TSTP Solution File: LCL840_5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL840_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n010.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 : Thu Aug 31 08:31:43 EDT 2023
% Result : Theorem 0.23s 0.53s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 155
% Syntax : Number of formulae : 314 ( 66 unt; 76 typ; 0 def)
% Number of atoms : 534 ( 30 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 488 ( 192 ~; 181 |; 41 &)
% ( 53 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 83 ( 43 >; 40 *; 0 +; 0 <<)
% Number of predicates : 60 ( 58 usr; 49 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 25 con; 0-5 aty)
% Number of variables : 173 (; 112 !; 36 ?; 173 :)
% ( 25 !>; 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(X0,fun(X1,X2)) * 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(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
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,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_13,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_14,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_15,type,
suc: nat > nat ).
tff(func_def_16,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_17,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_18,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_19,type,
fFalse: bool ).
tff(func_def_20,type,
fTrue: bool ).
tff(func_def_21,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_22,type,
t2: type ).
tff(func_def_23,type,
t: type ).
tff(func_def_24,type,
t_a: type ).
tff(func_def_25,type,
t1: type ).
tff(func_def_26,type,
ua1: type ).
tff(func_def_27,type,
a: dB ).
tff(func_def_28,type,
as: list(dB) ).
tff(func_def_29,type,
e: fun(nat,type) ).
tff(func_def_30,type,
ea: fun(nat,type) ).
tff(func_def_31,type,
i: nat ).
tff(func_def_32,type,
ia: nat ).
tff(func_def_33,type,
r: dB ).
tff(func_def_34,type,
t3: dB ).
tff(func_def_35,type,
u: dB ).
tff(func_def_36,type,
ua: dB ).
tff(func_def_37,type,
sK3: type ).
tff(func_def_38,type,
sK4: type ).
tff(func_def_39,type,
sK5: nat > nat ).
tff(func_def_40,type,
sK6: nat > nat ).
tff(func_def_41,type,
sK7: dB > dB ).
tff(func_def_42,type,
sK8: dB > list(dB) ).
tff(func_def_43,type,
sK9: dB > nat ).
tff(func_def_44,type,
sK10: dB > dB ).
tff(func_def_45,type,
sK11: dB > dB ).
tff(func_def_46,type,
sK12: dB > list(dB) ).
tff(func_def_47,type,
sK13: ( dB * dB ) > dB ).
tff(func_def_48,type,
sK14: fun(nat,bool) > nat ).
tff(func_def_49,type,
sK15: fun(nat,bool) > nat ).
tff(func_def_50,type,
sK16: ( dB * fun(nat,type) ) > type ).
tff(func_def_51,type,
sK17: ( dB * fun(nat,type) ) > type ).
tff(func_def_52,type,
sK18: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_53,type,
sK19: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_54,type,
sK20: ( dB * dB * dB ) > dB ).
tff(func_def_55,type,
sK21: ( dB * dB * dB ) > dB ).
tff(func_def_56,type,
sK22: ( dB * dB * dB ) > dB ).
tff(func_def_57,type,
sK23: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_58,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_59,type,
sK25: ( 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,
typing: ( fun(nat,type) * dB * type ) > $o ).
tff(pred_def_5,type,
typings: ( fun(nat,type) * list(dB) * list(type) ) > $o ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(pred_def_7,type,
sP0: dB > $o ).
tff(pred_def_8,type,
sP1: dB > $o ).
tff(pred_def_9,type,
sP2: ( dB * dB * dB ) > $o ).
tff(pred_def_10,type,
sQ26_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f1055,plain,
$false,
inference(avatar_smt_refutation,[],[f570,f574,f578,f582,f586,f590,f594,f598,f602,f606,f610,f614,f618,f622,f626,f630,f634,f638,f642,f651,f655,f659,f663,f679,f683,f687,f691,f727,f763,f767,f771,f775,f812,f816,f820,f824,f842,f846,f904,f908,f912,f916,f954,f958,f962,f966,f970,f1044,f1050,f1052,f1054]) ).
tff(f1054,plain,
( ~ spl27_48
| spl27_1
| ~ spl27_4
| ~ spl27_7
| ~ spl27_18 ),
inference(avatar_split_clause,[],[f1053,f636,f592,f580,f568,f1048]) ).
tff(f1048,plain,
( spl27_48
<=> beta(a,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_48])]) ).
tff(f568,plain,
( spl27_1
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).
tff(f580,plain,
( spl27_4
<=> typing(e,u,t1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_4])]) ).
tff(f592,plain,
( spl27_7
<=> pp(aa(dB,bool,it,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).
