TSTP Solution File: LCL825_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL825_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:50:17 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 180
% Syntax : Number of formulae : 355 ( 113 unt; 83 typ; 0 def)
% Number of atoms : 598 ( 212 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 509 ( 183 ~; 168 |; 76 &)
% ( 69 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 93 ( 45 >; 48 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 53 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 24 con; 0-5 aty)
% Number of variables : 489 ( 405 !; 45 ?; 489 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
type: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(X1,fun(X0,X2))) ).
tff(func_def_2,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
it: fun(dB,bool) ).
tff(func_def_6,type,
abs: dB > dB ).
tff(func_def_7,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_8,type,
var: nat > dB ).
tff(func_def_9,type,
dB_size: dB > nat ).
tff(func_def_10,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_11,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_12,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_13,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_14,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_15,type,
hd:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_16,type,
last:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_17,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_18,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_19,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_20,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_21,type,
shift:
!>[X0: $tType] : fun(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0)))) ).
tff(func_def_22,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_23,type,
type_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(type,fun(type,X0)) * type ) > X0 ) ).
tff(func_def_24,type,
typing: fun(fun(nat,type),fun(dB,fun(type,bool))) ).
tff(func_def_25,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_26,type,
fAll:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_27,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_28,type,
fFalse: bool ).
tff(func_def_29,type,
fTrue: bool ).
tff(func_def_30,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_31,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_32,type,
t1: type ).
tff(func_def_33,type,
t_a: type ).
tff(func_def_34,type,
t: type ).
tff(func_def_35,type,
ts: list(type) ).
tff(func_def_36,type,
e: fun(nat,type) ).
tff(func_def_37,type,
ea: fun(nat,type) ).
tff(func_def_38,type,
i: nat ).
tff(func_def_39,type,
ia: nat ).
tff(func_def_40,type,
n: nat ).
tff(func_def_41,type,
rs: list(dB) ).
tff(func_def_42,type,
t2: dB ).
tff(func_def_43,type,
u: dB ).
tff(func_def_44,type,
ua: dB ).
tff(func_def_45,type,
sK3: list(type) ).
tff(func_def_46,type,
sK4: dB > dB ).
tff(func_def_47,type,
sK5: dB > list(dB) ).
tff(func_def_48,type,
sK6: dB > nat ).
tff(func_def_49,type,
sK7: dB > dB ).
tff(func_def_50,type,
sK8: dB > dB ).
tff(func_def_51,type,
sK9: dB > list(dB) ).
tff(func_def_52,type,
sK10: ( dB * dB ) > dB ).
tff(func_def_53,type,
sK11: ( dB * dB * dB ) > dB ).
tff(func_def_54,type,
sK12: ( dB * dB * dB ) > dB ).
tff(func_def_55,type,
sK13: ( dB * dB * dB ) > dB ).
tff(func_def_56,type,
sK14: ( dB * fun(nat,type) ) > type ).
tff(func_def_57,type,
sK15: ( dB * fun(nat,type) ) > type ).
tff(func_def_58,type,
sK16: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_59,type,
sK17: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_60,type,
sK18: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_61,type,
sK19: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_62,type,
sK20: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_63,type,
sK21: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_64,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_65,type,
sK23:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_66,type,
sK24:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_67,type,
sK25:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_68,type,
sK26: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
typings: ( fun(nat,type) * list(dB) * list(type) ) > $o ).
tff(pred_def_5,type,
pp: bool > $o ).
tff(pred_def_6,type,
sP0: dB > $o ).
tff(pred_def_7,type,
sP1: dB > $o ).
tff(pred_def_8,type,
sP2: ( dB * dB * dB ) > $o ).
tff(f782,plain,
$false,
inference(avatar_sat_refutation,[],[f536,f541,f546,f551,f555,f559,f563,f567,f572,f577,f582,f586,f590,f594,f598,f602,f606,f610,f614,f618,f622,f633,f637,f641,f646,f650,f654,f658,f662,f669,f679,f683,f687,f694,f698,f703,f708,f712,f716,f724,f728,f732,f736,f740,f744,f748,f752,f756,f760,f764,f773,f779,f781]) ).
tff(f781,plain,
( ~ spl27_8
| spl27_52 ),
inference(avatar_contradiction_clause,[],[f780]) ).
tff(f780,plain,
( $false
| ~ spl27_8
| spl27_52 ),
inference(resolution,[],[f778,f566]) ).
