TPTP Problem File: SYN917+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN917+1 : TPTP v8.1.0. Released v3.1.0.
% Domain   : Syntactic
% Problem  : Combined problems from Smullyan
% Version  : Especial.
% English  :

% Refs     : [Smu68] Smullyan (1968), First-Order Logic
%            [Shu04] Shults (2004), Email to G. Sutcliffe
% Source   : [Shu04]
% Names    :

% Status   : Theorem
% Rating   : 0.13 v8.1.0, 0.07 v7.5.0, 0.05 v7.4.0, 0.00 v6.1.0, 0.08 v6.0.0, 0.25 v5.5.0, 0.21 v5.4.0, 0.22 v5.3.0, 0.30 v5.2.0, 0.21 v5.0.0, 0.20 v4.1.0, 0.22 v4.0.1, 0.21 v4.0.0, 0.25 v3.7.0, 0.33 v3.5.0, 0.12 v3.4.0, 0.17 v3.3.0, 0.33 v3.2.0, 0.78 v3.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :   94 (   0 equ)
%            Maximal formula atoms :   94 (  94 avg)
%            Number of connectives :   98 (   5   ~;   8   |;  39   &)
%                                         (  10 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  23 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   56 (  34   !;  22   ?)
% SPC      : FOF_THM_RFO_NEQ

%--------------------------------------------------------------------------
fof(prove_this,conjecture,
( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ( ? [X] :
( p(X)
=> c )
<=> ( ! [X] : p(X)
=> c ) )
& ( ! [X] :
( c
=> p(X) )
<=> ( c
=> ! [X] : p(X) ) )
& ( ! [X] :
( p(X)
=> c )
<=> ( ? [X] : p(X)
=> c ) ) ) ).

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