%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ARI734_1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 12:58:41 PM UTC 2026
% Result : Theorem 0.36s 1.33s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 60 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 135 ( 91 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 140 ( 65 ~; 48 |; 18 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 365 ( 43 atm; 115 fun; 95 num; 112 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 : 8 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 102 !; 10 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_1,type,
$bool: $tType ).
tff(func_def_7,type,
sK0: $int ).
tff(f1,conjecture,
! [X0: $int] :
( $greatereq(X0,0)
=> ? [X1: $int] :
( ( X1 = $product(2,X0) )
& ? [X2: $int] :
( ( ( X0 != 0 )
=> ( X1 = $sum(X2,2) ) )
& ( ( X0 = 0 )
=> ( X1 = 0 ) )
& ? [X3: $int] :
( ( X2 = $product(2,X3) )
& ( X3 = $difference(X0,1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
( $greatereq(X0,0)
=> ? [X1: $int] :
( ( X1 = $product(2,X0) )
& ? [X2: $int] :
( ( ( X0 != 0 )
=> ( X1 = $sum(X2,2) ) )
& ( ( X0 = 0 )
=> ( X1 = 0 ) )
& ? [X3: $int] :
( ( X2 = $product(2,X3) )
& ( X3 = $difference(X0,1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $int] :
( ~ $less(X0,0)
=> ? [X1: $int] :
( ( X1 = $product(2,X0) )
& ? [X2: $int] :
( ( ( X0 != 0 )
=> ( X1 = $sum(X2,2) ) )
& ( ( X0 = 0 )
=> ( X1 = 0 ) )
& ? [X3: $int] :
( ( X2 = $product(2,X3) )
& ( $sum(X0,$uminus(1)) = 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] : ( $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] :
( ~ $less(X0,0)
& ! [X1: $int] :
( ( $product(2,X0) != X1 )
| ! [X2: $int] :
( ( ( X0 != 0 )
& ( $sum(X2,2) != X1 ) )
| ( ( X0 = 0 )
& ( 0 != X1 ) )
| ! [X3: $int] :
( ( $product(2,X3) != X2 )
| ( $sum(X0,$uminus(1)) != X3 ) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f23,plain,
( ~ $less(sK0,0)
& ! [X1: $int] :
( ( $product(2,sK0) != X1 )
| ! [X2: $int] :
( ( ( 0 != sK0 )
& ( $sum(X2,2) != X1 ) )
| ( ( 0 = sK0 )
& ( 0 != X1 ) )
| ! [X3: $int] :
( ( $product(2,X3) != X2 )
| ( $sum(sK0,$uminus(1)) != X3 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f22]) ).
tff(f24,plain,
~ $less(sK0,0),
inference(cnf_transformation,[],[f23]) ).
tff(f27,plain,
! [X2: $int,X3: $int,X1: $int] :
( ( $product(2,sK0) != X1 )
| ( 0 != sK0 )
| ( 0 != X1 )
| ( $product(2,X3) != X2 )
| ( $sum(sK0,$uminus(1)) != X3 ) ),
inference(cnf_transformation,[],[f23]) ).
tff(f29,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( X2 = X3 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( 0 = X0 ) ),
inference(equality_resolution,[],[f20]) ).
tff(f33,plain,
! [X2: $int,X1: $int] :
( ( $product(2,sK0) != X1 )
| ( 0 != sK0 )
| ( 0 != X1 )
| ( $product(2,$sum(sK0,$uminus(1))) != X2 ) ),
inference(equality_resolution,[],[f27]) ).
tff(f34,plain,
! [X1: $int] :
( ( $product(2,sK0) != X1 )
| ( 0 != sK0 )
| ( 0 != X1 ) ),
inference(equality_resolution,[],[f33]) ).
tff(f35,plain,
( ( 0 != $product(2,sK0) )
| ( 0 != sK0 ) ),
inference(equality_resolution,[],[f34]) ).
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,[],[f29]) ).
tcf(c_51,negated_conjecture,
! [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,negated_conjecture,
! [X0_int: $int] : $product(X0_int,0) = 0,
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,negated_conjecture,
! [X0_int: $int] : $product(X0_int,1) = X0_int,
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,negated_conjecture,
! [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,negated_conjecture,
! [X0_int: $int,X1_int: $int] : $product(X0_int,X1_int) = $product(X1_int,X0_int),
inference(cnf_transformation,[],[f15]) ).
tcf(c_56,negated_conjecture,
! [X0_int: $int] : $uminus($uminus(X0_int)) = X0_int,
inference(cnf_transformation,[],[f14]) ).
tcf(c_57,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_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,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_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,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,$uminus(X0_int)) = 0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_63,negated_conjecture,
! [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,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,0) = X0_int,
inference(cnf_transformation,[],[f6]) ).
tcf(c_65,negated_conjecture,
! [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,negated_conjecture,
! [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 != 0 )
| ( $product(2,sK0) != 0 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_70,negated_conjecture,
~ $less(sK0,0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_71,plain,
$less(0,1),
theory(arith) ).
tcf(c_72,plain,
$less(1,2),
theory(arith) ).
tcf(c_89,negated_conjecture,
( ( sK0 != 0 )
| ( $product(sK0,2) != 0 ) ),
inference(theory_normalisation,[status(thm)],[c_68,c_54,c_55,c_65,c_66]) ).
tcf(c_91,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_92,plain,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_91]) ).
tcf(c_93,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_57]) ).
tcf(c_94,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_93]) ).
tcf(c_95,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(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_97,plain,
( ( $product(sK0,2) != 0 )
| ( sK0 != 0 ) ),
inference(prop_impl_just,[status(thm)],[c_89]) ).
tcf(c_98,plain,
( ( sK0 != 0 )
| ( $product(sK0,2) != 0 ) ),
inference(renaming,[status(thm)],[c_97]) ).
tcf(c_235,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_98,c_72,c_71,c_70,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_95,c_94,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI734_1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.53 % Computer : n001.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Fri Sep 25 06:29:25 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.54 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.57 Running TFA theorem proving
% 0.12/0.57 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
% 0.12/0.58
% 0.12/0.58 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.58
% 0.12/0.58 % Detected problem language: tptp
% 0.12/0.59 % Proving...
% 0.36/1.33 % SZS status Started for theBenchmark.p
% 0.36/1.33 ERROR - "ProverProcess:heur/schedule_none:304.9999797344208" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 0.36/1.33 Fatal error: exception Failure("undefined enum value")
% 0.36/1.33 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_l450d5a5/8tovj6ns 2>> /export/starexec/sandbox2/tmp/iprover_out_l450d5a5/8tovj6ns_error
% 0.36/1.33 % SZS status Theorem for theBenchmark.p
% 0.36/1.33
% 0.36/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.36/1.33
% 0.36/1.33 % ------ iProver source info
% 0.36/1.33
% 0.36/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 0.36/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.36/1.33 % git: non_committed_changes: false
% 0.36/1.33
% 0.36/1.33 % ------ Parsing...
% 0.36/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.36/1.33
% 0.36/1.33 % ------ Preprocessing...%
% 0.36/1.33
% 0.36/1.33 % SZS status Theorem for theBenchmark.p
% 0.36/1.33
% 0.36/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.36/1.33
% 0.36/1.33
%------------------------------------------------------------------------------