tff(f636,plain,
( spl27_18
<=> typing(shift(type,e,i,t1),a,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_18])]) ).
tff(f1053,plain,
( ~ beta(a,a)
| spl27_1
| ~ spl27_4
| ~ spl27_7
| ~ spl27_18 ),
inference(subsumption_resolution,[],[f1042,f581]) ).
tff(f581,plain,
( typing(e,u,t1)
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f580]) ).
tff(f1042,plain,
( ~ typing(e,u,t1)
| ~ beta(a,a)
| spl27_1
| ~ spl27_7
| ~ spl27_18 ),
inference(resolution,[],[f1035,f703]) ).
tff(f703,plain,
( ! [X6: dB] :
( typing(shift(type,e,i,t1),X6,sK3)
| ~ beta(a,X6) )
| ~ spl27_18 ),
inference(resolution,[],[f432,f637]) ).
tff(f637,plain,
( typing(shift(type,e,i,t1),a,sK3)
| ~ spl27_18 ),
inference(avatar_component_clause,[],[f636]) ).
tff(f432,plain,
! [X2: dB,X3: fun(nat,type),X0: dB,X1: type] :
( ~ typing(X3,X2,X1)
| ~ beta(X2,X0)
| typing(X3,X0,X1) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( typing(X3,X0,X1)
| ~ beta(X2,X0)
| ~ typing(X3,X2,X1) ),
inference(flattening,[],[f233]) ).
tff(f233,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( typing(X3,X0,X1)
| ~ beta(X2,X0)
| ~ typing(X3,X2,X1) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: dB,X1: type,X2: dB,X3: fun(nat,type)] :
( typing(X3,X2,X1)
=> ( beta(X2,X0)
=> typing(X3,X0,X1) ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X46: dB,X5: type,X8: dB,X7: fun(nat,type)] :
( typing(X7,X8,X5)
=> ( beta(X8,X46)
=> typing(X7,X46,X5) ) ),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_52_subject__reduction) ).
tff(f1035,plain,
( ! [X0: fun(nat,type),X1: type] :
( ~ typing(shift(type,X0,i,t1),a,X1)
| ~ typing(X0,u,t1) )
| spl27_1
| ~ spl27_7 ),
inference(subsumption_resolution,[],[f1029,f593]) ).
tff(f593,plain,
( pp(aa(dB,bool,it,u))
| ~ spl27_7 ),
inference(avatar_component_clause,[],[f592]) ).
tff(f1029,plain,
( ! [X0: fun(nat,type),X1: type] :
( ~ typing(X0,u,t1)
| ~ pp(aa(dB,bool,it,u))
| ~ typing(shift(type,X0,i,t1),a,X1) )
| spl27_1 ),
inference(resolution,[],[f433,f569]) ).
tff(f569,plain,
( ~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)))
| spl27_1 ),
inference(avatar_component_clause,[],[f568]) ).
tff(f433,plain,
! [X2: nat,X3: fun(nat,type),X0: dB,X1: type] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) ),
inference(flattening,[],[f235]) ).
tff(f235,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2)))
| ~ typing(X3,X0,t1)
| ~ pp(aa(dB,bool,it,X0))
| ~ typing(shift(type,X3,X2,t1),a,X1) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: dB,X1: type,X2: nat,X3: fun(nat,type)] :
( typing(shift(type,X3,X2,t1),a,X1)
=> ( pp(aa(dB,bool,it,X0))
=> ( typing(X3,X0,t1)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X0),X2))) ) ) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X4: dB,X15: type,X6: nat,X7: fun(nat,type)] :
( typing(shift(type,X7,X6,t1),a,X15)
=> ( pp(aa(dB,bool,it,X4))
=> ( typing(X7,X4,t1)
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X4),X6))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_12_SI2) ).
tff(f1052,plain,
( spl27_1
| ~ spl27_4
| ~ spl27_7
| ~ spl27_18 ),
inference(avatar_contradiction_clause,[],[f1051]) ).
tff(f1051,plain,
( $false
| spl27_1
| ~ spl27_4
| ~ spl27_7
| ~ spl27_18 ),
inference(subsumption_resolution,[],[f1040,f581]) ).
tff(f1040,plain,
( ~ typing(e,u,t1)
| spl27_1
| ~ spl27_7
| ~ spl27_18 ),
inference(resolution,[],[f1035,f637]) ).
tff(f1050,plain,
( ~ spl27_48
| spl27_1
| ~ spl27_4
| ~ spl27_7
| ~ spl27_9 ),
inference(avatar_split_clause,[],[f1046,f600,f592,f580,f568,f1048]) ).
