TSTP Solution File: LCL822_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL822_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:54:04 EDT 2024
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 87
% Syntax : Number of formulae : 99 ( 11 unt; 83 typ; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 2 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 96 ( 45 >; 51 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 24 con; 0-5 aty)
% Number of variables : 55 ( 15 !; 2 ?; 55 :)
% ( 38 !>; 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,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_12,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_13,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_14,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_15,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_16,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_17,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_18,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
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(f1989,plain,
$false,
inference(resolution,[],[f1987,f354]) ).
tff(f354,plain,
typings(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),rs,sK3),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
typings(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),rs,sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f218,f275]) ).
tff(f275,plain,
( ? [X0: list(type)] : typings(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),rs,X0)
=> typings(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),rs,sK3) ),
introduced(choice_axiom,[]) ).
tff(f218,plain,
? [X0: list(type)] : typings(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),rs,X0),
inference(ennf_transformation,[],[f118]) ).
tff(f118,plain,
~ ! [X0: list(type)] : ~ typings(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),rs,X0),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
~ ! [X4: list(type)] : ~ typings(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),rs,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096_B_Bthesis_O_A_I_B_BTs_O_Ae_060i_058T_062_A_124_124_N_Ars_A_058_ATs_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
tff(f1987,plain,
! [X0: list(type)] : ~ typings(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),rs,X0),
inference(resolution,[],[f418,f339]) ).
tff(f339,plain,
~ listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),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))),rs),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
~ listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),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))),rs),
inference(flattening,[],[f116]) ).
tff(f116,negated_conjecture,
~ listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),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))),rs),
inference(negated_conjecture,[],[f115]) ).
tff(f115,conjecture,
listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),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))),rs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f418,plain,
! [X2: fun(nat,type),X0: list(type),X1: list(dB)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1)
| ~ typings(X2,X1,X0) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1)
| ~ typings(X2,X1,X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: list(type),X1: list(dB),X2: fun(nat,type)] :
( typings(X2,X1,X0)
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X2)),X1) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X8: list(type),X9: list(dB),X10: fun(nat,type)] :
( typings(X10,X9,X8)
=> listsp(dB,aa(fun(dB,fun(type,bool)),fun(dB,bool),aa(fun(fun(type,bool),bool),fun(fun(dB,fun(type,bool)),fun(dB,bool)),combb(fun(type,bool),bool,dB),fEx(type)),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X10)),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_lists__typings) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : LCL822_5 : TPTP v8.1.2. Released v6.0.0.
% 0.04/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.30 % Computer : n019.cluster.edu
% 0.07/0.30 % Model : x86_64 x86_64
% 0.07/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.30 % Memory : 8042.1875MB
% 0.07/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.30 % CPULimit : 300
% 0.07/0.30 % WCLimit : 300
% 0.07/0.30 % DateTime : Fri May 3 13:13:58 EDT 2024
% 0.07/0.30 % CPUTime :
% 0.07/0.31 % (20976)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.33 % (20979)WARNING: value z3 for option sas not known
% 0.12/0.33 % (20980)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.33 % (20977)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.33 % (20978)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.33 % (20979)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)
% 0.12/0.33 % (20981)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)
% 0.12/0.33 % (20982)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)
% 0.12/0.33 % (20983)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)
% 0.12/0.33 % (20983)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.33 % Exception at run slice level
% 0.12/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.33 % Exception at run slice level
% 0.12/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.33 % Exception at run slice level
% 0.12/0.33 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.34 % (20984)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.12/0.34 % (20985)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)
% 0.12/0.34 % (20986)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)
% 0.12/0.35 % (20984)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.35 % (20985)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.35 % Exception at run slice level
% 0.12/0.35 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.35 % (20987)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.12/0.45 % (20986)First to succeed.
% 0.12/0.45 % (20986)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20976"
% 0.12/0.45 % (20986)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (20986)------------------------------
% 0.12/0.45 % (20986)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.45 % (20986)Termination reason: Refutation
% 0.12/0.45
% 0.12/0.45 % (20986)Memory used [KB]: 3067
% 0.12/0.45 % (20986)Time elapsed: 0.107 s
% 0.12/0.45 % (20986)Instructions burned: 328 (million)
% 0.12/0.45 % (20976)Success in time 0.142 s
%------------------------------------------------------------------------------