tff(f566,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0))
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f565]) ).
tff(f565,plain,
( spl27_8
<=> ! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_8])]) ).
tff(f778,plain,
( ~ listsp(dB,it,nil(dB))
| spl27_52 ),
inference(avatar_component_clause,[],[f776]) ).
tff(f776,plain,
( spl27_52
<=> listsp(dB,it,nil(dB)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_52])]) ).
tff(f779,plain,
( ~ spl27_52
| ~ spl27_33
| spl27_51 ),
inference(avatar_split_clause,[],[f774,f770,f685,f776]) ).
tff(f685,plain,
( spl27_33
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_33])]) ).
tff(f770,plain,
( spl27_51
<=> listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),nil(dB))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_51])]) ).
tff(f774,plain,
( ~ listsp(dB,it,nil(dB))
| ~ spl27_33
| spl27_51 ),
inference(forward_demodulation,[],[f772,f686]) ).
tff(f686,plain,
( ! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) )
| ~ spl27_33 ),
inference(avatar_component_clause,[],[f685]) ).
tff(f772,plain,
( ~ listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),nil(dB)))
| spl27_51 ),
inference(avatar_component_clause,[],[f770]) ).
tff(f773,plain,
~ spl27_51,
inference(avatar_split_clause,[],[f339,f770]) ).
tff(f339,plain,
~ listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),nil(dB))),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
~ listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),nil(dB))),
inference(flattening,[],[f116]) ).
tff(f116,negated_conjecture,
~ listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),nil(dB))),
inference(negated_conjecture,[],[f115]) ).
tff(f115,conjecture,
listsp(dB,it,map(dB,dB,aa(nat,fun(dB,dB),aa(fun(dB,fun(nat,dB)),fun(nat,fun(dB,dB)),combc(dB,nat,dB),aa(dB,fun(dB,fun(nat,dB)),aa(fun(dB,fun(dB,fun(nat,dB))),fun(dB,fun(dB,fun(nat,dB))),combc(dB,dB,fun(nat,dB)),subst),u)),i),nil(dB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f764,plain,
spl27_50,
inference(avatar_split_clause,[],[f530,f762]) ).
tff(f762,plain,
( spl27_50
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( substn(sK11(X0,X1,X2),X2,zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_50])]) ).
tff(f530,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( substn(sK11(X0,X1,X2),X2,zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) ),
inference(forward_demodulation,[],[f421,f384]) ).
tff(f384,plain,
! [X0: dB,X1: dB] : ( substn(X1,X0,zero_zero(nat)) = aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)) ),
inference(cnf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: dB,X1: dB] : ( substn(X1,X0,zero_zero(nat)) = aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X1),X0),zero_zero(nat)) ),
inference(rectify,[],[f99]) ).
tff(f99,axiom,
! [X22: dB,X13: dB] : ( substn(X13,X22,zero_zero(nat)) = aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X13),X22),zero_zero(nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_substn__subst__0) ).
tff(f421,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK11(X0,X1,X2)),X2),zero_zero(nat)) = X1 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: dB,X1: dB,X2: dB] :
( ( ( abs(sK11(X0,X1,X2)) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK11(X0,X1,X2)),X2),zero_zero(nat)) = X1 ) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f295,f296]) ).
tff(f296,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),zero_zero(nat)) = X1 ) )
=> ( ( abs(sK11(X0,X1,X2)) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK11(X0,X1,X2)),X2),zero_zero(nat)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f295,plain,
! [X0: dB,X1: dB,X2: dB] :
( ? [X3: dB] :
( ( abs(X3) = X0 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X2),zero_zero(nat)) = X1 ) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f294]) ).
tff(f294,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ sP2(X2,X0,X1) ),
inference(nnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X2: dB,X0: dB,X1: dB] :
( ? [X3: dB] :
( ( abs(X3) = X2 )
& ( aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X3),X1),zero_zero(nat)) = X0 ) )
| ~ sP2(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f760,plain,
spl27_49,
inference(avatar_split_clause,[],[f464,f758]) ).
tff(f758,plain,
( spl27_49
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: list(X1)] :
( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_49])]) ).
tff(f464,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ),
inference(cnf_transformation,[],[f323]) ).
