TPTP Problem File: SYO533^1.p
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% File : SYO533^1 : TPTP v8.2.0. Released v5.2.0.
% Domain : Syntactic
% Problem : Binary choice on individuals 4
% Version : Especial.
% English : There is an Epsa such that Epsa and (epsb Epsa) work together to
% give an a and b such that R a b holds, if such an a and b exist
% for a binary relation R on $i. A choice operator on i can be used
% to define a choice operator on i*i (Curried). In this version the
% prover must synthesize both parts of the solution.
% Refs : [Bac10] Backes (2010), Tableaux for Higher-Order Logic with If
% : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% Source : [Bro11]
% Names : CHOICE10 [Bro11]
% Status : Theorem
% Rating : 0.92 v8.2.0, 0.91 v8.1.0, 0.92 v7.4.0, 0.89 v7.3.0, 0.90 v7.2.0, 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 1.00 v5.2.0
% Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% Number of atoms : 0 ( 0 equ; 0 cnn)
% Maximal formula atoms : 0 ( 0 avg)
% Number of connectives : 7 ( 0 ~; 0 |; 0 &; 6 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 5 ( 0 ^; 1 !; 4 ?; 5 :)
% SPC : TH0_THM_NEQ_NAR
% Comments :
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thf(conj,conjecture,
? [Epsa: ( $i > $i > $o ) > $i,Epsb: ( $i > $i > $o ) > $i] :
! [R: $i > $i > $o] :
( ? [X: $i,Y: $i] : ( R @ X @ Y )
=> ( R @ ( Epsa @ R ) @ ( Epsb @ R ) ) ) ).
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