TSTP Solution File: LCL821_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL821_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 : n008.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 07:54:03 EDT 2024
% Result : Theorem 0.17s 0.58s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 70
% Syntax : Number of formulae : 84 ( 9 unt; 65 typ; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 14 ~; 5 |; 4 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 64 ( 32 >; 32 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 54 ( 54 usr; 21 con; 0-5 aty)
% Number of variables : 61 ( 33 !; 2 ?; 61 :)
% ( 26 !>; 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,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(fun(X0,X1),fun(X0,X2))) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
it: fun(dB,bool) ).
tff(func_def_5,type,
abs: dB > dB ).
tff(func_def_6,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_7,type,
var: nat > dB ).
tff(func_def_8,type,
dB_size: dB > nat ).
tff(func_def_9,type,
lift: ( dB * nat ) > dB ).
tff(func_def_10,type,
subst: fun(dB,fun(dB,fun(nat,dB))) ).
tff(func_def_11,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_12,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_13,type,
suc: nat > nat ).
tff(func_def_14,type,
shift:
!>[X0: $tType] : fun(fun(nat,X0),fun(nat,fun(X0,fun(nat,X0)))) ).
tff(func_def_15,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_16,type,
typing: fun(fun(nat,type),fun(dB,fun(type,bool))) ).
tff(func_def_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fAll:
!>[X0: $tType] : fun(fun(X0,bool),bool) ).
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,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_23,type,
t1: type ).
tff(func_def_24,type,
t_a: type ).
tff(func_def_25,type,
t: type ).
tff(func_def_26,type,
e: fun(nat,type) ).
tff(func_def_27,type,
ea: fun(nat,type) ).
tff(func_def_28,type,
i: nat ).
tff(func_def_29,type,
ia: nat ).
tff(func_def_30,type,
n: nat ).
tff(func_def_31,type,
rs: list(dB) ).
tff(func_def_32,type,
t2: dB ).
tff(func_def_33,type,
u: dB ).
tff(func_def_34,type,
ua: dB ).
tff(func_def_35,type,
sK1:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_36,type,
sK2:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_37,type,
sK3: nat > nat ).
tff(func_def_38,type,
sK4: nat > nat ).
tff(func_def_39,type,
sK5: nat > nat ).
tff(func_def_40,type,
sK6: nat > nat ).
tff(func_def_41,type,
sK7: ( nat * nat ) > nat ).
tff(func_def_42,type,
sK8: ( nat * nat ) > nat ).
tff(func_def_43,type,
sK9: fun(nat,bool) > nat ).
tff(func_def_44,type,
sK10: fun(nat,bool) > nat ).
tff(func_def_45,type,
sK11: ( nat * nat ) > nat ).
tff(func_def_46,type,
sK12: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_47,type,
sK13: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_48,type,
sK14: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_49,type,
sK15: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_50,type,
sK16:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_51,type,
sK17: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $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_8,type,
sP0: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).
tff(f4934,plain,
$false,
inference(resolution,[],[f3218,f367]) ).
tff(f367,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)),foldl(dB,dB,app,var(n),rs)),t1)),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
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)),foldl(dB,dB,app,var(n),rs)),t1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_nT) ).
tff(f3218,plain,
! [X0: dB,X1: 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)),foldl(dB,dB,app,X0,rs)),X1)),
inference(resolution,[],[f474,f536]) ).
tff(f536,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(subsumption_resolution,[],[f354,f353]) ).
tff(f353,plain,
~ thesis,
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
~ thesis,
inference(flattening,[],[f117]) ).
tff(f117,negated_conjecture,
~ thesis,
inference(negated_conjecture,[],[f116]) ).
tff(f116,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f354,plain,
! [X0: list(type)] :
( thesis
| ~ 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(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: list(type)] :
( thesis
| ~ 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,[],[f119]) ).
tff(f119,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)
=> thesis ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X73: 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,X73)
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f474,plain,
! [X2: dB,X3: fun(nat,type),X0: type,X1: list(dB)] :
( typings(X3,X1,sK12(X0,X1,X2,X3))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(cnf_transformation,[],[f334]) ).
tff(f334,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ( typings(X3,X1,sK12(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK12(X0,X1,X2,X3),X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f266,f333]) ).
tff(f333,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
=> ( typings(X3,X1,sK12(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,sK12(X0,X1,X2,X3),X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f266,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( ? [X4: list(type)] :
( typings(X3,X1,X4)
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0))) )
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0)) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: type,X1: list(dB),X2: dB,X3: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,X2,X1)),X0))
=> ~ ! [X4: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),X2),foldr(type,type,fun1,X4,X0)))
=> ~ typings(X3,X1,X4) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X3: type,X25: list(dB),X8: dB,X4: fun(nat,type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),foldl(dB,dB,app,X8,X25)),X3))
=> ~ ! [X65: list(type)] :
( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X4),X8),foldr(type,type,fun1,X65,X3)))
=> ~ typings(X4,X25,X65) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_list__app__typeE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL821_5 : TPTP v8.1.2. Released v6.0.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri May 3 14:02:27 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % (31734)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36 % (31737)WARNING: value z3 for option sas not known
% 0.12/0.36 % (31741)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)
% 0.12/0.36 % (31736)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.36 % (31740)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)
% 0.12/0.36 % (31737)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)
% 0.12/0.36 % (31738)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36 % (31739)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)
% 0.12/0.37 % (31735)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37 % (31741)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.37 % Exception at run slice level
% 0.12/0.37 % Exception at run slice level
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.37 % Exception at run slice level
% 0.12/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.38 % (31743)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)
% 0.12/0.38 % (31742)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.12/0.39 % (31744)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)
% 0.12/0.39 % (31743)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.39 % (31742)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.39 % Exception at run slice level
% 0.12/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.40 % (31745)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)
% 0.17/0.58 % (31744)First to succeed.
% 0.17/0.58 % (31744)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31734"
% 0.17/0.58 % (31744)Refutation found. Thanks to Tanya!
% 0.17/0.58 % SZS status Theorem for theBenchmark
% 0.17/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.58 % (31744)------------------------------
% 0.17/0.58 % (31744)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.58 % (31744)Termination reason: Refutation
% 0.17/0.58
% 0.17/0.58 % (31744)Memory used [KB]: 2744
% 0.17/0.58 % (31744)Time elapsed: 0.197 s
% 0.17/0.58 % (31744)Instructions burned: 421 (million)
% 0.17/0.58 % (31734)Success in time 0.235 s
%------------------------------------------------------------------------------