tff(f323,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( ( nil(X0) = map(X1,X0,X3,X2) )
| ( nil(X1) != X2 ) )
& ( ( nil(X1) = X2 )
| ( nil(X0) != map(X1,X0,X3,X2) ) ) ),
inference(nnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: $tType,X2: list(X1),X3: fun(X1,X0)] :
( ( nil(X0) = map(X1,X0,X3,X2) )
<=> ( nil(X1) = X2 ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType,X1: $tType,X5: list(X1),X6: fun(X1,X0)] :
( ( nil(X0) = map(X1,X0,X6,X5) )
<=> ( nil(X1) = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Nil__is__map__conv) ).
tff(f756,plain,
spl27_48,
inference(avatar_split_clause,[],[f439,f754]) ).
tff(f754,plain,
( spl27_48
<=> ! [X2: nat,X0: list(dB),X1: dB] :
( ( nil(dB) = X0 )
| ( var(X2) != foldl(dB,dB,app,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_48])]) ).
tff(f439,plain,
! [X2: nat,X0: list(dB),X1: dB] :
( ( nil(dB) = X0 )
| ( var(X2) != foldl(dB,dB,app,X1,X0) ) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: list(dB),X1: dB,X2: nat] :
( ( ( var(X2) = foldl(dB,dB,app,X1,X0) )
| ( nil(dB) != X0 )
| ( var(X2) != X1 ) )
& ( ( ( nil(dB) = X0 )
& ( var(X2) = X1 ) )
| ( var(X2) != foldl(dB,dB,app,X1,X0) ) ) ),
inference(flattening,[],[f310]) ).
tff(f310,plain,
! [X0: list(dB),X1: dB,X2: nat] :
( ( ( var(X2) = foldl(dB,dB,app,X1,X0) )
| ( nil(dB) != X0 )
| ( var(X2) != X1 ) )
& ( ( ( nil(dB) = X0 )
& ( var(X2) = X1 ) )
| ( var(X2) != foldl(dB,dB,app,X1,X0) ) ) ),
inference(nnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: list(dB),X1: dB,X2: nat] :
( ( var(X2) = foldl(dB,dB,app,X1,X0) )
<=> ( ( nil(dB) = X0 )
& ( var(X2) = X1 ) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X53: list(dB),X45: dB,X59: nat] :
( ( var(X59) = foldl(dB,dB,app,X45,X53) )
<=> ( ( nil(dB) = X53 )
& ( var(X59) = X45 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Var__eq__apps__conv) ).
tff(f752,plain,
spl27_47,
inference(avatar_split_clause,[],[f433,f750]) ).
tff(f750,plain,
( spl27_47
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( ( nil(dB) = X0 )
| ( abs(X2) != foldl(dB,dB,app,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_47])]) ).
tff(f433,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( ( nil(dB) = X0 )
| ( abs(X2) != foldl(dB,dB,app,X1,X0) ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( ( ( abs(X2) = foldl(dB,dB,app,X1,X0) )
| ( nil(dB) != X0 )
| ( abs(X2) != X1 ) )
& ( ( ( nil(dB) = X0 )
& ( abs(X2) = X1 ) )
| ( abs(X2) != foldl(dB,dB,app,X1,X0) ) ) ),
inference(flattening,[],[f306]) ).
tff(f306,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( ( ( abs(X2) = foldl(dB,dB,app,X1,X0) )
| ( nil(dB) != X0 )
| ( abs(X2) != X1 ) )
& ( ( ( nil(dB) = X0 )
& ( abs(X2) = X1 ) )
| ( abs(X2) != foldl(dB,dB,app,X1,X0) ) ) ),
inference(nnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( ( abs(X2) = foldl(dB,dB,app,X1,X0) )
<=> ( ( nil(dB) = X0 )
& ( abs(X2) = X1 ) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X53: list(dB),X45: dB,X54: dB] :
( ( abs(X54) = foldl(dB,dB,app,X45,X53) )
<=> ( ( nil(dB) = X53 )
& ( abs(X54) = X45 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Abs__eq__apps__conv) ).
tff(f748,plain,
spl27_46,
inference(avatar_split_clause,[],[f407,f746]) ).
tff(f746,plain,
( spl27_46
<=> ! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_46])]) ).
tff(f407,plain,
! [X2: dB,X0: dB,X1: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: dB,X1: dB,X2: dB] : ( abs(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X47: dB,X48: dB,X46: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,X48),X47) != abs(X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_dB_Osimps_I9_J) ).
tff(f744,plain,
spl27_45,
inference(avatar_split_clause,[],[f405,f742]) ).
tff(f742,plain,
( spl27_45
<=> ! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_45])]) ).
