TSTP Solution File: LCL773_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL773_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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:49:14 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 274
% Syntax : Number of formulae : 703 ( 217 unt; 59 typ; 0 def)
% Number of atoms : 1461 ( 392 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1328 ( 511 ~; 494 |; 90 &)
% ( 163 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 74 ( 40 >; 34 *; 0 +; 0 <<)
% Number of predicates : 143 ( 141 usr; 128 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 6 con; 0-5 aty)
% Number of variables : 928 ( 858 !; 49 ?; 928 :)
% ( 21 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
dB: $tType ).
tff(type_def_8,type,
list: $tType > $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
char: $tType ).
tff(type_def_11,type,
literal: $tType ).
tff(type_def_12,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
sgn_sgn:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
bool_size: bool > nat ).
tff(func_def_3,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
it: fun(dB,bool) ).
tff(func_def_5,type,
abs: dB > dB ).
tff(func_def_6,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_7,type,
var: nat > dB ).
tff(func_def_8,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_9,type,
dB_rec:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,fun(X0,fun(X0,X0)))) * fun(dB,fun(X0,X0)) * dB ) > X0 ) ).
tff(func_def_10,type,
dB_size: dB > nat ).
tff(func_def_11,type,
lift: ( dB * nat ) > dB ).
tff(func_def_12,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_13,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_14,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_15,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_16,type,
nat_size: nat > nat ).
tff(func_def_17,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_18,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_19,type,
char_size: char > nat ).
tff(func_def_20,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
i: nat ).
tff(func_def_24,type,
r: dB ).
tff(func_def_25,type,
sK4: int > nat ).
tff(func_def_26,type,
sK5: dB > dB ).
tff(func_def_27,type,
sK6: dB > list(dB) ).
tff(func_def_28,type,
sK7: dB > nat ).
tff(func_def_29,type,
sK8: dB > dB ).
tff(func_def_30,type,
sK9: dB > dB ).
tff(func_def_31,type,
sK10: dB > list(dB) ).
tff(func_def_32,type,
sK11: ( dB * dB ) > dB ).
tff(func_def_33,type,
sK12: ( dB * dB * dB ) > dB ).
tff(func_def_34,type,
sK13: ( dB * dB * dB ) > dB ).
tff(func_def_35,type,
sK14: ( dB * dB * dB ) > dB ).
tff(func_def_36,type,
sK15:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
sgn_if:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_8,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_9,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_10,type,
pp: bool > $o ).
tff(pred_def_11,type,
sP0: dB > $o ).
tff(pred_def_12,type,
sP1: dB > $o ).
tff(pred_def_13,type,
sP2: ( dB * dB * dB ) > $o ).
tff(pred_def_14,type,
sP3: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).
tff(f1350,plain,
$false,
inference(avatar_sat_refutation,[],[f557,f562,f567,f572,f577,f582,f587,f592,f597,f602,f607,f612,f617,f623,f627,f631,f635,f640,f646,f650,f654,f658,f664,f668,f674,f679,f683,f688,f693,f698,f703,f708,f722,f727,f731,f735,f739,f743,f747,f751,f755,f759,f763,f768,f773,f778,f785,f793,f797,f801,f806,f810,f816,f820,f824,f828,f832,f849,f853,f857,f861,f865,f869,f873,f877,f882,f903,f907,f917,f921,f925,f929,f933,f943,f948,f952,f956,f960,f964,f981,f986,f990,f994,f998,f1002,f1006,f1010,f1014,f1018,f1023,f1048,f1052,f1060,f1064,f1068,f1072,f1076,f1080,f1084,f1088,f1130,f1134,f1138,f1142,f1146,f1150,f1159,f1163,f1167,f1171,f1175,f1180,f1185,f1221,f1254,f1258,f1262,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1340,f1348,f1349]) ).
tff(f1349,plain,
( ~ spl16_26
| spl16_14
| ~ spl16_122 ),
inference(avatar_split_clause,[],[f1323,f1300,f620,f676]) ).
tff(f676,plain,
( spl16_26
<=> pp(aa(dB,bool,it,r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_26])]) ).
tff(f620,plain,
( spl16_14
<=> pp(aa(dB,bool,it,subst(r,var(i),bool_size(fTrue)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_14])]) ).
tff(f1300,plain,
( spl16_122
<=> ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,subst(X2,var(X1),X0)))
| ~ pp(aa(dB,bool,it,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_122])]) ).
tff(f1323,plain,
( ~ pp(aa(dB,bool,it,r))
| spl16_14
| ~ spl16_122 ),
inference(resolution,[],[f1301,f622]) ).
tff(f622,plain,
( ~ pp(aa(dB,bool,it,subst(r,var(i),bool_size(fTrue))))
| spl16_14 ),
inference(avatar_component_clause,[],[f620]) ).
tff(f1301,plain,
( ! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,subst(X2,var(X1),X0)))
| ~ pp(aa(dB,bool,it,X2)) )
| ~ spl16_122 ),
inference(avatar_component_clause,[],[f1300]) ).
tff(f1348,plain,
spl16_127,
inference(avatar_split_clause,[],[f475,f1346]) ).
tff(f1346,plain,
( spl16_127
<=> ! [X0: list(dB),X3: dB,X2: list(dB),X1: dB] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_127])]) ).
tff(f475,plain,
! [X2: list(dB),X3: dB,X0: list(dB),X1: dB] :
( ( X1 = X3 )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
inference(flattening,[],[f313]) ).
tff(f313,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
| ( X0 != X2 )
| ( X1 != X3 ) )
& ( ( ( X0 = X2 )
& ( X1 = X3 ) )
| ( foldl(dB,dB,app,abs(X1),X0) != foldl(dB,dB,app,abs(X3),X2) ) ) ),
inference(nnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: dB] :
( ( foldl(dB,dB,app,abs(X1),X0) = foldl(dB,dB,app,abs(X3),X2) )
<=> ( ( X0 = X2 )
& ( X1 = X3 ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X39: list(dB),X40: dB,X42: list(dB),X41: dB] :
( ( foldl(dB,dB,app,abs(X41),X42) = foldl(dB,dB,app,abs(X40),X39) )
<=> ( ( X39 = X42 )
& ( X40 = X41 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Abs__apps__eq__Abs__apps__conv) ).
tff(f1340,plain,
spl16_126,
inference(avatar_split_clause,[],[f321,f1337]) ).
tff(f1337,plain,
( spl16_126
<=> pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,r),var(i)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_126])]) ).
tff(f321,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,r),var(i)))),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,r),var(i)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f1314,plain,
spl16_125,
inference(avatar_split_clause,[],[f466,f1312]) ).
tff(f1312,plain,
( spl16_125
<=> ! [X2: dB,X0: dB,X1: list(dB)] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_125])]) ).
tff(f466,plain,
! [X2: dB,X0: dB,X1: list(dB)] :
( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( foldl(dB,dB,app,X2,X1) != foldl(dB,dB,app,X0,X1) ) ) ),
inference(nnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: dB,X1: list(dB),X2: dB] :
( ( foldl(dB,dB,app,X2,X1) = foldl(dB,dB,app,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X40: dB,X44: list(dB),X41: dB] :
( ( foldl(dB,dB,app,X41,X44) = foldl(dB,dB,app,X40,X44) )
<=> ( X40 = X41 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_apps__eq__tail__conv) ).
tff(f1310,plain,
( spl16_124
| ~ spl16_40
| ~ spl16_64 ),
inference(avatar_split_clause,[],[f895,f871,f749,f1308]) ).
tff(f1308,plain,
( spl16_124
<=> ! [X0: nat] : sP1(abs(var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_124])]) ).
tff(f749,plain,
( spl16_40
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_40])]) ).
tff(f871,plain,
( spl16_64
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_64])]) ).
tff(f895,plain,
( ! [X0: nat] : sP1(abs(var(X0)))
| ~ spl16_40
| ~ spl16_64 ),
inference(resolution,[],[f872,f750]) ).
tff(f750,plain,
( ! [X0: nat] : pp(aa(dB,bool,it,var(X0)))
| ~ spl16_40 ),
inference(avatar_component_clause,[],[f749]) ).
tff(f872,plain,
( ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) )
| ~ spl16_64 ),
inference(avatar_component_clause,[],[f871]) ).
tff(f1306,plain,
spl16_123,
inference(avatar_split_clause,[],[f461,f1304]) ).
tff(f1304,plain,
( spl16_123
<=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_123])]) ).
tff(f461,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,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) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f308]) ).
tff(f308,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) )
| ~ sP3(X2,X1,X0) ),
inference(nnf_transformation,[],[f265]) ).
tff(f265,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) )
| ~ sP3(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f1302,plain,
spl16_122,
inference(avatar_split_clause,[],[f452,f1300]) ).
tff(f452,plain,
! [X2: dB,X0: nat,X1: nat] :
( pp(aa(dB,bool,it,subst(X2,var(X1),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,subst(X2,var(X1),X0)))
| ~ pp(aa(dB,bool,it,X2)) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: nat,X1: nat,X2: dB] :
( pp(aa(dB,bool,it,X2))
=> pp(aa(dB,bool,it,subst(X2,var(X1),X0))) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X4: nat,X5: nat,X6: dB] :
( pp(aa(dB,bool,it,X6))
=> pp(aa(dB,bool,it,subst(X6,var(X5),X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_subst__Var__IT) ).
tff(f1298,plain,
spl16_121,
inference(avatar_split_clause,[],[f448,f1296]) ).
tff(f1296,plain,
( spl16_121
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( beta(foldl(dB,dB,app,X2,X0),foldl(dB,dB,app,X1,X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_121])]) ).
tff(f448,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( beta(foldl(dB,dB,app,X2,X0),foldl(dB,dB,app,X1,X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( beta(foldl(dB,dB,app,X2,X0),foldl(dB,dB,app,X1,X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(foldl(dB,dB,app,X2,X0),foldl(dB,dB,app,X1,X0)) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X39: list(dB),X40: dB,X41: dB] :
( beta(X41,X40)
=> beta(foldl(dB,dB,app,X41,X39),foldl(dB,dB,app,X40,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_apps__preserves__beta) ).
tff(f1294,plain,
spl16_120,
inference(avatar_split_clause,[],[f416,f1292]) ).
tff(f1292,plain,
( spl16_120
<=> ! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_120])]) ).
