TPTP Problem File: SYO803+1.p
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% File : SYO803+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain : Syntactic
% Problem : Theory of immediate successor reduced problem spSUC15
% Version : Especial.
% English :
% Refs : [Lam20] Lampert (2020), Email to Geoff Sutcliffe
% : [LN20] Lampert & Nakano (2020), Deciding Simple Infinity Axio
% Source : [Lam20]
% Names : spSUC14.p [Lam20]
% Status : Satisfiable
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 8 ( 1 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 36 ( 15 ~; 15 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 1 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 34 ( 22 !; 12 ?)
% SPC : FOF_SAT_RFO_NEQ
% Comments : Has only infinite models.
% Bugfixes : v7.5.0 - Fixed formulae that were finitely satisfiable.
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fof(axiom_1,axiom,
? [Y1] :
( ! [X1] : ~ f(Y1,X1)
& ! [X2] :
( ? [Y2] : f(Y2,X2)
| f(X2,Y1) ) ) ).
fof(axiom_2,axiom,
? [Y1] :
( ! [X1] : ~ f(Y1,X1)
& ! [X2] :
( ? [Y2] : f(Y2,X2)
| ~ f(X2,Y1) ) ) ).
fof(axiom_3,axiom,
? [Y1] :
( ? [Y2] : f(Y1,Y2)
& ! [X1] : ~ f(X1,Y1)
& ! [X2] :
( ! [X3] :
( f(X2,X3)
| ~ f(Y1,X3) )
| ? [Y3] : f(Y3,X2) ) ) ).
fof(axiom_4,axiom,
? [Y1] :
( ? [Y2] : f(Y1,Y2)
& ! [X1] : ~ f(X1,Y1)
& ! [X2] :
( ! [X3] :
( ~ f(X2,X3)
| f(Y1,X3) )
| ? [Y3] : f(Y3,X2) ) ) ).
fof(axiom_5,axiom,
! [X1,X2] :
( ! [X3] :
( ~ f(X1,X3)
| ~ f(X2,X3) )
| ! [X4] :
( ~ f(X4,X1)
| f(X4,X2) ) ) ).
fof(axiom_6,axiom,
! [X1,X2] :
( ! [X3] :
( ~ f(X3,X1)
| ~ f(X3,X2) )
| ! [X4] :
( ~ f(X1,X4)
| f(X2,X4) ) ) ).
fof(axiom_7,axiom,
! [X1] : ~ f(X1,X1) ).
fof(axiom_8,axiom,
! [X1] :
( ! [X2] :
( ! [X3] :
( ~ f(X1,X3)
| f(X2,X3) )
| ? [Y1] : f(Y1,X2) )
| ? [Y2] : f(Y2,X1) ) ).
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