tff(f405,plain,
! [X2: nat,X0: dB,X1: dB] : ( var(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: dB,X1: dB,X2: nat] : ( var(X2) != aa(dB,dB,aa(dB,fun(dB,dB),app,X1),X0) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X49: dB,X50: dB,X36: nat] : ( var(X36) != aa(dB,dB,aa(dB,fun(dB,dB),app,X50),X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_dB_Osimps_I4_J) ).
tff(f740,plain,
spl27_44,
inference(avatar_split_clause,[],[f390,f738]) ).
tff(f738,plain,
( spl27_44
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_44])]) ).
tff(f390,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X78: bool,X76: bool] :
( pp(X78)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X76),X78)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f736,plain,
spl27_43,
inference(avatar_split_clause,[],[f389,f734]) ).
tff(f734,plain,
( spl27_43
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_43])]) ).
tff(f389,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f110]) ).
tff(f110,axiom,
! [X78: bool,X76: bool] :
( pp(X76)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X76),X78)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f732,plain,
spl27_42,
inference(avatar_split_clause,[],[f388,f730]) ).
tff(f730,plain,
( spl27_42
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_42])]) ).
tff(f388,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X1),X0))
| pp(X1) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X78: bool,X76: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X76),X78))
| pp(X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
tff(f728,plain,
spl27_41,
inference(avatar_split_clause,[],[f387,f726]) ).
tff(f726,plain,
( spl27_41
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_41])]) ).
tff(f387,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X0),X1))
| ~ pp(X1) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X76: bool,X78: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,X76),X78))
| ~ pp(X78) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
tff(f724,plain,
spl27_40,
inference(avatar_split_clause,[],[f365,f722]) ).
tff(f722,plain,
( spl27_40
<=> ! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_40])]) ).
tff(f365,plain,
! [X0: dB] :
( sP0(X0)
| ( abs(sK4(X0)) = X0 )
| listsp(dB,it,sK5(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,sK4(X0)))
& ( abs(sK4(X0)) = X0 ) )
| ( listsp(dB,it,sK5(X0))
& ( foldl(dB,dB,app,var(sK6(X0)),sK5(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f280,f282,f281]) ).
tff(f281,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK4(X0)))
& ( abs(sK4(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,sK5(X0))
& ( foldl(dB,dB,app,var(sK6(X0)),sK5(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,[],[f271]) ).
tff(f271,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(f716,plain,
spl27_39,
inference(avatar_split_clause,[],[f438,f714]) ).
tff(f714,plain,
( spl27_39
<=> ! [X2: nat,X0: list(dB),X1: dB] :
( ( var(X2) = X1 )
| ( var(X2) != foldl(dB,dB,app,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_39])]) ).
tff(f438,plain,
! [X2: nat,X0: list(dB),X1: dB] :
( ( var(X2) = X1 )
| ( var(X2) != foldl(dB,dB,app,X1,X0) ) ),
inference(cnf_transformation,[],[f311]) ).
tff(f712,plain,
spl27_38,
inference(avatar_split_clause,[],[f432,f710]) ).
tff(f710,plain,
( spl27_38
<=> ! [X2: dB,X0: list(dB),X1: dB] :
( ( abs(X2) = X1 )
| ( abs(X2) != foldl(dB,dB,app,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_38])]) ).
tff(f432,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( ( abs(X2) = X1 )
| ( abs(X2) != foldl(dB,dB,app,X1,X0) ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f708,plain,
spl27_37,
inference(avatar_split_clause,[],[f363,f706]) ).
tff(f706,plain,
( spl27_37
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_37])]) ).
tff(f363,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X12: dB] :
( pp(aa(dB,bool,it,X12))
=> pp(aa(dB,bool,it,abs(X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Lambda) ).
tff(f703,plain,
( spl27_36
| ~ spl27_10
| ~ spl27_16 ),
inference(avatar_split_clause,[],[f626,f600,f574,f700]) ).
tff(f700,plain,
( spl27_36
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_36])]) ).
tff(f574,plain,
( spl27_10
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_10])]) ).
tff(f600,plain,
( spl27_16
<=> ! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_16])]) ).
tff(f626,plain,
( sP1(ua)
| ~ spl27_10
| ~ spl27_16 ),
inference(resolution,[],[f601,f576]) ).
tff(f576,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl27_10 ),
inference(avatar_component_clause,[],[f574]) ).
