%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ARI698_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 12:58:38 PM UTC 2026
% Result : Theorem 0.40s 1.18s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 32
% Syntax : Number of formulae : 107 ( 86 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 111 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 69 ( 28 ~; 31 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 1118 ( 36 atm; 688 fun; 307 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 : 14 ( 7 usr; 10 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 87 !; 0 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
n: $int ).
tff(func_def_1,type,
x6: $int ).
tff(func_def_2,type,
x5: $int ).
tff(func_def_3,type,
x4: $int ).
tff(func_def_4,type,
x3: $int ).
tff(func_def_5,type,
x2: $int ).
tff(func_def_6,type,
x1: $int ).
tff(f1,axiom,
n = 1000,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq1) ).
tff(f2,axiom,
$sum($sum($sum($sum($sum($product(1,x6),$product(n,x5)),$product(n,x4)),$product(n,x3)),$product(n,x2)),$product(n,x1)) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq2) ).
tff(f3,axiom,
$difference($difference($difference($difference($difference($product(n,x6),x5),x4),x3),x2),x1) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq3) ).
tff(f4,axiom,
$difference($difference($difference($difference($sum($product(n,x6),$product(1,x5)),x4),x3),x2),x1) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq4) ).
tff(f5,axiom,
$sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(1,x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq5) ).
tff(f6,axiom,
$sum($sum($sum($difference($sum($product(n,x6),$product(0,x5)),x4),$product(1,x3)),$product(1,x2)),$product(1,x1)) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq6) ).
tff(f7,axiom,
$difference($difference($difference($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),x3),x2),x1) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq7) ).
tff(f8,axiom,
$difference($difference($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),x2),x1) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq8) ).
tff(f9,axiom,
$sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(1,x2)),$product(1,x1)) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq9) ).
tff(f10,axiom,
$sum($difference($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),x2),$product(1,x1)) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq10) ).
tff(f11,axiom,
$difference($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(0,x2)),x1) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq11) ).
tff(f12,conjecture,
( ( x1 = 0 )
& ( x2 = 0 )
& ( x3 = 0 )
& ( x4 = 0 )
& ( x5 = 0 )
& ( x6 = 0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f13,negated_conjecture,
~ ( ( x1 = 0 )
& ( x2 = 0 )
& ( x3 = 0 )
& ( x4 = 0 )
& ( x5 = 0 )
& ( x6 = 0 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
tff(f14,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$uminus(x5)),$uminus(x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(theory_normalization,[],[f3]) ).
tff(f15,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(1,x5)),$uminus(x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(theory_normalization,[],[f4]) ).
tff(f16,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$uminus(x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
inference(theory_normalization,[],[f6]) ).
tff(f17,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(theory_normalization,[],[f7]) ).
tff(f18,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),$uminus(x2)),$uminus(x1)),
inference(theory_normalization,[],[f8]) ).
tff(f19,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$uminus(x2)),$product(1,x1)),
inference(theory_normalization,[],[f10]) ).
tff(f20,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(0,x2)),$uminus(x1)),
inference(theory_normalization,[],[f11]) ).
tff(f21,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f22,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f23,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f24,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f25,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f26,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f27,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| $less(X1,X0)
| $less(X0,X1) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f29,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_order_monotonicity]) ).
tff(f30,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f31,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f32,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f33,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f34,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(definition,[],[tha_right_identity]) ).
tff(f35,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(definition,[],[tha_times_zero]) ).
tff(f36,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(definition,[],[tha_distributivity]) ).
tff(f37,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(f38,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(definition,[],[tha_extra_integer_ordering]) ).
tff(f39,plain,
( ( x1 != 0 )
| ( x2 != 0 )
| ( x3 != 0 )
| ( x4 != 0 )
| ( x5 != 0 )
| ( x6 != 0 ) ),
inference(ennf_transformation,[],[f13]) ).
tff(f40,plain,
n = 1000,
inference(cnf_transformation,[],[f1]) ).
tff(f41,plain,
$sum($sum($sum($sum($sum($product(1,x6),$product(n,x5)),$product(n,x4)),$product(n,x3)),$product(n,x2)),$product(n,x1)) = 0,
inference(cnf_transformation,[],[f2]) ).
tff(f42,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$uminus(x5)),$uminus(x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(cnf_transformation,[],[f14]) ).
tff(f43,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(1,x5)),$uminus(x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(cnf_transformation,[],[f15]) ).
tff(f44,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(1,x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
inference(cnf_transformation,[],[f5]) ).
tff(f45,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$uminus(x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
inference(cnf_transformation,[],[f16]) ).
tff(f46,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(cnf_transformation,[],[f17]) ).
tff(f47,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),$uminus(x2)),$uminus(x1)),
inference(cnf_transformation,[],[f18]) ).
