## TPTP Problem File: SEV516+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV516+1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Set Theory
% Problem  : Condition for no universal set
% Version  : Especial.
% English  : The antecedent says that for every set z there is a subset of
%            it y containing just those elements x of z that are not elements
%            of themselves. The consequent says that there is no universal set.

% Refs     : [Pel16] Pelletier (2016), Email to Geoff Sutcliffe
%          : [PSH17] Pelletier et al. (2017), Automated Reasoning for the D
% Source   : [Pel16]
% Names    : 16 [PSH17]
%          : n02.p [Pel16]

% Status   : CounterSatisfiable
% Rating   : 0.00 v7.4.0, 0.33 v7.3.0, 0.00 v7.0.0
% Syntax   : Number of formulae    :    5 (   0 unit)
%            Number of atoms       :   84 (   0 equality)
%            Maximal formula depth :   17 (   8 average)
%            Number of connectives :  100 (  21   ~;  34   |;  42   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    5 (   0 propositional; 2-2 arity)
%            Number of functors    :    0 (   0 constant; --- arity)
%            Number of variables   :   27 (   0 sgn;  13   !;  14   ?)
%            Maximal term depth    :    1 (   1 average)
% SPC      : FOF_CSA_RFO_NEQ

% Comments : Translated from RM3 using the truth evaluation approach [PSH17].
%------------------------------------------------------------------------------
fof(nc2,conjecture,
( ? [A] :
! [B] :
? [C] :
( ( g_true_only(C,B)
& ( ( ( g_both(C,A)
| g_both(C,C) )
& ~ g_false_only(C,A)
& ~ g_true_only(C,C) )
| g_false_only(C,A)
| g_true_only(C,C) ) )
| ( g_both(C,B)
& ( ( g_true_only(C,A)
& g_false_only(C,C) )
| g_false_only(C,A)
| g_true_only(C,C) ) )
| ( g_false_only(C,B)
& ( ( g_true_only(C,A)
& g_false_only(C,C) )
| ( ( g_both(C,A)
| g_both(C,C) )
& ~ g_false_only(C,A)
& ~ g_true_only(C,C) ) ) ) )
| ! [D] :
? [E] : g_false_only(E,D)
| ( ? [A] :
( ? [B] :
( ? [C] :
( g_both(C,B)
& ( g_both(C,A)
| g_both(C,C) )
& ~ g_false_only(C,A)
& ~ g_true_only(C,C) )
& ~ ? [C] :
( ( g_true_only(C,B)
& ( ( ( g_both(C,A)
| g_both(C,C) )
& ~ g_false_only(C,A)
& ~ g_true_only(C,C) )
| g_false_only(C,A)
| g_true_only(C,C) ) )
| ( g_both(C,B)
& ( ( g_true_only(C,A)
& g_false_only(C,C) )
| g_false_only(C,A)
| g_true_only(C,C) ) )
| ( g_false_only(C,B)
& ( ( g_true_only(C,A)
& g_false_only(C,C) )
| ( ( g_both(C,A)
| g_both(C,C) )
& ~ g_false_only(C,A)
& ~ g_true_only(C,C) ) ) ) ) )
& ~ ? [B] :
! [C] :
( ( g_true_only(C,B)
& g_true_only(C,A)
& g_false_only(C,C) )
| ( g_false_only(C,B)
& ( g_false_only(C,A)
| g_true_only(C,C) ) ) ) )
& ~ ? [A] :
! [B] :
? [C] :
( ( g_true_only(C,B)
& ( ( ( g_both(C,A)
| g_both(C,C) )
& ~ g_false_only(C,A)
& ~ g_true_only(C,C) )
| g_false_only(C,A)
| g_true_only(C,C) ) )
| ( g_both(C,B)
& ( ( g_true_only(C,A)
& g_false_only(C,C) )
| g_false_only(C,A)
| g_true_only(C,C) ) )
| ( g_false_only(C,B)
& ( ( g_true_only(C,A)
& g_false_only(C,C) )
| ( ( g_both(C,A)
| g_both(C,C) )
& ~ g_false_only(C,A)
& ~ g_true_only(C,C) ) ) ) )
& ? [D] :
( ? [E] : g_both(E,D)
& ~ ? [E] : g_false_only(E,D) )
& ~ ? [D] :
! [E] : g_true_only(E,D) ) )).

fof(true_only_g,axiom,(
! [X_2,X_1] :
( g_true_only(X_2,X_1)
<=> ( g_true(X_2,X_1)
& ~ g_false(X_2,X_1) ) ) )).

fof(both_g,axiom,(
! [X_2,X_1] :
( g_both(X_2,X_1)
<=> ( g_true(X_2,X_1)
& g_false(X_2,X_1) ) ) )).

fof(false_only_g,axiom,(
! [X_2,X_1] :
( g_false_only(X_2,X_1)
<=> ( g_false(X_2,X_1)
& ~ g_true(X_2,X_1) ) ) )).

fof(exhaustion_g,axiom,(
! [X_2,X_1] :
( g_true_only(X_2,X_1)
| g_both(X_2,X_1)
| g_false_only(X_2,X_1) ) )).

%------------------------------------------------------------------------------
```