tff(f601,plain,
( ! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) )
| ~ spl27_16 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f698,plain,
spl27_35,
inference(avatar_split_clause,[],[f504,f696]) ).
tff(f696,plain,
( spl27_35
<=> ! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_35])]) ).
tff(f504,plain,
! [X2: list(dB),X3: nat] :
( sP1(foldl(dB,dB,app,var(X3),X2))
| ~ listsp(dB,it,X2) ),
inference(equality_resolution,[],[f368]) ).
tff(f368,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(f694,plain,
spl27_34,
inference(avatar_split_clause,[],[f422,f692]) ).
tff(f692,plain,
( spl27_34
<=> ! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK11(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_34])]) ).
tff(f422,plain,
! [X2: dB,X0: dB,X1: dB] :
( ( abs(sK11(X0,X1,X2)) = X0 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f297]) ).
tff(f687,plain,
spl27_33,
inference(avatar_split_clause,[],[f404,f685]) ).
tff(f404,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,X1)] : ( nil(X1) = map(X0,X1,X2,nil(X0)) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X1: $tType,X0: $tType,X6: fun(X1,X0)] : ( nil(X0) = map(X1,X0,X6,nil(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_map_Osimps_I1_J) ).
tff(f683,plain,
spl27_32,
inference(avatar_split_clause,[],[f402,f681]) ).
tff(f681,plain,
( spl27_32
<=> ! [X0: list(type),X1: fun(nat,type)] :
( ( nil(type) = X0 )
| ~ typings(X1,nil(dB),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_32])]) ).
tff(f402,plain,
! [X0: list(type),X1: fun(nat,type)] :
( ( nil(type) = X0 )
| ~ typings(X1,nil(dB),X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: list(type),X1: fun(nat,type)] :
( ( typings(X1,nil(dB),X0)
| ( nil(type) != X0 ) )
& ( ( nil(type) = X0 )
| ~ typings(X1,nil(dB),X0) ) ),
inference(nnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: list(type),X1: fun(nat,type)] :
( typings(X1,nil(dB),X0)
<=> ( nil(type) = X0 ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X37: list(type),X19: fun(nat,type)] :
( typings(X19,nil(dB),X37)
<=> ( nil(type) = X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_typings_Osimps_I1_J) ).
tff(f679,plain,
spl27_31,
inference(avatar_split_clause,[],[f393,f677]) ).
tff(f677,plain,
( spl27_31
<=> ! [X0: dB,X1: dB] :
( ( abs(sK10(X0,X1)) = X0 )
| ~ beta(abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_31])]) ).
tff(f393,plain,
! [X0: dB,X1: dB] :
( ( abs(sK10(X0,X1)) = X0 )
| ~ beta(abs(X1),X0) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: dB,X1: dB] :
( ( beta(X1,sK10(X0,X1))
& ( abs(sK10(X0,X1)) = X0 ) )
| ~ beta(abs(X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f221,f289]) ).
tff(f289,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( beta(X1,X2)
& ( abs(X2) = X0 ) )
=> ( beta(X1,sK10(X0,X1))
& ( abs(sK10(X0,X1)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f221,plain,
! [X0: dB,X1: dB] :
( ? [X2: dB] :
( beta(X1,X2)
& ( abs(X2) = X0 ) )
| ~ beta(abs(X1),X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),X0)
=> ~ ! [X2: dB] :
( ( abs(X2) = X0 )
=> ~ beta(X1,X2) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X22: dB,X12: dB] :
( beta(abs(X12),X22)
=> ~ ! [X70: dB] :
( ( abs(X70) = X22 )
=> ~ beta(X12,X70) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_beta__cases_I2_J) ).
tff(f669,plain,
( spl27_30
| ~ spl27_11
| ~ spl27_16 ),
inference(avatar_split_clause,[],[f625,f600,f579,f666]) ).
tff(f666,plain,
( spl27_30
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_30])]) ).
tff(f579,plain,
( spl27_11
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_11])]) ).
tff(f625,plain,
( sP1(u)
| ~ spl27_11
| ~ spl27_16 ),
inference(resolution,[],[f601,f581]) ).
tff(f581,plain,
( pp(aa(dB,bool,it,u))
| ~ spl27_11 ),
inference(avatar_component_clause,[],[f579]) ).
tff(f662,plain,
spl27_29,
inference(avatar_split_clause,[],[f503,f660]) ).
tff(f660,plain,
( spl27_29
<=> ! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_29])]) ).
