%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL834_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 11:56:48 AM UTC 2026
% Result : Theorem 0.18s 1.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 50 ( 50 usr; 19 con; 0-5 aty)
% Number of variables : 13 ( 13 !; 0 ?; 13 :)
% 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(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
beta: fun(dB,fun(dB,bool)) ).
tff(func_def_4,type,
abs: dB > dB ).
tff(func_def_5,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_6,type,
var: nat > dB ).
tff(func_def_7,type,
dB_size: dB > nat ).
tff(func_def_8,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_9,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_10,type,
substn: ( dB * dB * 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,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_14,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_15,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_16,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_17,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_18,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_19,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_20,type,
type_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(type,fun(type,X0)) * type ) > X0 ) ).
tff(func_def_21,type,
typing: ( fun(nat,type) * dB ) > fun(type,bool) ).
tff(func_def_22,type,
typings: ( fun(nat,type) * list(dB) ) > fun(list(type),bool) ).
tff(func_def_23,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_24,type,
fFalse: bool ).
tff(func_def_25,type,
fTrue: bool ).
tff(func_def_26,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_27,type,
t1: type ).
tff(func_def_28,type,
t_a: type ).
tff(func_def_29,type,
t: type ).
tff(func_def_30,type,
a: dB ).
tff(func_def_31,type,
as: list(dB) ).
tff(func_def_32,type,
e: fun(nat,type) ).
tff(func_def_33,type,
ea: fun(nat,type) ).
tff(func_def_34,type,
i: nat ).
tff(func_def_35,type,
ia: nat ).
tff(func_def_36,type,
r: dB ).
tff(func_def_37,type,
t2: dB ).
tff(func_def_38,type,
u: dB ).
tff(func_def_39,type,
ua: dB ).
tff(func_def_40,type,
sK0: ( dB * dB * dB ) > dB ).
tff(func_def_41,type,
sK1: ( dB * dB * dB ) > dB ).
tff(func_def_42,type,
sK2: ( dB * dB * dB ) > dB ).
tff(func_def_43,type,
sK3: ( dB * dB ) > dB ).
tff(func_def_44,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_45,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_46,type,
sK6:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_47,type,
sK7:
!>[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,
it: dB > $o ).
tff(pred_def_3,type,
step1:
!>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * list(X0) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_5,type,
pp: bool > $o ).
tff(f4,axiom,
! [X0: dB,X1: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),subst(X1,X0,zero_zero(nat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_beta) ).
tff(f11,axiom,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1))
=> pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_apps__preserves__beta) ).
tff(f110,conjecture,
pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f111,negated_conjecture,
~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))),
inference(negated_conjecture,[status(cth)],[f110]) ).
tff(f112,plain,
~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))),
inference(flattening,[],[f111]) ).
tff(f120,plain,
! [X0: list(dB),X1: dB,X2: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(ennf_transformation,[],[f11]) ).
tff(f143,plain,
~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))),
inference(cnf_transformation,[],[f112]) ).
tff(f157,plain,
! [X2: dB,X0: list(dB),X1: dB] :
( pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,X2,X0)),foldl(dB,dB,app,X1,X0)))
| ~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,X2),X1)) ),
inference(cnf_transformation,[],[f120]) ).
tff(f161,plain,
! [X0: dB,X1: dB] : pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(X1)),X0)),subst(X1,X0,zero_zero(nat)))),
inference(cnf_transformation,[],[f4]) ).
tff(f191,plain,
~ pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a)),subst(r,a,zero_zero(nat)))),
inference(resolution,[],[f143,f157]) ).
tff(f192,plain,
$false,
inference(forward_subsumption_resolution,[],[f191,f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL834_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 17:01:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/1.51 % (3739010)Detected formulas, will run a generic FOF schedule.
% 0.18/1.51 % (3739017)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=1108788702:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.18/1.51 % (3739017)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/1.51 % (3739019)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2453945767:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.18/1.51 % (3739016)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=2058749581:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.18/1.51 % (3739021)dis-21_1_sil=8000:lcm=predicate:random_seed=2813799687: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)
% 0.18/1.51 % (3739020)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=376781325:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.18/1.51 % (3739015)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=854708871:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.18/1.51 % (3739018)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2408776939:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.18/1.51 % (3739018)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/1.51 % (3739018)First to succeed.
% 0.18/1.51 % (3739018)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3739010"
% 0.18/1.51 % (3739019)Also succeeded, but the first one will report.
% 0.18/1.51 % (3739021)Also succeeded, but the first one will report.
% 0.18/1.51 % (3739020)Instruction limit reached!
% 0.18/1.51 % (3739020)------------------------------
% 0.18/1.51 % (3739020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (3739020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (3739020)CaDiCaL version: 2.1.3
% 0.18/1.51 % (3739020)Termination reason: Instruction limit
% 0.18/1.51 % (3739020)Termination phase: Saturation
% 0.18/1.51 % (3739020)Time elapsed: 0.082 s
% 0.18/1.51 % (3739020)Peak memory usage: 89 MB
% 0.18/1.51 % (3739020)Instructions burned: 139 (million)
% 0.18/1.51 % Exception at run slice level
% 0.18/1.51 User error: GNN currently only supports monomorphic FOL.
% 0.18/1.51 % (3739029)lrs+10_1_sil=8000:sp=occurrence:random_seed=593691178:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.18/1.51 % (3739029)Also succeeded, but the first one will report.
% 0.18/1.51 % (3739018)Refutation found. Thanks to Tanya!
% 0.18/1.51 % SZS status Theorem for theBenchmark
% 0.18/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (3739018)------------------------------
% 0.18/1.51 % (3739018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (3739018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (3739018)CaDiCaL version: 2.1.3
% 0.18/1.51 % (3739018)Termination reason: Refutation
% 0.18/1.51 % (3739018)Time elapsed: 0.005 s
% 0.18/1.51 % (3739018)Peak memory usage: 89 MB
% 0.18/1.51 % (3739018)Instructions burned: 7 (million)
% 0.18/1.51 % (3739018)------------------------------
% 0.18/1.51 % (3739018)------------------------------
% 0.18/1.51 % (3739010)Success in time 0.447 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------