%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ARI574_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 : n018.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 12:58:25 PM UTC 2026
% Result : Theorem 2.19s 1.31s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of formulae : 67 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 146 ( 70 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 133 ( 54 ~; 51 |; 24 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 406 ( 75 atm; 118 fun; 125 num; 88 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 : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 2 usr; 9 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 82 !; 6 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_1,type,
$bool: $tType ).
tff(func_def_10,type,
sK0: $int ).
tff(func_def_11,type,
sK1: $int ).
tff(f1,conjecture,
! [X0: $int,X1: $int] :
( ( $lesseq(X1,4)
& $lesseq($sum(X0,5),$product(2,X1))
& $lesseq(7,$sum(X0,X1)) )
<=> ( ( X1 = 4 )
& ( X0 = 3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq_sys_has_1_sol) ).
tff(f2,negated_conjecture,
~ ! [X0: $int,X1: $int] :
( ( $lesseq(X1,4)
& $lesseq($sum(X0,5),$product(2,X1))
& $lesseq(7,$sum(X0,X1)) )
<=> ( ( X1 = 4 )
& ( X0 = 3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $int,X1: $int] :
( ( ~ $less(4,X1)
& ~ $less($product(2,X1),$sum(X0,5))
& ~ $less($sum(X0,X1),7) )
<=> ( ( X1 = 4 )
& ( X0 = 3 ) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f5,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f6,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f7,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f8,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f9,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f11,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X0,X1) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f12,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_order_monotonicity]) ).
tff(f13,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f14,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f15,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f16,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f17,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f18,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(definition,[],[tha_times_zero]) ).
tff(f19,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(definition,[],[tha_distributivity]) ).
tff(f20,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( X2 = X3 )
| ( $product(X0,X3) != X1 )
| ( $product(X0,X2) != X1 )
| ( 0 = X0 ) ),
introduced(definition,[],[tha_divisibility]) ).
tff(f21,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_extra_integer_ordering]) ).
tff(f22,plain,
? [X0: $int,X1: $int] :
( ( ~ $less(4,X1)
& ~ $less($product(2,X1),$sum(X0,5))
& ~ $less($sum(X0,X1),7) )
<~> ( ( X1 = 4 )
& ( X0 = 3 ) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f23,plain,
? [X0: $int,X1: $int] :
( ( ( ~ $less(4,X1)
& ~ $less($product(2,X1),$sum(X0,5))
& ~ $less($sum(X0,X1),7) )
| ( ( X1 = 4 )
& ( X0 = 3 ) ) )
& ( $less(4,X1)
| $less($product(2,X1),$sum(X0,5))
| $less($sum(X0,X1),7)
| ( 4 != X1 )
| ( 3 != X0 ) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f24,plain,
? [X0: $int,X1: $int] :
( ( ( ~ $less(4,X1)
& ~ $less($product(2,X1),$sum(X0,5))
& ~ $less($sum(X0,X1),7) )
| ( ( X1 = 4 )
& ( X0 = 3 ) ) )
& ( $less(4,X1)
| $less($product(2,X1),$sum(X0,5))
| $less($sum(X0,X1),7)
| ( 4 != X1 )
| ( 3 != X0 ) ) ),
inference(flattening,[],[f23]) ).
tff(f25,plain,
( ( ( ~ $less(4,sK1)
& ~ $less($product(2,sK1),$sum(sK0,5))
& ~ $less($sum(sK0,sK1),7) )
| ( ( 4 = sK1 )
& ( 3 = sK0 ) ) )
& ( $less(4,sK1)
| $less($product(2,sK1),$sum(sK0,5))
| $less($sum(sK0,sK1),7)
| ( 4 != sK1 )
| ( 3 != sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
tff(f26,plain,
( ~ $less(4,sK1)
| ( 4 = sK1 ) ),
inference(cnf_transformation,[],[f25]) ).
