fun(X0,bool),set(X0),X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f313,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X7: X0] :
( ? [X8: X1] : ( aa(X1,X0,X2,X8) = X7 )
=> ( aa(X1,X0,X2,sK13(X0,X1,X2,X7)) = X7 ) ),
introduced(choice_axiom,[]) ).
tff(f310,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( ? [X4: list(X1)] : ( map(X1,X0,X2,X4) = X3 )
| ? [X5: X0] :
( ! [X6: X1] : ( aa(X1,X0,X2,X6) != X5 )
& member(X0,X5,aa(list(X0),fun(X0,bool),set(X0),X3)) ) )
& ( ! [X7: X0] :
( ? [X8: X1] : ( aa(X1,X0,X2,X8) = X7 )
| ~ member(X0,X7,aa(list(X0),fun(X0,bool),set(X0),X3)) )
| ! [X9: list(X1)] : ( map(X1,X0,X2,X9) != X3 ) ) ),
inference(rectify,[],[f309]) ).
tff(f309,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ( ? [X4: list(X1)] : ( map(X1,X0,X2,X4) = X3 )
| ? [X5: X0] :
( ! [X6: X1] : ( aa(X1,X0,X2,X6) != X5 )
& member(X0,X5,aa(list(X0),fun(X0,bool),set(X0),X3)) ) )
& ( ! [X5: X0] :
( ? [X6: X1] : ( aa(X1,X0,X2,X6) = X5 )
| ~ member(X0,X5,aa(list(X0),fun(X0,bool),set(X0),X3)) )
| ! [X4: list(X1)] : ( map(X1,X0,X2,X4) != X3 ) ) ),
inference(nnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ? [X4: list(X1)] : ( map(X1,X0,X2,X4) = X3 )
<=> ! [X5: X0] :
( ? [X6: X1] : ( aa(X1,X0,X2,X6) = X5 )
| ~ member(X0,X5,aa(list(X0),fun(X0,bool),set(X0),X3)) ) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: list(X0)] :
( ? [X4: list(X1)] : ( map(X1,X0,X2,X4) = X3 )
<=> ! [X5: X0] :
( member(X0,X5,aa(list(X0),fun(X0,bool),set(X0),X3))
=> ? [X6: X1] : ( aa(X1,X0,X2,X6) = X5 ) ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X1: $tType,X0: $tType,X11: fun(X0,X1),X16: list(X1)] :
( ? [X17: list(X0)] : ( map(X0,X1,X11,X17) = X16 )
<=> ! [X12: X1] :
( member(X1,X12,aa(list(X1),fun(X1,bool),set(X1),X16))
=> ? [X18: X0] : ( aa(X0,X1,X11,X18) = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ex__map__conv) ).
tff(f1329,plain,
spl22_122,
inference(avatar_split_clause,[],[f560,f1327]) ).
tff(f1327,plain,
( spl22_122
<=> ! [X1: $tType,X0: $tType,X7: X0,X9: list(X1),X2: fun(X1,X0)] :
( ( aa(X1,X0,X2,sK13(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,aa(list(X0),fun(X0,bool),member1(X0),map(X1,X0,X2,X9))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_122])]) ).
tff(f560,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X9: list(X1),X7: X0] :
( ( aa(X1,X0,X2,sK13(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,aa(list(X0),fun(X0,bool),member1(X0),map(X1,X0,X2,X9))) ),
inference(equality_resolution,[],[f535]) ).
tff(f535,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0),X9: list(X1),X7: X0] :
( ( aa(X1,X0,X2,sK13(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,aa(list(X0),fun(X0,bool),member1(X0),X3))
| ( map(X1,X0,X2,X9) != X3 ) ),
inference(definition_unfolding,[],[f482,f367]) ).
tff(f482,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0),X9: list(X1),X7: X0] :
( ( aa(X1,X0,X2,sK13(X0,X1,X2,X7)) = X7 )
| ~ member(X0,X7,aa(list(X0),fun(X0,bool),set(X0),X3))
| ( map(X1,X0,X2,X9) != X3 ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f1313,plain,
spl22_121,
inference(avatar_split_clause,[],[f506,f1311]) ).
tff(f1311,plain,
( spl22_121
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
| ( cons(X1,X3,X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_121])]) ).
tff(f506,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
| ( cons(X1,X3,X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f334]) ).
tff(f334,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( cons(X1,X3,X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( cons(X0,X6,X7) != X4 ) ) )
& ( ( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
& ( cons(X0,sK19(X0,X1,X2,X3,X4,X5),sK20(X0,X1,X2,X3,X4,X5)) = X4 ) )
| ( cons(X1,X3,X2) != map(X0,X1,X5,X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f332,f333]) ).
tff(f333,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( cons(X0,X8,X9) = X4 ) )
=> ( ( map(X0,X1,X5,sK20(X0,X1,X2,X3,X4,X5)) = X2 )
& ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
& ( cons(X0,sK19(X0,X1,X2,X3,X4,X5),sK20(X0,X1,X2,X3,X4,X5)) = X4 ) ) ),
introduced(choice_axiom,[]) ).
tff(f332,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( cons(X1,X3,X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( cons(X0,X6,X7) != X4 ) ) )
& ( ? [X8: X0,X9: list(X0)] :
( ( map(X0,X1,X5,X9) = X2 )
& ( aa(X0,X1,X5,X8) = X3 )
& ( cons(X0,X8,X9) = X4 ) )
| ( cons(X1,X3,X2) != map(X0,X1,X5,X4) ) ) ),
inference(rectify,[],[f331]) ).
tff(f331,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( ( cons(X1,X3,X2) = map(X0,X1,X5,X4) )
| ! [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) != X2 )
| ( aa(X0,X1,X5,X6) != X3 )
| ( cons(X0,X6,X7) != X4 ) ) )
& ( ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( cons(X0,X6,X7) = X4 ) )
| ( cons(X1,X3,X2) != map(X0,X1,X5,X4) ) ) ),
inference(nnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( cons(X1,X3,X2) = map(X0,X1,X5,X4) )
<=> ? [X6: X0,X7: list(X0)] :
( ( map(X0,X1,X5,X7) = X2 )
& ( aa(X0,X1,X5,X6) = X3 )
& ( cons(X0,X6,X7) = X4 ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X1: $tType,X0: $tType,X16: list(X0),X37: X0,X10: list(X1),X11: fun(X1,X0)] :
( ( map(X1,X0,X11,X10) = cons(X0,X37,X16) )
<=> ? [X44: X1,X45: list(X1)] :
( ( map(X1,X0,X11,X45) = X16 )
& ( aa(X1,X0,X11,X44) = X37 )
& ( cons(X1,X44,X45) = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_map__eq__Cons__conv) ).
tff(f1309,plain,
spl22_120,
inference(avatar_split_clause,[],[f502,f1307]) ).
tff(f1307,plain,
( spl22_120
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( map(X1,X0,X3,sK18(X0,X1,X2,X3,X4,X5)) = X4 )
| ( map(X1,X0,X3,X2) != cons(X0,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_120])]) ).
tff(f502,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( map(X1,X0,X3,sK18(X0,X1,X2,X3,X4,X5)) = X4 )
| ( map(X1,X0,X3,X2) != cons(X0,X5,X4) ) ),
inference(cnf_transformation,[],[f330]) ).
tff(f330,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( map(X1,X0,X3,X2) = cons(X0,X5,X4) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( cons(X1,X6,X7) != X2 ) ) )
& ( ( ( map(X1,X0,X3,sK18(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK17(X0,X1,X2,X3,X4,X5)) = X5 )
& ( cons(X1,sK17(X0,X1,X2,X3,X4,X5),sK18(X0,X1,X2,X3,X4,X5)) = X2 ) )
| ( map(X1,X0,X3,X2) != cons(X0,X5,X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f328,f329]) ).
tff(f329,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( cons(X1,X8,X9) = X2 ) )
=> ( ( map(X1,X0,X3,sK18(X0,X1,X2,X3,X4,X5)) = X4 )
& ( aa(X1,X0,X3,sK17(X0,X1,X2,X3,X4,X5)) = X5 )
& ( cons(X1,sK17(X0,X1,X2,X3,X4,X5),sK18(X0,X1,X2,X3,X4,X5)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f328,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( map(X1,X0,X3,X2) = cons(X0,X5,X4) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( cons(X1,X6,X7) != X2 ) ) )
& ( ? [X8: X1,X9: list(X1)] :
( ( map(X1,X0,X3,X9) = X4 )
& ( aa(X1,X0,X3,X8) = X5 )
& ( cons(X1,X8,X9) = X2 ) )
| ( map(X1,X0,X3,X2) != cons(X0,X5,X4) ) ) ),
inference(rectify,[],[f327]) ).
tff(f327,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( ( map(X1,X0,X3,X2) = cons(X0,X5,X4) )
| ! [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) != X4 )
| ( aa(X1,X0,X3,X6) != X5 )
| ( cons(X1,X6,X7) != X2 ) ) )
& ( ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( cons(X1,X6,X7) = X2 ) )
| ( map(X1,X0,X3,X2) != cons(X0,X5,X4) ) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( map(X1,X0,X3,X2) = cons(X0,X5,X4) )
<=> ? [X6: X1,X7: list(X1)] :
( ( map(X1,X0,X3,X7) = X4 )
& ( aa(X1,X0,X3,X6) = X5 )
& ( cons(X1,X6,X7) = X2 ) ) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X1: $tType,X16: list(X1),X11: fun(X1,X0),X10: list(X0),X4: X0] :
( ( cons(X0,X4,X10) = map(X1,X0,X11,X16) )
<=> ? [X44: X1,X45: list(X1)] :
( ( map(X1,X0,X11,X45) = X10 )
& ( aa(X1,X0,X11,X44) = X4 )
& ( cons(X1,X44,X45) = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Cons__eq__map__conv) ).
tff(f1290,plain,
spl22_119,
inference(avatar_split_clause,[],[f505,f1288]) ).
tff(f1288,plain,
( spl22_119
<=> ! [X1: $tType,X0: $tType,X3: X1,X4: list(X0),X5: fun(X0,X1),X2: list(X1)] :
( ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
| ( cons(X1,X3,X2) != map(X0,X1,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_119])]) ).
tff(f505,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: list(X0),X5: fun(X0,X1)] :
( ( aa(X0,X1,X5,sK19(X0,X1,X2,X3,X4,X5)) = X3 )
| ( cons(X1,X3,X2) != map(X0,X1,X5,X4) ) ),
inference(cnf_transformation,[],[f334]) ).
