%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL778_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 : 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 11:56:33 AM UTC 2026
% Result : Theorem 1.99s 0.87s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 34 ( 34 usr; 9 con; 0-5 aty)
% Number of variables : 0 ( 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,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
it: fun(dB,bool) ).
tff(func_def_2,type,
beta: fun(dB,fun(dB,bool)) ).
tff(func_def_3,type,
abs: dB > dB ).
tff(func_def_4,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_5,type,
var: nat > dB ).
tff(func_def_6,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
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,
append:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
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,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > X0 ) ).
tff(func_def_18,type,
list_size:
!>[X0: $tType] : ( ( fun(X0,nat) * list(X0) ) > nat ) ).
tff(func_def_19,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_20,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fFalse: bool ).
tff(func_def_23,type,
fTrue: bool ).
tff(func_def_24,type,
i: nat ).
tff(func_def_25,type,
r: dB ).
tff(func_def_26,type,
s: dB ).
tff(func_def_27,type,
ss: list(dB) ).
tff(func_def_28,type,
sK0:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_29,type,
sK1:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_30,type,
sK2:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_31,type,
sK3:
!>[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,
step1:
!>[X0: $tType] : ( ( fun(X0,fun(X0,bool)) * list(X0) * list(X0) ) > $o ) ).
tff(pred_def_3,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_5,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_6,type,
pp: bool > $o ).
tff(pred_def_7,type,
sP4: list(dB) > $o ).
tff(f104,axiom,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f107,conjecture,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f108,negated_conjecture,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
inference(negated_conjecture,[status(cth)],[f107]) ).
tff(f109,plain,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
inference(flattening,[],[f108]) ).
tff(f128,plain,
pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
inference(cnf_transformation,[],[f104]) ).
tff(f131,plain,
~ pp(aa(dB,bool,it,aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),var(i)))),
inference(cnf_transformation,[],[f109]) ).
tff(f165,plain,
$false,
inference(forward_subsumption_resolution,[],[f128,f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL778_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 16:48:49 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 1.99/0.87 % (2584350)Detected formulas, will run a generic FOF schedule.
% 1.99/0.87 % (2584360)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=543739519:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.99/0.87 % (2584358)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1402503628:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.99/0.87 % (2584357)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=3987736886:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.99/0.87 % (2584359)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1091315937:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.99/0.87 % (2584355)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=616440376:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.99/0.87 % (2584356)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=3184737669:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.99/0.87 % (2584358)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.99/0.87 % (2584358)First to succeed.
% 1.99/0.87 % (2584358)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2584350"
% 1.99/0.87 % (2584357)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.99/0.87 % (2584359)Also succeeded, but the first one will report.
% 1.99/0.87 % (2584360)Also succeeded, but the first one will report.
% 1.99/0.87 % (2584361)dis-21_1_sil=8000:lcm=predicate:random_seed=1592356428: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)
% 1.99/0.87 % (2584361)Also succeeded, but the first one will report.
% 1.99/0.87 % (2584358)Refutation found. Thanks to Tanya!
% 1.99/0.87 % SZS status Theorem for theBenchmark
% 1.99/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 1.99/0.87 % (2584358)------------------------------
% 1.99/0.87 % (2584358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.99/0.87 % (2584358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.99/0.87 % (2584358)CaDiCaL version: 2.1.3
% 1.99/0.87 % (2584358)Termination reason: Refutation
% 1.99/0.87 % (2584358)Time elapsed: 0.002 s
% 1.99/0.87 % (2584358)Peak memory usage: 89 MB
% 1.99/0.87 % (2584358)Instructions burned: 3 (million)
% 1.99/0.87 % (2584358)------------------------------
% 1.99/0.87 % (2584358)------------------------------
% 1.99/0.87 % (2584350)Success in time 0.26 s
% 1.99/0.87 % Vampire exiting
%------------------------------------------------------------------------------