tff(f600,plain,
( spl27_9
<=> typing(shift(type,e,i,t1),a,t2) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_9])]) ).
tff(f1046,plain,
( ~ beta(a,a)
| spl27_1
| ~ spl27_4
| ~ spl27_7
| ~ spl27_9 ),
inference(subsumption_resolution,[],[f1039,f581]) ).
tff(f1039,plain,
( ~ typing(e,u,t1)
| ~ beta(a,a)
| spl27_1
| ~ spl27_7
| ~ spl27_9 ),
inference(resolution,[],[f1035,f700]) ).
tff(f700,plain,
( ! [X3: dB] :
( typing(shift(type,e,i,t1),X3,t2)
| ~ beta(a,X3) )
| ~ spl27_9 ),
inference(resolution,[],[f432,f601]) ).
tff(f601,plain,
( typing(shift(type,e,i,t1),a,t2)
| ~ spl27_9 ),
inference(avatar_component_clause,[],[f600]) ).
tff(f1044,plain,
( spl27_1
| ~ spl27_4
| ~ spl27_7
| ~ spl27_9 ),
inference(avatar_contradiction_clause,[],[f1043]) ).
tff(f1043,plain,
( $false
| spl27_1
| ~ spl27_4
| ~ spl27_7
| ~ spl27_9 ),
inference(subsumption_resolution,[],[f1037,f581]) ).
tff(f1037,plain,
( ~ typing(e,u,t1)
| spl27_1
| ~ spl27_7
| ~ spl27_9 ),
inference(resolution,[],[f1035,f601]) ).
tff(f970,plain,
( spl27_47
| ~ spl27_13 ),
inference(avatar_split_clause,[],[f950,f616,f968]) ).
tff(f968,plain,
( spl27_47
<=> sP1(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_47])]) ).
tff(f616,plain,
( spl27_13
<=> 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,r),a),zero_zero(nat)),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_13])]) ).
tff(f950,plain,
( sP1(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as))
| ~ spl27_13 ),
inference(resolution,[],[f617,f372]) ).
tff(f372,plain,
! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(X0) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: dB] :
( ( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) )
& ( sP1(X0)
| ~ pp(aa(dB,bool,it,X0)) ) ),
inference(nnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
<=> sP1(X0) ),
inference(definition_folding,[],[f129,f262,f261]) ).
tff(f261,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(f262,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(f129,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,[],[f96]) ).
tff(f96,axiom,
! [X66: dB] :
( pp(aa(dB,bool,it,X66))
<=> ( ? [X77: dB,X78: dB,X79: list(dB)] :
( pp(aa(dB,bool,it,X78))
& 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,X77),X78),zero_zero(nat)),X79)))
& ( foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X77)),X78),X79) = X66 ) )
| ? [X77: dB] :
( pp(aa(dB,bool,it,X77))
& ( abs(X77) = X66 ) )
| ? [X75: list(dB),X76: nat] :
( listsp(dB,it,X75)
& ( foldl(dB,dB,app,var(X76),X75) = X66 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_95_IT_Osimps) ).
tff(f617,plain,
( 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,r),a),zero_zero(nat)),as)))
| ~ spl27_13 ),
inference(avatar_component_clause,[],[f616]) ).
tff(f966,plain,
( spl27_46
| ~ spl27_13 ),
inference(avatar_split_clause,[],[f949,f616,f964]) ).
tff(f964,plain,
( spl27_46
<=> sP1(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_46])]) ).
tff(f949,plain,
( sP1(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)))
| ~ spl27_13 ),
inference(resolution,[],[f617,f473]) ).
tff(f473,plain,
! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(X1)) ),
inference(equality_resolution,[],[f366]) ).
tff(f366,plain,
! [X0: dB,X1: dB] :
( sP1(X0)
| ~ pp(aa(dB,bool,it,X1))
| ( abs(X1) != X0 ) ),
inference(cnf_transformation,[],[f280]) ).
