%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ARI612_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 12:58:29 PM UTC 2026
% Result : Theorem 0.94s 1.29s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 45 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 13 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 150 ( 47 ~; 40 |; 47 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 254 ( 82 atm; 28 fun; 79 num; 65 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 : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 1 usr; 7 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 60 !; 5 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_1,type,
p: $int > $o ).
tff(pred_def_2,type,
q: $int > $o ).
tff(func_def_8,type,
sK0: $int ).
tff(f1,conjecture,
( ( ! [X0: $int] :
( ( $less(X0,12)
& $less(8,X0) )
<=> q(X0) )
& ! [X0: $int] :
( ( $less(X0,15)
& $less(5,X0) )
<=> p(X0) ) )
=> ! [X0: $int] :
( q(X0)
=> p(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interv_8_12_subset_5_15) ).
tff(f2,negated_conjecture,
~ ( ( ! [X0: $int] :
( ( $less(X0,12)
& $less(8,X0) )
<=> q(X0) )
& ! [X0: $int] :
( ( $less(X0,15)
& $less(5,X0) )
<=> p(X0) ) )
=> ! [X0: $int] :
( q(X0)
=> p(X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f4,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f5,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f6,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f7,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f9,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f10,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X0,X1) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f11,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_order_monotonicity]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f13,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f14,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_extra_integer_ordering]) ).
tff(f15,plain,
~ ( ( ! [X1: $int] :
( ( $less(X1,12)
& $less(8,X1) )
<=> q(X1) )
& ! [X0: $int] :
( ( $less(X0,15)
& $less(5,X0) )
<=> p(X0) ) )
=> ! [X2: $int] :
( q(X2)
=> p(X2) ) ),
inference(rectify,[],[f2]) ).
tff(f16,plain,
( ! [X1: $int] :
( ( $less(X1,12)
& $less(8,X1) )
<=> q(X1) )
& ! [X0: $int] :
( ( $less(X0,15)
& $less(5,X0) )
<=> p(X0) )
& ? [X2: $int] :
( q(X2)
& ~ p(X2) ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
( ! [X1: $int] :
( ( $less(X1,12)
& $less(8,X1) )
<=> q(X1) )
& ! [X0: $int] :
( ( $less(X0,15)
& $less(5,X0) )
<=> p(X0) )
& ? [X2: $int] :
( q(X2)
& ~ p(X2) ) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
( ! [X1: $int] :
( ( ~ $less(X1,12)
| ~ $less(8,X1)
| q(X1) )
& ( ~ q(X1)
| ( $less(X1,12)
& $less(8,X1) ) ) )
& ! [X0: $int] :
( ( ~ $less(X0,15)
| ~ $less(5,X0)
| p(X0) )
& ( ~ p(X0)
| ( $less(X0,15)
& $less(5,X0) ) ) )
& ? [X2: $int] :
( q(X2)
& ~ p(X2) ) ),
inference(nnf_transformation,[],[f17]) ).
tff(f19,plain,
( ! [X1: $int] :
( ( ~ $less(X1,12)
| ~ $less(8,X1)
| q(X1) )
& ( ~ q(X1)
| ( $less(X1,12)
& $less(8,X1) ) ) )
& ! [X0: $int] :
( ( ~ $less(X0,15)
| ~ $less(5,X0)
| p(X0) )
& ( ~ p(X0)
| ( $less(X0,15)
& $less(5,X0) ) ) )
& ? [X2: $int] :
( q(X2)
& ~ p(X2) ) ),
inference(flattening,[],[f18]) ).
tff(f20,plain,
( ! [X2: $int] :
( ( ~ $less(X2,12)
| ~ $less(8,X2)
| q(X2) )
& ( ~ q(X2)
| ( $less(X2,12)
& $less(8,X2) ) ) )
& ! [X1: $int] :
( ( ~ $less(X1,15)
| ~ $less(5,X1)
| p(X1) )
& ( ~ p(X1)
| ( $less(X1,15)
& $less(5,X1) ) ) )
& ? [X0: $int] :
( q(X0)
& ~ p(X0) ) ),
inference(rectify,[],[f19]) ).
tff(f21,plain,
( ! [X2: $int] :
( ( ~ $less(X2,12)
| ~ $less(8,X2)
| q(X2) )
& ( ~ q(X2)
| ( $less(X2,12)
& $less(8,X2) ) ) )
& ! [X1: $int] :
( ( ~ $less(X1,15)
| ~ $less(5,X1)
| p(X1) )
& ( ~ p(X1)
| ( $less(X1,15)
& $less(5,X1) ) ) )
& q(sK0)
& ~ p(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f20]) ).
tff(f23,plain,
! [X2: $int] :
( ~ q(X2)
| $less(X2,12) ),
inference(cnf_transformation,[],[f21]) ).
tff(f24,plain,
! [X2: $int] :
( ~ q(X2)
| $less(8,X2) ),
inference(cnf_transformation,[],[f21]) ).
