TPTP Problem File: SYN069+1.p
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% File : SYN069+1 : TPTP v8.2.0. Released v2.0.0.
% Domain : Syntactic
% Problem : Pelletier Problem 45
% Version : Especial.
% English :
% Refs : [KM64] Kalish & Montegue (1964), Logic: Techniques of Formal
% : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% : [Hah94] Haehnle (1994), Email to G. Sutcliffe
% Source : [Hah94]
% Names : Pelletier 45 [Pel86]
% Status : ContradictoryAxioms
% Rating : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v4.0.1, 0.05 v3.7.0, 0.00 v3.2.0, 0.11 v3.1.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1, 0.00 v2.1.0
% Syntax : Number of formulae : 4 ( 0 unt; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 16 ( 2 ~; 0 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 6 usr; 0 prp; 1-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 9 ( 5 !; 4 ?)
% SPC : FOF_CAX_RFO_NEQ
% Comments :
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fof(pel45_1,axiom,
! [X] :
( ( big_f(X)
& ! [Y] :
( ( big_g(Y)
& big_h(X,Y) )
=> big_j(X,Y) ) )
=> ! [Y1] :
( big_g(Y1)
& big_h(X,Y1)
& big_k(Y1) ) ) ).
fof(pel45_2,axiom,
~ ? [Y] :
( big_l(Y)
& big_k(Y) ) ).
fof(pel45_3,axiom,
? [X] :
( big_f(X)
& ! [Y] :
( big_h(X,Y)
=> big_l(Y) )
& ! [Y1] :
( ( big_g(Y1)
& big_h(X,Y1) )
=> big_j(X,Y1) ) ) ).
fof(pel45,conjecture,
? [X] :
( big_f(X)
& ~ ? [Y] :
( big_g(Y)
& big_h(X,Y) ) ) ).
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