TPTP Problem File: ARI697=1.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : ARI697=1 : TPTP v7.4.0. Released v6.3.0.
% Domain   : Arithmetic
% Problem  : Solve simple system of linear equations
% Version  : Especial.
% English  :

% Refs     : [BHS07] Beckert et al. (2007), Verification of Object-Oriented
%          : [Rue14] Ruemmer (2014), Email to Geoff Sutcliffe
% Source   : [Rue14]
% Names    : simplify20.pri [BHS07]
%          : poly_simplify20.p [Rue14]

% Status   : Theorem
% Rating   : 0.50 v7.0.0, 0.71 v6.4.0, 0.33 v6.3.0
% Syntax   : Number of formulae    :    9 (   4 unit;   5 type)
%            Number of atoms       :    4 (   4 equality)
%            Maximal formula depth :    2 (   2 average)
%            Number of connectives :    0 (   0   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 propositional; 0-2 arity)
%            Number of functors    :   22 (  18 constant; 0-2 arity)
%            Number of variables   :    0 (   0 sgn;   0   !;   0   ?)
%                                         (   0   :;   0  !>;   0  ?*)
%            Maximal term depth    :    7 (   3 average)
%            Arithmetic symbols    :   16 (   0 prd;   4 fun;  12 num;   0 var)
% SPC      : TF0_THM_EQU_ARI

% Comments : KeY arithmetic regression test, http://www.key-project.org
%------------------------------------------------------------------------------
tff(x1_type,type,(
    x1: $int )).

tff(x2_type,type,(
    x2: $int )).

tff(x3_type,type,(
    x3: $int )).

tff(x4_type,type,(
    x4: $int )).

tff(x5_type,type,(
    x5: $int )).

tff(eq1,axiom,(
    $sum($difference($sum($difference($product(-1,$product(2,x2)),$product(5,x1)),x3),x4),x5) = 0 )).

tff(eq2,axiom,(
    $sum($sum($sum($sum($product(9,x1),$product(62,x2)),$product(-1,$product(5,x3))),$product(-1,$product(3,x4))),$product(101,x5)) = 0 )).

tff(eq3,axiom,(
    $sum($sum($sum($sum($product(56,x1),$product(-1,$product(34,x2))),$product(-1,$product(11,x3))),$product(67,x4)),$product(-1,$product(98,x5))) = 0 )).

tff(conj,conjecture,(
    $remainder_t(x5,2) = 0 )).

%------------------------------------------------------------------------------