%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ARI615_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 0.16s 0.95s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 145 ( 22 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 171 ( 80 ~; 41 |; 32 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 315 ( 78 atm; 90 fun; 14 num; 133 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 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 113 !; 20 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_1,type,
p: ( $int * ( $int * $int ) ) > $o ).
tff(func_def_4,type,
sK0: $int ).
tff(func_def_5,type,
sK1: $int ).
tff(func_def_6,type,
sK2: $int ).
tff(func_def_7,type,
sK3: $int ).
tff(f1,conjecture,
( ! [X0: $int,X1: $int,X2: $int] :
( ( $lesseq(X0,$sum(X1,X2))
& $lesseq($sum(X1,$uminus(X2)),X0) )
<=> p(X0,X1,X2) )
=> ! [X0: $int,X1: $int,X2: $int,X3: $int] :
( $lesseq(X2,X3)
=> ( p(X0,X1,X2)
=> p(X0,X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interv_with_smaller_radius_contained) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int,X1: $int,X2: $int] :
( ( $lesseq(X0,$sum(X1,X2))
& $lesseq($sum(X1,$uminus(X2)),X0) )
<=> p(X0,X1,X2) )
=> ! [X0: $int,X1: $int,X2: $int,X3: $int] :
( $lesseq(X2,X3)
=> ( p(X0,X1,X2)
=> p(X0,X1,X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
<=> p(X0,X1,X2) )
=> ! [X0: $int,X1: $int,X2: $int,X3: $int] :
( ~ $less(X3,X2)
=> ( p(X0,X1,X2)
=> p(X0,X1,X3) ) ) ),
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] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_extra_integer_ordering]) ).
tff(f16,plain,
~ ( ! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
<=> p(X0,X1,X2) )
=> ! [X3: $int,X4: $int,X5: $int,X6: $int] :
( ~ $less(X6,X5)
=> ( p(X3,X4,X5)
=> p(X3,X4,X6) ) ) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( ! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
<=> p(X0,X1,X2) )
& ? [X3: $int,X4: $int,X5: $int,X6: $int] :
( ~ $less(X6,X5)
& p(X3,X4,X5)
& ~ p(X3,X4,X6) ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( ! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
<=> p(X0,X1,X2) )
& ? [X3: $int,X4: $int,X5: $int,X6: $int] :
( ~ $less(X6,X5)
& p(X3,X4,X5)
& ~ p(X3,X4,X6) ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( ! [X0: $int,X1: $int,X2: $int] :
( ( $less($sum(X1,X2),X0)
| $less(X0,$sum(X1,$uminus(X2)))
| p(X0,X1,X2) )
& ( ~ p(X0,X1,X2)
| ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) ) ) )
& ? [X3: $int,X4: $int,X5: $int,X6: $int] :
( ~ $less(X6,X5)
& p(X3,X4,X5)
& ~ p(X3,X4,X6) ) ),
inference(nnf_transformation,[],[f18]) ).
tff(f20,plain,
( ! [X0: $int,X1: $int,X2: $int] :
( ( $less($sum(X1,X2),X0)
| $less(X0,$sum(X1,$uminus(X2)))
| p(X0,X1,X2) )
& ( ~ p(X0,X1,X2)
| ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) ) ) )
& ? [X3: $int,X4: $int,X5: $int,X6: $int] :
( ~ $less(X6,X5)
& p(X3,X4,X5)
& ~ p(X3,X4,X6) ) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
( ! [X4: $int,X5: $int,X6: $int] :
( ( $less($sum(X5,X6),X4)
| $less(X4,$sum(X5,$uminus(X6)))
| p(X4,X5,X6) )
& ( ~ p(X4,X5,X6)
| ( ~ $less($sum(X5,X6),X4)
& ~ $less(X4,$sum(X5,$uminus(X6))) ) ) )
& ? [X0: $int,X1: $int,X2: $int,X3: $int] :
( ~ $less(X3,X2)
& p(X0,X1,X2)
& ~ p(X0,X1,X3) ) ),
inference(rectify,[],[f20]) ).
tff(f22,plain,
( ! [X4: $int,X5: $int,X6: $int] :
( ( $less($sum(X5,X6),X4)
| $less(X4,$sum(X5,$uminus(X6)))
| p(X4,X5,X6) )
& ( ~ p(X4,X5,X6)
| ( ~ $less($sum(X5,X6),X4)
& ~ $less(X4,$sum(X5,$uminus(X6))) ) ) )
& ~ $less(sK3,sK2)
& p(sK0,sK1,sK2)
& ~ p(sK0,sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f21]) ).
tff(f24,plain,
! [X6: $int,X4: $int,X5: $int] :
( ~ p(X4,X5,X6)
| ~ $less($sum(X5,X6),X4) ),
inference(cnf_transformation,[],[f22]) ).
tff(f25,plain,
! [X6: $int,X4: $int,X5: $int] :
( ~ p(X4,X5,X6)
| ~ $less(X4,$sum(X5,$uminus(X6))) ),
inference(cnf_transformation,[],[f22]) ).
tff(f26,plain,
~ $less(sK3,sK2),
inference(cnf_transformation,[],[f22]) ).
tff(f27,plain,
p(sK0,sK1,sK2),
inference(cnf_transformation,[],[f22]) ).
tff(f28,plain,
~ p(sK0,sK1,sK3),
inference(cnf_transformation,[],[f22]) ).
