TPTP Problem File: ARI740_1.p
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% File : ARI740_1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Arithmetic
% Problem : Integer power of real
% Version : Especial.
% English :
% Refs : [Pas16] Paskevich (2016), Email to Geoff Sutcliffe
% Source : [Pas16]
% Names : real-PowerIntTest-Pow_2_2.p [Pas16]
% Status : Theorem
% Rating : 0.25 v8.2.0, 0.38 v7.5.0, 0.40 v7.4.0, 0.38 v7.3.0, 0.33 v7.0.0
% Syntax : Number of formulae : 10 ( 3 unt; 1 typ; 0 def)
% Number of atoms : 18 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 0 ~; 0 |; 1 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 54 ( 10 atm; 9 fun; 18 num; 17 var)
% Number of types : 2 ( 0 usr; 2 ari)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 10 ( 1 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?; 17 :)
% SPC : TF0_THM_EQU_ARI
% Comments :
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tff(power,type,
power: ( $real * $int ) > $real ).
tff(power_0,axiom,
! [X: $real] : ( power(X,0) = 1.0 ) ).
tff(power_s,axiom,
! [X: $real,N: $int] :
( $lesseq(0,N)
=> ( power(X,$sum(N,1)) = $product(X,power(X,N)) ) ) ).
tff(power_s_alt,axiom,
! [X: $real,N: $int] :
( $less(0,N)
=> ( power(X,N) = $product(X,power(X,$difference(N,1))) ) ) ).
tff(power_1,axiom,
! [X: $real] : ( power(X,1) = X ) ).
tff(power_sum,axiom,
! [X: $real,N: $int,M: $int] :
( $lesseq(0,N)
=> ( $lesseq(0,M)
=> ( power(X,$sum(N,M)) = $product(power(X,N),power(X,M)) ) ) ) ).
tff(power_mult,axiom,
! [X: $real,N: $int,M: $int] :
( $lesseq(0,N)
=> ( $lesseq(0,M)
=> ( power(X,$product(N,M)) = power(power(X,N),M) ) ) ) ).
tff(power_mult2,axiom,
! [X: $real,Y: $real,N: $int] :
( $lesseq(0,N)
=> ( power($product(X,Y),N) = $product(power(X,N),power(Y,N)) ) ) ).
tff(pow_ge_one,axiom,
! [X: $real,N: $int] :
( ( $lesseq(0,N)
& $lesseq(1.0,X) )
=> $lesseq(1.0,power(X,N)) ) ).
tff(pow_2_2,conjecture,
power(2.0,2) = 4.0 ).
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