%------------------------------------------------------------------------------
% File : iProver-SAT---3.9.4
% Problem : SWV010+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT
% Computer : n015.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 : Fri Sep 25 03:24:43 PM UTC 2026
% Result : Satisfiable 1.21s 1.27s
% Output : Model 1.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
%------ Positive definition of a_holds
fof(lit_def,axiom,
! [X0] :
( a_holds(X0)
<=> ( X0 = key(generate_key(an_a_nonce),b)
| X0 = key(at,t) ) ) ).
%------ Positive definition of party_of_protocol
fof(lit_def_001,axiom,
! [X0] :
( party_of_protocol(X0)
<=> ( X0 = b
| X0 = a
| X0 = t ) ) ).
%------ Positive definition of message
fof(lit_def_002,axiom,
! [X0] :
( message(X0)
<=> ( ? [X1,X2] : X0 = sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),X1),bt),encrypt(X2,generate_key(an_a_nonce))))
| ? [X1,X2] : X0 = sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),X1),at),encrypt(triple(a,generate_key(an_a_nonce),X1),bt),X2))
| ? [X1,X2,X3] : X0 = sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3))
| ? [X1,X2,X3] :
( X1 != an_a_nonce
& X0 = sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)) )
| ? [X1,X2,X3] : X0 = sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3))
| ? [X1,X2,X3] : X0 = sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3))
| ? [X1] : X0 = sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(X1,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))
| X0 = sent(a,b,pair(a,an_a_nonce)) ) ) ).
%------ Positive definition of a_stored
fof(lit_def_003,axiom,
! [X0] :
( a_stored(X0)
<=> X0 = pair(b,an_a_nonce) ) ).
%------ Positive definition of b_holds
fof(lit_def_004,axiom,
! [X0] :
( b_holds(X0)
<=> ( ? [X1] : X0 = key(X1,a)
| X0 = key(bt,t) ) ) ).
%------ Positive definition of fresh_to_b
fof(lit_def_005,axiom,
! [X0] :
( fresh_to_b(X0)
<=> X0 = an_a_nonce ) ).
%------ Positive definition of b_stored
fof(lit_def_006,axiom,
! [X0] :
( b_stored(X0)
<=> X0 = pair(a,an_a_nonce) ) ).
%------ Positive definition of t_holds
fof(lit_def_007,axiom,
! [X0] :
( t_holds(X0)
<=> ( X0 = key(bt,b)
| X0 = key(at,a) ) ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV010+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 18:20:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p SAT
% 0.11/0.40 Running model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fnt_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 1.21/1.27 % SZS status Started for theBenchmark.p
% 1.21/1.27 % SZS status Satisfiable for theBenchmark.p
% 1.21/1.27
% 1.21/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.21/1.27
% 1.21/1.27 ------ iProver source info
% 1.21/1.27
% 1.21/1.27 git: date: 2026-07-19 20:42:38 +0200
% 1.21/1.27 git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.21/1.27 git: non_committed_changes: false
% 1.21/1.27
% 1.21/1.27 ------ Parsing...
% 1.21/1.27 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.21/1.27 ------ Proving...
% 1.21/1.27 ------ Problem Properties
% 1.21/1.27
% 1.21/1.27
% 1.21/1.27 clauses 16
% 1.21/1.27 conjectures 0
% 1.21/1.27 EPR 4
% 1.21/1.27 Horn 16
% 1.21/1.27 unary 10
% 1.21/1.27 binary 0
% 1.21/1.27 lits 29
% 1.21/1.27 lits eq 0
% 1.21/1.27 fd_pure 0
% 1.21/1.27 fd_pseudo 0
% 1.21/1.27 fd_cond 0
% 1.21/1.27 fd_pseudo_cond 0
% 1.21/1.27 AC symbols 0
% 1.21/1.27
% 1.21/1.27 ------ Schedule dynamic 5 is on
% 1.21/1.27
% 1.21/1.27 ------ no conjectures: strip conj schedule
% 1.21/1.27
% 1.21/1.27 ------ no equalities: superposition off
% 1.21/1.27
% 1.21/1.27 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.21/1.27
% 1.21/1.27
% 1.21/1.27 ------
% 1.21/1.27 Current options:
% 1.21/1.27 ------
% 1.21/1.27
% 1.21/1.27 ------ Input Options
% 1.21/1.27
% 1.21/1.27 --out_options all
% 1.21/1.27 --tptp_safe_out true
% 1.21/1.27 --problem_path ""
% 1.21/1.27 --include_path ""
% 1.21/1.27 --clausifier res/vclausify_rel
% 1.21/1.27 --clausifier_options --mode clausify -t 101.67 -updr off
% 1.21/1.27 --stdin false
% 1.21/1.27 --proof_out true
% 1.21/1.27 --proof_dot_file ""
% 1.21/1.27 --proof_reduce_dot []
% 1.21/1.27 --suppress_sat_res false
% 1.21/1.27 --suppress_unsat_res true
% 1.21/1.27 --stats_out none
% 1.21/1.27 --stats_mem false
% 1.21/1.27 --theory_stats_out false
% 1.21/1.27
% 1.21/1.27 ------ General Options
% 1.21/1.27
% 1.21/1.27 --fof false
% 1.21/1.27 --time_out_real 305.
