TPTP Axioms File: GEO011+0.ax
%------------------------------------------------------------------------------
% File : GEO011+0 : TPTP v8.2.0. Released v7.0.0.
% Domain : Geometry
% Axioms : Tarskian geometry
% Version : [Urb16] axioms : Especial.
% English :
% Refs : [Urb16] Urban (2016), Email to Geoff Sutcliffe
% : [BW17] Beeson & Wos (2017), Finding Proofs in Tarskian Geomet
% Source : [Urb16]
% Names :
% Status : Satisfiable
% Syntax : Number of formulae : 8 ( 1 unt; 0 def)
% Number of atoms : 27 ( 3 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 36 ( 17 ~; 15 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
fof(aA1,axiom,
! [X,Y] : s_e(X,Y,Y,X) ).
fof(aA2,axiom,
! [X,Y,Z,V,Z2,V2] :
( ~ s_e(X,Y,Z,V)
| ~ s_e(X,Y,Z2,V2)
| s_e(Z,V,Z2,V2) ) ).
fof(aA3,axiom,
! [X,Y,Z] :
( ~ s_e(X,Y,Z,Z)
| X = Y ) ).
fof(aA4,axiom,
! [X,Y,W,V] :
( s_t(X,Y,ext(X,Y,W,V))
& s_e(Y,ext(X,Y,W,V),W,V) ) ).
fof(aA5,axiom,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( ~ s_e(X,Y,X1,Y1)
| ~ s_e(Y,Z,Y1,Z1)
| ~ s_e(X,V,X1,V1)
| ~ s_e(Y,V,Y1,V1)
| ~ s_t(X,Y,Z)
| ~ s_t(X1,Y1,Z1)
| X = Y
| s_e(Z,V,Z1,V1) ) ).
fof(aA6,axiom,
! [X,Y] :
( ~ s_t(X,Y,X)
| X = Y ) ).
fof(aA7,axiom,
! [Xa,Xp,Xc,Xb,Xq] :
( ( ~ s_t(Xa,Xp,Xc)
| ~ s_t(Xb,Xq,Xc)
| s_t(Xp,ip(Xa,Xp,Xc,Xb,Xq),Xb) )
& ( ~ s_t(Xa,Xp,Xc)
| ~ s_t(Xb,Xq,Xc)
| s_t(Xq,ip(Xa,Xp,Xc,Xb,Xq),Xa) ) ) ).
fof(aA8,axiom,
( ~ s_t(alpha,beta,gamma)
& ~ s_t(beta,gamma,alpha)
& ~ s_t(gamma,alpha,beta) ) ).
%------------------------------------------------------------------------------