tff(f503,plain,
! [X1: dB] :
( sP1(abs(X1))
| ~ pp(aa(dB,bool,it,X1)) ),
inference(equality_resolution,[],[f369]) ).
tff(f369,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f658,plain,
spl27_28,
inference(avatar_split_clause,[],[f445,f656]) ).
tff(f656,plain,
( spl27_28
<=> ! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X3,X2,nil(X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_28])]) ).
tff(f445,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X3,X2,nil(X0)) = X2 ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: fun(X1,fun(X0,X1))] : ( foldl(X1,X0,X3,X2,nil(X0)) = X2 ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X1: $tType,X0: $tType,X51: X0,X6: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X6,X51,nil(X1)) = X51 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_foldl__Nil) ).
tff(f654,plain,
spl27_27,
inference(avatar_split_clause,[],[f444,f652]) ).
tff(f652,plain,
( spl27_27
<=> ! [X1: $tType,X0: $tType,X3: fun(X0,fun(X1,X1)),X2: X1] : ( foldr(X0,X1,X3,nil(X0),X2) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_27])]) ).
tff(f444,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X3,nil(X0),X2) = X2 ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: fun(X0,fun(X1,X1))] : ( foldr(X0,X1,X3,nil(X0),X2) = X2 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X1: $tType,X0: $tType,X51: X0,X6: fun(X1,fun(X0,X0))] : ( foldr(X1,X0,X6,nil(X1),X51) = X51 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_foldr_Osimps_I1_J) ).
tff(f650,plain,
spl27_26,
inference(avatar_split_clause,[],[f443,f648]) ).
tff(f648,plain,
( spl27_26
<=> ! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_26])]) ).
tff(f443,plain,
! [X1: $tType,X0: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: $tType,X2: fun(X0,fun(list(X0),X1)),X3: X1] : ( list_case(X1,X0,X3,X2,nil(X0)) = X3 ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X1: $tType,X0: $tType,X72: fun(X1,fun(list(X1),X0)),X73: X0] : ( list_case(X0,X1,X73,X72,nil(X1)) = X73 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_list_Osimps_I4_J) ).
tff(f646,plain,
( spl27_25
| ~ spl27_9
| ~ spl27_16 ),
inference(avatar_split_clause,[],[f624,f600,f569,f643]) ).
tff(f643,plain,
( spl27_25
<=> sP1(t2) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_25])]) ).
tff(f569,plain,
( spl27_9
<=> pp(aa(dB,bool,it,t2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_9])]) ).
tff(f624,plain,
( sP1(t2)
| ~ spl27_9
| ~ spl27_16 ),
inference(resolution,[],[f601,f571]) ).
tff(f571,plain,
( pp(aa(dB,bool,it,t2))
| ~ spl27_9 ),
inference(avatar_component_clause,[],[f569]) ).
tff(f641,plain,
spl27_24,
inference(avatar_split_clause,[],[f394,f639]) ).
tff(f639,plain,
( spl27_24
<=> ! [X0: dB,X1: dB] :
( beta(X1,sK10(X0,X1))
| ~ beta(abs(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_24])]) ).
tff(f394,plain,
! [X0: dB,X1: dB] :
( beta(X1,sK10(X0,X1))
| ~ beta(abs(X1),X0) ),
inference(cnf_transformation,[],[f290]) ).
tff(f637,plain,
spl27_23,
inference(avatar_split_clause,[],[f382,f635]) ).
tff(f635,plain,
( spl27_23
<=> ! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_23])]) ).
tff(f382,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType,X1: list(X0)] : ( map(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType,X8: list(X0)] : ( map(X0,X0,combi(X0),X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_map__ident) ).
tff(f633,plain,
spl27_22,
inference(avatar_split_clause,[],[f373,f631]) ).
tff(f631,plain,
( spl27_22
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,sK8(X0)))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_22])]) ).
tff(f373,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,sK8(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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),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,sK8(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(X0)) = X0 ) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),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,sK8(X0)))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,sK7(X0)),sK8(X0)),zero_zero(nat)),sK9(X0))))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(sK7(X0))),sK8(X0)),sK9(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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),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,[],[f270]) ).
tff(f270,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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),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(f622,plain,
spl27_21,
inference(avatar_split_clause,[],[f400,f620]) ).
tff(f620,plain,
( spl27_21
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_21])]) ).
