TPTP Problem File: SYN986+1.000.p
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% File : SYN986+1.000 : TPTP v9.0.0. Released v4.0.0.
% Domain : Syntactic
% Problem : Orevkov formula - size 0
% Version : [TS00] axioms : Especial.
% English : hyp(2,k,1) is defined. Each Ck has a non-normal natural deduction
% of size linear in k, and each normal deduction of Ck has at least
% hyp(2,k,1)=2_k nodes.
% Refs : [TS00] Troelstra & Schwichtenberg (2000), Basic Proof Theory
% : [Rat08] Raths (2008), Email to G. Sutcliffe
% Source : [Rat08]
% Names :
% Status : Theorem
% Rating : 0.07 v9.0.0, 0.00 v5.3.0, 0.04 v5.2.0, 0.07 v5.1.0, 0.14 v5.0.0, 0.10 v4.1.0, 0.11 v4.0.1, 0.47 v4.0.0
% Syntax : Number of formulae : 3 ( 2 unt; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 2 ( 0 ~; 0 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 6 ( 5 !; 1 ?)
% SPC : FOF_THM_RFO_NEQ
% Comments : Inspiration by Wolfgang Bibel, Helmut Schwichtenberg.
% : The complexity of proof seach is hyper-exponential with the size
% of the formulae: 2^0=1, 2^1=2, 2^2=4, 2^4=16, 2^16=65536,
% 2^65536 = mmmh... ?
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%----Include Orevkov formula
include('Axioms/SYN002+0.ax').
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fof(ck,conjecture,
? [Z0] : r(zero,zero,Z0) ).
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