tff(f1286,plain,
spl22_118,
inference(avatar_split_clause,[],[f501,f1284]) ).
tff(f1284,plain,
( spl22_118
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X4: list(X0),X5: X0,X2: list(X1)] :
( ( aa(X1,X0,X3,sK17(X0,X1,X2,X3,X4,X5)) = X5 )
| ( map(X1,X0,X3,X2) != cons(X0,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_118])]) ).
tff(f501,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0),X4: list(X0),X5: X0] :
( ( aa(X1,X0,X3,sK17(X0,X1,X2,X3,X4,X5)) = X5 )
| ( map(X1,X0,X3,X2) != cons(X0,X5,X4) ) ),
inference(cnf_transformation,[],[f330]) ).
tff(f1282,plain,
spl22_117,
inference(avatar_split_clause,[],[f474,f1280]) ).
tff(f1280,plain,
( spl22_117
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK10(X0,X1,X2,X3)) != aa(X1,X0,X2,sK10(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_117])]) ).
tff(f474,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK10(X0,X1,X2,X3)) != aa(X1,X0,X2,sK10(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK10(X0,X1,X2,X3)) != aa(X1,X0,X2,sK10(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f256,f303]) ).
tff(f303,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK10(X0,X1,X2,X3)) != aa(X1,X0,X2,sK10(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f256,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X1: $tType,X0: $tType,X9: fun(X0,X1),X11: fun(X0,X1)] :
( ! [X3: X0] : ( aa(X0,X1,X11,X3) = aa(X0,X1,X9,X3) )
=> ( X9 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ext) ).
tff(f1268,plain,
spl22_116,
inference(avatar_split_clause,[],[f523,f1266]) ).
tff(f1266,plain,
( spl22_116
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| member(X0,sK8(X0,X1,X2),aa(list(X0),fun(X0,bool),member1(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_116])]) ).
tff(f523,plain,
! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| member(X0,sK8(X0,X1,X2),aa(list(X0),fun(X0,bool),member1(X0),X2)) ),
inference(definition_unfolding,[],[f458,f367]) ).
tff(f458,plain,
! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| member(X0,sK8(X0,X1,X2),aa(list(X0),fun(X0,bool),set(X0),X2)) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: $tType,X1: fun(X0,X0),X2: list(X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| ( ( sK8(X0,X1,X2) != aa(X0,X0,X1,sK8(X0,X1,X2)) )
& member(X0,sK8(X0,X1,X2),aa(list(X0),fun(X0,bool),set(X0),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f250,f295]) ).
tff(f295,plain,
! [X0: $tType,X1: fun(X0,X0),X2: list(X0)] :
( ? [X3: X0] :
( ( aa(X0,X0,X1,X3) != X3 )
& member(X0,X3,aa(list(X0),fun(X0,bool),set(X0),X2)) )
=> ( ( sK8(X0,X1,X2) != aa(X0,X0,X1,sK8(X0,X1,X2)) )
& member(X0,sK8(X0,X1,X2),aa(list(X0),fun(X0,bool),set(X0),X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f250,plain,
! [X0: $tType,X1: fun(X0,X0),X2: list(X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| ? [X3: X0] :
( ( aa(X0,X0,X1,X3) != X3 )
& member(X0,X3,aa(list(X0),fun(X0,bool),set(X0),X2)) ) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType,X1: fun(X0,X0),X2: list(X0)] :
( ! [X3: X0] :
( member(X0,X3,aa(list(X0),fun(X0,bool),set(X0),X2))
=> ( aa(X0,X0,X1,X3) = X3 ) )
=> ( map(X0,X0,X1,X2) = X2 ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: $tType,X11: fun(X0,X0),X10: list(X0)] :
( ! [X3: X0] :
( member(X0,X3,aa(list(X0),fun(X0,bool),set(X0),X10))
=> ( aa(X0,X0,X11,X3) = X3 ) )
=> ( map(X0,X0,X11,X10) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_map__idI) ).
tff(f1264,plain,
spl22_115,
inference(avatar_split_clause,[],[f484,f1262]) ).
tff(f1262,plain,
( spl22_115
<=> ! [X1: $tType,X0: $tType,X6: X1,X3: list(X0),X2: fun(X1,X0)] :
( ( map(X1,X0,X2,sK11(X0,X1,X2,X3)) = X3 )
| ( aa(X1,X0,X2,X6) != sK12(X0,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_115])]) ).
tff(f484,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: list(X0),X6: X1] :
( ( map(X1,X0,X2,sK11(X0,X1,X2,X3)) = X3 )
| ( aa(X1,X0,X2,X6) != sK12(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f1260,plain,
spl22_114,
inference(avatar_split_clause,[],[f454,f1258]) ).
tff(f1258,plain,
( spl22_114
<=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ord_less(nat,X1,X2)
| ( X1 = X2 )
| sP0(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_114])]) ).
tff(f454,plain,
! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ord_less(nat,X1,X2)
| ( X1 = X2 )
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| sP0(X2,X1,X0) ),
inference(definition_folding,[],[f249,f262]) ).
tff(f262,plain,
! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) )
| ~ sP0(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f249,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) ) ),
inference(flattening,[],[f248]) ).
tff(f248,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) ) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( ( ord_less(nat,X2,X1)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> ( ( ( X1 = X2 )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> ( ( ord_less(nat,X1,X2)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) ) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X20: fun(nat,fun(nat,bool)),X51: nat,X53: nat] :
( ( ord_less(nat,X53,X51)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X20,X51),X53)) )
=> ( ( ( X51 = X53 )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X20,X51),X53)) )
=> ( ( ord_less(nat,X51,X53)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X20,X51),X53)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X20,X51),X53)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nat__less__cases) ).
tff(f1232,plain,
spl22_113,
inference(avatar_split_clause,[],[f519,f1230]) ).
tff(f1230,plain,
( spl22_113
<=> ! [X0: $tType,X2: X0,X1: list(X0)] :
( ( cons(X0,X2,X1) = insert(X0,X2,X1) )
| member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_113])]) ).
tff(f519,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( cons(X0,X2,X1) = insert(X0,X2,X1) )
| member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1)) ),
inference(definition_unfolding,[],[f449,f367]) ).
tff(f449,plain,
! [X0: $tType,X2: X0,X1: list(X0)] :
( ( cons(X0,X2,X1) = insert(X0,X2,X1) )
| member(X0,X2,aa(list(X0),fun(X0,bool),set(X0),X1)) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,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,[],[f175]) ).
tff(f175,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,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType,X10: list(X0),X4: X0] :
( ( ~ member(X0,X4,aa(list(X0),fun(X0,bool),set(X0),X10))
=> ( cons(X0,X4,X10) = insert(X0,X4,X10) ) )
& ( member(X0,X4,aa(list(X0),fun(X0,bool),set(X0),X10))
=> ( insert(X0,X4,X10) = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_List_Oinsert__def) ).
tff(f1228,plain,
spl22_112,
inference(avatar_split_clause,[],[f485,f1226]) ).
tff(f1226,plain,
( spl22_112
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: X1,X2: list(X1)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_112])]) ).
tff(f485,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: fun(X1,X0)] : ( map(X1,X0,X4,cons(X1,X3,X2)) = cons(X0,aa(X1,X0,X4,X3),map(X1,X0,X4,X2)) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType,X1: $tType,X10: list(X1),X4: X1,X11: fun(X1,X0)] : ( map(X1,X0,X11,cons(X1,X4,X10)) = cons(X0,aa(X1,X0,X11,X4),map(X1,X0,X11,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_map_Osimps_I2_J) ).
tff(f1222,plain,
spl22_111,
inference(avatar_split_clause,[],[f459,f1220]) ).
tff(f1220,plain,
( spl22_111
<=> ! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| ( sK8(X0,X1,X2) != aa(X0,X0,X1,sK8(X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_111])]) ).
tff(f459,plain,
! [X0: $tType,X2: list(X0),X1: fun(X0,X0)] :
( ( map(X0,X0,X1,X2) = X2 )
| ( sK8(X0,X1,X2) != aa(X0,X0,X1,sK8(X0,X1,X2)) ) ),
inference(cnf_transformation,[],[f296]) ).
tff(f1215,plain,
( ~ spl22_109
| spl22_110
| ~ spl22_1
| ~ spl22_104 ),
inference(avatar_split_clause,[],[f1189,f1177,f578,f1212,f1208]) ).
tff(f1208,plain,
( spl22_109
<=> ( zero_zero(int) = divisor(decr_Z(b)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_109])]) ).
tff(f1212,plain,
( spl22_110
<=> ( zero_zero(int) = divisor(b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_110])]) ).
tff(f1177,plain,
( spl22_104
<=> ! [X0: atom] :
( ( zero_zero(int) != divisor(decr_Z(X0)) )
| ( zero_zero(int) = divisor(X0) )
| ( zero_zero(int) != aa(atom,int,hd_coeff,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_104])]) ).
tff(f1189,plain,
( ( zero_zero(int) = divisor(b) )
| ( zero_zero(int) != divisor(decr_Z(b)) )
| ~ spl22_1
| ~ spl22_104 ),
inference(trivial_inequality_removal,[],[f1188]) ).
tff(f1188,plain,
( ( zero_zero(int) != zero_zero(int) )
| ( zero_zero(int) = divisor(b) )
| ( zero_zero(int) != divisor(decr_Z(b)) )
| ~ spl22_1
| ~ spl22_104 ),
inference(superposition,[],[f1178,f580]) ).
tff(f1178,plain,
( ! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,hd_coeff,X0) )
| ( zero_zero(int) = divisor(X0) )
| ( zero_zero(int) != divisor(decr_Z(X0)) ) )
| ~ spl22_104 ),
inference(avatar_component_clause,[],[f1177]) ).
tff(f1204,plain,
spl22_108,
inference(avatar_split_clause,[],[f576,f1202]) ).
tff(f1202,plain,
( spl22_108
<=> ! [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,[spl22_108])]) ).
tff(f576,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,[],[f446,f423]) ).
tff(f423,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ),
inference(cnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: X0] : ( insert(X0,X1,nil(X0)) = cons(X0,X1,nil(X0)) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType,X36: X0] : ( insert(X0,X36,nil(X0)) = cons(X0,X36,nil(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_insert__Nil) ).
tff(f446,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,[],[f244]) ).
tff(f244,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,[],[f174]) ).
