TPTP Problem File: SYO607+1.p
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% File : SYO607+1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Syntactic
% Problem : RM3 problem 6
% Version : Especial.
% English :
% Refs : [Pel16] Pelletier (2016), Email to Geoff Sutcliffe
% : [PSH17] Pelletier et al. (2017), Automated Reasoning for the D
% Source : [Pel16]
% Names : n06.p [Pel16]
% Status : Theorem
% Rating : 0.13 v9.0.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.00 v7.0.0
% Syntax : Number of formulae : 5 ( 0 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 28 ( 8 ~; 5 |; 12 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 5 usr; 0 prp; 2-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 23 ( 11 !; 12 ?)
% SPC : FOF_THM_RFO_NEQ
% Comments : Translated from RM3 using the truth evaluation approach [PSH17].
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fof(nc6,conjecture,
( ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
| ? [A] :
! [B] : g_true_only(A,B)
| ( ? [A] :
( ( g_both(a,A)
| ( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) ) )
& ~ g_true_only(a,A)
& ~ ! [B] : g_true_only(A,B) )
& ~ ? [A] :
( g_false_only(a,A)
& ? [B] : g_false_only(A,B) )
& ? [A] :
( ? [B] : g_both(A,B)
& ~ ? [B] : g_false_only(A,B) )
& ~ ? [A] :
! [B] : g_true_only(A,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) ) ).
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