TPTP Problem File: ARI655=1.p

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%------------------------------------------------------------------------------
% File     : ARI655=1 : TPTP v7.4.0. Released v6.3.0.
% Domain   : Arithmetic
% Problem  : a >= b, c >= d imply (a-b)*(c-d) >= 0
% Version  : Especial.
% English  :

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

% Status   : Theorem
% Rating   : 0.40 v7.4.0, 0.33 v7.3.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.67 v6.4.0, 1.00 v6.3.0
% Syntax   : Number of formulae    :    7 (   3 unit;   4 type)
%            Number of atoms       :    3 (   0 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  :    6 (   5 propositional; 0-2 arity)
%            Number of functors    :    7 (   5 constant; 0-2 arity)
%            Number of variables   :    0 (   0 sgn;   0   !;   0   ?)
%                                         (   0   :;   0  !>;   0  ?*)
%            Maximal term depth    :    3 (   1 average)
%            Arithmetic symbols    :    4 (   1 prd;   2 fun;   1 num;   0 var)
% SPC      : TF0_THM_NEQ_ARI

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

tff(b_type,type,(
    b: $int )).

tff(c_type,type,(
    c: $int )).

tff(d_type,type,(
    d: $int )).

tff(conj,axiom,(
    $lesseq(b,a) )).

tff(conj_001,axiom,(
    $lesseq(d,c) )).

tff(conj_002,conjecture,(
    $lesseq(0,$product($difference(a,b),$difference(c,d))) )).

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