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)
| ( pp(aa(dB,bool,it,sK7(X0)))
& ( abs(sK7(X0)) = X0 ) )
| ( listsp(dB,it,sK8(X0))
& ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 ) )
| ~ sP1(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f277,f279,f278]) ).
tff(f278,plain,
! [X0: dB] :
( ? [X4: dB] :
( pp(aa(dB,bool,it,X4))
& ( abs(X4) = X0 ) )
=> ( pp(aa(dB,bool,it,sK7(X0)))
& ( abs(sK7(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f279,plain,
! [X0: dB] :
( ? [X5: list(dB),X6: nat] :
( listsp(dB,it,X5)
& ( foldl(dB,dB,app,var(X6),X5) = X0 ) )
=> ( listsp(dB,it,sK8(X0))
& ( foldl(dB,dB,app,var(sK9(X0)),sK8(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f277,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,[],[f276]) ).
tff(f276,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,[],[f275]) ).
tff(f275,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,[],[f262]) ).
tff(f962,plain,
( spl27_45
| ~ spl27_13 ),
inference(avatar_split_clause,[],[f948,f616,f960]) ).
tff(f960,plain,
( spl27_45
<=> sP1(abs(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_45])]) ).
tff(f948,plain,
( sP1(abs(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as))))
| ~ spl27_13 ),
inference(resolution,[],[f617,f729]) ).
tff(f729,plain,
! [X0: dB] :
( ~ pp(aa(dB,bool,it,X0))
| sP1(abs(abs(X0))) ),
inference(resolution,[],[f360,f473]) ).
tff(f360,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,abs(X0)))
| ~ pp(aa(dB,bool,it,X0)) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
=> pp(aa(dB,bool,it,abs(X0))) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X13: dB] :
( pp(aa(dB,bool,it,X13))
=> pp(aa(dB,bool,it,abs(X13))) ),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_38_Lambda) ).
tff(f958,plain,
( spl27_44
| ~ spl27_13 ),
inference(avatar_split_clause,[],[f947,f616,f956]) ).
tff(f956,plain,
( spl27_44
<=> sP1(abs(abs(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_44])]) ).
tff(f947,plain,
( sP1(abs(abs(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)))))
| ~ spl27_13 ),
inference(resolution,[],[f617,f752]) ).
tff(f752,plain,
! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(abs(abs(X1)))) ),
inference(resolution,[],[f729,f360]) ).
tff(f954,plain,
( spl27_43
| ~ spl27_13 ),
inference(avatar_split_clause,[],[f946,f616,f952]) ).
tff(f952,plain,
( spl27_43
<=> sP1(abs(abs(abs(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_43])]) ).
tff(f946,plain,
( sP1(abs(abs(abs(abs(foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as))))))
| ~ spl27_13 ),
inference(resolution,[],[f617,f800]) ).
tff(f800,plain,
! [X1: dB] :
( ~ pp(aa(dB,bool,it,X1))
| sP1(abs(abs(abs(abs(X1))))) ),
inference(resolution,[],[f752,f360]) ).
tff(f916,plain,
( spl27_42
| ~ spl27_6 ),
inference(avatar_split_clause,[],[f898,f588,f914]) ).
tff(f914,plain,
( spl27_42
<=> sP1(abs(abs(abs(abs(ua))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_42])]) ).
tff(f588,plain,
( spl27_6
<=> pp(aa(dB,bool,it,ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_6])]) ).
tff(f898,plain,
( sP1(abs(abs(abs(abs(ua)))))
| ~ spl27_6 ),
inference(resolution,[],[f800,f589]) ).
tff(f589,plain,
( pp(aa(dB,bool,it,ua))
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f588]) ).
tff(f912,plain,
( spl27_41
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f897,f592,f910]) ).
tff(f910,plain,
( spl27_41
<=> sP1(abs(abs(abs(abs(u))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_41])]) ).
tff(f897,plain,
( sP1(abs(abs(abs(abs(u)))))
| ~ spl27_7 ),
inference(resolution,[],[f800,f593]) ).
tff(f908,plain,
( spl27_40
| ~ spl27_5 ),
inference(avatar_split_clause,[],[f896,f584,f906]) ).
tff(f906,plain,
( spl27_40
<=> sP1(abs(abs(abs(abs(t3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_40])]) ).
tff(f584,plain,
( spl27_5
<=> pp(aa(dB,bool,it,t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_5])]) ).
tff(f896,plain,
( sP1(abs(abs(abs(abs(t3)))))
| ~ spl27_5 ),
inference(resolution,[],[f800,f585]) ).
tff(f585,plain,
( pp(aa(dB,bool,it,t3))
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f584]) ).
tff(f904,plain,
( spl27_39
| ~ spl27_8 ),
inference(avatar_split_clause,[],[f895,f596,f902]) ).
tff(f902,plain,
( spl27_39
<=> sP1(abs(abs(abs(abs(a))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_39])]) ).
tff(f596,plain,
( spl27_8
<=> pp(aa(dB,bool,it,a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_8])]) ).
tff(f895,plain,
( sP1(abs(abs(abs(abs(a)))))
| ~ spl27_8 ),
inference(resolution,[],[f800,f597]) ).
