TPTP Problem File: ARI635_1.p
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% File : ARI635_1 : TPTP v9.0.0. Released v6.3.0.
% Domain : Arithmetic
% Problem : Example 9
% Version : Especial.
% English :
% Refs : [ALR14] Avigad et al. (2014), A Heuristic Prover for Real Ineq
% : [LAR14] Lewis et al. (2014), A Heuristic Prover for Real Inequ
% : [Lew14] Lewis (2014), Email to Geoff Sutcliffe
% Source : [Lew14]
% Names : Example 9 [Lew14]
% Status : Theorem
% Rating : 0.40 v9.0.0, 0.50 v7.5.0, 0.40 v7.4.0, 0.50 v7.3.0, 0.62 v7.1.0, 0.50 v7.0.0, 1.00 v6.3.0
% Syntax : Number of formulae : 14 ( 6 unt; 7 typ; 0 def)
% Number of atoms : 8 ( 0 equ)
% Maximal formula atoms : 2 ( 0 avg)
% Number of connectives : 1 ( 0 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 20 ( 8 atm; 6 fun; 4 num; 2 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 13 ( 7 usr; 9 con; 0-2 aty)
% Number of variables : 2 ( 2 !; 0 ?; 2 :)
% SPC : TF0_THM_NEQ_ARI
% Comments :
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tff(u_type,type,
u: $real ).
tff(v_type,type,
v: $real ).
tff(w_type,type,
w: $real ).
tff(x_type,type,
x: $real ).
tff(y_type,type,
y: $real ).
tff(s_type,type,
s: $real ).
tff(f_type,type,
f: $real > $real ).
tff(f_non_decreasing,axiom,
! [X: $real,Y: $real] :
( $greatereq(X,Y)
=> $greatereq(f(X),f(Y)) ) ).
tff(hypothesis,hypothesis,
$less(u,v) ).
tff(hypothesis_01,hypothesis,
$greater(w,1.0) ).
tff(hypothesis_02,hypothesis,
$greater(s,2.0) ).
tff(hypothesis_03,hypothesis,
$less($product($quotient(1.0,3.0),$sum(w,s)),v) ).
tff(hypothesis_04,hypothesis,
$lesseq(x,y) ).
tff(conclusion,conjecture,
$less($sum(f(x),u),$sum($product(v,v),f(y))) ).
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