tff(f400,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( var(X0) != var(X1) ) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: nat,X1: nat] :
( ( ( var(X0) = var(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( var(X0) != var(X1) ) ) ),
inference(nnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: nat,X1: nat] :
( ( var(X0) = var(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X20: nat,X21: nat] :
( ( var(X21) = var(X20) )
<=> ( X20 = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_dB_Osimps_I1_J) ).
tff(f618,plain,
spl27_20,
inference(avatar_split_clause,[],[f398,f616]) ).
tff(f616,plain,
( spl27_20
<=> ! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_20])]) ).
tff(f398,plain,
! [X0: dB,X1: dB] :
( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: dB,X1: dB] :
( ( ( abs(X0) = abs(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( abs(X0) != abs(X1) ) ) ),
inference(nnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: dB,X1: dB] :
( ( abs(X0) = abs(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X43: dB,X44: dB] :
( ( abs(X44) = abs(X43) )
<=> ( X43 = X44 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_dB_Osimps_I3_J) ).
tff(f614,plain,
spl27_19,
inference(avatar_split_clause,[],[f392,f612]) ).
tff(f612,plain,
( spl27_19
<=> ! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_19])]) ).
tff(f392,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: dB,X1: dB] :
( beta(abs(X1),abs(X0))
| ~ beta(X1,X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: dB,X1: dB] :
( beta(X1,X0)
=> beta(abs(X1),abs(X0)) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X13: dB,X22: dB] :
( beta(X22,X13)
=> beta(abs(X22),abs(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_abs) ).
tff(f610,plain,
spl27_18,
inference(avatar_split_clause,[],[f381,f608]) ).
tff(f608,plain,
( spl27_18
<=> ! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_18])]) ).
tff(f381,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: $tType,X1: X0] : ( aa(X0,X0,combi(X0),X1) = X1 ),
inference(rectify,[],[f107]) ).
tff(f107,axiom,
! [X0: $tType,X76: X0] : ( aa(X0,X0,combi(X0),X76) = X76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
tff(f606,plain,
spl27_17,
inference(avatar_split_clause,[],[f376,f604]) ).
tff(f604,plain,
( spl27_17
<=> ! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_17])]) ).
tff(f376,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,[],[f272]) ).
tff(f272,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f125,f271,f270]) ).
tff(f125,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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),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,[],[f73]) ).
tff(f73,axiom,
! [X51: dB] :
( pp(aa(dB,bool,it,X51))
<=> ( ? [X63: dB,X64: dB,X65: list(dB)] :
( pp(aa(dB,bool,it,X64))
& pp(aa(dB,bool,it,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,X63),X64),zero_zero(nat)),X65)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X63)),X64),X65) = X51 ) )
| ? [X63: dB] :
( pp(aa(dB,bool,it,X63))
& ( abs(X63) = X51 ) )
| ? [X61: list(dB),X62: nat] :
( listsp(dB,it,X61)
& ( foldl(dB,dB,app,var(X62),X61) = X51 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_IT_Osimps) ).
tff(f602,plain,
spl27_16,
inference(avatar_split_clause,[],[f375,f600]) ).
tff(f375,plain,
! [X0: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f288]) ).
tff(f598,plain,
spl27_15,
inference(avatar_split_clause,[],[f359,f596]) ).
tff(f596,plain,
( spl27_15
<=> ! [X0: nat] : pp(aa(dB,bool,it,var(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_15])]) ).
tff(f359,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X14: nat] : pp(aa(dB,bool,it,var(X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_Var__IT) ).
tff(f594,plain,
spl27_14,
inference(avatar_split_clause,[],[f358,f592]) ).
tff(f592,plain,
( spl27_14
<=> ! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_14])]) ).
tff(f358,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: nat] : ( zero_zero(nat) = size_size(dB,var(X0)) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X36: nat] : ( zero_zero(nat) = size_size(dB,var(X36)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_dB_Osize_I4_J) ).
tff(f590,plain,
spl27_13,
inference(avatar_split_clause,[],[f508,f588]) ).
tff(f588,plain,
( spl27_13
<=> ! [X1: fun(nat,type)] : typings(X1,nil(dB),nil(type)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_13])]) ).
tff(f508,plain,
! [X1: fun(nat,type)] : typings(X1,nil(dB),nil(type)),
inference(equality_resolution,[],[f403]) ).
tff(f403,plain,
! [X0: list(type),X1: fun(nat,type)] :
( typings(X1,nil(dB),X0)
| ( nil(type) != X0 ) ),
inference(cnf_transformation,[],[f293]) ).