tff(f597,plain,
( pp(aa(dB,bool,it,a))
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f596]) ).
tff(f846,plain,
( spl27_38
| ~ spl27_19 ),
inference(avatar_split_clause,[],[f836,f640,f844]) ).
tff(f844,plain,
( spl27_38
<=> typing(shift(type,e,i,t1),a,sK23(sK4,a,abs(r),shift(type,e,i,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_38])]) ).
tff(f640,plain,
( spl27_19
<=> typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_19])]) ).
tff(f836,plain,
( typing(shift(type,e,i,t1),a,sK23(sK4,a,abs(r),shift(type,e,i,t1)))
| ~ spl27_19 ),
inference(resolution,[],[f436,f641]) ).
tff(f641,plain,
( typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4)
| ~ spl27_19 ),
inference(avatar_component_clause,[],[f640]) ).
tff(f436,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: dB] :
( ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0)
| typing(X3,X1,sK23(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f309]) ).
tff(f309,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ( typing(X3,X1,sK23(X0,X1,X2,X3))
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK23(X0,X1,X2,X3)),X0)) )
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f238,f308]) ).
tff(f308,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( typing(X3,X1,X4)
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0)) )
=> ( typing(X3,X1,sK23(X0,X1,X2,X3))
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,sK23(X0,X1,X2,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f238,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( ? [X4: type] :
( typing(X3,X1,X4)
& typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0)) )
| ~ typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: type,X1: dB,X2: dB,X3: fun(nat,type)] :
( typing(X3,aa(dB,dB,aa(dB,fun(dB,dB),app,X2),X1),X0)
=> ~ ! [X4: type] :
( typing(X3,X2,aa(type,type,aa(type,fun(type,type),fun1,X4),X0))
=> ~ typing(X3,X1,X4) ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X5: type,X4: dB,X8: dB,X7: fun(nat,type)] :
( typing(X7,aa(dB,dB,aa(dB,fun(dB,dB),app,X8),X4),X5)
=> ~ ! [X31: type] :
( typing(X7,X8,aa(type,type,aa(type,fun(type,type),fun1,X31),X5))
=> ~ typing(X7,X4,X31) ) ),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_34_typing__elims_I2_J) ).
tff(f842,plain,
( spl27_37
| ~ spl27_10 ),
inference(avatar_split_clause,[],[f835,f604,f840]) ).
tff(f840,plain,
( spl27_37
<=> typing(shift(type,e,i,t1),a,sK23(ua1,a,abs(r),shift(type,e,i,t1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_37])]) ).
tff(f604,plain,
( spl27_10
<=> typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_10])]) ).
tff(f835,plain,
( typing(shift(type,e,i,t1),a,sK23(ua1,a,abs(r),shift(type,e,i,t1)))
| ~ spl27_10 ),
inference(resolution,[],[f436,f605]) ).
tff(f605,plain,
( typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1)
| ~ spl27_10 ),
inference(avatar_component_clause,[],[f604]) ).
tff(f824,plain,
( spl27_36
| ~ spl27_6 ),
inference(avatar_split_clause,[],[f806,f588,f822]) ).
tff(f822,plain,
( spl27_36
<=> sP1(abs(abs(abs(ua)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_36])]) ).
tff(f806,plain,
( sP1(abs(abs(abs(ua))))
| ~ spl27_6 ),
inference(resolution,[],[f752,f589]) ).
tff(f820,plain,
( spl27_35
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f805,f592,f818]) ).
tff(f818,plain,
( spl27_35
<=> sP1(abs(abs(abs(u)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_35])]) ).
tff(f805,plain,
( sP1(abs(abs(abs(u))))
| ~ spl27_7 ),
inference(resolution,[],[f752,f593]) ).
tff(f816,plain,
( spl27_34
| ~ spl27_5 ),
inference(avatar_split_clause,[],[f804,f584,f814]) ).
tff(f814,plain,
( spl27_34
<=> sP1(abs(abs(abs(t3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_34])]) ).
tff(f804,plain,
( sP1(abs(abs(abs(t3))))
| ~ spl27_5 ),
inference(resolution,[],[f752,f585]) ).
tff(f812,plain,
( spl27_33
| ~ spl27_8 ),
inference(avatar_split_clause,[],[f803,f596,f810]) ).
tff(f810,plain,
( spl27_33
<=> sP1(abs(abs(abs(a)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_33])]) ).
tff(f803,plain,
( sP1(abs(abs(abs(a))))
| ~ spl27_8 ),
inference(resolution,[],[f752,f597]) ).