% 1.21/1.27 --time_out_virtual -1.
% 1.21/1.27 --rnd_seed 13
% 1.21/1.27 --symbol_type_check false
% 1.21/1.27 --clausify_out false
% 1.21/1.27 --sig_cnt_out false
% 1.21/1.27 --trig_cnt_out false
% 1.21/1.27 --trig_cnt_out_tolerance 1.
% 1.21/1.27 --trig_cnt_out_sk_spl false
% 1.21/1.27 --abstr_cl_out false
% 1.21/1.27
% 1.21/1.27 ------ Interactive Mode
% 1.21/1.27
% 1.21/1.27 --interactive_mode false
% 1.21/1.27 --external_ip_address ""
% 1.21/1.27 --external_port 0
% 1.21/1.27
% 1.21/1.27 ------ Global Options
% 1.21/1.27
% 1.21/1.27 --schedule default
% 1.21/1.27 --add_important_lit false
% 1.21/1.27 --prop_solver_per_cl 500
% 1.21/1.27 --subs_bck_mult 8
% 1.21/1.27 --min_unsat_core false
% 1.21/1.27 --soft_assumptions false
% 1.21/1.27 --soft_lemma_size 3
% 1.21/1.27 --prop_impl_unit_size 0
% 1.21/1.27 --prop_impl_unit []
% 1.21/1.27 --share_sel_clauses true
% 1.21/1.27 --reset_solvers false
% 1.21/1.27 --bc_imp_inh [conj_cone]
% 1.21/1.27 --conj_cone_tolerance 3.
% 1.21/1.27 --extra_neg_conj none
% 1.21/1.27 --large_theory_mode true
% 1.21/1.27 --prolific_symb_bound 200
% 1.21/1.27 --lt_threshold 2000
% 1.21/1.27 --clause_weak_htbl true
% 1.21/1.27 --gc_record_bc_elim false
% 1.21/1.27
% 1.21/1.27 ------ Preprocessing Options
% 1.21/1.27
% 1.21/1.27 --preprocessing_flag false
% 1.21/1.27 --time_out_prep_mult 0.1
% 1.21/1.27 --splitting_mode input
% 1.21/1.27 --splitting_grd true
% 1.21/1.27 --splitting_cvd false
% 1.21/1.27 --splitting_cvd_svl false
% 1.21/1.27 --splitting_nvd 32
% 1.21/1.27 --sub_typing false
% 1.21/1.27 --prep_eq_flat_conj false
% 1.21/1.27 --prep_ineq_split false
% 1.21/1.27 --prep_eq_flat_all_gr false
% 1.21/1.27 --prep_gs_sim true
% 1.21/1.27 --prep_unflatten true
% 1.21/1.27 --prep_res_sim true
% 1.21/1.27 --prep_sup_sim_all true
% 1.21/1.27 --prep_sup_sim_sup false
% 1.21/1.27 --prep_upred true
% 1.21/1.27 --prep_well_definedness true
% 1.21/1.27 --prep_sem_filter exhaustive
% 1.21/1.27 --prep_sem_filter_out false
% 1.21/1.27 --pred_elim true
% 1.21/1.27 --res_sim_input true
% 1.21/1.27 --eq_ax_congr_red true
% 1.21/1.27 --pure_diseq_elim true
% 1.21/1.27 --brand_transform false
% 1.21/1.27 --non_eq_to_eq false
% 1.21/1.27 --prep_eq_proxy false
% 1.21/1.27 --prep_def_merge true
% 1.21/1.27 --prep_def_merge_prop_impl false
% 1.21/1.27 --prep_def_merge_mbd true
% 1.21/1.27 --prep_def_merge_tr_red false
% 1.21/1.27 --prep_def_merge_tr_cl false
% 1.21/1.27 --smt_preprocessing false
% 1.21/1.27 --smt_ac_axioms fast
% 1.21/1.27 --preprocessed_out false
% 1.21/1.27 --preprocessed_stats false
% 1.21/1.27
% 1.21/1.27 ------ Abstraction refinement Options
% 1.21/1.27
% 1.21/1.27 --abstr_ref []
% 1.21/1.27 --abstr_ref_prep false
% 1.21/1.27 --abstr_ref_until_sat false
% 1.21/1.27 --abstr_ref_sig_restrict funpre
