%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL821_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 11:56:44 AM UTC 2026
% Result : Theorem 0.69s 0.96s
% Output : Refutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 9 |; 2 &)
% ( 2 <=>; 3 =>; 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 : 10 ( 9 usr; 4 prp; 0-3 aty)
% Number of functors : 54 ( 54 usr; 21 con; 0-5 aty)
% Number of variables : 23 ( 0 sgn 22 !; 1 ?; 23 :)
% 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,
sK0: ( type * dB * dB * fun(nat,type) ) > type ).
tff(func_def_36,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_37,type,
sK2: ( nat * nat ) > nat ).
tff(func_def_38,type,
sK3: nat > nat ).
tff(func_def_39,type,
sK4: nat > nat ).
tff(func_def_40,type,
sK5:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_41,type,
sK6:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_42,type,
sK7: ( nat * nat ) > nat ).
tff(func_def_43,type,
sK8: ( nat * nat ) > nat ).
tff(func_def_44,type,
sK9: nat > nat ).
tff(func_def_45,type,
sK10: fun(nat,bool) > nat ).
tff(func_def_46,type,
sK11: nat > nat ).
tff(func_def_47,type,
sK12: fun(nat,bool) > nat ).
tff(func_def_48,type,
sK13: ( type * list(dB) * nat * fun(nat,type) ) > list(type) ).
tff(func_def_49,type,
sK14: ( type * type * list(dB) * fun(nat,type) ) > list(type) ).
tff(func_def_50,type,
sK15: ( type * list(dB) * dB * fun(nat,type) ) > list(type) ).
tff(func_def_51,type,
sK16: ( type * list(dB) * 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(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(f94,axiom,
! [X0: type,X1: list(dB),X2: nat,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,var(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),var(X2)),foldr(type,type,fun1,X4,X0)))
=> ~ typings(X3,X1,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_var__app__typesE) ).
tff(f115,axiom,
! [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 ),
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(f118,plain,
~ thesis,
inference(flattening,[],[f117]) ).
tff(f179,plain,
! [X0: type,X1: list(dB),X2: nat,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),var(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,var(X2),X1)),X0)) ),
inference(ennf_transformation,[],[f94]) ).
tff(f187,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,[],[f115]) ).
tff(f228,plain,
! [X0: type,X1: list(dB),X2: nat,X3: fun(nat,type)] :
( ( typings(X3,X1,sK13(X0,X1,X2,X3))
& pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),var(X2)),foldr(type,type,fun1,sK13(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,var(X2),X1)),X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X4,sK13(X0,X1,X2,X3))],[f179]) ).
tff(f235,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(f364,plain,
! [X2: nat,X3: fun(nat,type),X0: type,X1: list(dB)] :
( ~ pp(aa(type,bool,aa(dB,fun(type,bool),aa(fun(nat,type),fun(dB,fun(type,bool)),typing,X3),foldl(dB,dB,app,var(X2),X1)),X0))
| typings(X3,X1,sK13(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f228]) ).
tff(f388,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,[],[f187]) ).
tff(f389,plain,
~ thesis,
inference(cnf_transformation,[],[f118]) ).
tff(f421,definition,
( spl17_1
<=> ! [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) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
tff(f422,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)
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f421]) ).
tff(f424,definition,
( spl17_2
<=> thesis ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
tff(f427,plain,
( spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f388,f424,f421]) ).
tff(f428,plain,
~ spl17_2,
inference(avatar_split_clause,[],[f389,f424]) ).
tff(f647,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,sK13(t1,rs,n,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))),
inference(resolution,[],[f235,f364]) ).
tff(f654,plain,
( $false
| ~ spl17_1 ),
inference(forward_subsumption_resolution,[],[f647,f422]) ).
tff(f655,plain,
~ spl17_1,
inference(avatar_contradiction_clause,[],[f654]) ).
cnf(s1,plain,
( spl17_1
| spl17_2 ),
inference(sat_conversion,[],[f427]) ).
cnf(s2,plain,
~ spl17_2,
inference(sat_conversion,[],[f428]) ).
cnf(s5,plain,
~ spl17_1,
inference(sat_conversion,[],[f655]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s5]) ).
tff(f656,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL821_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 16:56:05 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.34 Running first-order theorem proving
% 0.07/0.34 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.69/0.95 % (2588085)Detected formulas, will run a generic FOF schedule.
% 0.69/0.95 % (2588108)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=127621675:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.69/0.95 % (2588108)First to succeed.
% 0.69/0.95 % (2588107)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3443623689:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.69/0.95 % (2588103)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=152637057:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.69/0.95 % (2588109)dis-21_1_sil=8000:lcm=predicate:random_seed=1069681682:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.69/0.95 % (2588105)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1553288265:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.69/0.95 % (2588106)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3503451730:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.69/0.96 % (2588104)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2342320451:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.69/0.96 % (2588108)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2588085"
% 0.69/0.96 % (2588106)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.69/0.96 % (2588106)Refutation not found, incomplete strategy
% 0.69/0.96 % (2588106)------------------------------
% 0.69/0.96 % (2588106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.69/0.96 % (2588106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.96 % (2588106)CaDiCaL version: 2.1.3
% 0.69/0.96 % (2588106)Termination reason: Refutation not found, incomplete strategy
% 0.69/0.96 % (2588106)Time elapsed: 0.002 s
% 0.69/0.96 % (2588106)Peak memory usage: 88 MB
% 0.69/0.96 % (2588106)Instructions burned: 3 (million)
% 0.69/0.96 % (2588105)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.69/0.96 % (2588109)Instruction limit reached!
% 0.69/0.96 % (2588109)------------------------------
% 0.69/0.96 % (2588109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.69/0.96 % (2588109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.96 % (2588109)CaDiCaL version: 2.1.3
% 0.69/0.96 % (2588109)Termination reason: Instruction limit
% 0.69/0.96 % (2588109)Termination phase: Saturation
% 0.69/0.96 % (2588109)Time elapsed: 0.047 s
% 0.69/0.96 % (2588109)Peak memory usage: 89 MB
% 0.69/0.96 % (2588109)Instructions burned: 129 (million)
% 0.69/0.96 % (2588107)Instruction limit reached!
% 0.69/0.96 % (2588107)------------------------------
% 0.69/0.96 % (2588107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.69/0.96 % (2588107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.96 % (2588107)CaDiCaL version: 2.1.3
% 0.69/0.96 % (2588107)Termination reason: Instruction limit
% 0.69/0.96 % (2588107)Termination phase: Saturation
% 0.69/0.96 % (2588107)Time elapsed: 0.051 s
% 0.69/0.96 % (2588107)Peak memory usage: 88 MB
% 0.69/0.96 % (2588107)Instructions burned: 121 (million)
% 0.69/0.96 % (2588108)Refutation found. Thanks to Tanya!
% 0.69/0.96 % SZS status Theorem for theBenchmark
% 0.69/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 2.98/1.07 % (2588108)------------------------------
% 2.98/1.07 % (2588108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.07 % (2588108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.07 % (2588108)CaDiCaL version: 2.1.3
% 2.98/1.07 % (2588108)Termination reason: Refutation
% 2.98/1.07 % (2588108)Time elapsed: 0.017 s
% 2.98/1.07 % (2588108)Peak memory usage: 90 MB
% 2.98/1.07 % (2588108)Instructions burned: 48 (million)
% 2.98/1.07 % (2588108)------------------------------
% 2.98/1.07 % (2588108)------------------------------
% 2.98/1.07 % (2588085)Success in time 0.4 s
% 2.98/1.07 % Vampire exiting
%------------------------------------------------------------------------------