tff(f775,plain,
( spl27_32
| ~ spl27_6 ),
inference(avatar_split_clause,[],[f757,f588,f773]) ).
tff(f773,plain,
( spl27_32
<=> sP1(abs(abs(ua))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_32])]) ).
tff(f757,plain,
( sP1(abs(abs(ua)))
| ~ spl27_6 ),
inference(resolution,[],[f729,f589]) ).
tff(f771,plain,
( spl27_31
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f756,f592,f769]) ).
tff(f769,plain,
( spl27_31
<=> sP1(abs(abs(u))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_31])]) ).
tff(f756,plain,
( sP1(abs(abs(u)))
| ~ spl27_7 ),
inference(resolution,[],[f729,f593]) ).
tff(f767,plain,
( spl27_30
| ~ spl27_5 ),
inference(avatar_split_clause,[],[f755,f584,f765]) ).
tff(f765,plain,
( spl27_30
<=> sP1(abs(abs(t3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_30])]) ).
tff(f755,plain,
( sP1(abs(abs(t3)))
| ~ spl27_5 ),
inference(resolution,[],[f729,f585]) ).
tff(f763,plain,
( spl27_29
| ~ spl27_8 ),
inference(avatar_split_clause,[],[f754,f596,f761]) ).
tff(f761,plain,
( spl27_29
<=> sP1(abs(abs(a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_29])]) ).
tff(f754,plain,
( sP1(abs(abs(a)))
| ~ spl27_8 ),
inference(resolution,[],[f729,f597]) ).
tff(f727,plain,
( ~ spl27_28
| spl27_1 ),
inference(avatar_split_clause,[],[f723,f568,f725]) ).
tff(f725,plain,
( spl27_28
<=> sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_28])]) ).
tff(f723,plain,
( ~ sP1(aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))
| spl27_1 ),
inference(resolution,[],[f569,f373]) ).
tff(f373,plain,
! [X0: dB] :
( pp(aa(dB,bool,it,X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f285]) ).
tff(f691,plain,
( spl27_27
| ~ spl27_6 ),
inference(avatar_split_clause,[],[f674,f588,f689]) ).
tff(f689,plain,
( spl27_27
<=> sP1(abs(ua)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_27])]) ).
tff(f674,plain,
( sP1(abs(ua))
| ~ spl27_6 ),
inference(resolution,[],[f473,f589]) ).
tff(f687,plain,
( spl27_26
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f673,f592,f685]) ).
tff(f685,plain,
( spl27_26
<=> sP1(abs(u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_26])]) ).
tff(f673,plain,
( sP1(abs(u))
| ~ spl27_7 ),
inference(resolution,[],[f473,f593]) ).
tff(f683,plain,
( spl27_25
| ~ spl27_5 ),
inference(avatar_split_clause,[],[f672,f584,f681]) ).
tff(f681,plain,
( spl27_25
<=> sP1(abs(t3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_25])]) ).
tff(f672,plain,
( sP1(abs(t3))
| ~ spl27_5 ),
inference(resolution,[],[f473,f585]) ).
tff(f679,plain,
( spl27_24
| ~ spl27_8 ),
inference(avatar_split_clause,[],[f671,f596,f677]) ).
tff(f677,plain,
( spl27_24
<=> sP1(abs(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_24])]) ).
tff(f671,plain,
( sP1(abs(a))
| ~ spl27_8 ),
inference(resolution,[],[f473,f597]) ).
tff(f663,plain,
( spl27_23
| ~ spl27_6 ),
inference(avatar_split_clause,[],[f647,f588,f661]) ).
tff(f661,plain,
( spl27_23
<=> sP1(ua) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_23])]) ).
tff(f647,plain,
( sP1(ua)
| ~ spl27_6 ),
inference(resolution,[],[f372,f589]) ).
tff(f659,plain,
( spl27_22
| ~ spl27_7 ),
inference(avatar_split_clause,[],[f646,f592,f657]) ).
tff(f657,plain,
( spl27_22
<=> sP1(u) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_22])]) ).
tff(f646,plain,
( sP1(u)
| ~ spl27_7 ),
inference(resolution,[],[f372,f593]) ).
tff(f655,plain,
( spl27_21
| ~ spl27_5 ),
inference(avatar_split_clause,[],[f645,f584,f653]) ).
tff(f653,plain,
( spl27_21
<=> sP1(t3) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_21])]) ).
tff(f645,plain,
( sP1(t3)
| ~ spl27_5 ),
inference(resolution,[],[f372,f585]) ).
tff(f651,plain,
( spl27_20
| ~ spl27_8 ),
inference(avatar_split_clause,[],[f644,f596,f649]) ).