tff(f174,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,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType,X4: X0,X48: fun(nat,bool)] :
( ( ~ member(nat,zero_zero(nat),X48)
=> ( nil(X0) = sublist(X0,cons(X0,X4,nil(X0)),X48) ) )
& ( member(nat,zero_zero(nat),X48)
=> ( cons(X0,X4,nil(X0)) = sublist(X0,cons(X0,X4,nil(X0)),X48) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_sublist__singleton) ).
tff(f1200,plain,
spl22_107,
inference(avatar_split_clause,[],[f515,f1198]) ).
tff(f515,plain,
! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,hd_coeff,X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
inference(definition_unfolding,[],[f412,f367]) ).
tff(f412,plain,
! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,hd_coeff,X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,hd_coeff,X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(ennf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: atom] :
( member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( zero_zero(int) != aa(atom,int,hd_coeff,X0) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X2: atom] :
( member(atom,X2,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( zero_zero(int) != aa(atom,int,hd_coeff,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hd0) ).
tff(f1187,plain,
spl22_106,
inference(avatar_split_clause,[],[f520,f1185]) ).
tff(f1185,plain,
( spl22_106
<=> ! [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,[spl22_106])]) ).
tff(f520,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,[],[f448,f367]) ).
tff(f448,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,[],[f245]) ).
tff(f1183,plain,
spl22_105,
inference(avatar_split_clause,[],[f516,f1181]) ).
tff(f1181,plain,
( spl22_105
<=> ! [X0: list(int)] :
( ord_less(int,zero_zero(int),zlcms(X0))
| member(int,sK3(X0),aa(list(int),fun(int,bool),member1(int),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_105])]) ).
tff(f516,plain,
! [X0: list(int)] :
( ord_less(int,zero_zero(int),zlcms(X0))
| member(int,sK3(X0),aa(list(int),fun(int,bool),member1(int),X0)) ),
inference(definition_unfolding,[],[f413,f367]) ).
tff(f413,plain,
! [X0: list(int)] :
( ord_less(int,zero_zero(int),zlcms(X0))
| member(int,sK3(X0),aa(list(int),fun(int,bool),set(int),X0)) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: list(int)] :
( ord_less(int,zero_zero(int),zlcms(X0))
| ( ( zero_zero(int) = sK3(X0) )
& member(int,sK3(X0),aa(list(int),fun(int,bool),set(int),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f237,f281]) ).
tff(f281,plain,
! [X0: list(int)] :
( ? [X1: int] :
( ( zero_zero(int) = X1 )
& member(int,X1,aa(list(int),fun(int,bool),set(int),X0)) )
=> ( ( zero_zero(int) = sK3(X0) )
& member(int,sK3(X0),aa(list(int),fun(int,bool),set(int),X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f237,plain,
! [X0: list(int)] :
( ord_less(int,zero_zero(int),zlcms(X0))
| ? [X1: int] :
( ( zero_zero(int) = X1 )
& member(int,X1,aa(list(int),fun(int,bool),set(int),X0)) ) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: list(int)] :
( ! [X1: int] :
( member(int,X1,aa(list(int),fun(int,bool),set(int),X0))
=> ( zero_zero(int) != X1 ) )
=> ord_less(int,zero_zero(int),zlcms(X0)) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X19: list(int)] :
( ! [X3: int] :
( member(int,X3,aa(list(int),fun(int,bool),set(int),X19))
=> ( zero_zero(int) != X3 ) )
=> ord_less(int,zero_zero(int),zlcms(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_zlcms__pos) ).
tff(f1179,plain,
spl22_104,
inference(avatar_split_clause,[],[f410,f1177]) ).
tff(f410,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(decr_Z(X0)) )
| ( zero_zero(int) = divisor(X0) )
| ( zero_zero(int) != aa(atom,int,hd_coeff,X0) ) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(decr_Z(X0)) )
| ( zero_zero(int) = divisor(X0) )
| ( zero_zero(int) != aa(atom,int,hd_coeff,X0) ) ),
inference(flattening,[],[f233]) ).
tff(f233,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(decr_Z(X0)) )
| ( zero_zero(int) = divisor(X0) )
| ( zero_zero(int) != aa(atom,int,hd_coeff,X0) ) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: atom] :
( ( zero_zero(int) = aa(atom,int,hd_coeff,X0) )
=> ( ( zero_zero(int) != divisor(X0) )
=> ( zero_zero(int) != divisor(decr_Z(X0)) ) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X7: atom] :
( ( zero_zero(int) = aa(atom,int,hd_coeff,X7) )
=> ( ( zero_zero(int) != divisor(X7) )
=> ( zero_zero(int) != divisor(decr_Z(X7)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Z_Oanormal__decr) ).
tff(f1173,plain,
( spl22_103
| ~ spl22_63
| ~ spl22_96 ),
inference(avatar_split_clause,[],[f1137,f1113,f868,f1170]) ).
tff(f1170,plain,
( spl22_103
<=> listMem(atom,b,as) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_103])]) ).
tff(f1113,plain,
( spl22_96
<=> ! [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,[spl22_96])]) ).
tff(f1137,plain,
( listMem(atom,b,as)
| ~ spl22_63
| ~ spl22_96 ),
inference(resolution,[],[f1114,f870]) ).
tff(f870,plain,
( member(atom,b,aa(list(atom),fun(atom,bool),member1(atom),as))
| ~ spl22_63 ),
inference(avatar_component_clause,[],[f868]) ).
tff(f1114,plain,
( ! [X0: $tType,X2: X0,X1: list(X0)] :
( ~ member(X0,X2,aa(list(X0),fun(X0,bool),member1(X0),X1))
| listMem(X0,X2,X1) )
| ~ spl22_96 ),
inference(avatar_component_clause,[],[f1113]) ).
tff(f1167,plain,
spl22_102,
inference(avatar_split_clause,[],[f518,f1165]) ).
tff(f1165,plain,
( spl22_102
<=> ! [X0: list(int)] :
( member(int,zero_zero(int),aa(list(int),fun(int,bool),member1(int),X0))
| ( zero_zero(int) != zlcms(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_102])]) ).
tff(f518,plain,
! [X0: list(int)] :
( member(int,zero_zero(int),aa(list(int),fun(int,bool),member1(int),X0))
| ( zero_zero(int) != zlcms(X0) ) ),
inference(definition_unfolding,[],[f417,f367]) ).
tff(f417,plain,
! [X0: list(int)] :
( member(int,zero_zero(int),aa(list(int),fun(int,bool),set(int),X0))
| ( zero_zero(int) != zlcms(X0) ) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: list(int)] :
( ( ( zero_zero(int) = zlcms(X0) )
| ~ member(int,zero_zero(int),aa(list(int),fun(int,bool),set(int),X0)) )
& ( member(int,zero_zero(int),aa(list(int),fun(int,bool),set(int),X0))
| ( zero_zero(int) != zlcms(X0) ) ) ),
inference(nnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
<=> member(int,zero_zero(int),aa(list(int),fun(int,bool),set(int),X0)) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X19: list(int)] :
( ( zero_zero(int) = zlcms(X19) )
<=> member(int,zero_zero(int),aa(list(int),fun(int,bool),set(int),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zlcms0__iff) ).
tff(f1163,plain,
spl22_101,
inference(avatar_split_clause,[],[f517,f1161]) ).
tff(f1161,plain,
( spl22_101
<=> ! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
| ~ member(int,zero_zero(int),aa(list(int),fun(int,bool),member1(int),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_101])]) ).
tff(f517,plain,
! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
| ~ member(int,zero_zero(int),aa(list(int),fun(int,bool),member1(int),X0)) ),
inference(definition_unfolding,[],[f418,f367]) ).
tff(f418,plain,
! [X0: list(int)] :
( ( zero_zero(int) = zlcms(X0) )
| ~ member(int,zero_zero(int),aa(list(int),fun(int,bool),set(int),X0)) ),
inference(cnf_transformation,[],[f284]) ).
tff(f1152,plain,
spl22_100,
inference(avatar_split_clause,[],[f575,f1150]) ).
tff(f1150,plain,
( spl22_100
<=> ! [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,[spl22_100])]) ).
tff(f575,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,[],[f447,f423]) ).
tff(f447,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,[],[f244]) ).
tff(f1148,plain,
spl22_99,
inference(avatar_split_clause,[],[f559,f1146]) ).
tff(f1146,plain,
( spl22_99
<=> ! [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,[spl22_99])]) ).
tff(f559,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,[],[f480]) ).
tff(f480,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,[],[f308]) ).
tff(f308,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,[],[f307]) ).
tff(f307,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,[],[f191]) ).
tff(f191,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,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType,X37: X0,X10: list(X0),X4: X0] :
( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),cons(X0,X4,X10)),X37))
<=> ( pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),X10),X37))
| ( X4 = X37 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_member__rec_I1_J) ).
tff(f1144,plain,
spl22_98,
inference(avatar_split_clause,[],[f514,f1142]) ).
tff(f1142,plain,
( spl22_98
<=> ! [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,[spl22_98])]) ).
tff(f514,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
inference(definition_unfolding,[],[f411,f367]) ).
tff(f411,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: atom] :
( ( zero_zero(int) != divisor(X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: atom] :
( member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( zero_zero(int) != divisor(X0) ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X2: atom] :
( member(atom,X2,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( divisor(X2) != zero_zero(int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_div0) ).
tff(f1119,plain,
spl22_97,
inference(avatar_split_clause,[],[f528,f1117]) ).
tff(f1117,plain,
( spl22_97
<=> ! [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,[spl22_97])]) ).
tff(f528,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,[],[f463,f367]) ).
tff(f463,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,[],[f299]) ).
tff(f299,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,[],[f181]) ).
tff(f181,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,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType,X10: list(X0),X4: X0] :
( listMem(X0,X4,X10)
<=> member(X0,X4,aa(list(X0),fun(X0,bool),set(X0),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ListMem__iff) ).
tff(f1115,plain,
spl22_96,
inference(avatar_split_clause,[],[f527,f1113]) ).
tff(f527,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,[],[f464,f367]) ).
tff(f464,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,[],[f299]) ).
tff(f1111,plain,
spl22_95,
inference(avatar_split_clause,[],[f453,f1109]) ).
tff(f1109,plain,
( spl22_95
<=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_95])]) ).
tff(f453,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: nat,X1: nat,X2: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
& ord_less(nat,X0,X1) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f293]) ).
tff(f293,plain,
! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) )
| ~ sP0(X2,X1,X0) ),
inference(nnf_transformation,[],[f262]) ).
tff(f1107,plain,
spl22_94,
inference(avatar_split_clause,[],[f445,f1105]) ).