tff(f416,plain,
! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: nat,X1: list(dB)] :
( pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1)))
| ~ listsp(dB,it,X1) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: nat,X1: list(dB)] :
( listsp(dB,it,X1)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X0),X1))) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X32: nat,X42: list(dB)] :
( listsp(dB,it,X42)
=> pp(aa(dB,bool,it,foldl(dB,dB,app,var(X32),X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_IT_OVar) ).
tff(f1290,plain,
spl16_119,
inference(avatar_split_clause,[],[f393,f1288]) ).
tff(f1288,plain,
( spl16_119
<=> ! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_119])]) ).
tff(f393,plain,
! [X0: dB] :
( sP0(X0)
| pp(aa(dB,bool,it,sK5(X0)))
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ( pp(aa(dB,bool,it,sK5(X0)))
& ( abs(sK5(X0)) = X0 ) )
| ( listsp(dB,it,sK6(X0))
& ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f280,f282,f281]) ).
tff(f281,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK5(X0)))
& ( abs(sK5(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f282,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK6(X0))
& ( foldl(dB,dB,app,var(sK7(X0)),sK6(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f280,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) )
& ! [X2: list(dB),X3: nat] :
( ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(rectify,[],[f279]) ).
tff(f279,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(flattening,[],[f278]) ).
tff(f278,plain,
! [X0: dB] :
( ( sP1(X0)
| ( ~ sP0(X0)
& ! [X4: dB] :
( ~ pp(aa(dB,bool,it,X4))
| ( abs(X4) != X0 ) )
& ! [X5: list(dB),X6: nat] :
( ~ listsp(dB,it,X5)
| ( foldl(dB,dB,app,var(X6),X5) != X0 ) ) ) )
& ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
| ~ sP1(X0) ) ),
inference(nnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: dB] :
( sP1(X0)
<=> ( sP0(X0)
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1286,plain,
spl16_118,
inference(avatar_split_clause,[],[f468,f1284]) ).
tff(f1284,plain,
( spl16_118
<=> ! [X2: list(dB),X0: list(dB),X1: dB,X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_118])]) ).
tff(f468,plain,
! [X2: list(dB),X3: nat,X0: list(dB),X1: dB] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: list(dB),X1: dB,X2: list(dB),X3: nat] : ( foldl(dB,dB,app,var(X3),X2) != foldl(dB,dB,app,abs(X1),X0) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X39: list(dB),X41: dB,X44: list(dB),X32: nat] : ( foldl(dB,dB,app,var(X32),X44) != foldl(dB,dB,app,abs(X41),X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Var__apps__neq__Abs__apps) ).
tff(f1262,plain,
( spl16_117
| ~ spl16_23
| ~ spl16_113 ),
inference(avatar_split_clause,[],[f1186,f1183,f661,f1260]) ).
tff(f1260,plain,
( spl16_117
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( subst(sK12(X0,X1,X2),X2,bool_size(fFalse)) = X1 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_117])]) ).
tff(f661,plain,
( spl16_23
<=> ( bool_size(fTrue) = bool_size(fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_23])]) ).
tff(f1183,plain,
( spl16_113
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( subst(sK12(X0,X1,X2),X2,bool_size(fTrue)) = X1 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_113])]) ).
tff(f1186,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( subst(sK12(X0,X1,X2),X2,bool_size(fFalse)) = X1 )
| ~ sP2(X0,X1,X2) )
| ~ spl16_23
| ~ spl16_113 ),
inference(forward_demodulation,[],[f1184,f663]) ).
tff(f663,plain,
( ( bool_size(fTrue) = bool_size(fFalse) )
| ~ spl16_23 ),
inference(avatar_component_clause,[],[f661]) ).
tff(f1184,plain,
( ! [X2: dB,X0: dB,X1: dB] :
( ( subst(sK12(X0,X1,X2),X2,bool_size(fTrue)) = X1 )
| ~ sP2(X0,X1,X2) )
| ~ spl16_113 ),
inference(avatar_component_clause,[],[f1183]) ).
tff(f1258,plain,
( spl16_116
| ~ spl16_23
| ~ spl16_112 ),
inference(avatar_split_clause,[],[f1181,f1178,f661,f1256]) ).
tff(f1256,plain,
( spl16_116
<=> ! [X0: $tType,X1: nat] :
( ord_less(nat,bool_size(fFalse),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_116])]) ).
tff(f1178,plain,
( spl16_112
<=> ! [X0: $tType,X1: nat] :
( ord_less(nat,bool_size(fTrue),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_112])]) ).
tff(f1181,plain,
( ! [X0: $tType,X1: nat] :
( ord_less(nat,bool_size(fFalse),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) )
| ~ spl16_23
| ~ spl16_112 ),
inference(forward_demodulation,[],[f1179,f663]) ).
tff(f1179,plain,
( ! [X0: $tType,X1: nat] :
( ord_less(nat,bool_size(fTrue),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) )
| ~ spl16_112 ),
inference(avatar_component_clause,[],[f1178]) ).
tff(f1254,plain,
( spl16_115
| ~ spl16_23
| ~ spl16_111 ),
inference(avatar_split_clause,[],[f1176,f1173,f661,f1252]) ).
tff(f1252,plain,
( spl16_115
<=> ! [X0: $tType,X1: nat] :
( ~ ord_less(nat,bool_size(fFalse),X1)
| ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_115])]) ).
tff(f1173,plain,
( spl16_111
<=> ! [X0: $tType,X1: nat] :
( ~ ord_less(nat,bool_size(fTrue),X1)
| ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_111])]) ).
tff(f1176,plain,
( ! [X0: $tType,X1: nat] :
( ~ ord_less(nat,bool_size(fFalse),X1)
| ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) )
| ~ spl16_23
| ~ spl16_111 ),
inference(forward_demodulation,[],[f1174,f663]) ).
tff(f1174,plain,
( ! [X0: $tType,X1: nat] :
( ~ ord_less(nat,bool_size(fTrue),X1)
| ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) )
| ~ spl16_111 ),
inference(avatar_component_clause,[],[f1173]) ).
tff(f1221,plain,
( spl16_114
| ~ spl16_39
| ~ spl16_52 ),
inference(avatar_split_clause,[],[f1151,f808,f745,f1219]) ).
tff(f1219,plain,
( spl16_114
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ~ sP1(subst(r,var(i),bool_size(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_114])]) ).
tff(f745,plain,
( spl16_39
<=> ! [X0: bool] :
( ~ pp(aa(dB,bool,it,subst(r,var(i),bool_size(X0))))
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_39])]) ).
tff(f808,plain,
( spl16_52
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_52])]) ).
tff(f1151,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ~ sP1(subst(r,var(i),bool_size(X0))) )
| ~ spl16_39
| ~ spl16_52 ),
inference(resolution,[],[f746,f809]) ).
tff(f809,plain,
( ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
| ~ spl16_52 ),
inference(avatar_component_clause,[],[f808]) ).
tff(f746,plain,
( ! [X0: bool] :
( ~ pp(aa(dB,bool,it,subst(r,var(i),bool_size(X0))))
| ( fFalse = X0 ) )
| ~ spl16_39 ),
inference(avatar_component_clause,[],[f745]) ).
tff(f1185,plain,
spl16_113,
inference(avatar_split_clause,[],[f550,f1183]) ).
tff(f550,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( subst(sK12(X0,X1,X2),X2,bool_size(fTrue)) = X1 )
| ~ sP2(X0,X1,X2) ),
inference(forward_demodulation,[],[f453,f336]) ).
tff(f336,plain,
zero_zero(nat) = bool_size(fTrue),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
zero_zero(nat) = bool_size(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_bool_Osize_I1_J) ).
tff(f453,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( subst(sK12(X0,X1,X2),X2,zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: dB,X1: dB,X2: dB] :
( ( ( abs(sK12(X0,X1,X2)) = X0 )
& ( subst(sK12(X0,X1,X2),X2,zero_zero(nat)) = X1 ) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f301,f302]) ).
tff(f302,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( subst(X3,X2,zero_zero(nat)) = X1 ) )
=> ( ( abs(sK12(X0,X1,X2)) = X0 )
& ( subst(sK12(X0,X1,X2),X2,zero_zero(nat)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f301,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( subst(X3,X2,zero_zero(nat)) = X1 ) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f300]) ).
tff(f300,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( subst(X3,X1,zero_zero(nat)) = X0 ) )
| ~ sP2(X2,X0,X1) ),
inference(nnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( subst(X3,X1,zero_zero(nat)) = X0 ) )
| ~ sP2(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f1180,plain,
spl16_112,
inference(avatar_split_clause,[],[f534,f1178]) ).
tff(f534,plain,
! [X0: $tType,X1: nat] :
( ord_less(nat,bool_size(fTrue),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ),
inference(forward_demodulation,[],[f376,f336]) ).
tff(f376,plain,
! [X0: $tType,X1: nat] :
( ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: nat] :
( ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,zero_zero(nat),X1) )
& ( ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1)) ) )
| ~ linordered_semidom(X0) ),
inference(nnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( ! [X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
<=> ord_less(nat,zero_zero(nat),X1) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
<=> ord_less(nat,zero_zero(nat),X1) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X32: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X32))
<=> ord_less(nat,zero_zero(nat),X32) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_of__nat__0__less__iff) ).
tff(f1175,plain,
spl16_111,
inference(avatar_split_clause,[],[f533,f1173]) ).
tff(f533,plain,
! [X0: $tType,X1: nat] :
( ~ ord_less(nat,bool_size(fTrue),X1)
| ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ),
inference(forward_demodulation,[],[f377,f336]) ).
tff(f377,plain,
! [X0: $tType,X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,zero_zero(nat),X1)
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f1171,plain,
spl16_110,
inference(avatar_split_clause,[],[f442,f1169]) ).
tff(f1169,plain,
( spl16_110
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_110])]) ).
tff(f442,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X28: dB,X29: dB,X30: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X30),X29) != abs(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_dB_Osimps_I8_J) ).
tff(f1167,plain,
spl16_109,
inference(avatar_split_clause,[],[f440,f1165]) ).
tff(f1165,plain,
( spl16_109
<=> ! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_109])]) ).
tff(f440,plain,
! [X2: dB,X0: nat,X1: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: nat,X1: dB,X2: dB] : ( var(X0) != aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X19: nat,X17: dB,X18: dB] : ( var(X19) != aa(dB,dB,aa(dB,fun(dB,dB),app,X18),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_dB_Osimps_I5_J) ).
