%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL774_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 11:56:32 AM UTC 2026
% Result : Theorem 3.40s 1.24s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 6 con; 0-5 aty)
% Number of variables : 3 ( 3 !; 0 ?; 3 :)
% 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] : fun(X0,fun(X0,X0)) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
it: 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_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_8,type,
dB_size: dB > nat ).
tff(func_def_9,type,
lift: ( dB * nat ) > dB ).
tff(func_def_10,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_11,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_12,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_13,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_14,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_15,type,
suc: nat > nat ).
tff(func_def_16,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_17,type,
fFalse: bool ).
tff(func_def_18,type,
fTrue: bool ).
tff(func_def_19,type,
i: nat ).
tff(func_def_20,type,
r: dB ).
tff(func_def_21,type,
sK0: fun(nat,bool) > nat ).
tff(func_def_22,type,
sK1: fun(nat,bool) > nat ).
tff(func_def_23,type,
sK2:
!>[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,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
beta: ( dB * dB ) > $o ).
tff(pred_def_10,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_11,type,
pp: bool > $o ).
tff(f1,axiom,
! [X3: nat] : pp(aa(dB,bool,it,var(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Var__IT) ).
tff(f110,conjecture,
pp(aa(dB,bool,it,var(i))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f111,negated_conjecture,
~ pp(aa(dB,bool,it,var(i))),
inference(negated_conjecture,[status(cth)],[f110]) ).
tff(f112,plain,
~ pp(aa(dB,bool,it,var(i))),
inference(flattening,[],[f111]) ).
tff(f113,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f1]) ).
tff(f131,plain,
~ pp(aa(dB,bool,it,var(i))),
inference(cnf_transformation,[],[f112]) ).
tff(f135,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f113]) ).
tff(f151,plain,
$false,
inference(forward_subsumption_resolution,[],[f131,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL774_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n009.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
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 16:47:15 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
% 3.40/1.24 % (2243859)Detected formulas, will run a generic FOF schedule.
% 3.40/1.24 % (2243868)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3316303494:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/1.24 % (2243869)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2217502336:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/1.24 % (2243866)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=778512599:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/1.24 % (2243870)dis-21_1_sil=8000:lcm=predicate:random_seed=4224724208: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)
% 3.40/1.24 % (2243867)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=230062710:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/1.24 % (2243865)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=2851368499:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/1.24 % (2243864)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=1261878756:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/1.24 % (2243867)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.40/1.24 % (2243867)First to succeed.
% 3.40/1.24 % (2243867)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2243859"
% 3.40/1.24 % (2243868)Also succeeded, but the first one will report.
% 3.40/1.24 % (2243866)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.40/1.24 % (2243870)Also succeeded, but the first one will report.
% 3.40/1.24 % (2243869)Also succeeded, but the first one will report.
% 3.40/1.24 % (2243867)Refutation found. Thanks to Tanya!
% 3.40/1.24 % SZS status Theorem for theBenchmark
% 3.40/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.24 % (2243867)------------------------------
% 3.40/1.24 % (2243867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.24 % (2243867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.24 % (2243867)CaDiCaL version: 2.1.3
% 3.40/1.24 % (2243867)Termination reason: Refutation
% 3.40/1.24 % (2243867)Time elapsed: 0.003 s
% 3.40/1.24 % (2243867)Peak memory usage: 88 MB
% 3.40/1.24 % (2243867)Instructions burned: 2 (million)
% 3.40/1.24 % (2243867)------------------------------
% 3.40/1.24 % (2243867)------------------------------
% 3.40/1.24 % (2243859)Success in time 0.426 s
% 3.40/1.24 % Vampire exiting
%------------------------------------------------------------------------------