tff(f1105,plain,
( spl22_94
<=> ! [X2: int,X0: int,X1: int] : ( dvd(X1,X0,nil(int)) = aa(atom,atom,hd_coeff1(X2),dvd(X1,X0,nil(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_94])]) ).
tff(f445,plain,
! [X2: int,X0: int,X1: int] : ( dvd(X1,X0,nil(int)) = aa(atom,atom,hd_coeff1(X2),dvd(X1,X0,nil(int))) ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: int,X1: int,X2: int] : ( dvd(X1,X0,nil(int)) = aa(atom,atom,hd_coeff1(X2),dvd(X1,X0,nil(int))) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X29: int,X30: int,X31: int] : ( dvd(X30,X29,nil(int)) = aa(atom,atom,hd_coeff1(X31),dvd(X30,X29,nil(int))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hd__coeff1_Osimps_I5_J) ).
tff(f1103,plain,
spl22_93,
inference(avatar_split_clause,[],[f433,f1101]) ).
tff(f1101,plain,
( spl22_93
<=> ! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_93])]) ).
tff(f433,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType,X1: list(X0)] :
( ( ( nil(X0) != X1 )
| ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) )
& ( ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f290,f291]) ).
tff(f291,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X4: X0,X5: list(X0)] : ( cons(X0,X4,X5) = X1 )
=> ( cons(X0,sK6(X0,X1),sK7(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f290,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,[],[f289]) ).
tff(f289,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,[],[f162]) ).
tff(f162,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != X1 )
<=> ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType,X10: list(X0)] :
( ( nil(X0) != X10 )
<=> ? [X21: X0,X49: list(X0)] : ( cons(X0,X21,X49) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_neq__Nil__conv) ).
tff(f1099,plain,
( ~ spl22_91
| spl22_92
| ~ spl22_18
| ~ spl22_85 ),
inference(avatar_split_clause,[],[f1071,f995,f663,f1097,f1093]) ).
tff(f1093,plain,
( spl22_91
<=> linordered_idom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_91])]) ).
tff(f1097,plain,
( spl22_92
<=> ! [X0: int] : ~ ord_less(int,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_92])]) ).
tff(f663,plain,
( spl22_18
<=> ! [X0: nat] : ~ ord_less(nat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_18])]) ).
tff(f995,plain,
( spl22_85
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1))
| ~ ord_less(int,X2,X1)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_85])]) ).
tff(f1071,plain,
( ! [X0: int] :
( ~ ord_less(int,X0,X0)
| ~ linordered_idom(nat) )
| ~ spl22_18
| ~ spl22_85 ),
inference(resolution,[],[f996,f664]) ).
tff(f664,plain,
( ! [X0: nat] : ~ ord_less(nat,X0,X0)
| ~ spl22_18 ),
inference(avatar_component_clause,[],[f663]) ).
tff(f996,plain,
( ! [X0: $tType,X2: int,X1: int] :
( ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1))
| ~ ord_less(int,X2,X1)
| ~ linordered_idom(X0) )
| ~ spl22_85 ),
inference(avatar_component_clause,[],[f995]) ).
tff(f1091,plain,
spl22_90,
inference(avatar_split_clause,[],[f429,f1089]) ).
tff(f1089,plain,
( spl22_90
<=> ! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_90])]) ).
tff(f429,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $tType,X1: list(X0)] :
( ( cons(X0,sK4(X0,X1),sK5(X0,X1)) = X1 )
| ( nil(X0) = X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f243,f285]) ).
tff(f285,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 )
=> ( cons(X0,sK4(X0,X1),sK5(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
tff(f243,plain,
! [X0: $tType,X1: list(X0)] :
( ? [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) = X1 )
| ( nil(X0) = X1 ) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType,X1: list(X0)] :
( ( nil(X0) != X1 )
=> ~ ! [X2: X0,X3: list(X0)] : ( cons(X0,X2,X3) != X1 ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType,X34: list(X0)] :
( ( nil(X0) != X34 )
=> ~ ! [X46: X0,X47: list(X0)] : ( cons(X0,X46,X47) != X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_list_Oexhaust) ).
tff(f1086,plain,
spl22_89,
inference(avatar_split_clause,[],[f424,f1084]) ).
tff(f1084,plain,
( spl22_89
<=> ! [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,[spl22_89])]) ).
tff(f424,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),nil(X0)),X1)),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),nil(X0)),X1)),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType,X34: X0] : ~ pp(aa(X0,bool,aa(list(X0),fun(X0,bool),member1(X0),nil(X0)),X34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_member__rec_I2_J) ).
tff(f1009,plain,
spl22_88,
inference(avatar_split_clause,[],[f489,f1007]) ).
tff(f1007,plain,
( spl22_88
<=> ! [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,[spl22_88])]) ).
tff(f489,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,[],[f318]) ).
tff(f318,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,[],[f317]) ).
tff(f317,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,[],[f195]) ).
tff(f195,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,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType,X22: list(X0),X23: X0,X24: list(X0),X13: X0] :
( ( cons(X0,X13,X24) = cons(X0,X23,X22) )
<=> ( ( X22 = X24 )
& ( X13 = X23 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_list_Oinject) ).
tff(f1005,plain,
spl22_87,
inference(avatar_split_clause,[],[f475,f1003]) ).
tff(f1003,plain,
( spl22_87
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: list(X1)] :
( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_87])]) ).
tff(f475,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( ( nil(X0) = map(X1,X0,X3,X2) )
| ( nil(X1) != X2 ) )
& ( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ) ),
inference(nnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( nil(X0) = map(X1,X0,X3,X2) )
<=> ( nil(X1) = X2 ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType,X1: $tType,X10: list(X1),X11: fun(X1,X0)] :
( ( map(X1,X0,X11,X10) = nil(X0) )
<=> ( nil(X1) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_map__is__Nil__conv) ).
tff(f1001,plain,
spl22_86,
inference(avatar_split_clause,[],[f471,f999]) ).
tff(f999,plain,
( spl22_86
<=> ! [X0: int,X3: int,X2: list(int),X1: int] : ( dvd(X1,X0,nil(int)) = asubst(X3,X2,dvd(X1,X0,nil(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_86])]) ).
tff(f471,plain,
! [X2: list(int),X3: int,X0: int,X1: int] : ( dvd(X1,X0,nil(int)) = asubst(X3,X2,dvd(X1,X0,nil(int))) ),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: int,X1: int,X2: list(int),X3: int] : ( dvd(X1,X0,nil(int)) = asubst(X3,X2,dvd(X1,X0,nil(int))) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X29: int,X30: int,X32: list(int),X33: int] : ( dvd(X30,X29,nil(int)) = asubst(X33,X32,dvd(X30,X29,nil(int))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_asubst_Osimps_I5_J) ).
tff(f997,plain,
spl22_85,
inference(avatar_split_clause,[],[f394,f995]) ).
tff(f394,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1))
| ~ ord_less(int,X2,X1)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1))
| ~ ord_less(int,X2,X1) )
& ( ord_less(int,X2,X1)
| ~ ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1)) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1))
<=> ord_less(int,X2,X1) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: int,X2: int] :
( ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1))
<=> ord_less(int,X2,X1) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X5: int,X8: int] :
( ord_less(X0,ring_1_of_int(X0,X8),ring_1_of_int(X0,X5))
<=> ord_less(int,X8,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_of__int__less__iff) ).
tff(f990,plain,
spl22_84,
inference(avatar_split_clause,[],[f393,f988]) ).
tff(f988,plain,
( spl22_84
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less(int,X2,X1)
| ~ ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_84])]) ).
tff(f393,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less(int,X2,X1)
| ~ ord_less(X0,ring_1_of_int(X0,X2),ring_1_of_int(X0,X1))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f986,plain,
spl22_83,
inference(avatar_split_clause,[],[f391,f984]) ).
tff(f984,plain,
( spl22_83
<=> ! [X0: $tType,X1: int] :
( ord_less(X0,ring_1_of_int(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,zero_zero(int))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_83])]) ).
tff(f391,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,ring_1_of_int(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,zero_zero(int))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,ring_1_of_int(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,zero_zero(int)) )
& ( ord_less(int,X1,zero_zero(int))
| ~ ord_less(X0,ring_1_of_int(X0,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,ring_1_of_int(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,zero_zero(int)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: int] :
( ord_less(X0,ring_1_of_int(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,zero_zero(int)) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X5: int] :
( ord_less(X0,ring_1_of_int(X0,X5),zero_zero(X0))
<=> ord_less(int,X5,zero_zero(int)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_of__int__less__0__iff) ).
tff(f982,plain,
spl22_82,
inference(avatar_split_clause,[],[f390,f980]) ).
tff(f980,plain,
( spl22_82
<=> ! [X0: $tType,X1: int] :
( ord_less(int,X1,zero_zero(int))
| ~ ord_less(X0,ring_1_of_int(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_82])]) ).
tff(f390,plain,
! [X0: $tType,X1: int] :
( ord_less(int,X1,zero_zero(int))
| ~ ord_less(X0,ring_1_of_int(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f978,plain,
spl22_81,
inference(avatar_split_clause,[],[f389,f976]) ).
tff(f976,plain,
( spl22_81
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,sgn_sgn(X0,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_81])]) ).
tff(f389,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,sgn_sgn(X0,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,sgn_sgn(X0,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0)) )
& ( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,sgn_sgn(X0,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,sgn_sgn(X0,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,sgn_sgn(X0,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) ) ),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X13: X0] :
( ord_less(X0,sgn_sgn(X0,X13),zero_zero(X0))
<=> ord_less(X0,X13,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_sgn__less) ).
tff(f974,plain,
spl22_80,
inference(avatar_split_clause,[],[f388,f972]) ).
tff(f972,plain,
( spl22_80
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,sgn_sgn(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_80])]) ).
tff(f388,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,sgn_sgn(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f970,plain,
spl22_79,
inference(avatar_split_clause,[],[f387,f968]) ).
tff(f968,plain,
( spl22_79
<=> ! [X0: $tType,X1: int] :
( ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X1))
| ~ ord_less(int,zero_zero(int),X1)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_79])]) ).
tff(f387,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X1))
| ~ ord_less(int,zero_zero(int),X1)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X1))
| ~ ord_less(int,zero_zero(int),X1) )
& ( ord_less(int,zero_zero(int),X1)
| ~ ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X1)) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X1))
<=> ord_less(int,zero_zero(int),X1) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: int] :
( ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X1))
<=> ord_less(int,zero_zero(int),X1) ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X5: int] :
( ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X5))
<=> ord_less(int,zero_zero(int),X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_of__int__0__less__iff) ).