tff(f1163,plain,
spl16_108,
inference(avatar_split_clause,[],[f420,f1161]) ).
tff(f1161,plain,
( spl16_108
<=> ! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,lift(X1,X0)))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_108])]) ).
tff(f420,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,lift(X1,X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,lift(X1,X0)))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: nat,X1: dB] :
( pp(aa(dB,bool,it,X1))
=> pp(aa(dB,bool,it,lift(X1,X0))) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X5: nat,X10: dB] :
( pp(aa(dB,bool,it,X10))
=> pp(aa(dB,bool,it,lift(X10,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_lift__IT) ).
tff(f1159,plain,
spl16_107,
inference(avatar_split_clause,[],[f391,f1157]) ).
tff(f1157,plain,
( spl16_107
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_107])]) ).
tff(f391,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK5(X0)) = X0 )
| listsp(dB,it,sK6(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f1150,plain,
spl16_106,
inference(avatar_split_clause,[],[f379,f1148]) ).
tff(f1148,plain,
( spl16_106
<=> ! [X0: $tType,X2: nat,X1: nat] :
( ord_less(nat,X2,X1)
| ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_106])]) ).
tff(f379,plain,
! [X0: $tType,X2: nat,X1: nat] :
( ord_less(nat,X2,X1)
| ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] :
( ord_less(nat,X2,X1)
| ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat,X2: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
=> ord_less(nat,X2,X1) ) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X3: nat,X38: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X38),semiring_1_of_nat(X0,X3))
=> ord_less(nat,X38,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_of__nat__less__imp__less) ).
tff(f1146,plain,
spl16_105,
inference(avatar_split_clause,[],[f378,f1144]) ).
tff(f1144,plain,
( spl16_105
<=> ! [X0: $tType,X2: nat,X1: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,X2,X1)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_105])]) ).
tff(f378,plain,
! [X0: $tType,X2: nat,X1: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,X2,X1)
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,X2,X1) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat,X2: nat] :
( ord_less(nat,X2,X1)
=> ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X3: nat,X38: nat] :
( ord_less(nat,X38,X3)
=> ord_less(X0,semiring_1_of_nat(X0,X38),semiring_1_of_nat(X0,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__imp__of__nat__less) ).
tff(f1142,plain,
spl16_104,
inference(avatar_split_clause,[],[f368,f1140]) ).
tff(f1140,plain,
( spl16_104
<=> ! [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,[spl16_104])]) ).
tff(f368,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,[],[f269]) ).
tff(f269,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,[],[f222]) ).
tff(f222,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,[],[f144]) ).
tff(f144,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,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X31: X0] :
( ord_less(X0,sgn_sgn(X0,X31),zero_zero(X0))
<=> ord_less(X0,X31,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_sgn__less) ).
tff(f1138,plain,
spl16_103,
inference(avatar_split_clause,[],[f367,f1136]) ).
tff(f1136,plain,
( spl16_103
<=> ! [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,[spl16_103])]) ).
tff(f367,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,[],[f269]) ).
tff(f1134,plain,
spl16_102,
inference(avatar_split_clause,[],[f366,f1132]) ).
tff(f1132,plain,
( spl16_102
<=> ! [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,[spl16_102])]) ).
tff(f366,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,[],[f268]) ).
tff(f268,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,[],[f221]) ).
tff(f221,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,[],[f143]) ).
tff(f143,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,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X31: X0] :
( ord_less(X0,zero_zero(X0),sgn_sgn(X0,X31))
<=> ord_less(X0,zero_zero(X0),X31) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_sgn__greater) ).
tff(f1130,plain,
spl16_101,
inference(avatar_split_clause,[],[f365,f1128]) ).
tff(f1128,plain,
( spl16_101
<=> ! [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,[spl16_101])]) ).
tff(f365,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,[],[f268]) ).
tff(f1088,plain,
spl16_100,
inference(avatar_split_clause,[],[f486,f1086]) ).
tff(f1086,plain,
( spl16_100
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(dB,fun(dB,X0)),X2: fun(dB,X0),X1: nat] : ( aa(nat,X0,X4,X1) = dB_case(X0,X4,X3,X2,var(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_100])]) ).
tff(f486,plain,
! [X0: $tType,X2: fun(dB,X0),X3: fun(dB,fun(dB,X0)),X1: nat,X4: fun(nat,X0)] : ( aa(nat,X0,X4,X1) = dB_case(X0,X4,X3,X2,var(X1)) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType,X1: nat,X2: fun(dB,X0),X3: fun(dB,fun(dB,X0)),X4: fun(nat,X0)] : ( aa(nat,X0,X4,X1) = dB_case(X0,X4,X3,X2,var(X1)) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType,X12: nat,X21: fun(dB,X0),X22: fun(dB,fun(dB,X0)),X23: fun(nat,X0)] : ( dB_case(X0,X23,X22,X21,var(X12)) = aa(nat,X0,X23,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_dB_Osimps_I10_J) ).
tff(f1084,plain,
spl16_99,
inference(avatar_split_clause,[],[f485,f1082]) ).
tff(f1082,plain,
( spl16_99
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(dB,fun(dB,X0)),X2: fun(dB,X0),X1: dB] : ( dB_case(X0,X4,X3,X2,abs(X1)) = aa(dB,X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_99])]) ).
tff(f485,plain,
! [X0: $tType,X2: fun(dB,X0),X3: fun(dB,fun(dB,X0)),X1: dB,X4: fun(nat,X0)] : ( dB_case(X0,X4,X3,X2,abs(X1)) = aa(dB,X0,X2,X1) ),
inference(cnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType,X1: dB,X2: fun(dB,X0),X3: fun(dB,fun(dB,X0)),X4: fun(nat,X0)] : ( dB_case(X0,X4,X3,X2,abs(X1)) = aa(dB,X0,X2,X1) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X26: dB,X21: fun(dB,X0),X22: fun(dB,fun(dB,X0)),X23: fun(nat,X0)] : ( dB_case(X0,X23,X22,X21,abs(X26)) = aa(dB,X0,X21,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_dB_Osimps_I12_J) ).
tff(f1080,plain,
spl16_98,
inference(avatar_split_clause,[],[f484,f1078]) ).
tff(f1078,plain,
( spl16_98
<=> ! [X0: $tType,X4: fun(nat,X0),X3: fun(dB,fun(dB,fun(X0,fun(X0,X0)))),X2: fun(dB,fun(X0,X0)),X1: nat] : ( aa(nat,X0,X4,X1) = dB_rec(X0,X4,X3,X2,var(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_98])]) ).
tff(f484,plain,
! [X0: $tType,X2: fun(dB,fun(X0,X0)),X3: fun(dB,fun(dB,fun(X0,fun(X0,X0)))),X1: nat,X4: fun(nat,X0)] : ( aa(nat,X0,X4,X1) = dB_rec(X0,X4,X3,X2,var(X1)) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType,X1: nat,X2: fun(dB,fun(X0,X0)),X3: fun(dB,fun(dB,fun(X0,fun(X0,X0)))),X4: fun(nat,X0)] : ( aa(nat,X0,X4,X1) = dB_rec(X0,X4,X3,X2,var(X1)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType,X12: nat,X21: fun(dB,fun(X0,X0)),X22: fun(dB,fun(dB,fun(X0,fun(X0,X0)))),X23: fun(nat,X0)] : ( aa(nat,X0,X23,X12) = dB_rec(X0,X23,X22,X21,var(X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_dB_Orecs_I1_J) ).
tff(f1076,plain,
spl16_97,
inference(avatar_split_clause,[],[f446,f1074]) ).
tff(f1074,plain,
( spl16_97
<=> ! [X2: bool,X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| pp(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_97])]) ).
tff(f446,plain,
! [X2: bool,X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| pp(X2) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: nat,X1: nat,X2: bool] :
( ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| pp(X2) )
& ( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| ~ pp(X2) ) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: nat,X1: nat,X2: bool] :
( ( ~ pp(X2)
=> ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) ) )
& ( pp(X2)
=> ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) ) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X56: nat,X20: nat,X36: bool] :
( ( ~ pp(X36)
=> ( semiring_1_of_nat(int,X56) = semiring_1_of_nat(int,if(nat,X36,X20,X56)) ) )
& ( pp(X36)
=> ( semiring_1_of_nat(int,X20) = semiring_1_of_nat(int,if(nat,X36,X20,X56)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_int__if__cong) ).
tff(f1072,plain,
spl16_96,
inference(avatar_split_clause,[],[f445,f1070]) ).
tff(f1070,plain,
( spl16_96
<=> ! [X2: bool,X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| ~ pp(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_96])]) ).
tff(f445,plain,
! [X2: bool,X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| ~ pp(X2) ),
inference(cnf_transformation,[],[f245]) ).
tff(f1068,plain,
spl16_95,
inference(avatar_split_clause,[],[f385,f1066]) ).
tff(f1066,plain,
( spl16_95
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_95])]) ).
tff(f385,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X6: dB] :
( pp(aa(dB,bool,it,X6))
=> pp(aa(dB,bool,it,abs(X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Lambda) ).
tff(f1064,plain,
spl16_94,
inference(avatar_split_clause,[],[f369,f1062]) ).
tff(f1062,plain,
( spl16_94
<=> ! [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,[spl16_94])]) ).
tff(f369,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,[],[f224]) ).
tff(f224,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f223]) ).
tff(f223,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,[],[f145]) ).
tff(f145,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 != X2 )
=> ( ~ ord_less(X0,X2,X1)
=> ord_less(X0,X1,X2) ) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X34: X0,X35: X0] :
( ( X34 != X35 )
=> ( ~ ord_less(X0,X35,X34)
=> ord_less(X0,X34,X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_linorder__neqE__linordered__idom) ).
tff(f1060,plain,
( spl16_93
| ~ spl16_40
| ~ spl16_51 ),
inference(avatar_split_clause,[],[f834,f804,f749,f1058]) ).
tff(f1058,plain,
( spl16_93
<=> ! [X0: nat] : sP1(var(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_93])]) ).
tff(f804,plain,
( spl16_51
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_51])]) ).
tff(f834,plain,
( ! [X0: nat] : sP1(var(X0))
| ~ spl16_40
| ~ spl16_51 ),
inference(resolution,[],[f805,f750]) ).
tff(f805,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl16_51 ),
inference(avatar_component_clause,[],[f804]) ).
