TPTP Axioms File: GEO004-2.ax
%--------------------------------------------------------------------------
% File : GEO004-2 : TPTP v8.2.0. Released v2.4.0.
% Domain : Geometry (Oriented curves)
% Axioms : Oriented curves
% Version : [EHK99] axioms.
% English :
% Refs : [KE99] Kulik & Eschenbach (1999), A Geometry of Oriented Curv
% : [EHK99] Eschenbach et al. (1999), Representing Simple Trajecto
% Source : [EHK99]
% Names :
% Status : Satisfiable
% Syntax : Number of clauses : 42 ( 2 unt; 20 nHn; 37 RR)
% Number of literals : 129 ( 17 equ; 64 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 0 prp; 1-4 aty)
% Number of functors : 11 ( 11 usr; 0 con; 1-5 aty)
% Number of variables : 125 ( 5 sgn)
% SPC :
% Comments : Requires GEO004-0.ax GEO004-1.ax
% : Created by tptp2X -f tptp -t clausify:otter GEO004+2.ax
%--------------------------------------------------------------------------
cnf(between_o_defn_1,axiom,
( ~ between_o(A,B,C,D)
| ordered_by(A,B,C)
| ordered_by(A,D,C) ) ).
cnf(between_o_defn_2,axiom,
( ~ between_o(A,B,C,D)
| ordered_by(A,B,C)
| ordered_by(A,C,B) ) ).
cnf(between_o_defn_3,axiom,
( ~ between_o(A,B,C,D)
| ordered_by(A,C,D)
| ordered_by(A,D,C) ) ).
cnf(between_o_defn_4,axiom,
( ~ between_o(A,B,C,D)
| ordered_by(A,C,D)
| ordered_by(A,C,B) ) ).
cnf(between_o_defn_5,axiom,
( ~ ordered_by(A,B,C)
| ~ ordered_by(A,C,D)
| between_o(A,B,C,D) ) ).
cnf(between_o_defn_6,axiom,
( ~ ordered_by(A,B,C)
| ~ ordered_by(A,C,D)
| between_o(A,D,C,B) ) ).
cnf(start_point_defn_7,axiom,
( ~ start_point(A,B)
| incident_o(A,B) ) ).
cnf(start_point_defn_8,axiom,
( ~ start_point(A,B)
| A = C
| ~ incident_o(C,B)
| ordered_by(B,A,C) ) ).
cnf(start_point_defn_9,axiom,
( ~ incident_o(A,B)
| A != ax2_sk1(B,A)
| start_point(A,B) ) ).
cnf(start_point_defn_10,axiom,
( ~ incident_o(A,B)
| incident_o(ax2_sk1(B,A),B)
| start_point(A,B) ) ).
cnf(start_point_defn_11,axiom,
( ~ incident_o(A,B)
| ~ ordered_by(B,A,ax2_sk1(B,A))
| start_point(A,B) ) ).
cnf(finish_point_defn_12,axiom,
( ~ finish_point(A,B)
| incident_o(A,B) ) ).
cnf(finish_point_defn_13,axiom,
( ~ finish_point(A,B)
| A = C
| ~ incident_o(C,B)
| ordered_by(B,C,A) ) ).
cnf(finish_point_defn_14,axiom,
( ~ incident_o(A,B)
| A != ax2_sk2(B,A)
| finish_point(A,B) ) ).
cnf(finish_point_defn_15,axiom,
( ~ incident_o(A,B)
| incident_o(ax2_sk2(B,A),B)
| finish_point(A,B) ) ).
cnf(finish_point_defn_16,axiom,
( ~ incident_o(A,B)
| ~ ordered_by(B,ax2_sk2(B,A),A)
| finish_point(A,B) ) ).
cnf(o1_17,axiom,
( ~ ordered_by(A,B,C)
| incident_o(B,A) ) ).
cnf(o1_18,axiom,
( ~ ordered_by(A,B,C)
| incident_o(C,A) ) ).
cnf(o2_19,axiom,
open(ax2_sk3(A)) ).
cnf(o2_20,axiom,
( ~ incident_o(A,B)
| incident_c(A,ax2_sk3(B)) ) ).
cnf(o2_21,axiom,
( ~ incident_c(A,ax2_sk3(B))
| incident_o(A,B) ) ).
cnf(o3_22,axiom,
( ~ between_o(A,B,C,D)
| ~ incident_o(E,A)
| incident_c(E,ax2_sk4(A,D,C,B)) ) ).