tff(f966,plain,
spl22_78,
inference(avatar_split_clause,[],[f386,f964]) ).
tff(f964,plain,
( spl22_78
<=> ! [X0: $tType,X1: int] :
( ord_less(int,zero_zero(int),X1)
| ~ ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X1))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_78])]) ).
tff(f386,plain,
! [X0: $tType,X1: int] :
( ord_less(int,zero_zero(int),X1)
| ~ ord_less(X0,zero_zero(X0),ring_1_of_int(X0,X1))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f962,plain,
spl22_77,
inference(avatar_split_clause,[],[f385,f960]) ).
tff(f960,plain,
( spl22_77
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),sgn_sgn(X0,X1))
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_77])]) ).
tff(f385,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),sgn_sgn(X0,X1))
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,zero_zero(X0),sgn_sgn(X0,X1))
| ~ ord_less(X0,zero_zero(X0),X1) )
& ( ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),sgn_sgn(X0,X1)) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,zero_zero(X0),sgn_sgn(X0,X1))
<=> ord_less(X0,zero_zero(X0),X1) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,zero_zero(X0),sgn_sgn(X0,X1))
<=> ord_less(X0,zero_zero(X0),X1) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X13: X0] :
( ord_less(X0,zero_zero(X0),sgn_sgn(X0,X13))
<=> ord_less(X0,zero_zero(X0),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_sgn__greater) ).
tff(f958,plain,
spl22_76,
inference(avatar_split_clause,[],[f384,f956]) ).
tff(f956,plain,
( spl22_76
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),sgn_sgn(X0,X1))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_76])]) ).
tff(f384,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),sgn_sgn(X0,X1))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f273]) ).
tff(f954,plain,
( spl22_75
| ~ spl22_32
| ~ spl22_50 ),
inference(avatar_split_clause,[],[f807,f802,f720,f952]) ).
tff(f952,plain,
( spl22_75
<=> ! [X0: bool] :
( ~ pp(X0)
| member(bool,X0,combi(bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_75])]) ).
tff(f720,plain,
( spl22_32
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_32])]) ).
tff(f802,plain,
( spl22_50
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_50])]) ).
tff(f807,plain,
( ! [X0: bool] :
( ~ pp(X0)
| member(bool,X0,combi(bool)) )
| ~ spl22_32
| ~ spl22_50 ),
inference(superposition,[],[f803,f721]) ).
tff(f721,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 )
| ~ spl22_32 ),
inference(avatar_component_clause,[],[f720]) ).
tff(f803,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X2))
| member(X0,X2,X1) )
| ~ spl22_50 ),
inference(avatar_component_clause,[],[f802]) ).
tff(f928,plain,
spl22_74,
inference(avatar_split_clause,[],[f509,f925]) ).
tff(f925,plain,
( spl22_74
<=> ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_74])]) ).
tff(f509,plain,
a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK21),
inference(cnf_transformation,[],[f336]) ).
tff(f336,plain,
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK21) )
& member(atom,sK21,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f201,f335]) ).
tff(f335,plain,
( ? [X0: atom] :
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X0) )
& member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) )
=> ( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK21) )
& member(atom,sK21,aa(list(atom),fun(atom,bool),set(atom),as)) ) ),
introduced(choice_axiom,[]) ).
tff(f201,plain,
? [X0: atom] :
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X0) )
& member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
? [X3: atom] :
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X3) )
& member(atom,X3,aa(list(atom),fun(atom,bool),set(atom),as)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096EX_Ab_058set_Aas_O_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_096) ).
tff(f923,plain,
spl22_73,
inference(avatar_split_clause,[],[f498,f921]) ).
tff(f921,plain,
( spl22_73
<=> ! [X2: int,X4: int,X0: list(int),X5: int,X3: list(int),X1: int] :
( ( X0 = X3 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_73])]) ).
tff(f498,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X0 = X3 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f326,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( ( dvd(X2,X1,X0) = dvd(X5,X4,X3) )
| ( X0 != X3 )
| ( X1 != X4 )
| ( X2 != X5 ) )
& ( ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
inference(flattening,[],[f325]) ).
tff(f325,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( ( dvd(X2,X1,X0) = dvd(X5,X4,X3) )
| ( X0 != X3 )
| ( X1 != X4 )
| ( X2 != X5 ) )
& ( ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
inference(nnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: list(int),X1: int,X2: int,X3: list(int),X4: int,X5: int] :
( ( dvd(X2,X1,X0) = dvd(X5,X4,X3) )
<=> ( ( X0 = X3 )
& ( X1 = X4 )
& ( X2 = X5 ) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X22: list(int),X25: int,X26: int,X24: list(int),X27: int,X28: int] :
( ( dvd(X28,X27,X24) = dvd(X26,X25,X22) )
<=> ( ( X22 = X24 )
& ( X25 = X27 )
& ( X26 = X28 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_atom_Osimps_I2_J) ).
tff(f919,plain,
spl22_72,
inference(avatar_split_clause,[],[f488,f917]) ).
tff(f917,plain,
( spl22_72
<=> ! [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,[spl22_72])]) ).
tff(f488,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,[],[f318]) ).
tff(f915,plain,
( spl22_71
| ~ spl22_32
| ~ spl22_49 ),
inference(avatar_split_clause,[],[f805,f798,f720,f913]) ).
tff(f913,plain,
( spl22_71
<=> ! [X0: bool] :
( pp(X0)
| ~ member(bool,X0,combi(bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_71])]) ).
tff(f798,plain,
( spl22_49
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_49])]) ).
tff(f805,plain,
( ! [X0: bool] :
( pp(X0)
| ~ member(bool,X0,combi(bool)) )
| ~ spl22_32
| ~ spl22_49 ),
inference(superposition,[],[f799,f721]) ).
tff(f799,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) )
| ~ spl22_49 ),
inference(avatar_component_clause,[],[f798]) ).
tff(f911,plain,
spl22_70,
inference(avatar_split_clause,[],[f392,f909]) ).
tff(f909,plain,
( spl22_70
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_70])]) ).
tff(f392,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f218]) ).
tff(f218,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 != X2 )
=> ( ~ ord_less(X0,X2,X1)
=> ord_less(X0,X1,X2) ) ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X34: X0,X36: X0] :
( ( X34 != X36 )
=> ( ~ ord_less(X0,X36,X34)
=> ord_less(X0,X34,X36) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_linorder__neqE__linordered__idom) ).
tff(f907,plain,
spl22_69,
inference(avatar_split_clause,[],[f382,f905]) ).
tff(f905,plain,
( spl22_69
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),X1)
| ( one_one(X0) != sgn_sgn(X0,X1) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_69])]) ).
tff(f382,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),X1)
| ( one_one(X0) != sgn_sgn(X0,X1) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( one_one(X0) = sgn_sgn(X0,X1) )
| ~ ord_less(X0,zero_zero(X0),X1) )
& ( ord_less(X0,zero_zero(X0),X1)
| ( one_one(X0) != sgn_sgn(X0,X1) ) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( one_one(X0) = sgn_sgn(X0,X1) )
<=> ord_less(X0,zero_zero(X0),X1) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ( one_one(X0) = sgn_sgn(X0,X1) )
<=> ord_less(X0,zero_zero(X0),X1) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X13: X0] :
( ( sgn_sgn(X0,X13) = one_one(X0) )
<=> ord_less(X0,zero_zero(X0),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_sgn__1__pos) ).
tff(f903,plain,
spl22_68,
inference(avatar_split_clause,[],[f379,f901]) ).
tff(f901,plain,
( spl22_68
<=> ! [X0: $tType,X1: X0] :
( ( one_one(X0) = sgn_sgn(X0,X1) )
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_68])]) ).
tff(f379,plain,
! [X0: $tType,X1: X0] :
( ( one_one(X0) = sgn_sgn(X0,X1) )
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( one_one(X0) = sgn_sgn(X0,X1) )
| ~ ord_less(X0,zero_zero(X0),X1) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,zero_zero(X0),X1)
=> ( one_one(X0) = sgn_sgn(X0,X1) ) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X7: X0] :
( ord_less(X0,zero_zero(X0),X7)
=> ( sgn_sgn(X0,X7) = one_one(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_sgn__pos) ).
tff(f899,plain,
spl22_67,
inference(avatar_split_clause,[],[f361,f896]) ).
tff(f896,plain,
( spl22_67
<=> ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_67])]) ).
tff(f361,plain,
a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK2),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK2) )
& member(atom,sK2,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f203,f266]) ).
tff(f266,plain,
( ? [X0: atom] :
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X0) )
& member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) )
=> ( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),sK2) )
& member(atom,sK2,aa(list(atom),fun(atom,bool),set(atom),as)) ) ),
introduced(choice_axiom,[]) ).
tff(f203,plain,
? [X0: atom] :
( ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X0) )
& member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(ennf_transformation,[],[f120]) ).
tff(f120,plain,
~ ! [X0: atom] :
( member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( a != aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X0) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
~ ! [X6: atom] :
( member(atom,X6,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( a != aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__096_B_Bthesis_O_A_I_B_Bb_O_A_091_124_Ab_A_058_Aset_Aas_059_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f894,plain,
spl22_66,
inference(avatar_split_clause,[],[f356,f891]) ).
tff(f891,plain,
( spl22_66
<=> ( a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_66])]) ).
tff(f356,plain,
a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),b),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
a = aa(atom,atom,hd_coeff1(zlcms(map(atom,int,hd_coeff,as))),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096a_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_096) ).
tff(f881,plain,
spl22_65,
inference(avatar_split_clause,[],[f540,f878]) ).
tff(f878,plain,
( spl22_65
<=> member(atom,sK21,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_65])]) ).
tff(f540,plain,
member(atom,sK21,aa(list(atom),fun(atom,bool),member1(atom),as)),
inference(definition_unfolding,[],[f508,f367]) ).
tff(f508,plain,
member(atom,sK21,aa(list(atom),fun(atom,bool),set(atom),as)),
inference(cnf_transformation,[],[f336]) ).
tff(f876,plain,
spl22_64,
inference(avatar_split_clause,[],[f513,f873]) ).
tff(f873,plain,
( spl22_64
<=> member(atom,sK2,aa(list(atom),fun(atom,bool),member1(atom),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_64])]) ).
tff(f513,plain,
member(atom,sK2,aa(list(atom),fun(atom,bool),member1(atom),as)),
inference(definition_unfolding,[],[f360,f367]) ).