tff(f1052,plain,
( spl16_92
| ~ spl16_23
| ~ spl16_90 ),
inference(avatar_split_clause,[],[f1024,f1021,f661,f1050]) ).
tff(f1050,plain,
( spl16_92
<=> ! [X0: nat] :
( ord_less(nat,bool_size(fFalse),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_92])]) ).
tff(f1021,plain,
( spl16_90
<=> ! [X0: nat] :
( ord_less(nat,bool_size(fTrue),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_90])]) ).
tff(f1024,plain,
( ! [X0: nat] :
( ord_less(nat,bool_size(fFalse),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) )
| ~ spl16_23
| ~ spl16_90 ),
inference(forward_demodulation,[],[f1022,f663]) ).
tff(f1022,plain,
( ! [X0: nat] :
( ord_less(nat,bool_size(fTrue),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) )
| ~ spl16_90 ),
inference(avatar_component_clause,[],[f1021]) ).
tff(f1048,plain,
( spl16_91
| ~ spl16_23
| ~ spl16_89 ),
inference(avatar_split_clause,[],[f1019,f1016,f661,f1046]) ).
tff(f1046,plain,
( spl16_91
<=> ! [X0: nat] :
( ~ ord_less(nat,bool_size(fFalse),X0)
| ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_91])]) ).
tff(f1016,plain,
( spl16_89
<=> ! [X0: nat] :
( ~ ord_less(nat,bool_size(fTrue),X0)
| ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_89])]) ).
tff(f1019,plain,
( ! [X0: nat] :
( ~ ord_less(nat,bool_size(fFalse),X0)
| ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) )
| ~ spl16_23
| ~ spl16_89 ),
inference(forward_demodulation,[],[f1017,f663]) ).
tff(f1017,plain,
( ! [X0: nat] :
( ~ ord_less(nat,bool_size(fTrue),X0)
| ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) )
| ~ spl16_89 ),
inference(avatar_component_clause,[],[f1016]) ).
tff(f1023,plain,
spl16_90,
inference(avatar_split_clause,[],[f545,f1021]) ).
tff(f545,plain,
! [X0: nat] :
( ord_less(nat,bool_size(fTrue),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ),
inference(forward_demodulation,[],[f403,f336]) ).
tff(f403,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: nat] :
( ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,zero_zero(nat),X0) )
& ( ord_less(nat,zero_zero(nat),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
inference(nnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
<=> ord_less(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X32: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X32))
<=> ord_less(nat,zero_zero(nat),X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zero__less__int__conv) ).
tff(f1018,plain,
spl16_89,
inference(avatar_split_clause,[],[f544,f1016]) ).
tff(f544,plain,
! [X0: nat] :
( ~ ord_less(nat,bool_size(fTrue),X0)
| ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ),
inference(forward_demodulation,[],[f404,f336]) ).
tff(f404,plain,
! [X0: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,zero_zero(nat),X0) ),
inference(cnf_transformation,[],[f289]) ).
tff(f1014,plain,
spl16_88,
inference(avatar_split_clause,[],[f499,f1012]) ).
tff(f1012,plain,
( spl16_88
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_88])]) ).
tff(f499,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f394]) ).
tff(f394,plain,
! [X2: list(dB),X3: nat,X0: dB] :
( sP1(X0)
| ~ listsp(dB,it,X2)
| ( foldl(dB,dB,app,var(X3),X2) != X0 ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f1010,plain,
spl16_87,
inference(avatar_split_clause,[],[f473,f1008]) ).
tff(f1008,plain,
( spl16_87
<=> ! [X0: nat,X3: dB,X2: dB,X1: dB] :
( beta(subst(X3,X1,X0),subst(X2,X1,X0))
| ~ beta(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_87])]) ).
tff(f473,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] :
( beta(subst(X3,X1,X0),subst(X2,X1,X0))
| ~ beta(X3,X2) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( beta(subst(X3,X1,X0),subst(X2,X1,X0))
| ~ beta(X3,X2) ),
inference(ennf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: nat,X1: dB,X2: dB,X3: dB] :
( beta(X3,X2)
=> beta(subst(X3,X1,X0),subst(X2,X1,X0)) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X5: nat,X10: dB,X8: dB,X6: dB] :
( beta(X6,X8)
=> beta(subst(X6,X10,X5),subst(X8,X10,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_subst__preserves__beta) ).
tff(f1006,plain,
spl16_86,
inference(avatar_split_clause,[],[f451,f1004]) ).
tff(f1004,plain,
( spl16_86
<=> ! [X2: nat,X0: dB,X1: nat] :
( ( var(X2) = subst(var(X2),X0,X1) )
| ~ ord_less(nat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_86])]) ).
tff(f451,plain,
! [X2: nat,X0: dB,X1: nat] :
( ( var(X2) = subst(var(X2),X0,X1) )
| ~ ord_less(nat,X2,X1) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: dB,X1: nat,X2: nat] :
( ( var(X2) = subst(var(X2),X0,X1) )
| ~ ord_less(nat,X2,X1) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: dB,X1: nat,X2: nat] :
( ord_less(nat,X2,X1)
=> ( var(X2) = subst(var(X2),X0,X1) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X9: dB,X5: nat,X4: nat] :
( ord_less(nat,X4,X5)
=> ( var(X4) = subst(var(X4),X9,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_subst__lt) ).
tff(f1002,plain,
spl16_85,
inference(avatar_split_clause,[],[f433,f1000]) ).
tff(f1000,plain,
( spl16_85
<=> ! [X0: nat,X1: nat] :
( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_85])]) ).
tff(f433,plain,
! [X0: nat,X1: nat] :
( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,X1,X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: nat,X1: nat] :
( ( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,X1,X0) )
& ( ord_less(nat,X1,X0)
| ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: nat,X1: nat] :
( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
<=> ord_less(nat,X1,X0) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X56: nat,X20: nat] :
( ord_less(int,semiring_1_of_nat(int,X20),semiring_1_of_nat(int,X56))
<=> ord_less(nat,X20,X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_transfer__int__nat__relations_I2_J) ).
tff(f998,plain,
spl16_84,
inference(avatar_split_clause,[],[f432,f996]) ).
tff(f996,plain,
( spl16_84
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_84])]) ).
tff(f432,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
inference(cnf_transformation,[],[f298]) ).
tff(f994,plain,
spl16_83,
inference(avatar_split_clause,[],[f373,f992]) ).
tff(f992,plain,
( spl16_83
<=> ! [X0: $tType,X2: nat,X1: nat] :
( ( X1 = X2 )
| ( semiring_1_of_nat(X0,X1) != semiring_1_of_nat(X0,X2) )
| ~ semiring_char_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_83])]) ).
tff(f373,plain,
! [X0: $tType,X2: nat,X1: nat] :
( ( X1 = X2 )
| ( semiring_1_of_nat(X0,X1) != semiring_1_of_nat(X0,X2) )
| ~ semiring_char_0(X0) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] :
( ( ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( semiring_1_of_nat(X0,X1) != semiring_1_of_nat(X0,X2) ) ) )
| ~ semiring_char_0(X0) ),
inference(nnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] :
( ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
<=> ( X1 = X2 ) )
| ~ semiring_char_0(X0) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType] :
( semiring_char_0(X0)
=> ! [X1: nat,X2: nat] :
( ( semiring_1_of_nat(X0,X1) = semiring_1_of_nat(X0,X2) )
<=> ( X1 = X2 ) ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X0: $tType] :
( semiring_char_0(X0)
=> ! [X32: nat,X37: nat] :
( ( semiring_1_of_nat(X0,X32) = semiring_1_of_nat(X0,X37) )
<=> ( X32 = X37 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_of__nat__eq__iff) ).
tff(f990,plain,
spl16_82,
inference(avatar_split_clause,[],[f363,f988]) ).
tff(f988,plain,
( spl16_82
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != sgn_sgn(X0,X1) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_82])]) ).
tff(f363,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != sgn_sgn(X0,X1) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,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,[],[f220]) ).
tff(f220,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = sgn_sgn(X0,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = sgn_sgn(X0,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X31: X0] :
( ( zero_zero(X0) = sgn_sgn(X0,X31) )
<=> ( zero_zero(X0) = X31 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_sgn__0__0) ).
tff(f986,plain,
( spl16_81
| ~ spl16_26
| ~ spl16_64 ),
inference(avatar_split_clause,[],[f896,f871,f676,f983]) ).
tff(f983,plain,
( spl16_81
<=> sP1(abs(r)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_81])]) ).
tff(f896,plain,
( sP1(abs(r))
| ~ spl16_26
| ~ spl16_64 ),
inference(resolution,[],[f872,f678]) ).
tff(f678,plain,
( pp(aa(dB,bool,it,r))
| ~ spl16_26 ),
inference(avatar_component_clause,[],[f676]) ).
tff(f981,plain,
( spl16_80
| ~ spl16_23
| ~ spl16_79 ),
inference(avatar_split_clause,[],[f965,f962,f661,f979]) ).
tff(f979,plain,
( spl16_80
<=> ! [X0: int] :
( ord_less(nat,bool_size(fFalse),sK4(X0))
| ~ ord_less(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_80])]) ).
tff(f962,plain,
( spl16_79
<=> ! [X0: int] :
( ord_less(nat,bool_size(fTrue),sK4(X0))
| ~ ord_less(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_79])]) ).
tff(f965,plain,
( ! [X0: int] :
( ord_less(nat,bool_size(fFalse),sK4(X0))
| ~ ord_less(int,zero_zero(int),X0) )
| ~ spl16_23
| ~ spl16_79 ),
inference(forward_demodulation,[],[f963,f663]) ).
tff(f963,plain,
( ! [X0: int] :
( ord_less(nat,bool_size(fTrue),sK4(X0))
| ~ ord_less(int,zero_zero(int),X0) )
| ~ spl16_79 ),
inference(avatar_component_clause,[],[f962]) ).
tff(f964,plain,
spl16_79,
inference(avatar_split_clause,[],[f537,f962]) ).
tff(f537,plain,
! [X0: int] :
( ord_less(nat,bool_size(fTrue),sK4(X0))
| ~ ord_less(int,zero_zero(int),X0) ),
inference(forward_demodulation,[],[f383,f336]) ).