tff(f649,plain,
( spl27_20
<=> sP1(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_20])]) ).
tff(f644,plain,
( sP1(a)
| ~ spl27_8 ),
inference(resolution,[],[f372,f597]) ).
tff(f642,plain,
spl27_19,
inference(avatar_split_clause,[],[f344,f640]) ).
tff(f344,plain,
typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f203,f268]) ).
tff(f268,plain,
( ? [X0: type] : typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0)
=> typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),sK4) ),
introduced(choice_axiom,[]) ).
tff(f203,plain,
? [X0: type] : typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0),
inference(ennf_transformation,[],[f113]) ).
tff(f113,plain,
~ ! [X0: type] : ~ typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X0),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
~ ! [X19: type] : ~ typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),X19),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_16__096_B_Bthesis_O_A_I_B_BU_O_Ae_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f638,plain,
spl27_18,
inference(avatar_split_clause,[],[f343,f636]) ).
tff(f343,plain,
typing(shift(type,e,i,t1),a,sK3),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
typing(shift(type,e,i,t1),a,sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f202,f266]) ).
tff(f266,plain,
( ? [X0: type] : typing(shift(type,e,i,t1),a,X0)
=> typing(shift(type,e,i,t1),a,sK3) ),
introduced(choice_axiom,[]) ).
tff(f202,plain,
? [X0: type] : typing(shift(type,e,i,t1),a,X0),
inference(ennf_transformation,[],[f112]) ).
tff(f112,plain,
~ ! [X0: type] : ~ typing(shift(type,e,i,t1),a,X0),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
~ ! [X3: type] : ~ typing(shift(type,e,i,t1),a,X3),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_6__096_B_Bthesis_O_A_I_B_BT_H_H_O_Ae_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f634,plain,
spl27_17,
inference(avatar_split_clause,[],[f342,f632]) ).
tff(f632,plain,
( spl27_17
<=> 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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_17])]) ).
tff(f342,plain,
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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))),
inference(cnf_transformation,[],[f67]) ).
tff(f67,axiom,
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,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),aa(nat,dB,aa(dB,fun(nat,dB),lift,u),zero_zero(nat))),suc(i))),aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i)),zero_zero(nat)),map(dB,dB,combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)))),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_66__096IT_A_Ir_091lift_Au_A0_PSuc_Ai_093_091a_091u_Pi_093_P0_093_A_092_060degree_062_092_060degree_062_Amap_A_I_Ft_O_At_091u_Pi_093_J_Aas_J_096) ).
tff(f630,plain,
spl27_16,
inference(avatar_split_clause,[],[f341,f628]) ).
tff(f628,plain,
( spl27_16
<=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),u),i))) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_16])]) ).
tff(f341,plain,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),u),i))),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),u),i))),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_11__096IT_A_I_Ir_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_J_091u_Pi_093_J_096) ).
tff(f626,plain,
spl27_15,
inference(avatar_split_clause,[],[f340,f624]) ).
tff(f624,plain,
( spl27_15
<=> beta(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_15])]) ).
tff(f340,plain,
beta(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),
inference(cnf_transformation,[],[f36]) ).
tff(f36,axiom,
beta(foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as)),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_35__096Abs_Ar_A_092_060degree_062_Aa_A_092_060degree_062_092_060degree_062_Aas_A_092_060rightarrow_062_092_060_094sub_062_092_060beta_062r_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_096) ).
tff(f622,plain,
spl27_14,
inference(avatar_split_clause,[],[f339,f620]) ).
tff(f620,plain,
( spl27_14
<=> typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_14])]) ).
tff(f339,plain,
typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),t),
inference(cnf_transformation,[],[f29]) ).
tff(f29,axiom,
typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,r),a),zero_zero(nat)),as),t),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_28__096e_060i_058T_062_A_092_060turnstile_062_Ar_091a_P0_093_A_092_060degree_062_092_060degree_062_Aas_A_058_AT_H_096) ).
tff(f618,plain,
spl27_13,
inference(avatar_split_clause,[],[f338,f616]) ).
tff(f338,plain,
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,r),a),zero_zero(nat)),as))),
inference(cnf_transformation,[],[f18]) ).
tff(f18,axiom,
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,r),a),zero_zero(nat)),as))),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_17_Beta_I1_J) ).
tff(f614,plain,
spl27_12,
inference(avatar_split_clause,[],[f337,f612]) ).
tff(f612,plain,
( spl27_12
<=> typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_12])]) ).
tff(f337,plain,
typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t),
inference(cnf_transformation,[],[f24]) ).