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,[],[f15]) ).
tcf(c_50,negated_conjecture,
! [X0_int: $int] : $uminus($uminus(X0_int)) = X0_int,
inference(cnf_transformation,[],[f14]) ).
tcf(c_51,negated_conjecture,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_53,negated_conjecture,
! [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_55,negated_conjecture,
! [X0_int: $int] : ~ $less(X0_int,X0_int),
inference(cnf_transformation,[],[f9]) ).
tcf(c_56,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,$uminus(X0_int)) = 0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_58,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,0) = X0_int,
inference(cnf_transformation,[],[f6]) ).
tcf(c_60,negated_conjecture,
! [X0_int: $int,X1_int: $int] : $sum(X0_int,X1_int) = $sum(X1_int,X0_int),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,negated_conjecture,
~ p(sK0,sK1,sK3),
inference(cnf_transformation,[],[f28]) ).
tcf(c_62,negated_conjecture,
p(sK0,sK1,sK2),
inference(cnf_transformation,[],[f27]) ).
tcf(c_63,negated_conjecture,
~ $less(sK3,sK2),
inference(cnf_transformation,[],[f26]) ).
tcf(c_64,negated_conjecture,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( ~ p(X0_int,X1_int,X2_int)
| ~ $less(X0_int,$sum(X1_int,$uminus(X2_int))) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_65,negated_conjecture,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( ~ p(X2_int,X0_int,X1_int)
| ~ $less($sum(X0_int,X1_int),X2_int) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_67,plain,
$less(0,1),
theory(arith) ).
tcf(c_86,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( ~ p(X0_int,X1_int,X2_int)
| ~ $less(X0_int,$sum(X1_int,$uminus(X2_int))) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
tcf(c_90,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( ~ p(X2_int,X0_int,X1_int)
| ~ $less($sum(X0_int,X1_int),X2_int) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_212,plain,
( ( sK2 != sK3 )
| ( sK1 != sK1 )
| ( sK0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_62]) ).
tcf(c_230,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( ~ $less(X0_int,$sum(X1_int,$uminus(X2_int)))
| ( X2_int != sK2 )
| ( X1_int != sK1 )
| ( X0_int != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_86]) ).
tcf(c_231,plain,
~ $less(sK0,$sum(sK1,$uminus(sK2))),
inference(unflattening,[status(thm)],[c_230]) ).
tcf(c_235,plain,
! [X0_int: $int,X1_int: $int,X2_int: $int] :
( ~ $less($sum(X1_int,X2_int),X0_int)
| ( X2_int != sK2 )
| ( X1_int != sK1 )
| ( X0_int != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_90]) ).
tcf(c_236,plain,
~ $less($sum(sK1,sK2),sK0),
inference(unflattening,[status(thm)],[c_235]) ).
tcf(c_249,plain,
sK2 != sK3,
inference(equality_resolution_simp,[status(thm)],[c_212]) ).
tcf(c_250,plain,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X0_int,$sum(X1_int,1))
| ~ $less(X1_int,X0_int) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_251,plain,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_250]) ).
tcf(c_252,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X0_int,$sum(X1_int,1))
| $less(X1_int,X0_int) ),
inference(prop_impl_just,[status(thm)],[c_51]) ).
tcf(c_253,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_252]) ).
tcf(c_347,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_249,c_236,c_231,c_67,c_63,c_60,c_58,c_56,c_55,c_53,c_253,c_50,c_251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ARI615_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Fri Sep 25 06:17:50 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.32 Running TFA theorem proving
% 0.02/0.32 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
% 0.02/0.32
% 0.02/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.32
% 0.06/0.32 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 0.16/0.95 % SZS status Started for theBenchmark.p
% 0.16/0.95 ERROR - "ProverProcess:heur/schedule_none:304.99999046325684" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 0.16/0.95 Fatal error: exception Failure("undefined enum value")
% 0.16/0.95 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_dtebm9w2/19w8dszj 2>> /export/starexec/sandbox/tmp/iprover_out_dtebm9w2/19w8dszj_error
% 0.16/0.95 % SZS status Theorem for theBenchmark.p
% 0.16/0.95
% 0.16/0.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.16/0.95
% 0.16/0.95 % ------ iProver source info
% 0.16/0.95
% 0.16/0.95 % git: date: 2026-07-19 20:42:38 +0200
% 0.16/0.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.16/0.95 % git: non_committed_changes: false
% 0.16/0.95
% 0.16/0.95 % ------ Parsing...
% 0.16/0.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.16/0.95
% 0.16/0.95 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 0.16/0.95
% 0.16/0.95 % SZS status Theorem for theBenchmark.p
% 0.16/0.95
% 0.16/0.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.16/0.95
% 0.16/0.95
%------------------------------------------------------------------------------