tff(f383,plain,
! [X0: int] :
( ord_less(nat,zero_zero(nat),sK4(X0))
| ~ ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: int] :
( ( ( semiring_1_of_nat(int,sK4(X0)) = X0 )
& ord_less(nat,zero_zero(nat),sK4(X0)) )
| ~ ord_less(int,zero_zero(int),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f234,f274]) ).
tff(f274,plain,
! [X0: int] :
( ? [X1: nat] :
( ( semiring_1_of_nat(int,X1) = X0 )
& ord_less(nat,zero_zero(nat),X1) )
=> ( ( semiring_1_of_nat(int,sK4(X0)) = X0 )
& ord_less(nat,zero_zero(nat),sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f234,plain,
! [X0: int] :
( ? [X1: nat] :
( ( semiring_1_of_nat(int,X1) = X0 )
& ord_less(nat,zero_zero(nat),X1) )
| ~ ord_less(int,zero_zero(int),X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: int] :
( ord_less(int,zero_zero(int),X0)
=> ? [X1: nat] :
( ( semiring_1_of_nat(int,X1) = X0 )
& ord_less(nat,zero_zero(nat),X1) ) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X7: int] :
( ord_less(int,zero_zero(int),X7)
=> ? [X55: nat] :
( ( semiring_1_of_nat(int,X55) = X7 )
& ord_less(nat,zero_zero(nat),X55) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__less__imp__eq__int) ).
tff(f960,plain,
spl16_78,
inference(avatar_split_clause,[],[f454,f958]) ).
tff(f958,plain,
( spl16_78
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK12(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_78])]) ).
tff(f454,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK12(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f303]) ).
tff(f956,plain,
spl16_77,
inference(avatar_split_clause,[],[f412,f954]) ).
tff(f954,plain,
( spl16_77
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_77])]) ).
tff(f412,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(flattening,[],[f236]) ).
tff(f236,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ord_less(nat,X1,X0)
=> ord_less(nat,X0,X1) ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X34: nat,X35: nat] :
( ( X34 != X35 )
=> ( ~ ord_less(nat,X35,X34)
=> ord_less(nat,X34,X35) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_linorder__neqE__nat) ).
tff(f952,plain,
spl16_76,
inference(avatar_split_clause,[],[f384,f950]) ).
tff(f950,plain,
( spl16_76
<=> ! [X0: int] :
( ( semiring_1_of_nat(int,sK4(X0)) = X0 )
| ~ ord_less(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_76])]) ).
tff(f384,plain,
! [X0: int] :
( ( semiring_1_of_nat(int,sK4(X0)) = X0 )
| ~ ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f275]) ).
tff(f948,plain,
spl16_75,
inference(avatar_split_clause,[],[f362,f946]) ).
tff(f946,plain,
( spl16_75
<=> ! [X0: $tType,X1: X0] :
( ( sgn_sgn(X0,X1) = sgn_sgn(X0,sgn_sgn(X0,X1)) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_75])]) ).
tff(f362,plain,
! [X0: $tType,X1: X0] :
( ( sgn_sgn(X0,X1) = sgn_sgn(X0,sgn_sgn(X0,X1)) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ! [X1: X0] : ( sgn_sgn(X0,X1) = sgn_sgn(X0,sgn_sgn(X0,X1)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ( sgn_sgn(X0,X1) = sgn_sgn(X0,sgn_sgn(X0,X1)) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X33: X0] : ( sgn_sgn(X0,X33) = sgn_sgn(X0,sgn_sgn(X0,X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_sgn__sgn) ).
tff(f943,plain,
( spl16_74
| ~ spl16_23
| ~ spl16_73 ),
inference(avatar_split_clause,[],[f934,f931,f661,f941]) ).
tff(f941,plain,
( spl16_74
<=> ! [X0: nat] :
( ( bool_size(fFalse) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_74])]) ).
tff(f931,plain,
( spl16_73
<=> ! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_73])]) ).
tff(f934,plain,
( ! [X0: nat] :
( ( bool_size(fFalse) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) )
| ~ spl16_23
| ~ spl16_73 ),
inference(forward_demodulation,[],[f932,f663]) ).
tff(f932,plain,
( ! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) )
| ~ spl16_73 ),
inference(avatar_component_clause,[],[f931]) ).
tff(f933,plain,
spl16_73,
inference(avatar_split_clause,[],[f541,f931]) ).
tff(f541,plain,
! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ),
inference(forward_demodulation,[],[f388,f336]) ).
tff(f388,plain,
! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: nat] :
( ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
| ( zero_zero(nat) != X0 ) )
& ( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
inference(nnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: nat] :
( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
<=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X32: nat] :
( ( zero_zero(int) = semiring_1_of_nat(int,X32) )
<=> ( zero_zero(nat) = X32 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_int__eq__0__conv) ).
tff(f929,plain,
spl16_72,
inference(avatar_split_clause,[],[f447,f927]) ).
tff(f927,plain,
( spl16_72
<=> ! [X2: dB,X0: nat,X1: dB] :
( beta(lift(X2,X0),lift(X1,X0))
| ~ beta(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_72])]) ).
tff(f447,plain,
! [X2: dB,X0: nat,X1: dB] :
( beta(lift(X2,X0),lift(X1,X0))
| ~ beta(X2,X1) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: nat,X1: dB,X2: dB] :
( beta(lift(X2,X0),lift(X1,X0))
| ~ beta(X2,X1) ),
inference(ennf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: nat,X1: dB,X2: dB] :
( beta(X2,X1)
=> beta(lift(X2,X0),lift(X1,X0)) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X5: nat,X8: dB,X6: dB] :
( beta(X6,X8)
=> beta(lift(X6,X5),lift(X8,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_lift__preserves__beta) ).
tff(f925,plain,
spl16_71,
inference(avatar_split_clause,[],[f428,f923]) ).
tff(f923,plain,
( spl16_71
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_71])]) ).
tff(f428,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: nat,X1: nat] :
( ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X56: nat,X20: nat] :
( ( semiring_1_of_nat(int,X20) = semiring_1_of_nat(int,X56) )
<=> ( X20 = X56 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_transfer__int__nat__relations_I1_J) ).
tff(f921,plain,
spl16_70,
inference(avatar_split_clause,[],[f414,f919]) ).
tff(f919,plain,
( spl16_70
<=> ! [X0: dB,X1: dB] :
( ( abs(sK11(X0,X1)) = X0 )
| ~ beta(abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_70])]) ).
tff(f414,plain,
! [X0: dB,X1: dB] :
( ( abs(sK11(X0,X1)) = X0 )
| ~ beta(abs(X1),X0) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: dB,X1: dB] :
( ( beta(X1,sK11(X0,X1))
& ( abs(sK11(X0,X1)) = X0 ) )
| ~ beta(abs(X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f239,f290]) ).
tff(f290,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( beta(X1,X2)
& ( abs(X2) = X0 ) )
=> ( beta(X1,sK11(X0,X1))
& ( abs(sK11(X0,X1)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f239,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( beta(X1,X2)
& ( abs(X2) = X0 ) )
| ~ beta(abs(X1),X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),X0)
=> ~ ! [X2: dB] :
( ( abs(X2) = X0 )
=> ~ beta(X1,X2) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X8: dB,X6: dB] :
( beta(abs(X6),X8)
=> ~ ! [X43: dB] :
( ( abs(X43) = X8 )
=> ~ beta(X6,X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_beta__cases_I2_J) ).
tff(f917,plain,
( spl16_69
| ~ spl16_26
| ~ spl16_51 ),
inference(avatar_split_clause,[],[f833,f804,f676,f914]) ).
tff(f914,plain,
( spl16_69
<=> sP1(r) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_69])]) ).
tff(f833,plain,
( sP1(r)
| ~ spl16_26
| ~ spl16_51 ),
inference(resolution,[],[f805,f678]) ).
tff(f907,plain,
( spl16_68
| ~ spl16_23
| ~ spl16_66 ),
inference(avatar_split_clause,[],[f884,f880,f661,f905]) ).
tff(f905,plain,
( spl16_68
<=> ! [X0: nat] :
( ord_less(nat,bool_size(fFalse),X0)
| ( bool_size(fFalse) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_68])]) ).
tff(f880,plain,
( spl16_66
<=> ! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ord_less(nat,bool_size(fTrue),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_66])]) ).
tff(f884,plain,
( ! [X0: nat] :
( ord_less(nat,bool_size(fFalse),X0)
| ( bool_size(fFalse) = X0 ) )
| ~ spl16_23
| ~ spl16_66 ),
inference(forward_demodulation,[],[f883,f663]) ).
tff(f883,plain,
( ! [X0: nat] :
( ( bool_size(fFalse) = X0 )
| ord_less(nat,bool_size(fTrue),X0) )
| ~ spl16_23
| ~ spl16_66 ),
inference(forward_demodulation,[],[f881,f663]) ).
tff(f881,plain,
( ! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ord_less(nat,bool_size(fTrue),X0) )
| ~ spl16_66 ),
inference(avatar_component_clause,[],[f880]) ).
tff(f903,plain,
( spl16_67
| ~ spl16_23
| ~ spl16_65 ),
inference(avatar_split_clause,[],[f878,f875,f661,f901]) ).
tff(f901,plain,
( spl16_67
<=> ! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,bool_size(fFalse)) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_67])]) ).
tff(f875,plain,
( spl16_65
<=> ! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,bool_size(fTrue)) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_65])]) ).
tff(f878,plain,
( ! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,bool_size(fFalse)) )
| ~ semiring_1(X0) )
| ~ spl16_23
| ~ spl16_65 ),
inference(forward_demodulation,[],[f876,f663]) ).
tff(f876,plain,
( ! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,bool_size(fTrue)) )
| ~ semiring_1(X0) )
| ~ spl16_65 ),
inference(avatar_component_clause,[],[f875]) ).
tff(f882,plain,
spl16_66,
inference(avatar_split_clause,[],[f536,f880]) ).
tff(f536,plain,
! [X0: nat] :
( ( bool_size(fTrue) = X0 )
| ord_less(nat,bool_size(fTrue),X0) ),
inference(forward_demodulation,[],[f535,f336]) ).
tff(f535,plain,
! [X0: nat] :
( ord_less(nat,bool_size(fTrue),X0)
| ( zero_zero(nat) = X0 ) ),
inference(forward_demodulation,[],[f382,f336]) ).
tff(f382,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ord_less(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X3: nat] :
( ( zero_zero(nat) != X3 )
=> ord_less(nat,zero_zero(nat),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_gr0I) ).
