TPTP Problem File: PHI044_1.p
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%------------------------------------------------------------------------------
% File : PHI044_1 : TPTP v9.0.0. Released v7.5.0.
% Domain : Philosophy
% Problem : Impossibility theorem
% Version : [Gus20] axioms.
% English :
% Refs : [Gus20] Gustafsson (2020), A Paradox for the Intrinsic Value o
% Source : [Gus20]
% Names :
% Status : Unsatisfiable
% Rating : 0.00 v7.5.0
% Syntax : Number of formulae : 16 ( 0 unt; 8 typ; 0 def)
% Number of atoms : 55 ( 12 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 51 ( 4 ~; 4 |; 26 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 0 prp; 2-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 37 ( 29 !; 8 ?; 37 :)
% SPC : TF0_UNS_EQU_NAR
% Comments :
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%----Type declarations
tff(option_type,type,
option: $tType ).
tff(option_set_type,type,
option_set: $tType ).
tff(subset_type,type,
subset: ( option_set * option_set ) > $o ).
tff(member_type,type,
member: ( option * option_set ) > $o ).
tff(weakly_better_type,type,
weakly_better: ( option_set * option_set ) > $o ).
tff(better_type,type,
better: ( option_set * option_set ) > $o ).
tff(permitted_preference_type,type,
permitted_preference: ( option * option ) > $o ).
tff(required_preference_type,type,
required_preference: ( option * option ) > $o ).
%----Supplementary axioms
tff(subset,axiom,
! [A: option_set,B: option_set] :
( subset(A,B)
<=> ! [X: option] :
( member(X,A)
=> member(X,B) ) ) ).
tff(better,axiom,
! [X: option_set,Y: option_set] :
( better(X,Y)
<=> ( weakly_better(X,Y)
& ~ weakly_better(Y,X) ) ) ).
%----Substantial axioms
tff(value_of_rational_diversity,axiom,
! [X: option,Y: option,U: option_set,V: option_set] :
( ( permitted_preference(X,Y)
& permitted_preference(Y,X)
& member(X,U)
& member(Y,U)
& member(X,V)
& ! [Z: option] :
( member(Z,U)
=> ( ( Z = X )
| ( Z = Y ) ) )
& ! [Z: option] :
( member(Z,V)
=> ( Z = X ) ) )
=> better(U,V) ) ).
tff(insignificance_of_dominated_options,axiom,
! [X: option_set,Y: option_set] :
( ( subset(X,Y)
& ? [U: option] :
( member(U,X)
& ! [V: option] :
( ( member(V,Y)
& ~ member(V,X) )
=> required_preference(U,V) ) ) )
=> ~ better(Y,X) ) ).
tff(harmlessness_of_expansions,axiom,
! [X: option_set,Y: option_set] :
( subset(X,Y)
=> weakly_better(Y,X) ) ).
tff(parity_of_no_choice_situations,axiom,
! [X: option,Y: option,U: option_set,V: option_set] :
( ( ! [Z: option] :
( member(Z,U)
<=> ( Z = X ) )
& ! [Z: option] :
( member(Z,V)
<=> ( Z = Y ) ) )
=> ~ better(U,V) ) ).
tff(transitivity_of_weakly_better_freedom_of_choice,axiom,
! [X: option_set,Y: option_set,Z: option_set] :
( ( weakly_better(X,Y)
& weakly_better(Y,Z) )
=> weakly_better(X,Z) ) ).
tff(existence_of_dominated_diversity,axiom,
? [X: option,Y: option,Z: option,A: option_set,B: option_set,C: option_set,D: option_set] :
( permitted_preference(X,Y)
& permitted_preference(Y,X)
& required_preference(Z,X)
& required_preference(Z,Y)
& member(X,A)
& member(Z,B)
& member(X,C)
& member(Y,C)
& member(X,D)
& member(Y,D)
& member(Z,D)
& ! [U: option] :
( member(U,A)
<=> ( U = X ) )
& ! [U: option] :
( member(U,B)
<=> ( U = Z ) )
& ! [U: option] :
( member(U,C)
<=> ( ( U = X )
| ( U = Y ) ) )
& ! [U: option] :
( member(U,D)
<=> ( ( U = X )
| ( U = Y )
| ( U = Z ) ) ) ) ).
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