%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : DAT091_1 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p 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 : Fri Sep 25 01:13:59 PM UTC 2026
% Result : Theorem 1.38s 1.32s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 40 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 41 ( 24 ~; 12 |; 0 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 31 ( 31 fml; 0 var)
% Number arithmetic : 47 ( 0 atm; 0 fun; 20 num; 27 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 51 ( 1 sgn 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
nil: list ).
tff(pred_def_1,type,
in: ( list * $int ) > $o ).
tff(pred_def_2,type,
inRange: ( list * $int ) > $o ).
tff(func_def_3,type,
tail: list > list ).
tff(func_def_5,type,
length: list > $int ).
tff(func_def_8,type,
count: ( list * $int ) > $int ).
tff(func_def_9,type,
append: ( list * list ) > list ).
tff(func_def_11,type,
sK0: ( list * $int ) > $int ).
tff(func_def_12,type,
sK1: ( list * $int ) > list ).
tff(func_def_13,type,
sK2: ( list * $int ) > $int ).
tff(func_def_14,type,
sK3: ( list * $int ) > list ).
tff(func_def_15,type,
sK4: ( list * $int ) > $int ).
tff(func_def_16,type,
sK5: ( list * $int ) > list ).
tff(f4,axiom,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(f10,axiom,
! [X0: $int,X1: $int,X2: list,X3: $int] :
( ( X0 != X1 )
=> ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_3) ).
tff(f15,conjecture,
~ ! [X0: list,X1: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f16,negated_conjecture,
~ ~ ! [X0: list,X1: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f32,plain,
! [X0: $int,X1: $int,X2: list] :
( ( X0 != X1 )
=> ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
inference(rectify,[],[f10]) ).
tff(f34,plain,
! [X0: list,X1: list] :
( ( X0 != X1 )
=> ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
inference(flattening,[],[f16]) ).
tff(f35,plain,
! [X0: $int,X1: $int,X2: list] :
( ( X0 = X1 )
| ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
inference(ennf_transformation,[],[f32]) ).
tff(f37,plain,
! [X0: list,X1: list] :
( ( X0 = X1 )
| ! [X2: $int] : ( count(X2,X0) != count(X2,X1) ) ),
inference(ennf_transformation,[],[f34]) ).
tff(f50,plain,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
inference(cnf_transformation,[],[f4]) ).
tff(f66,plain,
! [X2: list,X0: $int,X1: $int] :
( ( X0 = X1 )
| ( count(X0,cons(X1,X2)) = count(X0,X2) ) ),
inference(cnf_transformation,[],[f35]) ).
tff(f72,plain,
! [X2: $int,X0: list,X1: list] :
( ( X0 = X1 )
| ( count(X2,X0) != count(X2,X1) ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_64,plain,
! [X0_int: $int,X0_list: list] : cons(X0_int,X0_list) != nil,
inference(cnf_transformation,[],[f50]) ).
tcf(c_80,plain,
! [X0_int: $int,X0_list: list,X1_int: $int] :
( ( X0_int = X1_int )
| ( count(X0_int,cons(X1_int,X0_list)) = count(X0_int,X0_list) ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_86,negated_conjecture,
! [X0_int: $int,X0_list: list,X1_list: list] :
( ( X0_list = X1_list )
| ( count(X0_int,X0_list) != count(X0_int,X1_list) ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_114,plain,
cons(0,nil) != nil,
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_143,plain,
! [X0_int: $int,X0_list: list,X1_int: $int] :
( ( cons(X1_int,X0_list) = nil )
| ( count(X0_int,cons(X1_int,X0_list)) != count(X0_int,nil) ) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_144,plain,
( ( cons(0,nil) = nil )
| ( count(0,cons(0,nil)) != count(0,nil) ) ),
inference(instantiation,[status(thm)],[c_143]) ).
tcf(c_145,plain,
! [X0_int: $int,X0_list: list,X1_int: $int,X1_list: list] :
( ( count(X0_int,cons(X1_int,X0_list)) = count(X0_int,nil) )
| ( count(count(X0_int,cons(X1_int,X0_list)),cons(count(X0_int,nil),X1_list)) = count(count(X0_int,cons(X1_int,X0_list)),X1_list) ) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_148,plain,
( ( count(0,cons(0,nil)) = count(0,nil) )
| ( count(count(0,cons(0,nil)),cons(count(0,nil),nil)) = count(count(0,cons(0,nil)),nil) ) ),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_184,plain,
! [X0_int: $int,X0_list: list,X1_int: $int] :
( ( cons(count(X0_int,nil),nil) = nil )
| ( count(count(X0_int,cons(X1_int,X0_list)),cons(count(X0_int,nil),nil)) != count(count(X0_int,cons(X1_int,X0_list)),nil) ) ),
inference(instantiation,[status(thm)],[c_143]) ).