tff(f360,plain,
member(atom,sK2,aa(list(atom),fun(atom,bool),set(atom),as)),
inference(cnf_transformation,[],[f267]) ).
tff(f871,plain,
spl22_63,
inference(avatar_split_clause,[],[f510,f868]) ).
tff(f510,plain,
member(atom,b,aa(list(atom),fun(atom,bool),member1(atom),as)),
inference(definition_unfolding,[],[f355,f367]) ).
tff(f355,plain,
member(atom,b,aa(list(atom),fun(atom,bool),set(atom),as)),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
member(atom,b,aa(list(atom),fun(atom,bool),set(atom),as)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096b_A_058_Aset_Aas_096) ).
tff(f866,plain,
spl22_62,
inference(avatar_split_clause,[],[f497,f864]) ).
tff(f864,plain,
( spl22_62
<=> ! [X2: int,X3: list(int),X4: int,X0: list(int),X5: int,X1: int] :
( ( X1 = X4 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_62])]) ).
tff(f497,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X1 = X4 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f862,plain,
spl22_61,
inference(avatar_split_clause,[],[f496,f860]) ).
tff(f860,plain,
( spl22_61
<=> ! [X3: list(int),X4: int,X0: list(int),X5: int,X2: int,X1: int] :
( ( X2 = X5 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_61])]) ).
tff(f496,plain,
! [X2: int,X3: list(int),X0: list(int),X1: int,X4: int,X5: int] :
( ( X2 = X5 )
| ( dvd(X2,X1,X0) != dvd(X5,X4,X3) ) ),
inference(cnf_transformation,[],[f326]) ).
tff(f858,plain,
spl22_60,
inference(avatar_split_clause,[],[f423,f856]) ).
tff(f854,plain,
( spl22_59
| ~ spl22_4
| ~ spl22_39 ),
inference(avatar_split_clause,[],[f781,f748,f593,f851]) ).
tff(f851,plain,
( spl22_59
<=> ( one_one(int) = ring_1_of_int(int,one_one(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_59])]) ).
tff(f593,plain,
( spl22_4
<=> ring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_4])]) ).
tff(f748,plain,
( spl22_39
<=> ! [X0: $tType] :
( ( ring_1_of_int(X0,one_one(int)) = one_one(X0) )
| ~ ring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_39])]) ).
tff(f781,plain,
( ( one_one(int) = ring_1_of_int(int,one_one(int)) )
| ~ spl22_4
| ~ spl22_39 ),
inference(resolution,[],[f749,f595]) ).
tff(f595,plain,
( ring_1(int)
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f593]) ).
tff(f749,plain,
( ! [X0: $tType] :
( ~ ring_1(X0)
| ( ring_1_of_int(X0,one_one(int)) = one_one(X0) ) )
| ~ spl22_39 ),
inference(avatar_component_clause,[],[f748]) ).
tff(f849,plain,
spl22_58,
inference(avatar_split_clause,[],[f380,f847]) ).
tff(f847,plain,
( spl22_58
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != sgn_sgn(X0,X1) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_58])]) ).
tff(f380,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != sgn_sgn(X0,X1) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = sgn_sgn(X0,X1) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != sgn_sgn(X0,X1) ) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = sgn_sgn(X0,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = sgn_sgn(X0,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X13: X0] :
( ( zero_zero(X0) = sgn_sgn(X0,X13) )
<=> ( zero_zero(X0) = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_sgn__0__0) ).
tff(f845,plain,
spl22_57,
inference(avatar_split_clause,[],[f376,f843]) ).
tff(f843,plain,
( spl22_57
<=> ! [X0: $tType,X2: int,X1: int] :
( ( X1 = X2 )
| ( ring_1_of_int(X0,X1) != ring_1_of_int(X0,X2) )
| ~ ring_char_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_57])]) ).
tff(f376,plain,
! [X0: $tType,X2: int,X1: int] :
( ( X1 = X2 )
| ( ring_1_of_int(X0,X1) != ring_1_of_int(X0,X2) )
| ~ ring_char_0(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ( ring_1_of_int(X0,X1) = ring_1_of_int(X0,X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( ring_1_of_int(X0,X1) != ring_1_of_int(X0,X2) ) ) )
| ~ ring_char_0(X0) ),
inference(nnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ring_1_of_int(X0,X1) = ring_1_of_int(X0,X2) )
<=> ( X1 = X2 ) )
| ~ ring_char_0(X0) ),
inference(ennf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType] :
( ring_char_0(X0)
=> ! [X1: int,X2: int] :
( ( ring_1_of_int(X0,X1) = ring_1_of_int(X0,X2) )
<=> ( X1 = X2 ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X0: $tType] :
( ring_char_0(X0)
=> ! [X5: int,X8: int] :
( ( ring_1_of_int(X0,X5) = ring_1_of_int(X0,X8) )
<=> ( X5 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_of__int__eq__iff) ).
tff(f841,plain,
spl22_56,
inference(avatar_split_clause,[],[f372,f839]) ).
tff(f839,plain,
( spl22_56
<=> ! [X0: $tType,X1: int] :
( ( zero_zero(int) = X1 )
| ( zero_zero(X0) != ring_1_of_int(X0,X1) )
| ~ ring_char_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_56])]) ).
tff(f372,plain,
! [X0: $tType,X1: int] :
( ( zero_zero(int) = X1 )
| ( zero_zero(X0) != ring_1_of_int(X0,X1) )
| ~ ring_char_0(X0) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ( zero_zero(X0) = ring_1_of_int(X0,X1) )
| ( zero_zero(int) != X1 ) )
& ( ( zero_zero(int) = X1 )
| ( zero_zero(X0) != ring_1_of_int(X0,X1) ) ) )
| ~ ring_char_0(X0) ),
inference(nnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( zero_zero(X0) = ring_1_of_int(X0,X1) )
<=> ( zero_zero(int) = X1 ) )
| ~ ring_char_0(X0) ),
inference(ennf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: $tType] :
( ring_char_0(X0)
=> ! [X1: int] :
( ( zero_zero(X0) = ring_1_of_int(X0,X1) )
<=> ( zero_zero(int) = X1 ) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( ring_char_0(X0)
=> ! [X5: int] :
( ( zero_zero(X0) = ring_1_of_int(X0,X5) )
<=> ( zero_zero(int) = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_of__int__eq__0__iff) ).
tff(f828,plain,
spl22_55,
inference(avatar_split_clause,[],[f472,f826]) ).
tff(f826,plain,
( spl22_55
<=> ! [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,[spl22_55])]) ).
tff(f472,plain,
! [X0: $tType,X2: list(X0),X3: X0,X1: X0] :
( listMem(X0,X3,cons(X0,X1,X2))
| ~ listMem(X0,X3,X2) ),
inference(cnf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: $tType,X1: X0,X2: list(X0),X3: X0] :
( listMem(X0,X3,cons(X0,X1,X2))
| ~ listMem(X0,X3,X2) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType,X1: X0,X2: list(X0),X3: X0] :
( listMem(X0,X3,X2)
=> listMem(X0,X3,cons(X0,X1,X2)) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType,X34: X0,X35: list(X0),X36: X0] :
( listMem(X0,X36,X35)
=> listMem(X0,X36,cons(X0,X34,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_insert) ).
tff(f824,plain,
spl22_54,
inference(avatar_split_clause,[],[f425,f822]) ).
tff(f822,plain,
( spl22_54
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_54])]) ).
tff(f425,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(flattening,[],[f238]) ).
tff(f238,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ord_less(nat,X1,X0)
=> ord_less(nat,X0,X1) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X34: nat,X36: nat] :
( ( X34 != X36 )
=> ( ~ ord_less(nat,X36,X34)
=> ord_less(nat,X34,X36) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_linorder__neqE__nat) ).
tff(f820,plain,
spl22_53,
inference(avatar_split_clause,[],[f414,f818]) ).
tff(f818,plain,
( spl22_53
<=> ! [X0: list(int)] :
( ord_less(int,zero_zero(int),zlcms(X0))
| ( zero_zero(int) = sK3(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_53])]) ).
tff(f414,plain,
! [X0: list(int)] :
( ord_less(int,zero_zero(int),zlcms(X0))
| ( zero_zero(int) = sK3(X0) ) ),
inference(cnf_transformation,[],[f282]) ).
tff(f816,plain,
( spl22_52
| ~ spl22_4
| ~ spl22_38 ),
inference(avatar_split_clause,[],[f780,f744,f593,f813]) ).
tff(f813,plain,
( spl22_52
<=> ( zero_zero(int) = ring_1_of_int(int,zero_zero(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_52])]) ).
tff(f744,plain,
( spl22_38
<=> ! [X0: $tType] :
( ( zero_zero(X0) = ring_1_of_int(X0,zero_zero(int)) )
| ~ ring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_38])]) ).
tff(f780,plain,
( ( zero_zero(int) = ring_1_of_int(int,zero_zero(int)) )
| ~ spl22_4
| ~ spl22_38 ),
inference(resolution,[],[f745,f595]) ).
tff(f745,plain,
( ! [X0: $tType] :
( ~ ring_1(X0)
| ( zero_zero(X0) = ring_1_of_int(X0,zero_zero(int)) ) )
| ~ spl22_38 ),
inference(avatar_component_clause,[],[f744]) ).
tff(f811,plain,
spl22_51,
inference(avatar_split_clause,[],[f378,f809]) ).
tff(f809,plain,
( spl22_51
<=> ! [X0: $tType,X1: X0] :
( ( sgn_sgn(X0,X1) = sgn_sgn(X0,sgn_sgn(X0,X1)) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_51])]) ).
tff(f378,plain,
! [X0: $tType,X1: X0] :
( ( sgn_sgn(X0,X1) = sgn_sgn(X0,sgn_sgn(X0,X1)) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType] :
( ! [X1: X0] : ( sgn_sgn(X0,X1) = sgn_sgn(X0,sgn_sgn(X0,X1)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ( sgn_sgn(X0,X1) = sgn_sgn(X0,sgn_sgn(X0,X1)) ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X7: X0] : ( sgn_sgn(X0,X7) = sgn_sgn(X0,sgn_sgn(X0,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_sgn__sgn) ).
tff(f804,plain,
spl22_50,
inference(avatar_split_clause,[],[f466,f802]) ).
tff(f466,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,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,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( member(X0,X2,X1)
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X0: $tType,X48: fun(X0,bool),X4: X0] :
( member(X0,X4,X48)
<=> pp(aa(X0,bool,X48,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_mem__def) ).
