TPTP Problem File: SEV429^1.p
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% File : SEV429^1 : TPTP v8.2.0. Released v5.2.0.
% Domain : Set Theory
% Problem : Injective functions f:I->I have left inverses
% Version : Especial.
% English :
% Refs : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% Source : [Bro11]
% Names : INVEXISTS [Bro11]
% Status : Theorem
% Rating : 0.50 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.29 v7.4.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v6.1.0, 0.86 v5.5.0, 1.00 v5.2.0
% Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 0 def)
% Number of atoms : 3 ( 3 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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thf(f,type,
f: $i > $i ).
thf(finj,axiom,
! [X: $i,Y: $i] :
( ( ( f @ X )
= ( f @ Y ) )
=> ( X = Y ) ) ).
thf(invexists,conjecture,
? [G: $i > $i] :
! [X: $i] :
( ( G @ ( f @ X ) )
= X ) ).
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