%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL800_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 : n014.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 11:56:39 AM UTC 2026
% Result : Theorem 3.45s 1.24s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 10 con; 0-5 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% 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,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
app: ( dB * dB ) > dB ).
tff(func_def_3,type,
var: nat > dB ).
tff(func_def_4,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_5,type,
dB_rec:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,fun(X0,fun(X0,X0)))) * fun(dB,fun(X0,X0)) * dB ) > X0 ) ).
tff(func_def_6,type,
dB_size: dB > nat ).
tff(func_def_7,type,
lift: ( dB * nat ) > dB ).
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,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_13,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_14,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_15,type,
list_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),fun(X0,X0))) * list(X1) ) > 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,
suc: nat > nat ).
tff(func_def_19,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_20,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
a: dB ).
tff(func_def_24,type,
as: list(dB) ).
tff(func_def_25,type,
i: nat ).
tff(func_def_26,type,
n: nat ).
tff(func_def_27,type,
rs: list(dB) ).
tff(func_def_28,type,
t: dB ).
tff(func_def_29,type,
u: dB ).
tff(func_def_30,type,
ua: dB ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
equal_equal:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_8,type,
it: dB > $o ).
tff(pred_def_9,type,
listMem:
!>[X0: $tType] : ( ( X0 * list(X0) ) > $o ) ).
tff(pred_def_10,type,
member1:
!>[X0: $tType] : ( ( list(X0) * X0 ) > $o ) ).
tff(pred_def_11,type,
null:
!>[X0: $tType] : ( list(X0) > $o ) ).
tff(pred_def_12,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(f5,axiom,
it(subst(app(lift(u,zero_zero(nat)),var(zero_zero(nat))),subst(a,u,i),zero_zero(nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096IT_A_I_Ilift_Au_A0_A_092_060degree_062_AVar_A0_J_091a_091u_Pi_093_P0_093_J_096) ).
tff(f7,axiom,
! [X0: nat,X1: dB,X2: dB,X3: dB] : ( subst(app(X3,X2),X1,X0) = app(subst(X3,X1,X0),subst(X2,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subst__App) ).
tff(f14,axiom,
! [X0: dB,X1: nat,X2: dB] : ( subst(lift(X2,X1),X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_subst__lift) ).
tff(f15,axiom,
! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_subst__eq) ).
tff(f106,conjecture,
it(app(u,subst(a,u,i))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f107,negated_conjecture,
~ it(app(u,subst(a,u,i))),
inference(negated_conjecture,[status(cth)],[f106]) ).
tff(f108,plain,
~ it(app(u,subst(a,u,i))),
inference(flattening,[],[f107]) ).
tff(f115,plain,
~ it(app(u,subst(a,u,i))),
inference(cnf_transformation,[],[f108]) ).
tff(f121,plain,
! [X0: dB,X1: nat] : ( subst(var(X1),X0,X1) = X0 ),
inference(cnf_transformation,[],[f15]) ).
tff(f123,plain,
! [X2: dB,X3: dB,X0: nat,X1: dB] : ( subst(app(X3,X2),X1,X0) = app(subst(X3,X1,X0),subst(X2,X1,X0)) ),
inference(cnf_transformation,[],[f7]) ).
tff(f124,plain,
it(subst(app(lift(u,zero_zero(nat)),var(zero_zero(nat))),subst(a,u,i),zero_zero(nat))),
inference(cnf_transformation,[],[f5]) ).
tff(f130,plain,
! [X2: dB,X0: dB,X1: nat] : ( subst(lift(X2,X1),X0,X1) = X2 ),
inference(cnf_transformation,[],[f14]) ).
tff(f149,plain,
! [X2: dB,X3: dB,X0: dB,X1: nat] : ( subst(app(lift(X0,X1),X2),X3,X1) = app(X0,subst(X2,X3,X1)) ),
inference(superposition,[],[f123,f130]) ).
tff(f312,plain,
it(app(u,subst(var(zero_zero(nat)),subst(a,u,i),zero_zero(nat)))),
inference(superposition,[],[f124,f149]) ).
tff(f318,plain,
it(app(u,subst(a,u,i))),
inference(forward_demodulation,[],[f312,f121]) ).
tff(f323,plain,
$false,
inference(forward_subsumption_resolution,[],[f318,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL800_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 16:52:31 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.45/1.24 % (1009281)Detected formulas, will run a generic FOF schedule.
% 3.45/1.24 % (1009292)dis-21_1_sil=8000:lcm=predicate:random_seed=3386444145: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)
% 3.45/1.24 % (1009292)Instruction limit reached!
% 3.45/1.24 % (1009292)------------------------------
% 3.45/1.24 % (1009292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.24 % (1009292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.24 % (1009292)CaDiCaL version: 2.1.3
% 3.45/1.24 % (1009292)Termination reason: Instruction limit
% 3.45/1.24 % (1009292)Termination phase: Saturation
% 3.45/1.24 % (1009292)Time elapsed: 0.039 s
% 3.45/1.24 % (1009292)Peak memory usage: 89 MB
% 3.45/1.24 % (1009292)Instructions burned: 130 (million)
% 3.45/1.24 % (1009286)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=2573283964:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.45/1.24 % (1009289)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3254943375:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.45/1.24 % (1009291)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=376871822:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.45/1.24 % (1009288)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=1792847541:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.45/1.24 % (1009290)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2280693798:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.45/1.24 % (1009287)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=3721626250:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.45/1.24 % (1009289)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.45/1.24 % (1009289)Refutation not found, incomplete strategy
% 3.45/1.24 % (1009289)------------------------------
% 3.45/1.24 % (1009289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.24 % (1009289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.24 % (1009289)CaDiCaL version: 2.1.3
% 3.45/1.24 % (1009289)Termination reason: Refutation not found, incomplete strategy
% 3.45/1.24 % (1009289)Time elapsed: 0.002 s
% 3.45/1.24 % (1009289)Peak memory usage: 88 MB
% 3.45/1.24 % (1009289)Instructions burned: 1 (million)
% 3.45/1.24 % (1009288)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.45/1.24 % (1009290)First to succeed.
% 3.45/1.24 % (1009290)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1009281"
% 3.45/1.24 % (1009291)Also succeeded, but the first one will report.
% 3.45/1.24 % (1009294)lrs+10_1_sil=8000:sp=occurrence:random_seed=117438798:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.45/1.24 % (1009294)Also succeeded, but the first one will report.
% 3.45/1.24 % (1009289)------------------------------
% 3.45/1.24 % (1009289)------------------------------
% 3.45/1.24 % (1009290)Refutation found. Thanks to Tanya!
% 3.45/1.24 % SZS status Theorem for theBenchmark
% 3.45/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.24 % (1009290)------------------------------
% 3.45/1.24 % (1009290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.24 % (1009290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.24 % (1009290)CaDiCaL version: 2.1.3
% 3.45/1.24 % (1009290)Termination reason: Refutation
% 3.45/1.24 % (1009290)Time elapsed: 0.009 s
% 3.45/1.24 % (1009290)Peak memory usage: 88 MB
% 3.45/1.24 % (1009290)Instructions burned: 12 (million)
% 3.45/1.24 % (1009290)------------------------------
% 3.45/1.24 % (1009290)------------------------------
% 3.45/1.24 % (1009281)Success in time 0.435 s
% 3.45/1.24 % Vampire exiting
%------------------------------------------------------------------------------