tff(f800,plain,
spl22_49,
inference(avatar_split_clause,[],[f465,f798]) ).
tff(f465,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f300]) ).
tff(f796,plain,
spl22_48,
inference(avatar_split_clause,[],[f444,f794]) ).
tff(f794,plain,
( spl22_48
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_48])]) ).
tff(f444,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
inference(cnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X1: $tType,X0: $tType,X11: fun(X1,X0)] : ( nil(X0) = map(X1,X0,X11,nil(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_map_Osimps_I1_J) ).
tff(f790,plain,
( spl22_47
| ~ spl22_3
| ~ spl22_37 ),
inference(avatar_split_clause,[],[f779,f740,f588,f787]) ).
tff(f787,plain,
( spl22_47
<=> ( zero_zero(int) = sgn_sgn(int,zero_zero(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_47])]) ).
tff(f588,plain,
( spl22_3
<=> sgn_if(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_3])]) ).
tff(f740,plain,
( spl22_37
<=> ! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ sgn_if(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_37])]) ).
tff(f779,plain,
( ( zero_zero(int) = sgn_sgn(int,zero_zero(int)) )
| ~ spl22_3
| ~ spl22_37 ),
inference(resolution,[],[f741,f590]) ).
tff(f590,plain,
( sgn_if(int)
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f588]) ).
tff(f741,plain,
( ! [X0: $tType] :
( ~ sgn_if(X0)
| ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) ) )
| ~ spl22_37 ),
inference(avatar_component_clause,[],[f740]) ).
tff(f778,plain,
spl22_46,
inference(avatar_split_clause,[],[f544,f776]) ).
tff(f776,plain,
( spl22_46
<=> ! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_46])]) ).
tff(f544,plain,
! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f381]) ).
tff(f381,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = sgn_sgn(X0,X1) )
| ( zero_zero(X0) != X1 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f774,plain,
spl22_45,
inference(avatar_split_clause,[],[f541,f772]) ).
tff(f772,plain,
( spl22_45
<=> ! [X0: $tType] :
( ( zero_zero(X0) = ring_1_of_int(X0,zero_zero(int)) )
| ~ ring_char_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_45])]) ).
tff(f541,plain,
! [X0: $tType] :
( ( zero_zero(X0) = ring_1_of_int(X0,zero_zero(int)) )
| ~ ring_char_0(X0) ),
inference(equality_resolution,[],[f373]) ).
tff(f373,plain,
! [X0: $tType,X1: int] :
( ( zero_zero(X0) = ring_1_of_int(X0,X1) )
| ( zero_zero(int) != X1 )
| ~ ring_char_0(X0) ),
inference(cnf_transformation,[],[f268]) ).
tff(f770,plain,
spl22_44,
inference(avatar_split_clause,[],[f443,f768]) ).
tff(f768,plain,
( spl22_44
<=> ! [X2: int,X0: list(int),X1: int] : ( zero_zero(nat) = size_size(atom,dvd(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_44])]) ).
tff(f443,plain,
! [X2: int,X0: list(int),X1: int] : ( zero_zero(nat) = size_size(atom,dvd(X2,X1,X0)) ),
inference(cnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: list(int),X1: int,X2: int] : ( zero_zero(nat) = size_size(atom,dvd(X2,X1,X0)) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X41: list(int),X42: int,X43: int] : ( zero_zero(nat) = size_size(atom,dvd(X43,X42,X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_atom_Osize_I5_J) ).
tff(f766,plain,
spl22_43,
inference(avatar_split_clause,[],[f422,f764]) ).
tff(f764,plain,
( spl22_43
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_43])]) ).
tff(f422,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType,X2: list(X0)] : ( map(X0,X0,combi(X0),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_map__ident) ).
tff(f762,plain,
spl22_42,
inference(avatar_split_clause,[],[f421,f760]) ).
tff(f760,plain,
( spl22_42
<=> ! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_42])]) ).
tff(f421,plain,
! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType,X1: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X1) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType,X48: fun(nat,bool)] : ( nil(X0) = sublist(X0,nil(X0),X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_sublist__nil) ).
tff(f758,plain,
spl22_41,
inference(avatar_split_clause,[],[f409,f756]) ).
tff(f756,plain,
( spl22_41
<=> ! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_41])]) ).
tff(f409,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ord_less(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X50: nat] :
( ( zero_zero(nat) != X50 )
=> ord_less(nat,zero_zero(nat),X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_gr0I) ).
tff(f754,plain,
spl22_40,
inference(avatar_split_clause,[],[f407,f752]) ).
tff(f752,plain,
( spl22_40
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ~ iszero(X0,X1)
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_40])]) ).
tff(f407,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ~ iszero(X0,X1)
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( iszero(X0,X1)
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ~ iszero(X0,X1) ) )
| ~ semiring_1(X0) ),
inference(nnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType] :
( ! [X1: X0] :
( iszero(X0,X1)
<=> ( zero_zero(X0) = X1 ) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] :
( semiring_1(X0)
=> ! [X1: X0] :
( iszero(X0,X1)
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ! [X5: X0] :
( iszero(X0,X5)
<=> ( zero_zero(X0) = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_iszero__def) ).
tff(f750,plain,
spl22_39,
inference(avatar_split_clause,[],[f371,f748]) ).
tff(f371,plain,
! [X0: $tType] :
( ( ring_1_of_int(X0,one_one(int)) = one_one(X0) )
| ~ ring_1(X0) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType] :
( ( ring_1_of_int(X0,one_one(int)) = one_one(X0) )
| ~ ring_1(X0) ),
inference(ennf_transformation,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( ring_1(X0)
=> ( ring_1_of_int(X0,one_one(int)) = one_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_of__int__1) ).
tff(f746,plain,
spl22_38,
inference(avatar_split_clause,[],[f370,f744]) ).
tff(f370,plain,
! [X0: $tType] :
( ( zero_zero(X0) = ring_1_of_int(X0,zero_zero(int)) )
| ~ ring_1(X0) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType] :
( ( zero_zero(X0) = ring_1_of_int(X0,zero_zero(int)) )
| ~ ring_1(X0) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( ring_1(X0)
=> ( zero_zero(X0) = ring_1_of_int(X0,zero_zero(int)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_of__int__0) ).
tff(f742,plain,
spl22_37,
inference(avatar_split_clause,[],[f369,f740]) ).
tff(f369,plain,
! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ sgn_if(X0) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ sgn_if(X0) ),
inference(ennf_transformation,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType] :
( sgn_if(X0)
=> ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_sgn0) ).
tff(f738,plain,
spl22_36,
inference(avatar_split_clause,[],[f556,f736]) ).
tff(f736,plain,
( spl22_36
<=> ! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != cons(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_36])]) ).
tff(f556,plain,
! [X0: $tType,X2: X0,X3: list(X0)] : ( nil(X0) != cons(X0,X2,X3) ),
inference(equality_resolution,[],[f434]) ).
tff(f434,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: list(X0)] :
( ( nil(X0) != X1 )
| ( cons(X0,X2,X3) != X1 ) ),
inference(cnf_transformation,[],[f292]) ).
tff(f734,plain,
spl22_35,
inference(avatar_split_clause,[],[f452,f732]) ).
tff(f732,plain,
( spl22_35
<=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_35])]) ).
tff(f452,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f294]) ).
tff(f730,plain,
spl22_34,
inference(avatar_split_clause,[],[f442,f728]) ).
tff(f728,plain,
( spl22_34
<=> ! [X2: int,X0: list(int),X1: int] : ( zero_zero(nat) = atom_size(dvd(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_34])]) ).
tff(f442,plain,
! [X2: int,X0: list(int),X1: int] : ( zero_zero(nat) = atom_size(dvd(X2,X1,X0)) ),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: list(int),X1: int,X2: int] : ( zero_zero(nat) = atom_size(dvd(X2,X1,X0)) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X41: list(int),X42: int,X43: int] : ( atom_size(dvd(X43,X42,X41)) = zero_zero(nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_atom_Osize_I2_J) ).
tff(f726,plain,
spl22_33,
inference(avatar_split_clause,[],[f441,f724]) ).
tff(f724,plain,
( spl22_33
<=> ! [X2: int,X0: atom,X1: list(int)] : ( divisor(X0) = divisor(asubst(X2,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_33])]) ).
tff(f441,plain,
! [X2: int,X0: atom,X1: list(int)] : ( divisor(X0) = divisor(asubst(X2,X1,X0)) ),
inference(cnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: atom,X1: list(int),X2: int] : ( divisor(X0) = divisor(asubst(X2,X1,X0)) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X7: atom,X14: list(int),X15: int] : ( divisor(X7) = divisor(asubst(X15,X14,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_divisor__asubst) ).
tff(f722,plain,
spl22_32,
inference(avatar_split_clause,[],[f420,f720]) ).
tff(f420,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X0: $tType,X57: X0] : ( aa(X0,X0,combi(X0),X57) = X57 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f718,plain,
spl22_31,
inference(avatar_split_clause,[],[f406,f716]) ).
tff(f716,plain,
( spl22_31
<=> ! [X0: $tType] :
( member(X0,zero_zero(X0),semiring_1_Nats(X0))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_31])]) ).
tff(f406,plain,
! [X0: $tType] :
( member(X0,zero_zero(X0),semiring_1_Nats(X0))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType] :
( member(X0,zero_zero(X0),semiring_1_Nats(X0))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> member(X0,zero_zero(X0),semiring_1_Nats(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Nats__0) ).
tff(f714,plain,
spl22_30,
inference(avatar_split_clause,[],[f405,f712]) ).
tff(f712,plain,
( spl22_30
<=> ! [X0: $tType] :
( member(X0,one_one(X0),semiring_1_Nats(X0))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_30])]) ).
tff(f405,plain,
! [X0: $tType] :
( member(X0,one_one(X0),semiring_1_Nats(X0))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( member(X0,one_one(X0),semiring_1_Nats(X0))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> member(X0,one_one(X0),semiring_1_Nats(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Nats__1) ).
tff(f710,plain,
spl22_29,
inference(avatar_split_clause,[],[f402,f708]) ).
tff(f708,plain,
( spl22_29
<=> ! [X0: $tType] :
( ord_less(X0,zero_zero(X0),one_one(X0))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_29])]) ).
tff(f402,plain,
! [X0: $tType] :
( ord_less(X0,zero_zero(X0),one_one(X0))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType] :
( ord_less(X0,zero_zero(X0),one_one(X0))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ord_less(X0,zero_zero(X0),one_one(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_zero__less__one) ).