tff(f48,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(1,x2)),$product(1,x1)),
inference(cnf_transformation,[],[f9]) ).
tff(f49,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$uminus(x2)),$product(1,x1)),
inference(cnf_transformation,[],[f19]) ).
tff(f50,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(0,x2)),$uminus(x1)),
inference(cnf_transformation,[],[f20]) ).
tff(f52,plain,
0 = $sum($sum($sum($sum($sum($product(1,x6),$product(1000,x5)),$product(1000,x4)),$product(1000,x3)),$product(1000,x2)),$product(1000,x1)),
inference(definition_unfolding,[],[f41,f40,f40,f40,f40,f40]) ).
tff(f53,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$uminus(x5)),$uminus(x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(definition_unfolding,[],[f42,f40]) ).
tff(f54,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$product(1,x5)),$uminus(x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(definition_unfolding,[],[f43,f40]) ).
tff(f55,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(1,x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
inference(definition_unfolding,[],[f44,f40]) ).
tff(f56,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$uminus(x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
inference(definition_unfolding,[],[f45,f40]) ).
tff(f57,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)),
inference(definition_unfolding,[],[f46,f40]) ).
tff(f58,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),$uminus(x2)),$uminus(x1)),
inference(definition_unfolding,[],[f47,f40]) ).
tff(f59,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(1,x2)),$product(1,x1)),
inference(definition_unfolding,[],[f48,f40]) ).
tff(f60,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$uminus(x2)),$product(1,x1)),
inference(definition_unfolding,[],[f49,f40]) ).
tff(f61,plain,
0 = $sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(0,x2)),$uminus(x1)),
inference(definition_unfolding,[],[f50,f40]) ).
tff(f62,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( X2 = X3 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( 0 = X0 ) ),
inference(equality_resolution,[],[f37]) ).
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,[],[f38]) ).
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,[],[f62]) ).
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,[],[f36]) ).
tcf(c_52,negated_conjecture,
! [X0_int: $int] : $product(X0_int,0) = 0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,negated_conjecture,
! [X0_int: $int] : $product(X0_int,1) = X0_int,
inference(cnf_transformation,[],[f34]) ).
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,[],[f33]) ).
tcf(c_55,negated_conjecture,
! [X0_int: $int,X1_int: $int] : $product(X0_int,X1_int) = $product(X1_int,X0_int),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,negated_conjecture,
! [X0_int: $int] : $uminus($uminus(X0_int)) = X0_int,
inference(cnf_transformation,[],[f31]) ).
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,[],[f30]) ).
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,[],[f29]) ).
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,[],[f28]) ).
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,[],[f27]) ).
tcf(c_61,negated_conjecture,
! [X0_int: $int] : ~ $less(X0_int,X0_int),
inference(cnf_transformation,[],[f26]) ).
tcf(c_62,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,$uminus(X0_int)) = 0,
inference(cnf_transformation,[],[f25]) ).
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,[],[f24]) ).
tcf(c_64,negated_conjecture,
! [X0_int: $int] : $sum(X0_int,0) = X0_int,
inference(cnf_transformation,[],[f23]) ).
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,[],[f22]) ).
tcf(c_66,negated_conjecture,
! [X0_int: $int,X1_int: $int] : $sum(X0_int,X1_int) = $sum(X1_int,X0_int),
inference(cnf_transformation,[],[f21]) ).
tcf(c_67,negated_conjecture,
$sum($sum($sum($sum($sum($product(1,x6),$product(1000,x5)),$product(1000,x4)),$product(1000,x3)),$product(1000,x2)),$product(1000,x1)) = 0,
inference(cnf_transformation,[],[f52]) ).
tcf(c_68,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$uminus(x5)),$uminus(x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)) = 0,
inference(cnf_transformation,[],[f53]) ).
tcf(c_69,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$product(1,x5)),$uminus(x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)) = 0,
inference(cnf_transformation,[],[f54]) ).
tcf(c_70,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(1,x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)) = 0,
inference(cnf_transformation,[],[f55]) ).
tcf(c_71,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$uminus(x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)) = 0,
inference(cnf_transformation,[],[f56]) ).
tcf(c_72,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$uminus(x3)),$uminus(x2)),$uminus(x1)) = 0,
inference(cnf_transformation,[],[f57]) ).
tcf(c_73,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),$uminus(x2)),$uminus(x1)) = 0,
inference(cnf_transformation,[],[f58]) ).
tcf(c_74,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(1,x2)),$product(1,x1)) = 0,
inference(cnf_transformation,[],[f59]) ).
tcf(c_75,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$uminus(x2)),$product(1,x1)) = 0,
inference(cnf_transformation,[],[f60]) ).