% 1.21/1.27 --abstr_ref_af_restrict_to_split_sk false
% 1.21/1.27 --abstr_ref_under []
% 1.21/1.27
% 1.21/1.27 ------ SAT Options
% 1.21/1.27
% 1.21/1.27 --sat_mode false
% 1.21/1.27 --sat_fm_restart_options ""
% 1.21/1.27 --sat_gr_def false
% 1.21/1.27 --sat_epr_types true
% 1.21/1.27 --sat_non_cyclic_types false
% 1.21/1.27 --sat_finite_models false
% 1.21/1.27 --sat_fm_lemmas false
% 1.21/1.27 --sat_fm_prep false
% 1.21/1.27 --sat_fm_uc_incr true
% 1.21/1.27 --sat_out_model pos
% 1.21/1.27 --sat_out_clauses false
% 1.21/1.27
% 1.21/1.27 ------ QBF Options
% 1.21/1.27
% 1.21/1.27 --qbf_mode false
% 1.21/1.27 --qbf_elim_univ false
% 1.21/1.27 --qbf_dom_inst none
% 1.21/1.27 --qbf_dom_pre_inst false
% 1.21/1.27 --qbf_sk_in false
% 1.21/1.27 --qbf_pred_elim true
% 1.21/1.27 --qbf_split 512
% 1.21/1.27
% 1.21/1.27 ------ BMC1 Options
% 1.21/1.27
% 1.21/1.27 --bmc1_incremental false
% 1.21/1.27 --bmc1_axioms reachable_all
% 1.21/1.27 --bmc1_min_bound 0
% 1.21/1.27 --bmc1_max_bound -1
% 1.21/1.27 --bmc1_max_bound_default -1
% 1.21/1.27 --bmc1_symbol_reachability true
% 1.21/1.27 --bmc1_property_lemmas false
% 1.21/1.27 --bmc1_k_induction false
% 1.21/1.27 --bmc1_non_equiv_states false
% 1.21/1.27 --bmc1_deadlock false
% 1.21/1.27 --bmc1_ucm false
% 1.21/1.27 --bmc1_add_unsat_core none
% 1.21/1.27 --bmc1_unsat_core_children false
% 1.21/1.27 --bmc1_unsat_core_extrapolate_axioms false
% 1.21/1.27 --bmc1_out_stat full
% 1.21/1.27 --bmc1_ground_init false
% 1.21/1.27 --bmc1_pre_inst_next_state false
% 1.21/1.27 --bmc1_pre_inst_state false
% 1.21/1.27 --bmc1_pre_inst_reach_state false
% 1.21/1.27 --bmc1_out_unsat_core false
% 1.21/1.27 --bmc1_aig_witness_out false
% 1.21/1.27 --bmc1_verbose false
% 1.21/1.27 --bmc1_dump_clauses_tptp false
% 1.21/1.27 --bmc1_dump_unsat_core_tptp false
% 1.21/1.27 --bmc1_dump_file -
% 1.21/1.27 --bmc1_ucm_expand_uc_limit 128
% 1.21/1.27 --bmc1_ucm_n_expand_iterations 6
% 1.21/1.27 --bmc1_ucm_extend_mode 1
% 1.21/1.27 --bmc1_ucm_init_mode 2
% 1.21/1.27 --bmc1_ucm_cone_mode none
% 1.21/1.27 --bmc1_ucm_reduced_relation_type 0
% 1.21/1.27 --bmc1_ucm_relax_model 4
% 1.21/1.27 --bmc1_ucm_full_tr_after_sat true
% 1.21/1.27 --bmc1_ucm_expand_neg_assumptions false
% 1.21/1.27 --bmc1_ucm_layered_model none
% 1.21/1.27 --bmc1_ucm_max_lemma_size 10
% 1.21/1.27
% 1.21/1.27 ------ AIG Options
% 1.21/1.27
% 1.21/1.27 --aig_mode false
% 1.21/1.27
% 1.21/1.27 ------ Instantiation Options
% 1.21/1.27
% 1.21/1.27 --instantiation_flag true
% 1.21/1.27 --inst_sos_flag false
% 1.21/1.27 --inst_sos_phase true
% 1.21/1.27 --inst_sos_sth_lit_sel [+prop;+non_prol_conj_symb;-eq;+ground;-num_var;-num_symb]
% 1.21/1.27 --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.21/1.27 --inst_lit_sel_side none
% 1.21/1.27 --inst_solver_per_active 1400
% 1.21/1.27 --inst_solver_calls_frac 1.