tff(f877,plain,
spl16_65,
inference(avatar_split_clause,[],[f532,f875]) ).
tff(f532,plain,
! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,bool_size(fTrue)) )
| ~ semiring_1(X0) ),
inference(forward_demodulation,[],[f370,f336]) ).
tff(f370,plain,
! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f83]) ).
tff(f83,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_of__nat__0) ).
tff(f873,plain,
spl16_64,
inference(avatar_split_clause,[],[f498,f871]) ).
tff(f498,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f395]) ).
tff(f395,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f869,plain,
spl16_63,
inference(avatar_split_clause,[],[f492,f867]) ).
tff(f867,plain,
( spl16_63
<=> ! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_63])]) ).
tff(f492,plain,
! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f364]) ).
tff(f364,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = sgn_sgn(X0,X1) )
| ( zero_zero(X0) != X1 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f865,plain,
spl16_62,
inference(avatar_split_clause,[],[f415,f863]) ).
tff(f863,plain,
( spl16_62
<=> ! [X0: dB,X1: dB] :
( beta(X1,sK11(X0,X1))
| ~ beta(abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_62])]) ).
tff(f415,plain,
! [X0: dB,X1: dB] :
( beta(X1,sK11(X0,X1))
| ~ beta(abs(X1),X0) ),
inference(cnf_transformation,[],[f291]) ).
tff(f861,plain,
spl16_61,
inference(avatar_split_clause,[],[f399,f859]) ).
tff(f859,plain,
( spl16_61
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_61])]) ).
tff(f399,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK9(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ( pp(aa(dB,bool,it,sK9(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK8(X0),sK9(X0),zero_zero(nat)),sK10(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f285,f286]) ).
tff(f286,plain,
! [X0: dB] :
( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X4,X5,zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
=> ( pp(aa(dB,bool,it,sK9(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(sK8(X0),sK9(X0),zero_zero(nat)),sK10(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK8(X0))),sK9(X0)),sK10(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f285,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X4: dB,X5: dB,X6: list(dB)] :
( pp(aa(dB,bool,it,X5))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X4,X5,zero_zero(nat)),X6)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X4)),X5),X6) = X0 ) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f284]) ).
tff(f284,plain,
! [X0: dB] :
( ( sP0(X0)
| ! [X1: dB,X2: dB,X3: list(dB)] :
( ~ pp(aa(dB,bool,it,X2))
| ~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
| ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) != X0 ) ) )
& ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: dB] :
( sP0(X0)
<=> ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f857,plain,
spl16_60,
inference(avatar_split_clause,[],[f375,f855]) ).
tff(f855,plain,
( spl16_60
<=> ! [X0: $tType,X1: nat] :
( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_60])]) ).
tff(f375,plain,
! [X0: $tType,X1: nat] :
( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType] :
( ! [X1: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0)) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X38: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X38),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_of__nat__less__0__iff) ).
tff(f853,plain,
spl16_59,
inference(avatar_split_clause,[],[f361,f851]) ).
tff(f851,plain,
( spl16_59
<=> ! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ sgn_if(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_59])]) ).
tff(f361,plain,
! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ sgn_if(X0) ),
inference(cnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: $tType] :
( ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) )
| ~ sgn_if(X0) ),
inference(ennf_transformation,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType] :
( sgn_if(X0)
=> ( zero_zero(X0) = sgn_sgn(X0,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_sgn0) ).
tff(f849,plain,
( ~ spl16_58
| spl16_14
| ~ spl16_23
| ~ spl16_52 ),
inference(avatar_split_clause,[],[f842,f808,f661,f620,f846]) ).
tff(f846,plain,
( spl16_58
<=> sP1(subst(r,var(i),bool_size(fFalse))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_58])]) ).
tff(f842,plain,
( ~ sP1(subst(r,var(i),bool_size(fFalse)))
| spl16_14
| ~ spl16_23
| ~ spl16_52 ),
inference(forward_demodulation,[],[f837,f663]) ).
tff(f837,plain,
( ~ sP1(subst(r,var(i),bool_size(fTrue)))
| spl16_14
| ~ spl16_52 ),
inference(resolution,[],[f809,f622]) ).
tff(f832,plain,
spl16_57,
inference(avatar_split_clause,[],[f460,f830]) ).
tff(f830,plain,
( spl16_57
<=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_57])]) ).
tff(f460,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f309]) ).
tff(f828,plain,
spl16_56,
inference(avatar_split_clause,[],[f438,f826]) ).
tff(f826,plain,
( spl16_56
<=> ! [X2: dB,X0: dB,X1: nat] : ( subst(lift(X2,X1),X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_56])]) ).
tff(f438,plain,
! [X2: dB,X0: dB,X1: nat] : ( subst(lift(X2,X1),X0,X1) = X2 ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: dB,X1: nat,X2: dB] : ( subst(lift(X2,X1),X0,X1) = X2 ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X8: dB,X7: nat,X10: dB] : ( subst(lift(X10,X7),X8,X7) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_subst__lift) ).
tff(f824,plain,
spl16_55,
inference(avatar_split_clause,[],[f426,f822]) ).
tff(f822,plain,
( spl16_55
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_55])]) ).
tff(f426,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X11: nat,X12: nat] :
( ( var(X12) = var(X11) )
<=> ( X11 = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_dB_Osimps_I1_J) ).
tff(f820,plain,
spl16_54,
inference(avatar_split_clause,[],[f424,f818]) ).
tff(f818,plain,
( spl16_54
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_54])]) ).
tff(f424,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X27: dB,X26: dB] :
( ( abs(X26) = abs(X27) )
<=> ( X26 = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_dB_Osimps_I3_J) ).
tff(f816,plain,
spl16_53,
inference(avatar_split_clause,[],[f413,f814]) ).
tff(f814,plain,
( spl16_53
<=> ! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_53])]) ).
tff(f413,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: dB,X1: dB] :
( beta(X1,X0)
=> beta(abs(X1),abs(X0)) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X10: dB,X8: dB] :
( beta(X8,X10)
=> beta(abs(X8),abs(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_abs) ).
tff(f810,plain,
spl16_52,
inference(avatar_split_clause,[],[f402,f808]) ).
tff(f402,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f158,f261,f260]) ).
tff(f158,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> ( ? [X1: dB,X2: dB,X3: list(dB)] :
( pp(aa(dB,bool,it,X2))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X1,X2,zero_zero(nat)),X3)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X2),X3) = X0 ) )
| ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
| ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) ) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X31: dB] :
( pp(aa(dB,bool,it,X31))
<=> ( ? [X52: dB,X53: dB,X54: list(dB)] :
( pp(aa(dB,bool,it,X53))
& pp(aa(dB,bool,it,foldl(dB,dB,app,subst(X52,X53,zero_zero(nat)),X54)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X52)),X53),X54) = X31 ) )
| ? [X52: dB] :
( pp(aa(dB,bool,it,X52))
& ( abs(X52) = X31 ) )
| ? [X50: list(dB),X51: nat] :
( listsp(dB,it,X50)
& ( foldl(dB,dB,app,var(X51),X50) = X31 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_IT_Osimps) ).
tff(f806,plain,
spl16_51,
inference(avatar_split_clause,[],[f401,f804]) ).
tff(f401,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f288]) ).
tff(f801,plain,
( spl16_50
| ~ spl16_23
| ~ spl16_46 ),
inference(avatar_split_clause,[],[f779,f776,f661,f799]) ).
tff(f799,plain,
( spl16_50
<=> ! [X0: nat,X1: dB] : ( liftn(bool_size(fFalse),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_50])]) ).
tff(f776,plain,
( spl16_46
<=> ! [X0: nat,X1: dB] : ( liftn(bool_size(fTrue),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_46])]) ).
tff(f779,plain,
( ! [X0: nat,X1: dB] : ( liftn(bool_size(fFalse),X1,X0) = X1 )
| ~ spl16_23
| ~ spl16_46 ),
inference(forward_demodulation,[],[f777,f663]) ).
tff(f777,plain,
( ! [X0: nat,X1: dB] : ( liftn(bool_size(fTrue),X1,X0) = X1 )
| ~ spl16_46 ),
inference(avatar_component_clause,[],[f776]) ).
tff(f797,plain,
( spl16_49
| ~ spl16_23
| ~ spl16_45 ),
inference(avatar_split_clause,[],[f774,f771,f661,f795]) ).
tff(f795,plain,
( spl16_49
<=> ! [X0: nat] : ( bool_size(fFalse) = size_size(dB,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_49])]) ).
tff(f771,plain,
( spl16_45
<=> ! [X0: nat] : ( bool_size(fTrue) = size_size(dB,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_45])]) ).
tff(f774,plain,
( ! [X0: nat] : ( bool_size(fFalse) = size_size(dB,var(X0)) )
| ~ spl16_23
| ~ spl16_45 ),
inference(forward_demodulation,[],[f772,f663]) ).
tff(f772,plain,
( ! [X0: nat] : ( bool_size(fTrue) = size_size(dB,var(X0)) )
| ~ spl16_45 ),
inference(avatar_component_clause,[],[f771]) ).
tff(f793,plain,
( spl16_48
| ~ spl16_23
| ~ spl16_44 ),
inference(avatar_split_clause,[],[f769,f765,f661,f790]) ).
tff(f790,plain,
( spl16_48
<=> ( zero_zero(int) = semiring_1_of_nat(int,bool_size(fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_48])]) ).
tff(f765,plain,
( spl16_44
<=> ( zero_zero(int) = semiring_1_of_nat(int,bool_size(fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_44])]) ).
tff(f769,plain,
( ( zero_zero(int) = semiring_1_of_nat(int,bool_size(fFalse)) )
| ~ spl16_23
| ~ spl16_44 ),
inference(forward_demodulation,[],[f767,f663]) ).
tff(f767,plain,
( ( zero_zero(int) = semiring_1_of_nat(int,bool_size(fTrue)) )
| ~ spl16_44 ),
inference(avatar_component_clause,[],[f765]) ).
tff(f785,plain,
( ~ spl16_12
| spl16_47
| spl16_14
| ~ spl16_23
| ~ spl16_27 ),
inference(avatar_split_clause,[],[f717,f681,f661,f620,f782,f609]) ).
tff(f609,plain,
( spl16_12
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_12])]) ).
tff(f782,plain,
( spl16_47
<=> ( fFalse = aa(dB,bool,it,subst(r,var(i),bool_size(fFalse))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_47])]) ).