tff(f28,plain,
q(sK0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0_int: $int] : $uminus($uminus(X0_int)) = X0_int,
inference(cnf_transformation,[],[f13]) ).
tcf(c_51,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_55,negated_conjecture,
! [X0_int: $int] : ~ $less(X0_int,X0_int),
inference(cnf_transformation,[],[f8]) ).
tcf(c_56,plain,
! [X0_int: $int] : $sum(X0_int,$uminus(X0_int)) = 0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_58,plain,
! [X0_int: $int] : $sum(X0_int,0) = X0_int,
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,plain,
! [X0_int: $int,X1_int: $int] : $sum(X0_int,X1_int) = $sum(X1_int,X0_int),
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,negated_conjecture,
q(sK0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_66,negated_conjecture,
! [X0_int: $int] :
( $less(8,X0_int)
| ~ q(X0_int) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_67,negated_conjecture,
! [X0_int: $int] :
( $less(X0_int,12)
| ~ q(X0_int) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_69,plain,
$less(0,1),
theory(arith) ).
tcf(c_70,plain,
$less(1,5),
theory(arith) ).
tcf(c_71,plain,
$less(5,8),
theory(arith) ).
tcf(c_72,plain,
$less(8,12),
theory(arith) ).
tcf(c_73,plain,
$less(12,15),
theory(arith) ).
tcf(c_103,plain,
! [X0_int: $int] :
( $less(8,X0_int)
| ~ q(X0_int) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
tcf(c_105,plain,
! [X0_int: $int] :
( $less(X0_int,12)
| ~ q(X0_int) ),
inference(prop_impl_just,[status(thm)],[c_67]) ).
tcf(c_257,plain,
! [X0_int: $int] :
( $less(X0_int,12)
| ( X0_int != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_105]) ).
tcf(c_258,plain,
$less(sK0,12),
inference(unflattening,[status(thm)],[c_257]) ).
tcf(c_262,plain,
! [X0_int: $int] :
( $less(8,X0_int)
| ( X0_int != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_103]) ).
tcf(c_263,plain,
$less(8,sK0),
inference(unflattening,[status(thm)],[c_262]) ).
tcf(c_651,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_263,c_258,c_73,c_72,c_71,c_70,c_69,c_60,c_58,c_56,c_55,c_51,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI612_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 06:22:58 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.41 Running TFA theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s tfa_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 0.94/1.29 % SZS status Started for theBenchmark.p
% 0.94/1.29 ERROR - "ProverProcess:heur/schedule_none:304.9999740123749" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 0.94/1.29 Fatal error: exception Failure("undefined enum value")
% 0.94/1.29 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_c6cne_1h/tju67u7p 2>> /export/starexec/sandbox2/tmp/iprover_out_c6cne_1h/tju67u7p_error
% 0.94/1.29 ERROR - "ProverProcess:heur/vip_65520:11.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 0.94/1.29 Fatal error: exception Failure("undefined enum value")
% 0.94/1.29 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/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_c6cne_1h/z3mnlxf9 2>> /export/starexec/sandbox2/tmp/iprover_out_c6cne_1h/z3mnlxf9_error
% 0.94/1.29 % SZS status Theorem for theBenchmark.p
% 0.94/1.29
% 0.94/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.94/1.29
% 0.94/1.29 % ------ iProver source info
% 0.94/1.29
% 0.94/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.94/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.94/1.29 % git: non_committed_changes: false
% 0.94/1.29
% 0.94/1.29 % ------ Parsing...
% 0.94/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.94/1.29
% 0.94/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 3 0s sf_e pe_s pe_e %
% 0.94/1.29
% 0.94/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.94/1.29
% 0.94/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.94/1.29 % ------ Proving...
% 0.94/1.29 % ------ Problem Properties
% 0.94/1.29
% 0.94/1.29 %
% 0.94/1.29 % clauses 20
% 0.94/1.29 % conjectures 2
% 0.94/1.29 % EPR 11
% 0.94/1.29 % Horn 18
% 0.94/1.29 % unary 14
% 0.94/1.29 % binary 4
% 0.94/1.29 % lits 28
% 0.94/1.29 % lits eq 7
% 0.94/1.29 % fd_pure 0
% 0.94/1.29 % fd_pseudo 0
% 0.94/1.29 % fd_cond 0
% 0.94/1.29 % fd_pseudo_cond 1
% 0.94/1.29 % AC symbols 1
% 0.94/1.29
% 0.94/1.29 % ------ Input Options Time Limit: Unbounded
% 0.94/1.29
% 0.94/1.29
% 0.94/1.29 % ------
% 0.94/1.29 % Current options:
% 0.94/1.29 % ------
% 0.94/1.29
% 0.94/1.29
% 0.94/1.29 %
% 0.94/1.29
% 0.94/1.29 % ------ Proving...
% 0.94/1.29 %
% 0.94/1.29
% 0.94/1.29 % SZS status Theorem for theBenchmark.p
% 0.94/1.29
% 0.94/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.94/1.29
% 0.94/1.29
%------------------------------------------------------------------------------