%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL827_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:00:46 PM UTC 2026
% Result : Theorem 0.18s 0.53s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 12 |; 3 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-4 aty)
% Number of functors : 79 ( 79 usr; 28 con; 0-5 aty)
% Number of variables : 20 ( 0 sgn 17 !; 3 ?; 20 :)
% 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: list(type) ).
tff(func_def_48,type,
sK2: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_49,type,
sK3: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(func_def_50,type,
sK4: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_51,type,
sK5: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_52,type,
sK6: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_53,type,
sK7: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_54,type,
sK8: ( type * dB * fun(nat,type) ) > type ).
tff(func_def_55,type,
sK9: ( dB * fun(nat,type) ) > type ).
tff(func_def_56,type,
sK10: ( dB * fun(nat,type) ) > type ).
tff(func_def_57,type,
sK11: dB > dB ).
tff(func_def_58,type,
sK12: dB > dB ).
tff(func_def_59,type,
sK13: dB > list(dB) ).
tff(func_def_60,type,
sK14: dB > dB ).
tff(func_def_61,type,
sK15: dB > list(dB) ).
tff(func_def_62,type,
sK16: dB > nat ).
tff(func_def_63,type,
sK17:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_64,type,
sK18: ( dB * dB ) > dB ).
tff(func_def_65,type,
sK19: ( dB * dB * dB ) > dB ).
tff(func_def_66,type,
sK20: ( dB * dB * dB ) > dB ).
tff(func_def_67,type,
sK21: ( dB * dB * dB ) > dB ).
tff(func_def_68,type,
sK22:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_69,type,
sK23:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_70,type,
sK24:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_71,type,
sK25: ( dB * list(dB) * nat ) > list(dB) ).
tff(func_def_72,type,
sK26: ( dB * list(dB) * dB ) > dB ).
tff(func_def_73,type,
sK27: ( dB * list(dB) * dB ) > list(dB) ).
tff(func_def_74,type,
sK28: ( dB * list(dB) * dB ) > dB ).
tff(func_def_75,type,
sK29: ( dB * list(dB) * dB ) > dB ).
tff(func_def_76,type,
sK30: ( dB * list(dB) * dB ) > list(dB) ).
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(f3,axiom,
( ! [X0: fun(nat,type),X1: type,X2: dB,X3: 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),X0),X3),t)),a),X1))
=> ( pp(aa(dB,bool,it,X2))
=> ( pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
=> pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X2),X3))) ) ) )
& ? [X4: 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),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Cons_I1_J) ).
tff(f115,axiom,
! [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 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f116,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f117,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f116]) ).
tff(f120,plain,
~ thesis,
inference(flattening,[],[f117]) ).
tff(f121,plain,
( ! [X0: fun(nat,type),X1: type,X2: dB,X3: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X2),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
| ~ pp(aa(dB,bool,it,X2))
| ~ 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),X0),X3),t)),a),X1)) )
& ? [X4: 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),X4)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f122,plain,
( ! [X0: fun(nat,type),X1: type,X2: dB,X3: nat] :
( pp(aa(dB,bool,it,aa(nat,dB,aa(dB,fun(nat,dB),aa(dB,fun(dB,fun(nat,dB)),subst,a),X2),X3)))
| ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X0),X2),t))
| ~ pp(aa(dB,bool,it,X2))
| ~ 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),X0),X3),t)),a),X1)) )
& ? [X4: 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),X4)) ),
inference(flattening,[],[f121]) ).
tff(f181,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,[],[f115]) ).
tff(f185,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,[],[f122]) ).
tff(f351,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(cnf_transformation,[],[f181]) ).
tff(f352,plain,
~ thesis,
inference(cnf_transformation,[],[f120]) ).
tff(f395,definition,
( spl31_1
<=> thesis ),
introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition]) ).
tff(f399,definition,
( spl31_2
<=> ! [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(definition,[new_symbols(definition,[spl31_2])],[avatar_definition]) ).
tff(f400,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))
| ~ spl31_2 ),
inference(avatar_component_clause,[],[f399]) ).
tff(f401,plain,
( spl31_1
| spl31_2 ),
inference(avatar_split_clause,[],[f351,f399,f395]) ).
tff(f402,plain,
~ spl31_1,
inference(avatar_split_clause,[],[f352,f395]) ).
tff(f736,plain,
( $false
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f185,f400]) ).
tff(f737,plain,
~ spl31_2,
inference(avatar_contradiction_clause,[],[f736]) ).
cnf(s1,plain,
( spl31_1
| spl31_2 ),
inference(sat_conversion,[],[f401]) ).
cnf(s2,plain,
~ spl31_1,
inference(sat_conversion,[],[f402]) ).
cnf(s17,plain,
~ spl31_2,
inference(sat_conversion,[],[f737]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s17,s2]) ).
tff(f738,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL827_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:00:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.53 % (1855762)Will run a generic schedule for satisfiability detection.
% 0.18/0.53 % (1855773)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4204117286:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.53 % (1855768)% WARNING: option uhcvi not known.
% 0.18/0.53 % (1855767)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3811928391_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.53 % (1855768)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1554427734:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.53 % (1855772)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3621826732:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.53 % (1855769)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1718934768:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.53 % (1855770)dis+10_1_sil=32000:sp=arity:random_seed=1305157118:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.53 % (1855771)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2126917279:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.53 % Exception at run slice level
% 0.18/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.53 % (1855781)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1222549406:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.53 % Exception at run slice level
% 0.18/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.53 % (1855768) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1855762-1855768"...
% 0.18/0.53 % (1855768)...printing done.
% 0.18/0.53 % (1855773)Instruction limit reached!
% 0.18/0.53 % (1855773)------------------------------
% 0.18/0.53 % (1855773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.53 % (1855773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.53 % (1855773)CaDiCaL version: 2.1.3
% 0.18/0.53 % (1855773)Termination reason: Instruction limit
% 0.18/0.53 % (1855773)Termination phase: Saturation
% 0.18/0.53 % (1855773)Time elapsed: 0.051 s
% 0.18/0.53 % (1855773)Peak memory usage: 14 MB
% 0.18/0.53 % (1855773)Instructions burned: 161 (million)
% 0.18/0.53 % (1855768)Refutation found. Thanks to Tanya!
% 0.18/0.53 % SZS status Theorem for theBenchmark
% 0.18/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.53 % (1855768)------------------------------
% 0.18/0.53 % (1855768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.53 % (1855768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.53 % (1855768)CaDiCaL version: 2.1.3
% 0.18/0.53 % (1855768)Termination reason: Refutation
% 0.18/0.53 % (1855768)Time elapsed: 0.043 s
% 0.18/0.53 % (1855768)Peak memory usage: 13 MB
% 0.18/0.53 % (1855768)Instructions burned: 73 (million)
% 0.18/0.53 % (1855762)Success in time 0.11 s
% 0.18/0.53 % Vampire exiting
%------------------------------------------------------------------------------