## TPTP Problem File: SYO605+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO605+1 : TPTP v8.0.0. Released v7.0.0.
% Domain   : Syntactic
% Problem  : RM3 problem 4
% Version  : Especial.
% English  :

% Refs     : [Pel16] Pelletier (2016), Email to Geoff Sutcliffe
%          : [PSH17] Pelletier et al. (2017), Automated Reasoning for the D
% Source   : [Pel16]
% Names    : 18 [PSH17]
%          : n04.p [Pel16]

% Status   : Theorem
% Rating   : 0.21 v7.5.0, 0.29 v7.4.0, 0.06 v7.3.0, 0.14 v7.2.0, 0.17 v7.1.0, 0.25 v7.0.0
% Syntax   : Number of formulae    :    5 (   0 unt;   0 def)
%            Number of atoms       :   69 (   0 equ)
%            Maximal formula atoms :   57 (  13 avg)
%            Number of connectives :   71 (   7   ~;  31   |;  30   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   5 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   27 (  13   !;  14   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments : Translated from RM3 using the truth evaluation approach [PSH17].
%------------------------------------------------------------------------------
fof(nc4,conjecture,
( ! [A] :
? [B] :
( ( g_true_only(B,A)
& ( g_both(B,B)
| g_false_only(B,B) ) )
| ( g_both(B,A)
& ( g_true_only(B,B)
| g_false_only(B,B) ) )
| ( g_false_only(B,A)
& ( g_true_only(B,B)
| g_both(B,B) ) ) )
| ? [B] :
! [A] :
? [C] :
( ( g_true_only(C,A)
& ( g_both(C,B)
| g_true_only(C,B) ) )
| ( g_both(C,A)
& ( g_false_only(C,B)
| g_true_only(C,B) ) )
| ( g_false_only(C,A)
& ( g_false_only(C,B)
| g_both(C,B) ) ) )
| ( ? [A] :
( ? [B] :
( g_both(B,A)
& g_both(B,B) )
& ~ ? [B] :
( ( g_true_only(B,A)
& ( g_both(B,B)
| g_false_only(B,B) ) )
| ( g_both(B,A)
& ( g_true_only(B,B)
| g_false_only(B,B) ) )
| ( g_false_only(B,A)
& ( g_true_only(B,B)
| g_both(B,B) ) ) ) )
& ~ ? [A] :
! [B] :
( ( g_true_only(B,A)
& g_true_only(B,B) )
| ( g_false_only(B,A)
& g_false_only(B,B) ) )
& ? [B] :
( ? [A] :
( ? [C] :
( g_both(C,A)
& g_both(C,B) )
& ~ ? [C] :
( ( g_true_only(C,A)
& ( g_both(C,B)
| g_true_only(C,B) ) )
| ( g_both(C,A)
& ( g_false_only(C,B)
| g_true_only(C,B) ) )
| ( g_false_only(C,A)
& ( g_false_only(C,B)
| g_both(C,B) ) ) ) )
& ~ ? [A] :
! [C] :
( ( g_true_only(C,A)
& g_false_only(C,B) )
| ( g_false_only(C,A)
& g_true_only(C,B) ) ) )
& ~ ? [B] :
! [A] :
? [C] :
( ( g_true_only(C,A)
& ( g_both(C,B)
| g_true_only(C,B) ) )
| ( g_both(C,A)
& ( g_false_only(C,B)
| g_true_only(C,B) ) )
| ( g_false_only(C,A)
& ( g_false_only(C,B)
| g_both(C,B) ) ) ) ) ) ).

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) ) ).

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