tff(f24,axiom,
typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_23_T) ).
tff(f610,plain,
spl27_11,
inference(avatar_split_clause,[],[f336,f608]) ).
tff(f608,plain,
( spl27_11
<=> typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_11])]) ).
tff(f336,plain,
typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t_a),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
typing(shift(type,ea,ia,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as),t_a),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_27_Beta_I5_J) ).
tff(f606,plain,
spl27_10,
inference(avatar_split_clause,[],[f335,f604]) ).
tff(f335,plain,
typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
typing(shift(type,e,i,t1),aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),ua1),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_15__096e_060i_058T_062_A_092_060turnstile_062_AAbs_Ar_A_092_060degree_062_Aa_A_058_AU_096) ).
tff(f602,plain,
spl27_9,
inference(avatar_split_clause,[],[f334,f600]) ).
tff(f334,plain,
typing(shift(type,e,i,t1),a,t2),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
typing(shift(type,e,i,t1),a,t2),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_5__096e_060i_058T_062_A_092_060turnstile_062_Aa_A_058_AT_H_H_096) ).
tff(f598,plain,
spl27_8,
inference(avatar_split_clause,[],[f333,f596]) ).
tff(f333,plain,
pp(aa(dB,bool,it,a)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
pp(aa(dB,bool,it,a)),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_4_Beta_I3_J) ).
tff(f594,plain,
spl27_7,
inference(avatar_split_clause,[],[f332,f592]) ).
tff(f332,plain,
pp(aa(dB,bool,it,u)),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
pp(aa(dB,bool,it,u)),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_2_uIT) ).
tff(f590,plain,
spl27_6,
inference(avatar_split_clause,[],[f331,f588]) ).
tff(f331,plain,
pp(aa(dB,bool,it,ua)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
pp(aa(dB,bool,it,ua)),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_1_Beta_I6_J) ).
tff(f586,plain,
spl27_5,
inference(avatar_split_clause,[],[f330,f584]) ).
tff(f330,plain,
pp(aa(dB,bool,it,t3)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
pp(aa(dB,bool,it,t3)),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_0__096IT_At_096) ).
tff(f582,plain,
spl27_4,
inference(avatar_split_clause,[],[f329,f580]) ).
tff(f329,plain,
typing(e,u,t1),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
typing(e,u,t1),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_3_uT) ).
tff(f578,plain,
spl27_3,
inference(avatar_split_clause,[],[f328,f576]) ).
tff(f576,plain,
( spl27_3
<=> typing(ea,ua,t1) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_3])]) ).
tff(f328,plain,
typing(ea,ua,t1),
inference(cnf_transformation,[],[f19]) ).
tff(f19,axiom,
typing(ea,ua,t1),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',fact_18_Beta_I7_J) ).
tff(f574,plain,
~ spl27_2,
inference(avatar_split_clause,[],[f325,f572]) ).
tff(f572,plain,
( spl27_2
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).
tff(f325,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',help_pp_1_1_U) ).
tff(f570,plain,
~ spl27_1,
inference(avatar_split_clause,[],[f324,f568]) ).
tff(f324,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(cnf_transformation,[],[f111]) ).
tff(f111,plain,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(flattening,[],[f110]) ).
tff(f110,negated_conjecture,
~ pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
inference(negated_conjecture,[],[f109]) ).
tff(f109,conjecture,
pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),u),i))),
file('/export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL840_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n010.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 24 18:11:36 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a TF1_THM_EQU_NAR problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.h0zu15EJbL/Vampire---4.8_18517
% 0.16/0.38 % (18638)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.45 % (18641)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.23/0.45 % (18642)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.45 % (18643)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.45 % (18644)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.45 % (18639)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.45 % (18640)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.45 % (18645)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.45 % (18642)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.45 % (18639)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.52 % (18645)First to succeed.
% 0.23/0.53 % (18645)Refutation found. Thanks to Tanya!
% 0.23/0.53 % SZS status Theorem for Vampire---4
% 0.23/0.53 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.53 % (18645)------------------------------
% 0.23/0.53 % (18645)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.53 % (18645)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.53 % (18645)Termination reason: Refutation
% 0.23/0.53
% 0.23/0.53 % (18645)Memory used [KB]: 1918
% 0.23/0.53 % (18645)Time elapsed: 0.078 s
% 0.23/0.53 % (18645)------------------------------
% 0.23/0.53 % (18645)------------------------------
% 0.23/0.53 % (18638)Success in time 0.148 s
% 0.23/0.53 % Vampire---4.8 exiting
%------------------------------------------------------------------------------