## TPTP Problem File: SYO606+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO606+1 : TPTP v8.1.0. Released v7.0.0.
% Domain   : Syntactic
% Problem  : RM3 problem 5
% Version  : Especial.
% English  :

% Refs     : [Pel16] Pelletier (2016), Email to Geoff Sutcliffe
%          : [PSH17] Pelletier et al. (2017), Automated Reasoning for the D
% Source   : [Pel16]
% Names    : n05.p [Pel16]

% Status   : Theorem
% Rating   : 0.27 v8.1.0, 0.21 v7.5.0, 0.33 v7.4.0, 0.25 v7.3.0, 0.29 v7.2.0, 0.17 v7.1.0, 0.00 v7.0.0
% Syntax   : Number of formulae    :    9 (   0 unt;   0 def)
%            Number of atoms       :   65 (   0 equ)
%            Maximal formula atoms :   41 (   7 avg)
%            Number of connectives :   70 (  14   ~;  19   |;  31   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   10 (  10 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   55 (  27   !;  28   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments : Translated from RM3 using the truth evaluation approach [PSH17].
%------------------------------------------------------------------------------
fof(nc5,conjecture,
( ( ! [A] :
( ! [B] : g_false_only(A,B)
| ? [B] : h_true_only(A,B) )
& ! [A,B] :
? [C] :
( g_false_only(A,B)
| h_true_only(A,C) ) )
| ( ? [A] :
( ( ? [B] : g_true_only(A,B)
& ( ( ? [B] : h_both(A,B)
& ~ ? [B] : h_true_only(A,B) )
| ! [B] : h_false_only(A,B) ) )
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_true_only(A,B)
& ! [B] : h_false_only(A,B) ) )
& ? [A,B] :
! [C] :
( ( g_true_only(A,B)
& ( h_both(A,C)
| h_false_only(A,C) ) )
| ( g_both(A,B)
& h_false_only(A,C) ) ) )
| ( ? [A] :
( ? [B] : g_both(A,B)
& ~ ? [B] : g_true_only(A,B)
& ? [B] : h_both(A,B)
& ~ ? [B] : h_true_only(A,B) )
& ~ ? [A] :
( ( ? [B] : g_true_only(A,B)
& ( ( ? [B] : h_both(A,B)
& ~ ? [B] : h_true_only(A,B) )
| ! [B] : h_false_only(A,B) ) )
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_true_only(A,B)
& ! [B] : h_false_only(A,B) ) )
& ? [A] :
( ? [B] :
( ? [C] :
( g_both(A,B)
& h_both(A,C) )
& ~ ? [C] :
( g_false_only(A,B)
| h_true_only(A,C) ) )
& ~ ? [B] :
! [C] :
( ( g_true_only(A,B)
& ( h_both(A,C)
| h_false_only(A,C) ) )
| ( g_both(A,B)
& h_false_only(A,C) ) ) )
& ~ ? [A,B] :
! [C] :
( ( g_true_only(A,B)
& ( h_both(A,C)
| h_false_only(A,C) ) )
| ( g_both(A,B)
& h_false_only(A,C) ) ) ) ) ).

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) ) ).

fof(true_only_h,axiom,
! [X_2,X_1] :
( h_true_only(X_2,X_1)
<=> ( h_true(X_2,X_1)
& ~ h_false(X_2,X_1) ) ) ).

fof(both_h,axiom,
! [X_2,X_1] :
( h_both(X_2,X_1)
<=> ( h_true(X_2,X_1)
& h_false(X_2,X_1) ) ) ).

fof(false_only_h,axiom,
! [X_2,X_1] :
( h_false_only(X_2,X_1)
<=> ( h_false(X_2,X_1)
& ~ h_true(X_2,X_1) ) ) ).

fof(exhaustion_h,axiom,
! [X_2,X_1] :
( h_true_only(X_2,X_1)
| h_both(X_2,X_1)
| h_false_only(X_2,X_1) ) ).

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