%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL777_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 : n009.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 3.65s 1.48s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 2 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 47 ( 47 usr; 9 con; 0-5 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% 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_size: dB > nat ).
tff(func_def_7,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_8,type,
append:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_9,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_10,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_11,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_13,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_14,type,
maps:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).
tff(func_def_15,type,
rotate1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_16,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_17,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_18,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_19,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_20,type,
fFalse: bool ).
tff(func_def_21,type,
fTrue: bool ).
tff(func_def_22,type,
i: nat ).
tff(func_def_23,type,
r: dB ).
tff(func_def_24,type,
s: dB ).
tff(func_def_25,type,
ss: list(dB) ).
tff(func_def_26,type,
sK0: ( dB * dB * dB ) > dB ).
tff(func_def_27,type,
sK1: ( dB * dB * dB ) > dB ).
tff(func_def_28,type,
sK2: ( dB * dB * dB ) > dB ).
tff(func_def_29,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_30,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_31,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_32,type,
sK6: ( list(dB) * dB * dB * dB ) > list(dB) ).
tff(func_def_33,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_34,type,
sK8:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_35,type,
sK9:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_36,type,
sK10:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_37,type,
sK11:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_38,type,
sK12:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_39,type,
sK13:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).
tff(func_def_40,type,
sK14:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_41,type,
sK15:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_42,type,
sK16:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_43,type,
sK17:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_44,type,
sK18:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
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,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_5,type,
pp: bool > $o ).
tff(pred_def_6,type,
sP19: list(dB) > $o ).
tff(pred_def_7,type,
sP20: list(dB) > $o ).
tff(pred_def_8,type,
sP21: list(dB) > $o ).
tff(pred_def_9,type,
sP22: list(dB) > $o ).
tff(f7,axiom,
! [X0: dB,X1: list(dB),X2: dB] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,append(dB,X1,cons(dB,X0,nil(dB)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_app__last) ).
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,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),append(dB,ss,cons(dB,var(i),nil(dB)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
tff(f108,negated_conjecture,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),append(dB,ss,cons(dB,var(i),nil(dB)))))),
inference(negated_conjecture,[status(cth)],[f107]) ).
tff(f109,plain,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),append(dB,ss,cons(dB,var(i),nil(dB)))))),
inference(flattening,[],[f108]) ).
tff(f178,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(f181,plain,
~ pp(aa(dB,bool,it,foldl(dB,dB,app,subst(r,s,zero_zero(nat)),append(dB,ss,cons(dB,var(i),nil(dB)))))),
inference(cnf_transformation,[],[f109]) ).
tff(f207,plain,
! [X2: dB,X0: dB,X1: list(dB)] : ( aa(dB,dB,aa(dB,fun(dB,dB),app,foldl(dB,dB,app,X2,X1)),X0) = foldl(dB,dB,app,X2,append(dB,X1,cons(dB,X0,nil(dB)))) ),
inference(cnf_transformation,[],[f7]) ).
tff(f336,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(forward_demodulation,[],[f181,f207]) ).
tff(f337,plain,
$false,
inference(forward_subsumption_resolution,[],[f336,f178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL777_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 16:47:45 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.65/1.48 % (2244275)Detected formulas, will run a generic FOF schedule.
% 3.65/1.48 % (2244282)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=2057048617:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.65/1.48 % (2244282)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.65/1.48 % (2244286)dis-21_1_sil=8000:lcm=predicate:random_seed=1452334415: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)
% 3.65/1.48 % (2244283)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3275371589:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.65/1.48 % (2244280)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=3257020201:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.65/1.48 % (2244281)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=3704003134:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.65/1.48 % (2244284)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=391308890:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.65/1.48 % (2244285)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2256205470:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.65/1.48 % (2244283)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.65/1.48 % (2244283)First to succeed.
% 3.65/1.48 % (2244283)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2244275"
% 3.65/1.48 % (2244284)Also succeeded, but the first one will report.
% 3.65/1.48 % (2244285)Also succeeded, but the first one will report.
% 3.65/1.48 % (2244286)Instruction limit reached!
% 3.65/1.48 % (2244286)------------------------------
% 3.65/1.48 % (2244286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.48 % (2244286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.48 % (2244286)CaDiCaL version: 2.1.3
% 3.65/1.48 % (2244286)Termination reason: Instruction limit
% 3.65/1.48 % (2244286)Termination phase: Saturation
% 3.65/1.48 % (2244286)Time elapsed: 0.072 s
% 3.65/1.48 % (2244286)Peak memory usage: 89 MB
% 3.65/1.48 % (2244286)Instructions burned: 129 (million)
% 3.65/1.48 % Exception at run slice level
% 3.65/1.48 User error: GNN currently only supports monomorphic FOL.
% 3.65/1.48 % (2244294)lrs+10_1_sil=8000:sp=occurrence:random_seed=646358572:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.65/1.48 % (2244294)Also succeeded, but the first one will report.
% 3.65/1.48 % (2244283)Refutation found. Thanks to Tanya!
% 3.65/1.48 % SZS status Theorem for theBenchmark
% 3.65/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.48 % (2244283)------------------------------
% 3.65/1.48 % (2244283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.48 % (2244283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.48 % (2244283)CaDiCaL version: 2.1.3
% 3.65/1.48 % (2244283)Termination reason: Refutation
% 3.65/1.48 % (2244283)Time elapsed: 0.008 s
% 3.65/1.48 % (2244283)Peak memory usage: 89 MB
% 3.65/1.48 % (2244283)Instructions burned: 12 (million)
% 3.65/1.48 % (2244283)------------------------------
% 3.65/1.48 % (2244283)------------------------------
% 3.65/1.48 % (2244275)Success in time 0.444 s
% 3.65/1.48 % Vampire exiting
%------------------------------------------------------------------------------