tff(f706,plain,
spl22_28,
inference(avatar_split_clause,[],[f401,f704]) ).
tff(f704,plain,
( spl22_28
<=> ! [X0: $tType] :
( ~ ord_less(X0,one_one(X0),zero_zero(X0))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_28])]) ).
tff(f401,plain,
! [X0: $tType] :
( ~ ord_less(X0,one_one(X0),zero_zero(X0))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType] :
( ~ ord_less(X0,one_one(X0),zero_zero(X0))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ~ ord_less(X0,one_one(X0),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_not__one__less__zero) ).
tff(f702,plain,
spl22_27,
inference(avatar_split_clause,[],[f438,f700]) ).
tff(f700,plain,
( spl22_27
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : listMem(X0,X2,cons(X0,X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_27])]) ).
tff(f438,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : listMem(X0,X2,cons(X0,X2,X1)),
inference(cnf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType,X1: list(X0),X2: X0] : listMem(X0,X2,cons(X0,X2,X1)),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X35: list(X0),X36: X0] : listMem(X0,X36,cons(X0,X36,X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_elem) ).
tff(f698,plain,
spl22_26,
inference(avatar_split_clause,[],[f437,f696]) ).
tff(f696,plain,
( spl22_26
<=> ! [X2: int,X0: list(int),X1: int] : ( divisor(dvd(X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_26])]) ).
tff(f437,plain,
! [X2: int,X0: list(int),X1: int] : ( divisor(dvd(X2,X1,X0)) = X2 ),
inference(cnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: list(int),X1: int,X2: int] : ( divisor(dvd(X2,X1,X0)) = X2 ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X14: list(int),X15: int,X40: int] : ( divisor(dvd(X40,X15,X14)) = X40 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_divisor_Osimps_I2_J) ).
tff(f694,plain,
spl22_25,
inference(avatar_split_clause,[],[f435,f692]) ).
tff(f692,plain,
( spl22_25
<=> ! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_25])]) ).
tff(f435,plain,
! [X0: $tType,X2: X0,X1: list(X0)] : ( cons(X0,X2,X1) != X1 ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType,X1: list(X0),X2: X0] : ( cons(X0,X2,X1) != X1 ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType,X35: list(X0),X36: X0] : ( cons(X0,X36,X35) != X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_not__Cons__self2) ).
tff(f690,plain,
spl22_24,
inference(avatar_split_clause,[],[f399,f688]) ).
tff(f688,plain,
( spl22_24
<=> ! [X0: $tType] :
( ( zero_zero(X0) != one_one(X0) )
| ~ zero_neq_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_24])]) ).
tff(f399,plain,
! [X0: $tType] :
( ( zero_zero(X0) != one_one(X0) )
| ~ zero_neq_one(X0) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType] :
( ( zero_zero(X0) != one_one(X0) )
| ~ zero_neq_one(X0) ),
inference(ennf_transformation,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType] :
( zero_neq_one(X0)
=> ( zero_zero(X0) != one_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_one__neq__zero) ).
tff(f686,plain,
spl22_23,
inference(avatar_split_clause,[],[f404,f684]) ).
tff(f684,plain,
( spl22_23
<=> ! [X0: $tType] :
( iszero(X0,zero_zero(X0))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_23])]) ).
tff(f404,plain,
! [X0: $tType] :
( iszero(X0,zero_zero(X0))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType] :
( iszero(X0,zero_zero(X0))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> iszero(X0,zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_iszero__0) ).
tff(f682,plain,
spl22_22,
inference(avatar_split_clause,[],[f403,f680]) ).
tff(f680,plain,
( spl22_22
<=> ! [X0: $tType] :
( ~ iszero(X0,one_one(X0))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_22])]) ).
tff(f403,plain,
! [X0: $tType] :
( ~ iszero(X0,one_one(X0))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ~ iszero(X0,one_one(X0))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ~ iszero(X0,one_one(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_not__iszero__1) ).
tff(f678,plain,
spl22_21,
inference(avatar_split_clause,[],[f354,f675]) ).
tff(f675,plain,
( spl22_21
<=> ( one_one(int) = zlcms(nil(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_21])]) ).
tff(f354,plain,
one_one(int) = zlcms(nil(int)),
inference(cnf_transformation,[],[f43]) ).
tff(f43,axiom,
one_one(int) = zlcms(nil(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_zlcms_Osimps_I1_J) ).
tff(f673,plain,
spl22_20,
inference(avatar_split_clause,[],[f419,f671]) ).
tff(f671,plain,
( spl22_20
<=> ! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_20])]) ).
tff(f419,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType,X1: fun(X0,bool)] : ~ list_ex1(X0,X1,nil(X0)),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType,X20: fun(X0,bool)] : ~ list_ex1(X0,X20,nil(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_list__ex1__simps_I1_J) ).
tff(f669,plain,
spl22_19,
inference(avatar_split_clause,[],[f364,f667]) ).
tff(f667,plain,
( spl22_19
<=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_19])]) ).
tff(f364,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(cnf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X50: nat] : ~ ord_less(nat,X50,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_less__zeroE) ).
tff(f665,plain,
spl22_18,
inference(avatar_split_clause,[],[f362,f663]) ).
tff(f362,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X50: nat] : ~ ord_less(nat,X50,X50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_less__irrefl__nat) ).
tff(f661,plain,
spl22_17,
inference(avatar_split_clause,[],[f353,f658]) ).
tff(f658,plain,
( spl22_17
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_17])]) ).
tff(f353,plain,
pp(fTrue),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f656,plain,
spl22_16,
inference(avatar_split_clause,[],[f352,f653]) ).
tff(f653,plain,
( spl22_16
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_16])]) ).
tff(f352,plain,
semiring_1(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f651,plain,
spl22_15,
inference(avatar_split_clause,[],[f351,f648]) ).
tff(f648,plain,
( spl22_15
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_15])]) ).
tff(f351,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
tff(f646,plain,
spl22_14,
inference(avatar_split_clause,[],[f350,f643]) ).
tff(f643,plain,
( spl22_14
<=> zero_neq_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_14])]) ).
tff(f350,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
tff(f641,plain,
spl22_13,
inference(avatar_split_clause,[],[f349,f638]) ).
tff(f638,plain,
( spl22_13
<=> linordered_semidom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_13])]) ).
tff(f349,plain,
linordered_semidom(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
tff(f636,plain,
spl22_12,
inference(avatar_split_clause,[],[f348,f633]) ).
tff(f633,plain,
( spl22_12
<=> linordered_semidom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_12])]) ).
tff(f348,plain,
linordered_semidom(nat),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
tff(f631,plain,
spl22_11,
inference(avatar_split_clause,[],[f347,f628]) ).
tff(f628,plain,
( spl22_11
<=> zero_neq_one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_11])]) ).
tff(f347,plain,
zero_neq_one(nat),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
tff(f626,plain,
spl22_10,
inference(avatar_split_clause,[],[f346,f623]) ).
tff(f623,plain,
( spl22_10
<=> one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_10])]) ).
tff(f346,plain,
one(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
tff(f621,plain,
spl22_9,
inference(avatar_split_clause,[],[f345,f618]) ).
tff(f618,plain,
( spl22_9
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_9])]) ).
tff(f345,plain,
zero(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f616,plain,
spl22_8,
inference(avatar_split_clause,[],[f344,f613]) ).
tff(f613,plain,
( spl22_8
<=> one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_8])]) ).
tff(f344,plain,
one(nat),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
tff(f611,plain,
spl22_7,
inference(avatar_split_clause,[],[f343,f608]) ).
tff(f608,plain,
( spl22_7
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_7])]) ).
tff(f343,plain,
zero(nat),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f606,plain,
spl22_6,
inference(avatar_split_clause,[],[f342,f603]) ).
tff(f603,plain,
( spl22_6
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_6])]) ).
tff(f342,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f601,plain,
spl22_5,
inference(avatar_split_clause,[],[f341,f598]) ).
tff(f598,plain,
( spl22_5
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_5])]) ).
tff(f341,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
ring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
tff(f596,plain,
spl22_4,
inference(avatar_split_clause,[],[f340,f593]) ).
tff(f340,plain,
ring_1(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
ring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
tff(f591,plain,
spl22_3,
inference(avatar_split_clause,[],[f339,f588]) ).
tff(f339,plain,
sgn_if(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
sgn_if(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Osgn__if) ).
tff(f586,plain,
~ spl22_2,
inference(avatar_split_clause,[],[f338,f583]) ).
tff(f583,plain,
( spl22_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_2])]) ).
tff(f338,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
tff(f581,plain,
spl22_1,
inference(avatar_split_clause,[],[f337,f578]) ).
tff(f337,plain,
zero_zero(int) = aa(atom,int,hd_coeff,b),
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
zero_zero(int) = aa(atom,int,hd_coeff,b),
inference(flattening,[],[f117]) ).
tff(f117,negated_conjecture,
( ~ zero_zero(int) != aa(atom,int,hd_coeff,b) ),
inference(negated_conjecture,[],[f116]) ).
tff(f116,conjecture,
zero_zero(int) != aa(atom,int,hd_coeff,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM122_5 : TPTP v8.1.2. Released v6.0.0.
% 0.11/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n019.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 : Fri May 3 21:24:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (9013)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (9016)WARNING: value z3 for option sas not known
% 0.13/0.37 % (9014)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (9015)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 % (9017)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (9016)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 % (9018)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 % (9019)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 % (9020)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 % (9020)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39 % (9021)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.39 % (9023)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)
% 0.13/0.39 % (9022)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)
% 0.13/0.39 % (9021)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.39 % Exception at run slice level
% 0.13/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39 % (9022)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.40 % (9018)First to succeed.
% 0.13/0.40 % (9019)Also succeeded, but the first one will report.
% 0.13/0.41 % (9024)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.20/0.41 % (9018)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9013"
% 0.20/0.41 % (9018)Refutation found. Thanks to Tanya!
% 0.20/0.41 % SZS status Theorem for theBenchmark
% 0.20/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.42 % (9018)------------------------------
% 0.20/0.42 % (9018)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.42 % (9018)Termination reason: Refutation
% 0.20/0.42
% 0.20/0.42 % (9018)Memory used [KB]: 1457
% 0.20/0.42 % (9018)Time elapsed: 0.043 s
% 0.20/0.42 % (9018)Instructions burned: 70 (million)
% 0.20/0.42 % (9013)Success in time 0.063 s
%------------------------------------------------------------------------------