tff(f27,plain,
( ~ $less($product(2,sK1),$sum(sK0,5))
| ( 4 = sK1 ) ),
inference(cnf_transformation,[],[f25]) ).
tff(f28,plain,
( ~ $less($sum(sK0,sK1),7)
| ( 4 = sK1 ) ),
inference(cnf_transformation,[],[f25]) ).
tff(f29,plain,
( ~ $less(4,sK1)
| ( 3 = sK0 ) ),
inference(cnf_transformation,[],[f25]) ).
tff(f30,plain,
( ~ $less($product(2,sK1),$sum(sK0,5))
| ( 3 = sK0 ) ),
inference(cnf_transformation,[],[f25]) ).
tff(f31,plain,
( ~ $less($sum(sK0,sK1),7)
| ( 3 = sK0 ) ),
inference(cnf_transformation,[],[f25]) ).
tff(f33,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( X2 = X3 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( 0 = X0 ) ),
inference(equality_resolution,[],[f20]) ).
tcf(c_49,negated_conjecture,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ $less(X0_int,$sum(X1_int,1)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( ( X1_int = X2_int )
| ( X0_int = 0 )
| ( $product(X0_int,X1_int) != $product(X0_int,X2_int) ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_51,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] : $sum($product(X0_int,X1_int),$product(X0_int,X2_int)) = $product(X0_int,$sum(X1_int,X2_int)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0_int: $int] : $product(X0_int,0) = 0,
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,plain,
! [X0_int: $int] : $product(X0_int,1) = X0_int,
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] : $product($product(X0_int,X1_int),X2_int) = $product(X0_int,$product(X1_int,X2_int)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_55,plain,
! [X0_int: $int,X1_int: $int] : $product(X0_int,X1_int) = $product(X1_int,X0_int),
inference(cnf_transformation,[],[f15]) ).
tcf(c_56,plain,
! [X0_int: $int] : $uminus($uminus(X0_int)) = X0_int,
inference(cnf_transformation,[],[f14]) ).
tcf(c_57,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_58,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( $less($sum(X0_int,X2_int),$sum(X1_int,X2_int))
| ~ $less(X0_int,X1_int) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_59,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,X1_int)
| ( X0_int = X1_int ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_60,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( $less(X0_int,X2_int)
| ~ $less(X1_int,X2_int)
| ~ $less(X0_int,X1_int) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_61,negated_conjecture,
! [X0_int: $int] : ~ $less(X0_int,X0_int),
inference(cnf_transformation,[],[f9]) ).
tcf(c_62,plain,
! [X0_int: $int] : $sum(X0_int,$uminus(X0_int)) = 0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_63,plain,
! [X0_int: $int,X1_int: $int] : $sum($uminus(X0_int),$uminus(X1_int)) = $uminus($sum(X1_int,X0_int)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,plain,
! [X0_int: $int] : $sum(X0_int,0) = X0_int,
inference(cnf_transformation,[],[f6]) ).
tcf(c_65,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] : $sum($sum(X0_int,X1_int),X2_int) = $sum(X0_int,$sum(X1_int,X2_int)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0_int: $int,X1_int: $int] : $sum(X0_int,X1_int) = $sum(X1_int,X0_int),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,negated_conjecture,
( ( sK0 = 3 )
| ~ $less($sum(sK0,sK1),7) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_69,negated_conjecture,
( ( sK0 = 3 )
| ~ $less($product(2,sK1),$sum(sK0,5)) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_70,negated_conjecture,
( ( sK0 = 3 )
| ~ $less(4,sK1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_71,negated_conjecture,
( ( sK1 = 4 )
| ~ $less($sum(sK0,sK1),7) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_72,negated_conjecture,
( ( sK1 = 4 )
| ~ $less($product(2,sK1),$sum(sK0,5)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_73,negated_conjecture,
( ( sK1 = 4 )
| ~ $less(4,sK1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_74,plain,
$less(0,1),
theory(arith) ).
tcf(c_75,plain,
$less(1,2),
theory(arith) ).