cnf(o3_23,axiom,
( ~ between_o(A,B,C,D)
| ~ incident_c(E,ax2_sk4(A,D,C,B))
| incident_o(E,A) ) ).
cnf(o3_24,axiom,
( ~ between_o(A,B,C,D)
| between_c(ax2_sk4(A,D,C,B),B,C,D) ) ).
cnf(o3_25,axiom,
( incident_o(ax2_sk5(A,B,C,D,E),B)
| incident_c(ax2_sk5(A,B,C,D,E),A)
| ~ between_c(A,E,D,C)
| between_o(B,E,D,C) ) ).
cnf(o3_26,axiom,
( incident_o(ax2_sk5(A,B,C,D,E),B)
| ~ incident_o(ax2_sk5(A,B,C,D,E),B)
| ~ between_c(A,E,D,C)
| between_o(B,E,D,C) ) ).
cnf(o3_27,axiom,
( ~ incident_c(ax2_sk5(A,B,C,D,E),A)
| incident_c(ax2_sk5(A,B,C,D,E),A)
| ~ between_c(A,E,D,C)
| between_o(B,E,D,C) ) ).
cnf(o3_28,axiom,
( ~ incident_c(ax2_sk5(A,B,C,D,E),A)
| ~ incident_o(ax2_sk5(A,B,C,D,E),B)
| ~ between_c(A,E,D,C)
| between_o(B,E,D,C) ) ).
cnf(o4_29,axiom,
start_point(ax2_sk6(A),A) ).
cnf(o5_30,axiom,
( ~ open(A)
| B = C
| ~ incident_c(B,A)
| ~ incident_c(C,A)
| ~ incident_o(D,ax2_sk7(A,C,B))
| incident_c(D,A) ) ).
cnf(o5_31,axiom,
( ~ open(A)
| B = C
| ~ incident_c(B,A)
| ~ incident_c(C,A)
| ~ incident_c(D,A)
| incident_o(D,ax2_sk7(A,C,B)) ) ).
cnf(o5_32,axiom,
( ~ open(A)
| B = C
| ~ incident_c(B,A)
| ~ incident_c(C,A)
| ordered_by(ax2_sk7(A,C,B),B,C) ) ).
cnf(o6_33,axiom,
( ordered_by(A,ax2_sk8(B,A),ax2_sk9(B,A))
| ordered_by(B,ax2_sk8(B,A),ax2_sk9(B,A))
| A = B ) ).
cnf(o6_34,axiom,
( ordered_by(A,ax2_sk8(B,A),ax2_sk9(B,A))
| ~ ordered_by(A,ax2_sk8(B,A),ax2_sk9(B,A))
| A = B ) ).
cnf(o6_35,axiom,
( ~ ordered_by(A,ax2_sk8(A,B),ax2_sk9(A,B))
| ordered_by(A,ax2_sk8(A,B),ax2_sk9(A,B))
| B = A ) ).
cnf(o6_36,axiom,
( ~ ordered_by(A,ax2_sk8(A,B),ax2_sk9(A,B))
| ~ ordered_by(B,ax2_sk8(A,B),ax2_sk9(A,B))
| B = A ) ).
cnf(underlying_curve_defn_37,axiom,
( A != underlying_curve(B)
| ~ incident_o(C,B)
| incident_c(C,A) ) ).
cnf(underlying_curve_defn_38,axiom,
( A != underlying_curve(B)
| ~ incident_c(C,A)
| incident_o(C,B) ) ).
cnf(underlying_curve_defn_39,axiom,
( incident_o(ax2_sk10(A,B),A)
| incident_c(ax2_sk10(A,B),B)
| B = underlying_curve(A) ) ).
cnf(underlying_curve_defn_40,axiom,
( incident_o(ax2_sk10(A,B),A)
| ~ incident_o(ax2_sk10(A,B),A)
| B = underlying_curve(A) ) ).
cnf(underlying_curve_defn_41,axiom,
( ~ incident_c(ax2_sk10(A,B),B)
| incident_c(ax2_sk10(A,B),B)
| B = underlying_curve(A) ) ).
cnf(underlying_curve_defn_42,axiom,
( ~ incident_c(ax2_sk10(A,B),B)
| ~ incident_o(ax2_sk10(A,B),A)
| B = underlying_curve(A) ) ).
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