tff(f681,plain,
( spl16_27
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_27])]) ).
tff(f717,plain,
( ( fFalse = aa(dB,bool,it,subst(r,var(i),bool_size(fFalse))) )
| ~ pp(fTrue)
| spl16_14
| ~ spl16_23
| ~ spl16_27 ),
inference(forward_demodulation,[],[f714,f663]) ).
tff(f714,plain,
( ~ pp(fTrue)
| ( fFalse = aa(dB,bool,it,subst(r,var(i),bool_size(fTrue))) )
| spl16_14
| ~ spl16_27 ),
inference(superposition,[],[f622,f682]) ).
tff(f682,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = X0 ) )
| ~ spl16_27 ),
inference(avatar_component_clause,[],[f681]) ).
tff(f778,plain,
spl16_46,
inference(avatar_split_clause,[],[f546,f776]) ).
tff(f546,plain,
! [X0: nat,X1: dB] : ( liftn(bool_size(fTrue),X1,X0) = X1 ),
inference(forward_demodulation,[],[f408,f336]) ).
tff(f408,plain,
! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: nat,X1: dB] : ( liftn(zero_zero(nat),X1,X0) = X1 ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X7: nat,X10: dB] : ( liftn(zero_zero(nat),X10,X7) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_liftn__0) ).
tff(f773,plain,
spl16_45,
inference(avatar_split_clause,[],[f531,f771]) ).
tff(f531,plain,
! [X0: nat] : ( bool_size(fTrue) = size_size(dB,var(X0)) ),
inference(forward_demodulation,[],[f356,f336]) ).
tff(f356,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X19: nat] : ( zero_zero(nat) = size_size(dB,var(X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_dB_Osize_I4_J) ).
tff(f768,plain,
spl16_44,
inference(avatar_split_clause,[],[f521,f765]) ).
tff(f521,plain,
zero_zero(int) = semiring_1_of_nat(int,bool_size(fTrue)),
inference(forward_demodulation,[],[f341,f336]) ).
tff(f341,plain,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_transfer__int__nat__numerals_I1_J) ).
tff(f763,plain,
spl16_43,
inference(avatar_split_clause,[],[f437,f761]) ).
tff(f761,plain,
( spl16_43
<=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_43])]) ).
tff(f437,plain,
! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X0: $tType,X34: X0,X35: X0] : ( if(X0,fFalse,X35,X34) = X34 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
tff(f759,plain,
spl16_42,
inference(avatar_split_clause,[],[f436,f757]) ).
tff(f757,plain,
( spl16_42
<=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_42])]) ).
tff(f436,plain,
! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X0: $tType,X34: X0,X35: X0] : ( if(X0,fTrue,X35,X34) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
tff(f755,plain,
spl16_41,
inference(avatar_split_clause,[],[f409,f753]) ).
tff(f753,plain,
( spl16_41
<=> ! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_41])]) ).
tff(f409,plain,
! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
inference(cnf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X9: dB,X7: nat] : ( subst(var(X7),X9,X7) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_subst__eq) ).
tff(f751,plain,
spl16_40,
inference(avatar_split_clause,[],[f357,f749]) ).
tff(f357,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X3: nat] : pp(aa(dB,bool,it,var(X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Var__IT) ).
tff(f747,plain,
( spl16_39
| spl16_14
| ~ spl16_27 ),
inference(avatar_split_clause,[],[f712,f681,f620,f745]) ).
tff(f712,plain,
( ! [X0: bool] :
( ~ pp(aa(dB,bool,it,subst(r,var(i),bool_size(X0))))
| ( fFalse = X0 ) )
| spl16_14
| ~ spl16_27 ),
inference(superposition,[],[f622,f682]) ).
tff(f743,plain,
spl16_38,
inference(avatar_split_clause,[],[f355,f741]) ).
tff(f741,plain,
( spl16_38
<=> ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_38])]) ).
tff(f355,plain,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X7: nat] : ~ ord_less(int,semiring_1_of_nat(int,X7),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_int__less__0__conv) ).
tff(f739,plain,
( spl16_37
| ~ spl16_23
| ~ spl16_32 ),
inference(avatar_split_clause,[],[f709,f706,f661,f737]) ).
tff(f737,plain,
( spl16_37
<=> ! [X0: nat] : ( bool_size(fFalse) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_37])]) ).
tff(f706,plain,
( spl16_32
<=> ! [X0: nat] : ( bool_size(fTrue) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_32])]) ).
tff(f709,plain,
( ! [X0: nat] : ( bool_size(fFalse) = dB_size(var(X0)) )
| ~ spl16_23
| ~ spl16_32 ),
inference(forward_demodulation,[],[f707,f663]) ).
tff(f707,plain,
( ! [X0: nat] : ( bool_size(fTrue) = dB_size(var(X0)) )
| ~ spl16_32 ),
inference(avatar_component_clause,[],[f706]) ).
tff(f735,plain,
( spl16_36
| ~ spl16_23
| ~ spl16_31 ),
inference(avatar_split_clause,[],[f704,f701,f661,f733]) ).
tff(f733,plain,
( spl16_36
<=> ! [X0: bool] : ( bool_size(fFalse) = size_size(bool,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_36])]) ).
tff(f701,plain,
( spl16_31
<=> ! [X0: bool] : ( bool_size(fTrue) = size_size(bool,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_31])]) ).
tff(f704,plain,
( ! [X0: bool] : ( bool_size(fFalse) = size_size(bool,X0) )
| ~ spl16_23
| ~ spl16_31 ),
inference(forward_demodulation,[],[f702,f663]) ).
tff(f702,plain,
( ! [X0: bool] : ( bool_size(fTrue) = size_size(bool,X0) )
| ~ spl16_31 ),
inference(avatar_component_clause,[],[f701]) ).
tff(f731,plain,
( spl16_35
| ~ spl16_23
| ~ spl16_30 ),
inference(avatar_split_clause,[],[f699,f696,f661,f729]) ).
tff(f729,plain,
( spl16_35
<=> ! [X0: char] : ( bool_size(fFalse) = size_size(char,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_35])]) ).
tff(f696,plain,
( spl16_30
<=> ! [X0: char] : ( bool_size(fTrue) = size_size(char,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_30])]) ).
tff(f699,plain,
( ! [X0: char] : ( bool_size(fFalse) = size_size(char,X0) )
| ~ spl16_23
| ~ spl16_30 ),
inference(forward_demodulation,[],[f697,f663]) ).
tff(f697,plain,
( ! [X0: char] : ( bool_size(fTrue) = size_size(char,X0) )
| ~ spl16_30 ),
inference(avatar_component_clause,[],[f696]) ).
tff(f727,plain,
( spl16_34
| ~ spl16_23
| ~ spl16_29 ),
inference(avatar_split_clause,[],[f694,f691,f661,f725]) ).
tff(f725,plain,
( spl16_34
<=> ! [X0: literal] : ( bool_size(fFalse) = size_size(literal,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_34])]) ).
tff(f691,plain,
( spl16_29
<=> ! [X0: literal] : ( bool_size(fTrue) = size_size(literal,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_29])]) ).
tff(f694,plain,
( ! [X0: literal] : ( bool_size(fFalse) = size_size(literal,X0) )
| ~ spl16_23
| ~ spl16_29 ),
inference(forward_demodulation,[],[f692,f663]) ).
tff(f692,plain,
( ! [X0: literal] : ( bool_size(fTrue) = size_size(literal,X0) )
| ~ spl16_29 ),
inference(avatar_component_clause,[],[f691]) ).
tff(f722,plain,
( spl16_33
| ~ spl16_23
| ~ spl16_28 ),
inference(avatar_split_clause,[],[f689,f685,f661,f719]) ).
tff(f719,plain,
( spl16_33
<=> ( bool_size(fFalse) = nat_size(bool_size(fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_33])]) ).
tff(f685,plain,
( spl16_28
<=> ( bool_size(fTrue) = nat_size(bool_size(fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_28])]) ).
tff(f689,plain,
( ( bool_size(fFalse) = nat_size(bool_size(fFalse)) )
| ~ spl16_23
| ~ spl16_28 ),
inference(forward_demodulation,[],[f687,f663]) ).
tff(f687,plain,
( ( bool_size(fTrue) = nat_size(bool_size(fTrue)) )
| ~ spl16_28 ),
inference(avatar_component_clause,[],[f685]) ).
tff(f708,plain,
spl16_32,
inference(avatar_split_clause,[],[f530,f706]) ).
tff(f530,plain,
! [X0: nat] : ( bool_size(fTrue) = dB_size(var(X0)) ),
inference(forward_demodulation,[],[f354,f336]) ).
tff(f354,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X19: nat] : ( dB_size(var(X19)) = zero_zero(nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_dB_Osize_I1_J) ).
tff(f703,plain,
spl16_31,
inference(avatar_split_clause,[],[f529,f701]) ).
tff(f529,plain,
! [X0: bool] : ( bool_size(fTrue) = size_size(bool,X0) ),
inference(forward_demodulation,[],[f353,f336]) ).
tff(f353,plain,
! [X0: bool] : ( zero_zero(nat) = size_size(bool,X0) ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: bool] : ( zero_zero(nat) = size_size(bool,X0) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X24: bool] : ( zero_zero(nat) = size_size(bool,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_size__bool) ).
tff(f698,plain,
spl16_30,
inference(avatar_split_clause,[],[f528,f696]) ).
tff(f528,plain,
! [X0: char] : ( bool_size(fTrue) = size_size(char,X0) ),
inference(forward_demodulation,[],[f352,f336]) ).
tff(f352,plain,
! [X0: char] : ( zero_zero(nat) = size_size(char,X0) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: char] : ( zero_zero(nat) = size_size(char,X0) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X25: char] : ( zero_zero(nat) = size_size(char,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_size__char) ).
tff(f693,plain,
spl16_29,
inference(avatar_split_clause,[],[f527,f691]) ).
tff(f527,plain,
! [X0: literal] : ( bool_size(fTrue) = size_size(literal,X0) ),
inference(forward_demodulation,[],[f351,f336]) ).
tff(f351,plain,
! [X0: literal] : ( zero_zero(nat) = size_size(literal,X0) ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: literal] : ( zero_zero(nat) = size_size(literal,X0) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X8: literal] : ( zero_zero(nat) = size_size(literal,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_size__literal__def) ).