tcf(c_76,plain,
$less(2,3),
theory(arith) ).
tcf(c_77,plain,
$less(3,4),
theory(arith) ).
tcf(c_78,plain,
$less(4,5),
theory(arith) ).
tcf(c_79,plain,
$less(5,7),
theory(arith) ).
tcf(c_730,plain,
( ( sK0 = 3 )
| ~ $less($sum(sK1,sK0),7) ),
inference(demodulation,[status(thm)],[c_68,c_66]) ).
tcf(c_731,plain,
( ( sK1 = 4 )
| ~ $less($sum(sK1,sK0),7) ),
inference(demodulation,[status(thm)],[c_71,c_66]) ).
tcf(c_732,plain,
( ( sK0 = 3 )
| ~ $less($product(sK1,2),$sum(sK0,5)) ),
inference(demodulation,[status(thm)],[c_69,c_55]) ).
tcf(c_733,plain,
sK1 = 4,
inference(global_subsumption_just,[status(thm)],[c_72]) ).
tcf(c_736,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_733,c_732,c_731,c_730,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_70,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_57,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI574_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 06:18:19 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.42 Running TFA theorem proving
% 0.13/0.42 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
% 0.13/0.43
% 0.13/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.43
% 0.13/0.43 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 2.19/1.31 % SZS status Started for theBenchmark.p
% 2.19/1.31 ERROR - "ProverProcess:heur/schedule_none:304.9999759197235" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 2.19/1.31 Fatal error: exception Failure("undefined enum value")
% 2.19/1.31 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_8o_gzfau/lykijmzc 2>> /export/starexec/sandbox2/tmp/iprover_out_8o_gzfau/lykijmzc_error
% 2.19/1.31 ERROR - "ProverProcess:heur/vip_65520:11.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 2.19/1.31 Fatal error: exception Failure("undefined enum value")
% 2.19/1.31 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_8o_gzfau/y72yww3n 2>> /export/starexec/sandbox2/tmp/iprover_out_8o_gzfau/y72yww3n_error
% 2.19/1.31 % SZS status Theorem for theBenchmark.p
% 2.19/1.31
% 2.19/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.19/1.31
% 2.19/1.31 % ------ iProver source info
% 2.19/1.31
% 2.19/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.19/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.19/1.31 % git: non_committed_changes: false
% 2.19/1.31
% 2.19/1.31 % ------ Parsing...
% 2.19/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.19/1.31
% 2.19/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.19/1.31
% 2.19/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.19/1.31
% 2.19/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.19/1.31 % ------ Proving...
% 2.19/1.31 % ------ Problem Properties
% 2.19/1.31
% 2.19/1.31 %
% 2.19/1.31 % clauses 31
% 2.19/1.31 % conjectures 9
% 2.19/1.31 % EPR 11
% 2.19/1.31 % Horn 27
% 2.19/1.31 % unary 18
% 2.19/1.31 % binary 9
% 2.19/1.31 % lits 50
% 2.19/1.31 % lits eq 23
% 2.19/1.31 % fd_pure 0
% 2.19/1.31 % fd_pseudo 0
% 2.19/1.31 % fd_cond 0
% 2.19/1.31 % fd_pseudo_cond 2
% 2.19/1.31 % AC symbols 2
% 2.19/1.31
% 2.19/1.31 % ------ Input Options Time Limit: Unbounded
% 2.19/1.31
% 2.19/1.31
% 2.19/1.31 % ------
% 2.19/1.31 % Current options:
% 2.19/1.31 % ------
% 2.19/1.31
% 2.19/1.31
% 2.19/1.31 %
% 2.19/1.31
% 2.19/1.31 % ------ Proving...
% 2.19/1.31 %
% 2.19/1.31
% 2.19/1.31 % SZS status Theorem for theBenchmark.p
% 2.19/1.31
% 2.19/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.19/1.31
% 2.19/1.31
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