tcf(c_185,plain,
( ( cons(count(0,nil),nil) = nil )
| ( count(count(0,cons(0,nil)),cons(count(0,nil),nil)) != count(count(0,cons(0,nil)),nil) ) ),
inference(instantiation,[status(thm)],[c_184]) ).
tcf(c_313,plain,
! [X0_int: $int] : cons(count(X0_int,nil),nil) != nil,
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_314,plain,
cons(count(0,nil),nil) != nil,
inference(instantiation,[status(thm)],[c_313]) ).
tcf(c_315,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_314,c_185,c_148,c_144,c_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT091_1 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.52 % Computer : n009.cluster.edu
% 0.11/0.52 % Model : x86_64 x86_64
% 0.11/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52 % Memory : 8046.5625MB
% 0.11/0.52 % OS : Linux 6.8.0-71-generic
% 0.11/0.52 % CPULimit : 300
% 0.11/0.52 % WCLimit : 300
% 0.11/0.52 % DateTime : Fri Sep 25 10:24:45 UTC 2026
% 0.11/0.52 % CPUTime :
% 0.11/0.52 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.54 Running TFA theorem proving
% 0.11/0.54 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s tfa_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.56
% 0.11/0.56 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.56
% 0.11/0.56 % Detected problem language: tptp
% 0.15/0.57 % Proving...
% 1.38/1.32 % SZS status Started for theBenchmark.p
% 1.38/1.32 ERROR - "ProverProcess:heur/schedule_none:304.99997878074646" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 1.38/1.32 Fatal error: exception Failure("undefined enum value")
% 1.38/1.32 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --schedule none --sub_typing false --suppress_sat_res true --tptp_safe_out true --stats_out none --out_options none --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 101.67 --show_fool true" --time_out_real 305.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_5v4hz1n6/wqv3yhzs 2>> /export/starexec/sandbox/tmp/iprover_out_5v4hz1n6/wqv3yhzs_error
% 1.38/1.32 ERROR - "ProverProcess:heur/vip_65520:11.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 1.38/1.32 Fatal error: exception Failure("undefined enum value")
% 1.38/1.32 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_mode time_based --comb_res_mult 6 --comb_sup_deep_mult 0 --comb_sup_mult 6 --conj_cone_tolerance 1.8969679945890683 --demod_completeness_check fullold --demod_use_ground false --extra_neg_conj all_neg --instantiation_flag false --out_options none --preprocessed_out false --preprocessing_flag false --prolific_symb_bound 1024 --proof_out true --prop_solver_per_cl 512 --res_to_smt_solver false --resolution_flag true --schedule none --share_sel_clauses true --stats_out none --subs_bck_mult 16 --sup_bw_gjoin_interval 100 --sup_cache_sim none --sup_full_bw "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_full_fixpoint false --sup_full_fw "[]" --sup_fun_splitting false --sup_immed_bw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_immed_bw_main "[SubsumptionRes;UnitSubsAndRes;FullSubsAndRes;Demod;ACDemod]" --sup_immed_fixpoint false --sup_immed_fw_immed "[Subsumption;SubsumptionRes;FullSubsAndRes;Demod;LightNorm;ACDemod]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;FullSubsAndRes;Demod;LightNorm;ACNormalisation;GroundJoinability;Connectedness]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_fixpoint false --sup_main_fixpoint true --sup_ordering lpo --sup_passive_queue_type priority_queues --sup_passive_queues "[[+has_eq;-has_eq];[-num_var;-num_var];[+conj_dist;+ground;-max_atom_input_occur]]" --sup_passive_queues_freq "[1;4;4]" --sup_prop_simpl_given false --sup_prop_simpl_new false --sup_score sim_d_gen --sup_share_max_num_cl 10 --sup_share_score_frac 0.2 --sup_smt_interval 32 --sup_symb_ordering invfreq_arity --sup_term_weight default --sup_to_prop_solver passive --sup_unprocessed_bound 10 --superposition_flag true --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 3.67 --show_fool true" --time_out_real 11.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_5v4hz1n6/_sv29x5t 2>> /export/starexec/sandbox/tmp/iprover_out_5v4hz1n6/_sv29x5t_error
% 1.38/1.32 ERROR - "ProverProcess:heur/vip_65097:3.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 1.38/1.32 Fatal error: exception Failure("undefined enum value")