tff(f688,plain,
spl16_28,
inference(avatar_split_clause,[],[f518,f685]) ).
tff(f518,plain,
bool_size(fTrue) = nat_size(bool_size(fTrue)),
inference(forward_demodulation,[],[f338,f336]) ).
tff(f338,plain,
zero_zero(nat) = nat_size(zero_zero(nat)),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
zero_zero(nat) = nat_size(zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_nat_Osize_I1_J) ).
tff(f683,plain,
spl16_27,
inference(avatar_split_clause,[],[f358,f681]) ).
tff(f358,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X57: bool] :
( ( fFalse = X57 )
| ( fTrue = X57 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
tff(f679,plain,
spl16_26,
inference(avatar_split_clause,[],[f320,f676]) ).
tff(f320,plain,
pp(aa(dB,bool,it,r)),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
pp(aa(dB,bool,it,r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f674,plain,
( ~ spl16_25
| spl16_14
| ~ spl16_23 ),
inference(avatar_split_clause,[],[f669,f661,f620,f671]) ).
tff(f671,plain,
( spl16_25
<=> pp(aa(dB,bool,it,subst(r,var(i),bool_size(fFalse)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_25])]) ).
tff(f669,plain,
( ~ pp(aa(dB,bool,it,subst(r,var(i),bool_size(fFalse))))
| spl16_14
| ~ spl16_23 ),
inference(superposition,[],[f622,f663]) ).
tff(f668,plain,
( spl16_24
| ~ spl16_18
| ~ spl16_22 ),
inference(avatar_split_clause,[],[f659,f656,f637,f666]) ).
tff(f666,plain,
( spl16_24
<=> ! [X0: nat] : ~ ord_less(nat,X0,bool_size(fFalse)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_24])]) ).
tff(f637,plain,
( spl16_18
<=> ( zero_zero(nat) = bool_size(fTrue) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_18])]) ).
tff(f656,plain,
( spl16_22
<=> ! [X0: nat] : ~ ord_less(nat,X0,bool_size(fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_22])]) ).
tff(f659,plain,
( ! [X0: nat] : ~ ord_less(nat,X0,bool_size(fFalse))
| ~ spl16_18
| ~ spl16_22 ),
inference(forward_demodulation,[],[f657,f641]) ).
tff(f641,plain,
( ( bool_size(fTrue) = bool_size(fFalse) )
| ~ spl16_18 ),
inference(forward_demodulation,[],[f639,f337]) ).
tff(f337,plain,
zero_zero(nat) = bool_size(fFalse),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
zero_zero(nat) = bool_size(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_bool_Osize_I2_J) ).
tff(f639,plain,
( ( zero_zero(nat) = bool_size(fTrue) )
| ~ spl16_18 ),
inference(avatar_component_clause,[],[f637]) ).
tff(f657,plain,
( ! [X0: nat] : ~ ord_less(nat,X0,bool_size(fTrue))
| ~ spl16_22 ),
inference(avatar_component_clause,[],[f656]) ).
tff(f664,plain,
( spl16_23
| ~ spl16_18 ),
inference(avatar_split_clause,[],[f641,f637,f661]) ).
tff(f658,plain,
spl16_22,
inference(avatar_split_clause,[],[f524,f656]) ).
tff(f524,plain,
! [X0: nat] : ~ ord_less(nat,X0,bool_size(fTrue)),
inference(forward_demodulation,[],[f346,f336]) ).
tff(f346,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X3: nat] : ~ ord_less(nat,X3,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__nat__zero__code) ).
tff(f654,plain,
spl16_21,
inference(avatar_split_clause,[],[f406,f652]) ).
tff(f652,plain,
( spl16_21
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_21])]) ).
tff(f406,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X28: dB,X19: nat] : ( var(X19) != abs(X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_dB_Osimps_I6_J) ).
tff(f650,plain,
spl16_20,
inference(avatar_split_clause,[],[f350,f648]) ).
tff(f648,plain,
( spl16_20
<=> ! [X0: nat] : ( size_size(nat,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_20])]) ).
tff(f350,plain,
! [X0: nat] : ( size_size(nat,X0) = X0 ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: nat] : ( size_size(nat,X0) = X0 ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X3: nat] : ( size_size(nat,X3) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_nat__size) ).
tff(f646,plain,
spl16_19,
inference(avatar_split_clause,[],[f337,f643]) ).
tff(f643,plain,
( spl16_19
<=> ( zero_zero(nat) = bool_size(fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_19])]) ).
tff(f640,plain,
spl16_18,
inference(avatar_split_clause,[],[f336,f637]) ).
tff(f635,plain,
spl16_17,
inference(avatar_split_clause,[],[f405,f633]) ).
tff(f633,plain,
( spl16_17
<=> ! [X0: dB,X1: nat] : ~ beta(var(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_17])]) ).
tff(f405,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(cnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X10: dB,X5: nat] : ~ beta(var(X5),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_beta__cases_I1_J) ).
tff(f631,plain,
spl16_16,
inference(avatar_split_clause,[],[f396,f629]) ).
tff(f629,plain,
( spl16_16
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_16])]) ).
tff(f396,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f627,plain,
spl16_15,
inference(avatar_split_clause,[],[f344,f625]) ).
tff(f625,plain,
( spl16_15
<=> ! [X0: nat] : ~ ord_less(nat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_15])]) ).
tff(f344,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(cnf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X3: nat] : ~ ord_less(nat,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__irrefl__nat) ).
tff(f623,plain,
( ~ spl16_14
| spl16_13 ),
inference(avatar_split_clause,[],[f618,f614,f620]) ).
tff(f614,plain,
( spl16_13
<=> pp(aa(dB,bool,it,subst(r,var(i),zero_zero(nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_13])]) ).
tff(f618,plain,
( ~ pp(aa(dB,bool,it,subst(r,var(i),bool_size(fTrue))))
| spl16_13 ),
inference(forward_demodulation,[],[f616,f336]) ).
tff(f616,plain,
( ~ pp(aa(dB,bool,it,subst(r,var(i),zero_zero(nat))))
| spl16_13 ),
inference(avatar_component_clause,[],[f614]) ).
tff(f617,plain,
~ spl16_13,
inference(avatar_split_clause,[],[f319,f614]) ).
tff(f319,plain,
~ pp(aa(dB,bool,it,subst(r,var(i),zero_zero(nat)))),
inference(cnf_transformation,[],[f123]) ).
tff(f123,plain,
~ pp(aa(dB,bool,it,subst(r,var(i),zero_zero(nat)))),
inference(flattening,[],[f122]) ).
tff(f122,negated_conjecture,
~ pp(aa(dB,bool,it,subst(r,var(i),zero_zero(nat)))),
inference(negated_conjecture,[],[f121]) ).
tff(f121,conjecture,
pp(aa(dB,bool,it,subst(r,var(i),zero_zero(nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f612,plain,
spl16_12,
inference(avatar_split_clause,[],[f334,f609]) ).
tff(f334,plain,
pp(fTrue),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
tff(f607,plain,
spl16_11,
inference(avatar_split_clause,[],[f333,f604]) ).
tff(f604,plain,
( spl16_11
<=> linordered_semidom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_11])]) ).
tff(f333,plain,
linordered_semidom(nat),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
tff(f602,plain,
spl16_10,
inference(avatar_split_clause,[],[f332,f599]) ).
tff(f599,plain,
( spl16_10
<=> linordered_semidom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_10])]) ).
tff(f332,plain,
linordered_semidom(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
tff(f597,plain,
spl16_9,
inference(avatar_split_clause,[],[f331,f594]) ).
tff(f594,plain,
( spl16_9
<=> semiring_char_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_9])]) ).
tff(f331,plain,
semiring_char_0(nat),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
semiring_char_0(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
tff(f592,plain,
spl16_8,
inference(avatar_split_clause,[],[f330,f589]) ).
tff(f589,plain,
( spl16_8
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).
tff(f330,plain,
zero(nat),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f587,plain,
spl16_7,
inference(avatar_split_clause,[],[f329,f584]) ).
tff(f584,plain,
( spl16_7
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_7])]) ).
tff(f329,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
tff(f582,plain,
spl16_6,
inference(avatar_split_clause,[],[f328,f579]) ).
tff(f579,plain,
( spl16_6
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).
tff(f328,plain,
semiring_1(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f577,plain,
spl16_5,
inference(avatar_split_clause,[],[f327,f574]) ).
tff(f574,plain,
( spl16_5
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
tff(f327,plain,
zero(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f572,plain,
spl16_4,
inference(avatar_split_clause,[],[f326,f569]) ).
tff(f569,plain,
( spl16_4
<=> semiring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
tff(f326,plain,
semiring_char_0(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
semiring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
tff(f567,plain,
spl16_3,
inference(avatar_split_clause,[],[f325,f564]) ).
tff(f564,plain,
( spl16_3
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).
tff(f325,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f562,plain,
spl16_2,
inference(avatar_split_clause,[],[f324,f559]) ).
tff(f559,plain,
( spl16_2
<=> sgn_if(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
tff(f324,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(f557,plain,
~ spl16_1,
inference(avatar_split_clause,[],[f322,f554]) ).
tff(f554,plain,
( spl16_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
tff(f322,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LCL773_5 : TPTP v8.1.2. Released v6.0.0.
% 0.05/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32 % Computer : n006.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 22:54:20 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (16289)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34 % (16295)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)
% 0.10/0.35 % (16292)WARNING: value z3 for option sas not known
% 0.10/0.35 % (16292)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)
% 0.10/0.35 % (16291)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.35 % (16293)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.35 % (16294)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)
% 0.10/0.35 % (16296)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)
% 0.10/0.36 % (16296)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.10/0.36 % (16290)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.36 % Exception at run slice level
% 0.10/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.36 % Exception at run slice level
% 0.10/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.37 % Exception at run slice level
% 0.15/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38 % (16294)First to succeed.
% 0.15/0.39 % (16294)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (16294)------------------------------
% 0.15/0.40 % (16294)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40 % (16294)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (16294)Memory used [KB]: 1366
% 0.15/0.40 % (16294)Time elapsed: 0.034 s
% 0.15/0.40 % (16294)Instructions burned: 56 (million)
% 0.15/0.40 % (16294)------------------------------
% 0.15/0.40 % (16294)------------------------------
% 0.15/0.40 % (16289)Success in time 0.071 s
%------------------------------------------------------------------------------