tcf(c_76,negated_conjecture,
$sum($sum($sum($sum($sum($product(1000,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(0,x2)),$uminus(x1)) = 0,
inference(cnf_transformation,[],[f61]) ).
tcf(c_78,plain,
$less(0,1),
theory(arith) ).
tcf(c_79,plain,
$less(1,1000),
theory(arith) ).
tcf(c_95,negated_conjecture,
$sum($product(1,x6),$sum($product(1000,x5),$sum($product(1000,x4),$sum($product(1000,x3),$sum($product(1000,x2),$product(1000,x1)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_67,c_54,c_55,c_65,c_66]) ).
tcf(c_96,negated_conjecture,
$sum($uminus(x5),$sum($uminus(x4),$sum($uminus(x3),$sum($uminus(x2),$sum($uminus(x1),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_68,c_54,c_55,c_65,c_66]) ).
tcf(c_97,negated_conjecture,
$sum($uminus(x4),$sum($uminus(x3),$sum($uminus(x2),$sum($uminus(x1),$sum($product(1,x5),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_69,c_54,c_55,c_65,c_66]) ).
tcf(c_98,negated_conjecture,
$sum($product(0,x5),$sum($product(1,x4),$sum($product(1,x3),$sum($product(1,x2),$sum($product(1,x1),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_70,c_54,c_55,c_65,c_66]) ).
tcf(c_99,negated_conjecture,
$sum($uminus(x4),$sum($product(0,x5),$sum($product(1,x3),$sum($product(1,x2),$sum($product(1,x1),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_71,c_54,c_55,c_65,c_66]) ).
tcf(c_100,negated_conjecture,
$sum($uminus(x3),$sum($uminus(x2),$sum($uminus(x1),$sum($product(0,x5),$sum($product(0,x4),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_72,c_54,c_55,c_65,c_66]) ).
tcf(c_101,negated_conjecture,
$sum($uminus(x2),$sum($uminus(x1),$sum($product(0,x5),$sum($product(0,x4),$sum($product(1,x3),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_73,c_54,c_55,c_65,c_66]) ).
tcf(c_102,negated_conjecture,
$sum($product(0,x5),$sum($product(0,x4),$sum($product(0,x3),$sum($product(1,x2),$sum($product(1,x1),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_74,c_54,c_55,c_65,c_66]) ).
tcf(c_103,negated_conjecture,
$sum($uminus(x2),$sum($product(0,x5),$sum($product(0,x4),$sum($product(0,x3),$sum($product(1,x1),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_75,c_54,c_55,c_65,c_66]) ).
tcf(c_104,negated_conjecture,
$sum($uminus(x1),$sum($product(0,x5),$sum($product(0,x4),$sum($product(0,x3),$sum($product(0,x2),$product(1000,x6)))))) = 0,
inference(theory_normalisation,[status(thm)],[c_76,c_54,c_55,c_65,c_66]) ).
tcf(c_105,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_106,plain,
! [X0_int: $int,X1_int: $int] :
( ~ $less(X1_int,X0_int)
| ~ $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_105]) ).
tcf(c_107,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_108,plain,
! [X0_int: $int,X1_int: $int] :
( $less(X1_int,X0_int)
| $less(X0_int,$sum(X1_int,1)) ),
inference(renaming,[status(thm)],[c_107]) ).
tcf(c_109,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_267,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_104,c_103,c_102,c_101,c_100,c_99,c_98,c_97,c_96,c_95,c_79,c_78,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_109,c_108,c_56,c_55,c_54,c_53,c_52,c_51,c_50,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI698_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 06:24:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running TFA theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.40/1.18 % SZS status Started for theBenchmark.p
% 0.40/1.18 ERROR - "ProverProcess:heur/schedule_none:304.99997901916504" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("undefined enum value")
% 0.40/1.18 Fatal error: exception Failure("undefined enum value")
% 0.40/1.18 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_hgmsvgbt/ej340vgm 2>> /export/starexec/sandbox/tmp/iprover_out_hgmsvgbt/ej340vgm_error
% 0.40/1.18 % SZS status Theorem for theBenchmark.p
% 0.40/1.18
% 0.40/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.40/1.18
% 0.40/1.18 % ------ iProver source info
% 0.40/1.18
% 0.40/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.40/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.40/1.18 % git: non_committed_changes: false
% 0.40/1.18
% 0.40/1.18 % ------ Parsing...
% 0.40/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.40/1.18
% 0.40/1.18 % ------ Preprocessing...%
% 0.40/1.18
% 0.40/1.18 % SZS status Theorem for theBenchmark.p
% 0.40/1.18
% 0.40/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.40/1.18
% 0.40/1.18
%------------------------------------------------------------------------------