%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ARI685_1 : TPTP v9.3.1. Released v6.3.0.
% 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 12:58:37 PM UTC 2026
% Result : Theorem 0.38s 6.15s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 24
% Syntax : Number of formulae : 55 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 81 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 24 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 18 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 554 ( 38 atm; 320 fun; 109 num; 87 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 4 usr; 9 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 87 !; 0 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
c: $int ).
tff(func_def_3,type,
d: $int ).
tff(f1,axiom,
$sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(f2,conjecture,
$sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),b),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f3,negated_conjecture,
( ( ~ $sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),b),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))) ) = 0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
( ( ~ 0 ) = $sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),$uminus(b)),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))) ),
inference(theory_normalization,[],[f3]) ).
tff(f5,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f6,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f7,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f8,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f9,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f10,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f11,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X0,X1) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f13,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_order_monotonicity]) ).
tff(f14,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f15,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f16,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f17,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f18,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f19,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(definition,[],[tha_times_zero]) ).
tff(f20,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(definition,[],[tha_distributivity]) ).
tff(f21,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(f22,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_extra_integer_ordering]) ).
tff(f23,plain,
0 != $sum($product($product(d,b),a),$product(-1,$sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(-2,$product(a,a)),$product(-1,$product(c,a))),$uminus(b)),$product(-1,$product(b,a))),$product(2,c)),$product(-1,$product(c,b))),$product(c,c)),$product(-1,$product($product(c,a),a))),$product(-1,$product(2,$product(d,a)))),$product(-1,$product(2,$product(d,b)))),$product(-1,$product($product(c,b),a))),$product(d,c)),$product(-1,$product($product(d,a),a))),$product(2,d)))),
inference(flattening,[],[f4]) ).
tff(f24,plain,
$sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
inference(cnf_transformation,[],[f1]) ).
tff(f26,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( X2 = X3 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( 0 = X0 ) ),
inference(equality_resolution,[],[f21]) ).
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,[],[f22]) ).
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,[],[f26]) ).
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,[],[f20]) ).
tcf(c_52,negated_conjecture,
! [X0_int: $int] : $product(X0_int,0) = 0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,negated_conjecture,
! [X0_int: $int] : $product(X0_int,1) = X0_int,
inference(cnf_transformation,[],[f18]) ).
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,[],[f17]) ).
tcf(c_55,negated_conjecture,
! [X0_int: $int,X1_int: $int] : $product(X0_int,X1_int) = $product(X1_int,X0_int),
inference(cnf_transformation,[],[f16]) ).
tcf(c_56,negated_conjecture,
! [X0_int: $int] : $uminus($uminus(X0_int)) = X0_int,
inference(cnf_transformation,[],[f15]) ).
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,[],[f14]) ).
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,[],[f13]) ).
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,[],[f12]) ).
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,[],[f11]) ).
tcf(c_61,negated_conjecture,
! [X0_int: $int] : ~ $less(X0_int,X0_int),
inference(cnf_transformation,[],[f10]) ).
tcf(c_62,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,$uminus(X0_int)) = 0,
inference(cnf_transformation,[],[f9]) ).
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,[],[f8]) ).
tcf(c_64,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,0) = X0_int,
inference(cnf_transformation,[],[f7]) ).
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,[],[f6]) ).
tcf(c_66,negated_conjecture,
! [X0_int: $int,X1_int: $int] : $sum(X0_int,X1_int) = $sum(X1_int,X0_int),
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,negated_conjecture,
$sum($sum($sum($product(a,a),$product($product($sum(a,b),$sum($sum(c,d),1)),$sum(a,2))),b),$product(-1,$product($sum($sum($sum(a,b),c),d),$sum(2,c)))) = 0,
inference(cnf_transformation,[],[f24]) ).
tcf(c_69,plain,
$less(-2,-1),
theory(arith) ).
tcf(c_70,plain,
$less(-1,0),
theory(arith) ).
tcf(c_71,plain,
$less(0,1),
theory(arith) ).
tcf(c_72,plain,
$less(1,2),
theory(arith) ).
tcf(c_88,negated_conjecture,
$sum(b,$sum($product(a,a),$sum($product(-1,$product($sum(c,2),$sum(a,$sum(c,$sum(b,d))))),$product($sum(a,b),$product($sum(a,2),$sum(c,$sum(d,1))))))) = 0,
inference(theory_normalisation,[status(thm)],[c_67,c_54,c_55,c_65,c_66]) ).
tcf(c_90,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_91,plain,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_90]) ).
tcf(c_92,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_93,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_92]) ).
tcf(c_94,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_210,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_88,c_72,c_71,c_70,c_69,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_94,c_93,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI685_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.35 % Computer : n016.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.35 % CPULimit : 300
% 0.08/5.35 % WCLimit : 300
% 0.08/5.36 % DateTime : Fri Sep 25 06:26:34 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.38 Running TFA theorem proving
% 0.08/5.38 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
% 0.08/5.39
% 0.08/5.39 % ======== iProver multi-core TPTP/SMT =========
% 0.08/5.39
% 0.08/5.39 % Detected problem language: tptp
% 0.12/5.41 % Proving...
% 0.38/6.15 % SZS status Started for theBenchmark.p
% 0.38/6.15 ERROR - "ProverProcess:heur/schedule_none:304.99997997283936" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 0.38/6.15 Fatal error: exception Failure("undefined enum value")
% 0.38/6.15 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_hbtg5pbp/1_2vo4wn 2>> /export/starexec/sandbox2/tmp/iprover_out_hbtg5pbp/1_2vo4wn_error
% 0.38/6.15 % SZS status Theorem for theBenchmark.p
% 0.38/6.15
% 0.38/6.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.38/6.15
% 0.38/6.15 % ------ iProver source info
% 0.38/6.15
% 0.38/6.15 % git: date: 2026-07-19 20:42:38 +0200
% 0.38/6.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.38/6.15 % git: non_committed_changes: false
% 0.38/6.15
% 0.38/6.15 % ------ Parsing...
% 0.38/6.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.38/6.15
% 0.38/6.15 % ------ Preprocessing...%
% 0.38/6.15
% 0.38/6.15 % SZS status Theorem for theBenchmark.p
% 0.38/6.15
% 0.38/6.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.38/6.15
% 0.38/6.15
%------------------------------------------------------------------------------