TPTP Problem File: SEU709_8.p
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%------------------------------------------------------------------------------
% File : SEU709_8 : TPTP v9.0.0. Released v8.0.0.
% Domain : Set Theory
% Problem : Conditionals
% Version : Especial * Reduced > Especial.
% English : (! A:i.! phi:o.! x:i.in x A -> (! y:i.in y A ->
% in (if A phi x y) (setadjoin x (setadjoin y emptyset))))
% Refs :
% Source : [TPTP]
% Names :
% Status : Theorem
% Rating : 0.00 v8.1.0
% Syntax : Number of formulae : 15 ( 5 unt; 9 typ; 5 def)
% Number of atoms : 30 ( 9 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 17 ( 1 ~; 0 |; 0 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 15 ( 10 fml; 5 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 3 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-4 aty)
% Number of variables : 20 ( 20 !; 0 ?; 20 :)
% SPC : TX0_THM_EQU_NAR
% Comments : Translated to TXF from the THF version.
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tff(in_type,type,
in: ( $i * $i ) > $o ).
tff(emptyset_type,type,
emptyset: $i ).
tff(setadjoin_type,type,
setadjoin: ( $i * $i ) > $i ).
tff(setadjoinIL_type,type,
setadjoinIL: $o ).
tff(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : in(Xx,setadjoin(Xx,Xy)) ) ) ).
tff(in__Cong_type,type,
in__Cong: $o ).
tff(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in(Xx,A)
<=> in(Xy,B) ) ) ) ) ) ).
tff(secondinupair_type,type,
secondinupair: $o ).
tff(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))) ) ) ).
tff(if_type,type,
if: ( $i * $o * $i * $i ) > $i ).
tff(iftrue_type,type,
iftrue: $o ).
tff(iftrue,definition,
( iftrue
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( in(Xx,A)
=> ! [Xy: $i] :
( in(Xy,A)
=> ( (Xphi)
=> ( if(A,(Xphi),Xx,Xy) = Xx ) ) ) ) ) ) ).
tff(iffalse_type,type,
iffalse: $o ).
tff(iffalse,definition,
( iffalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( in(Xx,A)
=> ! [Xy: $i] :
( in(Xy,A)
=> ( ~ (Xphi)
=> ( if(A,(Xphi),Xx,Xy) = Xy ) ) ) ) ) ) ).
tff(iftrueorfalse,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,Xphi: $o,Xx: $i] :
( in(Xx,A)
=> ! [Xy: $i] :
( in(Xy,A)
=> in(if(A,(Xphi),Xx,Xy),setadjoin(Xx,setadjoin(Xy,emptyset))) ) ) ) ) ) ) ) ).
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