% 1.21/1.27 --inst_to_smt_solver true
% 1.21/1.27 --inst_passive_queue_type priority_queues
% 1.21/1.27 --inst_passive_queues [[-num_var];[+age;-num_symb]]
% 1.21/1.27 --inst_passive_queues_freq [25;2]
% 1.21/1.27 --inst_dismatching true
% 1.21/1.27 --inst_eager_unprocessed_to_passive true
% 1.21/1.27 --inst_unprocessed_bound 1000
% 1.21/1.27 --inst_prop_sim_given true
% 1.21/1.27 --inst_prop_sim_new false
% 1.21/1.27 --inst_subs_new false
% 1.21/1.27 --inst_eq_res_simp false
% 1.21/1.27 --inst_subs_given false
% 1.21/1.27 --inst_orphan_elimination true
% 1.21/1.27 --inst_learning_loop_flag true
% 1.21/1.27 --inst_learning_start 3000
% 1.21/1.27 --inst_learning_factor 2
% 1.21/1.27 --inst_start_prop_sim_after_learn 3
% 1.21/1.27 --inst_sel_renew solver
% 1.21/1.27 --inst_lit_activity_flag true
% 1.21/1.27 --inst_restr_to_given false
% 1.21/1.27 --inst_activity_threshold 500
% 1.21/1.27
% 1.21/1.27 ------ Resolution Options
% 1.21/1.27
% 1.21/1.27 --resolution_flag false
% 1.21/1.27 --res_lit_sel adaptive
% 1.21/1.27 --res_lit_sel_side none
% 1.21/1.27 --res_ordering kbo
% 1.21/1.27 --res_to_prop_solver active
% 1.21/1.27 --res_prop_simpl_new false
% 1.21/1.27 --res_prop_simpl_given true
% 1.21/1.27 --res_to_smt_solver true
% 1.21/1.27 --res_passive_queue_type priority_queues
% 1.21/1.27 --res_passive_queues [[-num_symb];[+age;-num_symb]]
% 1.21/1.27 --res_passive_queues_freq [15;5]
% 1.21/1.27 --res_forward_subs full
% 1.21/1.27 --res_backward_subs full
% 1.21/1.27 --res_forward_subs_resolution true
% 1.21/1.27 --res_backward_subs_resolution true
% 1.21/1.27 --res_orphan_elimination true
% 1.21/1.27 --res_time_limit 300.
