TSTP Solution File: LCL827_5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL827_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:42:48 EDT 2024
% Result : Theorem 0.60s 0.77s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 66
% Syntax : Number of formulae : 83 ( 8 unt; 60 typ; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 50 ( 20 ~; 14 |; 5 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 41 ( 20 >; 21 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 4 prp; 0-4 aty)
% Number of functors : 50 ( 50 usr; 27 con; 0-5 aty)
% Number of variables : 62 ( 26 !; 5 ?; 62 :)
% ( 31 !>; 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,
beta: fun(dB,fun(dB,bool)) ).
tff(func_def_7,type,
abs: dB > dB ).
tff(func_def_8,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_9,type,
var: nat > dB ).
tff(func_def_10,type,
dB_size: dB > nat ).
tff(func_def_11,type,
lift: fun(dB,fun(nat,dB)) ).
tff(func_def_12,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_13,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_14,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_15,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_16,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_17,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_18,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_19,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_20,type,
shift:
!>[X0: $tType] : fun(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0)))) ).
tff(func_def_21,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_22,type,
type_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(type,fun(type,X0)) * type ) > X0 ) ).
tff(func_def_23,type,
typing: fun(fun(nat,type),fun(dB,fun(type,bool))) ).
tff(func_def_24,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_25,type,
fAll:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_26,type,
fEx:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
tff(func_def_27,type,
fFalse: bool ).
tff(func_def_28,type,
fTrue: bool ).
tff(func_def_29,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_30,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_31,type,
t2: type ).
tff(func_def_32,type,
t_a: type ).
tff(func_def_33,type,
t: type ).
tff(func_def_34,type,
ts: list(type) ).
tff(func_def_35,type,
a: dB ).
tff(func_def_36,type,
as: list(dB) ).
tff(func_def_37,type,
e: fun(nat,type) ).
tff(func_def_38,type,
ea: fun(nat,type) ).
tff(func_def_39,type,
i: nat ).
tff(func_def_40,type,
ia: nat ).
tff(func_def_41,type,
n: nat ).
tff(func_def_42,type,
rs: list(dB) ).
tff(func_def_43,type,
t1: dB ).
tff(func_def_44,type,
u: dB ).
tff(func_def_45,type,
ua: dB ).
tff(func_def_46,type,
sK0: type ).
tff(func_def_47,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
step1:
!>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * list(X0) * list(X0) ) > $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_7,type,
sQ2_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f177,plain,
$false,
inference(avatar_sat_refutation,[],[f173,f174,f176]) ).
tff(f176,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f175]) ).
tff(f175,plain,
( $false
| ~ spl3_1 ),
inference(resolution,[],[f168,f151]) ).
tff(f151,plain,
pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK0)),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f137,f141]) ).
tff(f141,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
=> pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),sK0)) ),
introduced(choice_axiom,[]) ).
tff(f137,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2)) ) ),
inference(flattening,[],[f136]) ).
tff(f136,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
| ~ pp(aa(dB,bool,it,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2)) ) ),
inference(ennf_transformation,[],[f123]) ).
tff(f123,plain,
( ? [X0: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
& ! [X1: fun(nat,type),X2: type,X3: dB,X4: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X1),X4),t)),a),X2))
=> ( pp(aa(dB,bool,it,X3))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X1),X3),t))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X3),X4))) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
( ? [X8: type] : pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X8))
& ! [X4: fun(nat,type),X5: type,X6: dB,X7: nat] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),X4),X7),t)),a),X5))
=> ( pp(aa(dB,bool,it,X6))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X6),t))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X6),X7))) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9IuW2lpV4m/Vampire---4.8_25234',fact_2_Cons_I1_J) ).
tff(f168,plain,
( ! [X0: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f167]) ).
tff(f167,plain,
( spl3_1
<=> ! [X0: type] : ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
tff(f174,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f146,f170]) ).
tff(f170,plain,
( spl3_2
<=> thesis ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
tff(f146,plain,
~ thesis,
inference(cnf_transformation,[],[f119]) ).
tff(f119,plain,
~ thesis,
inference(flattening,[],[f117]) ).
tff(f117,negated_conjecture,
~ thesis,
inference(negated_conjecture,[],[f116]) ).
tff(f116,conjecture,
thesis,
file('/export/starexec/sandbox2/tmp/tmp.9IuW2lpV4m/Vampire---4.8_25234',conj_1) ).
tff(f173,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f145,f170,f167]) ).
tff(f145,plain,
! [X0: type] :
( thesis
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0)) ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: type] :
( thesis
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0)) ),
inference(ennf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X0))
=> thesis ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X93: type] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,aa(type,fun(nat,type),aa(nat,fun(type,fun(nat,type)),aa(fun(nat,type),fun(nat,fun(type,fun(nat,type))),shift(type),e),i),t)),a),X93))
=> thesis ),
file('/export/starexec/sandbox2/tmp/tmp.9IuW2lpV4m/Vampire---4.8_25234',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : LCL827_5 : TPTP v8.1.2. Released v6.0.0.
% 0.09/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31 % Computer : n018.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 13:58:46 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 This is a TF1_THM_EQU_NAR problem
% 0.16/0.31 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.9IuW2lpV4m/Vampire---4.8_25234
% 0.60/0.76 % (25347)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.60/0.76 % (25350)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.60/0.76 % (25348)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.60/0.76 % (25349)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.60/0.76 % (25353)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.60/0.76 % (25351)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.60/0.76 % (25354)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.60/0.76 % (25352)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.60/0.77 % (25354)First to succeed.
% 0.60/0.77 % (25350)Also succeeded, but the first one will report.
% 0.60/0.77 % (25352)Also succeeded, but the first one will report.
% 0.60/0.77 % (25354)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25346"
% 0.60/0.77 % (25354)Refutation found. Thanks to Tanya!
% 0.60/0.77 % SZS status Theorem for Vampire---4
% 0.60/0.77 % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.77 % (25354)------------------------------
% 0.60/0.77 % (25354)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77 % (25354)Termination reason: Refutation
% 0.60/0.77
% 0.60/0.77 % (25354)Memory used [KB]: 1148
% 0.60/0.77 % (25354)Time elapsed: 0.006 s
% 0.60/0.77 % (25354)Instructions burned: 10 (million)
% 0.60/0.77 % (25346)Success in time 0.444 s
% 0.60/0.77 % Vampire---4.8 exiting
%------------------------------------------------------------------------------