% 1.38/1.32 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 3 --comb_sup_deep_mult 0 --comb_sup_mult 0 --conj_cone_tolerance 4.0357851670394345 --extra_neg_conj none --inst_activity_threshold 512 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp true --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 2048 --inst_lit_activity_flag true --inst_lit_sel "[+split;-sign;-depth]" --inst_lit_sel_side none --inst_orphan_elimination true --inst_passive_queue_type queue --inst_passive_queues "[[+age;+num_lits;-age];[-age;-min_def_symb;+bc_imp_inh]]" --inst_passive_queues_freq "[2;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given true --inst_sel_renew solver --inst_solver_calls_frac 1.0 --inst_solver_per_active 1024 --inst_sos_flag true --inst_sos_phase false --inst_sos_sth_lit_sel "[+split;-ground;-depth]" --inst_start_prop_sim_after_learn 3 --inst_subs_given true --inst_subs_new false --instantiation_flag true --out_options none --prep_sup_sim_all true --prep_sup_sim_sup false --preprocessed_out false --preprocessing_flag true --prolific_symb_bound 256 --proof_out true --prop_solver_per_cl 16384 --resolution_flag true --schedule none --share_sel_clauses false --stats_out none --subs_bck_mult 8 --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 1.00 --show_fool true" --time_out_real 3.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_5v4hz1n6/2qnhyq3t 2>> /export/starexec/sandbox/tmp/iprover_out_5v4hz1n6/2qnhyq3t_error
% 1.38/1.32 ERROR - "ProverProcess:heur/vip_65080:40.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 1.38/1.32 Fatal error: exception Failure("undefined enum value")
% 1.38/1.32 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --comb_mode time_based --comb_res_mult 6 --comb_sup_deep_mult 4 --comb_sup_mult 6 --conj_cone_tolerance 1.895766803319499 --demod_completeness_check fullold --demod_use_ground false --extra_neg_conj all_pos_neg --instantiation_flag false --out_options none --preprocessed_out false --preprocessing_flag false --prolific_symb_bound 1024 --proof_out true --prop_solver_per_cl 128 --res_to_smt_solver false --resolution_flag true --schedule none --share_sel_clauses true --stats_out none --subs_bck_mult 16 --sup_bw_gjoin_interval 100 --sup_cache_sim none --sup_full_bw "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_full_fixpoint false --sup_full_fw "[]" --sup_fun_splitting false --sup_immed_bw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes]" --sup_immed_bw_main "[SubsumptionRes;UnitSubsAndRes;FullSubsAndRes;Demod;ACDemod]" --sup_immed_fixpoint false --sup_immed_fw_immed "[Subsumption;SubsumptionRes;FullSubsAndRes;Demod;LightNorm;ACDemod]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;FullSubsAndRes;Demod;LightNorm;ACNormalisation;GroundJoinability;Connectedness]" --sup_immed_triv "[]" --sup_indices_passive "[]" --sup_input_fixpoint false --sup_iter_deepening 2 --sup_main_fixpoint true --sup_ordering lpo --sup_passive_queue_type priority_queues --sup_passive_queues "[[+has_eq;-has_eq];[-num_var;-num_var];[+conj_dist;+ground;-max_atom_input_occur]]" --sup_passive_queues_freq "[1;4;4]" --sup_prop_simpl_given false --sup_prop_simpl_new false --sup_restarts_mult 4 --sup_score sim_d_gen --sup_share_max_num_cl 10 --sup_share_score_frac 0.2 --sup_smt_interval 32 --sup_symb_ordering invfreq_arity --sup_term_weight default --sup_to_prop_solver passive --sup_unprocessed_bound 10 --superposition_flag true --suppress_sat_res true --tptp_safe_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode tclausify -t 13.33 --show_fool true" --time_out_real 40.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_5v4hz1n6/_4u7chs4 2>> /export/starexec/sandbox/tmp/iprover_out_5v4hz1n6/_4u7chs4_error
% 1.38/1.32 % SZS status Theorem for theBenchmark.p
% 1.38/1.32
% 1.38/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.38/1.32
% 1.38/1.32 % ------ iProver source info
% 1.38/1.32
% 1.38/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 1.38/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.38/1.32 % git: non_committed_changes: false
% 1.38/1.32
% 1.38/1.32 % ------ Parsing...
% 1.38/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.38/1.32 % ------ Proving...
% 1.38/1.32 % ------ Problem Properties
% 1.38/1.32
% 1.38/1.32 %
% 1.38/1.32 % clauses 39
% 1.38/1.32 % conjectures 1
% 1.38/1.32 % EPR 5
% 1.38/1.32 % Horn 27
% 1.38/1.32 % unary 19
% 1.38/1.32 % binary 9
% 1.38/1.32 % lits 71
% 1.38/1.32 % lits eq 33
% 1.38/1.32 % fd_pure 0
% 1.38/1.32 % fd_pseudo 0
% 1.38/1.32 % fd_cond 3
% 1.38/1.32 % fd_pseudo_cond 3
% 1.38/1.32 % AC symbols 1
% 1.38/1.32
% 1.38/1.32 % ------ Input Options Time Limit: Unbounded
% 1.38/1.32
% 1.38/1.32
% 1.38/1.32 % ------
% 1.38/1.32 % Current options:
% 1.38/1.32 % ------
% 1.38/1.32
% 1.38/1.32
% 1.38/1.32 %
% 1.38/1.32
% 1.38/1.32 % ------ Proving...
% 1.38/1.32 %
% 1.38/1.32
% 1.38/1.32 % SZS status Theorem for theBenchmark.p
% 1.38/1.32
% 1.38/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.38/1.32
% 1.38/1.32
%------------------------------------------------------------------------------