tff(f586,plain,
spl27_12,
inference(avatar_split_clause,[],[f357,f584]) ).
tff(f584,plain,
( spl27_12
<=> ! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_12])]) ).
tff(f357,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(cnf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: nat] : ( zero_zero(nat) = dB_size(var(X0)) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X36: nat] : ( zero_zero(nat) = dB_size(var(X36)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_dB_Osize_I1_J) ).
tff(f582,plain,
spl27_11,
inference(avatar_split_clause,[],[f346,f579]) ).
tff(f346,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_uIT) ).
tff(f577,plain,
spl27_10,
inference(avatar_split_clause,[],[f345,f574]) ).
tff(f345,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Var_I3_J) ).
tff(f572,plain,
spl27_9,
inference(avatar_split_clause,[],[f344,f569]) ).
tff(f344,plain,
pp(aa(dB,bool,it,t2)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(dB,bool,it,t2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096IT_At_096) ).
tff(f567,plain,
spl27_8,
inference(avatar_split_clause,[],[f380,f565]) ).
tff(f380,plain,
! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType,X4: fun(X0,bool)] : listsp(X0,X4,nil(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_listsp_ONil) ).
tff(f563,plain,
spl27_7,
inference(avatar_split_clause,[],[f378,f561]) ).
tff(f561,plain,
( spl27_7
<=> ! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).
tff(f378,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(cnf_transformation,[],[f127]) ).
tff(f127,plain,
! [X0: dB,X1: nat] : ( abs(X0) != var(X1) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X46: dB,X36: nat] : ( var(X36) != abs(X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_dB_Osimps_I6_J) ).
tff(f559,plain,
spl27_6,
inference(avatar_split_clause,[],[f377,f557]) ).
tff(f557,plain,
( spl27_6
<=> ! [X0: dB,X1: nat] : ~ beta(var(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_6])]) ).
tff(f377,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(cnf_transformation,[],[f126]) ).
tff(f126,plain,
! [X0: dB,X1: nat] : ~ beta(var(X1),X0),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X13: dB,X11: nat] : ~ beta(var(X11),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_beta__cases_I1_J) ).
tff(f555,plain,
spl27_5,
inference(avatar_split_clause,[],[f370,f553]) ).
tff(f553,plain,
( spl27_5
<=> ! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_5])]) ).
tff(f370,plain,
! [X0: dB] :
( sP1(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f551,plain,
~ spl27_4,
inference(avatar_split_clause,[],[f343,f548]) ).
tff(f548,plain,
( spl27_4
<=> ( n = i ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_4])]) ).
tff(f343,plain,
n != i,
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
n != i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_False) ).
tff(f546,plain,
spl27_3,
inference(avatar_split_clause,[],[f342,f543]) ).
tff(f543,plain,
( spl27_3
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_3])]) ).
tff(f342,plain,
pp(fTrue),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f541,plain,
spl27_2,
inference(avatar_split_clause,[],[f341,f538]) ).
tff(f538,plain,
( spl27_2
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).
tff(f341,plain,
zero(nat),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f536,plain,
~ spl27_1,
inference(avatar_split_clause,[],[f340,f533]) ).
tff(f533,plain,
( spl27_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).
tff(f340,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL825_5 : TPTP v8.1.2. Released v6.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 23:01:49 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (10068)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (10071)WARNING: value z3 for option sas not known
% 0.22/0.42 % (10069)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.42 % (10073)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)
% 0.22/0.42 % (10072)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.42 % (10071)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)
% 0.22/0.42 % (10070)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.42 % (10074)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)
% 0.22/0.42 % (10075)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)
% 0.22/0.43 % Exception at run slice level% (10075)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.43 % Exception at run slice level
% 0.22/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.43
% 0.22/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.43 % Exception at run slice level
% 0.22/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.44 % (10073)First to succeed.
% 0.22/0.45 % (10079)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.45 % (10078)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.45 % (10080)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.45 % (10073)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (10073)------------------------------
% 0.22/0.45 % (10073)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.45 % (10073)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (10073)Memory used [KB]: 1408
% 0.22/0.45 % (10073)Time elapsed: 0.027 s
% 0.22/0.45 % (10073)Instructions burned: 46 (million)
% 0.22/0.45 % (10073)------------------------------
% 0.22/0.45 % (10073)------------------------------
% 0.22/0.45 % (10068)Success in time 0.079 s
%------------------------------------------------------------------------------