% 1.21/1.27
% 1.21/1.27 ------ Superposition Options
% 1.21/1.27
% 1.21/1.27 --superposition_flag true
% 1.21/1.27 --sup_passive_queue_type priority_queues
% 1.21/1.27 --sup_passive_queues [[-conj_dist;-num_symb];[+score;+min_def_symb;-max_atom_input_occur;+conj_non_prolific_symb];[+age;-num_symb];[+score;-num_symb]]
% 1.21/1.27 --sup_passive_queues_freq [8;1;4;4]
% 1.21/1.27 --twee_lhs_weight 4
% 1.21/1.27 --sup_set_join false
% 1.21/1.27 --sup_set_join_goals true
% 1.21/1.27 --sup_set_join_limit 1000
% 1.21/1.27 --demod_completeness_check fast
% 1.21/1.27 --demod_use_ground true
% 1.21/1.27 --sup_unprocessed_bound 0
% 1.21/1.27 --sup_to_prop_solver passive
% 1.21/1.27 --sup_prop_simpl_new true
% 1.21/1.27 --sup_prop_simpl_given true
% 1.21/1.27 --sup_fun_splitting false
% 1.21/1.27 --sup_iter_deepening 2
% 1.21/1.27 --sup_restarts_mult 12
% 1.21/1.27 --sup_score sim_d_gen
% 1.21/1.27 --sup_share_score_frac 0.2
% 1.21/1.27 --sup_share_max_num_cl 500
% 1.21/1.27 --sup_ordering kbo
% 1.21/1.27 --sup_symb_ordering invfreq
% 1.21/1.27 --sup_term_weight default
% 1.21/1.27
% 1.21/1.27 ------ Superposition Simplification Setup
% 1.21/1.27
% 1.21/1.27 --sup_indices_passive [LightNormIndex;FwDemodIndex]
% 1.21/1.27 --sup_full_triv [SMTSimplify;PropSubs]
% 1.21/1.27 --sup_full_fw [ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability]
% 1.21/1.27 --sup_full_bw [BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 1.21/1.27 --sup_immed_triv []
% 1.21/1.27 --sup_immed_fw_main [ACNormalisation;FwLightNorm;FwUnitSubsAndRes]
% 1.21/1.27 --sup_immed_fw_immed [ACNormalisation;FwUnitSubsAndRes]
% 1.21/1.27 --sup_immed_bw_main [BwUnitSubsAndRes;BwDemod]
% 1.21/1.27 --sup_immed_bw_immed [BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 1.21/1.27 --sup_input_triv [Unflattening;SMTSimplify]
% 1.21/1.27 --sup_input_fw [FwACDemod;ACNormalisation;FwLightNorm;FwDemod;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes;FwGroundJoinability]
% 1.21/1.27 --sup_input_bw [BwACDemod;BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]
% 1.21/1.27 --sup_full_fixpoint true
% 1.21/1.27 --sup_main_fixpoint true
% 1.21/1.27 --sup_immed_fixpoint false
% 1.21/1.27 --sup_input_fixpoint true
% 1.21/1.27 --sup_cache_sim none
% 1.21/1.27 --sup_smt_interval 500
% 1.21/1.27 --sup_bw_gjoin_interval 0
% 1.21/1.27
% 1.21/1.27 ------ Combination Options
% 1.21/1.27
% 1.21/1.27 --comb_mode clause_based
% 1.21/1.27 --comb_inst_mult 5
% 1.21/1.27 --comb_res_mult 1
% 1.21/1.27 --comb_sup_mult 1
% 1.21/1.27 --comb_sup_deep_mult 1
% 1.21/1.27
% 1.21/1.27 ------ Debug Options
% 1.21/1.27
% 1.21/1.27 --dbg_backtrace false
% 1.21/1.27 --dbg_dump_prop_clauses false
% 1.21/1.27 --dbg_dump_prop_clauses_file -
% 1.21/1.27 --dbg_out_stat false
% 1.21/1.27 --dbg_just_parse false
% 1.21/1.27
% 1.21/1.27
% 1.21/1.27
% 1.21/1.27
% 1.21/1.27 ------ Proving...
% 1.21/1.27
% 1.21/1.27
% 1.21/1.27 % SZS status Satisfiable for theBenchmark.p
% 1.21/1.27
% 1.21/1.27 ------ Building Model...Done
% 1.21/1.27
% 1.21/1.27 %------ The model is defined over ground terms (initial term algebra).
% 1.21/1.27 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n))))
% 1.21/1.27 %------ where \phi is a formula over the term algebra.
% 1.21/1.27 %------ If we have equality in the problem then it is also defined as a predicate above,
% 1.21/1.27 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type
% 1.21/1.27 %------ See help for --sat_out_model for different model outputs.
% 1.21/1.27 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
% 1.21/1.27 %------ where the first argument stands for the sort ($i in the unsorted case)
% 1.21/1.27 % SZS output start Model for theBenchmark.p
% See solution above
% 1.21/1.28
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