TPTP Problem File: GEO033-3.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : GEO033-3 : TPTP v8.2.0. Bugfixed v1.2.1.
% Domain : Geometry
% Problem : First inner five-segment theorem
% Version : [Qua89] axioms : Augmented.
% English :
% Refs : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
% : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% Source : [Qua89]
% Names : D14 [Qua89]
% Status : Unsatisfiable
% Rating : 0.15 v8.2.0, 0.24 v8.1.0, 0.16 v7.4.0, 0.18 v7.3.0, 0.08 v7.2.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.29 v6.0.0, 0.20 v5.5.0, 0.35 v5.3.0, 0.33 v5.2.0, 0.31 v5.1.0, 0.29 v4.1.0, 0.15 v4.0.1, 0.36 v4.0.0, 0.18 v3.7.0, 0.20 v3.5.0, 0.09 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0, 0.23 v3.1.0, 0.18 v2.7.0, 0.42 v2.6.0, 0.22 v2.5.0, 0.36 v2.4.0, 0.38 v2.2.1, 0.43 v2.2.0, 0.20 v2.1.0, 0.25 v2.0.0
% Syntax : Number of clauses : 74 ( 30 unt; 15 nHn; 55 RR)
% Number of literals : 182 ( 39 equ; 99 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-4 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-6 aty)
% Number of variables : 232 ( 13 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
% Bugfixes : v1.2.1 - Clause d12 fixed.
%--------------------------------------------------------------------------
%----Include Tarski geometry axioms
include('Axioms/GEO002-0.ax').
%----Include definition of reflection
include('Axioms/GEO002-2.ax').
%--------------------------------------------------------------------------
cnf(d1,axiom,
equidistant(U,V,U,V) ).
cnf(d2,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(W,X,U,V) ) ).
cnf(d3,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(V,U,W,X) ) ).
cnf(d4_1,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(U,V,X,W) ) ).
cnf(d4_2,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(V,U,X,W) ) ).
cnf(d4_3,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(W,X,V,U) ) ).
cnf(d4_4,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(X,W,U,V) ) ).
cnf(d4_5,axiom,
( ~ equidistant(U,V,W,X)
| equidistant(X,W,V,U) ) ).
cnf(d5,axiom,
( ~ equidistant(U,V,W,X)
| ~ equidistant(W,X,Y,Z)
| equidistant(U,V,Y,Z) ) ).
cnf(e1,axiom,
V = extension(U,V,W,W) ).
cnf(b0,axiom,
( Y != extension(U,V,W,X)
| between(U,V,Y) ) ).
cnf(r2_1,axiom,
between(U,V,reflection(U,V)) ).
cnf(r2_2,axiom,
equidistant(V,reflection(U,V),U,V) ).
cnf(r3_1,axiom,
( U != V
| V = reflection(U,V) ) ).
cnf(r3_2,axiom,
U = reflection(U,U) ).
cnf(r4,axiom,
( V != reflection(U,V)
| U = V ) ).
cnf(d7,axiom,
equidistant(U,U,V,V) ).
cnf(d8,axiom,
( ~ equidistant(U,V,U1,V1)
| ~ equidistant(V,W,V1,W1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(U,W,U1,W1) ) ).
cnf(d9,axiom,
( ~ between(U,V,W)
| ~ between(U,V,X)
| ~ equidistant(V,W,V,X)
| U = V
| W = X ) ).
cnf(d10_1,axiom,
( ~ between(U,V,W)
| U = V
| W = extension(U,V,V,W) ) ).
cnf(d10_2,axiom,
( ~ equidistant(W,X,Y,Z)
| extension(U,V,W,X) = extension(U,V,Y,Z)
| U = V ) ).
cnf(d10_3,axiom,
( extension(U,V,U,V) = extension(U,V,V,U)
| U = V ) ).
cnf(r5,axiom,
equidistant(V,U,V,reflection(reflection(U,V),V)) ).
cnf(r6,axiom,
U = reflection(reflection(U,V),V) ).
cnf(t3,axiom,
between(U,V,V) ).
cnf(b1,axiom,
( ~ between(U,W,X)
| U != X
| between(V,W,X) ) ).
cnf(t1,axiom,
( ~ between(U,V,W)
| between(W,V,U) ) ).
cnf(t2,axiom,
between(U,U,V) ).
cnf(b2,axiom,
( ~ between(U,V,W)
| ~ between(V,U,W)
| U = V ) ).
cnf(b3,axiom,
( ~ between(U,V,W)
| ~ between(U,W,V)
| V = W ) ).
cnf(t6_1,axiom,
( ~ between(U,V,W)
| ~ between(V,U,W)
| U = V
| V = W ) ).
cnf(t6_2,axiom,
( ~ between(U,V,W)
| ~ between(U,W,V)
| U = V
| V = W ) ).
cnf(b4,axiom,
( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,V,W) ) ).
cnf(b5,axiom,
( ~ between(U,V,W)
| ~ between(U,W,X)
| between(V,W,X) ) ).
cnf(b6,axiom,
( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,W,X)
| V = W ) ).
cnf(b7,axiom,
( ~ between(U,V,W)
| ~ between(V,W,X)
| between(U,V,X)
| V = W ) ).
cnf(b8,axiom,
( ~ between(U,V,X)
| ~ between(V,W,X)
| between(U,W,X) ) ).
cnf(b9,axiom,
( ~ between(U,V,W)
| ~ between(U,W,X)
| between(U,V,X) ) ).
cnf(e2_1,axiom,
lower_dimension_point_1 != lower_dimension_point_2 ).
cnf(e2_2,axiom,
lower_dimension_point_2 != lower_dimension_point_3 ).
cnf(e2_3,axiom,
lower_dimension_point_1 != lower_dimension_point_3 ).
cnf(e3_1,axiom,
V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ).
cnf(e3_2,axiom,
equidistant(V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2),X,extension(W,X,lower_dimension_point_1,lower_dimension_point_2)) ).
cnf(e3_3,axiom,
between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) ).
cnf(b10,axiom,
( ~ between(U,V,W)
| ~ between(U1,V1,W)
| ~ between(U,X,U1)
| between(X,inner_pasch(V1,inner_pasch(U,X,U1,V1,W),U,V,W),W)
| between(V,inner_pasch(V1,inner_pasch(U,X,U1,V1,W),U,V,W),V1) ) ).
cnf(d11,axiom,
( ~ between(U,V,W)
| ~ equidistant(U,W,U,W1)
| ~ equidistant(V,W,V,W1)
| U = V
| W = W1 ) ).
cnf(d12,axiom,
( ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(W,X,W1,X1)
| ~ between(U,V,W)
| ~ between(U1,V1,W1)
| equidistant(V,X,V1,X1) ) ).
cnf(d13,axiom,
( ~ between(U,V,W)
| ~ between(U1,V1,W1)
| ~ equidistant(U,V,U1,V1)
| ~ equidistant(U,W,U1,W1)
| equidistant(V,W,V1,W1) ) ).
cnf(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1) ).
cnf(v_to_w_equals_v1_to_w1,hypothesis,
equidistant(v,w,v1,w1) ).
cnf(u_to_x_equals_u1_to_x1,hypothesis,
equidistant(u,x,u1,x1) ).
cnf(w_to_x_equals_w1_to_x1,hypothesis,
equidistant(w,x,w1,x1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(v1_between_u1_and_w1,hypothesis,
between(u1,v1,w1) ).
cnf(prove_v_to_x_equals_v1_to_x1,negated_conjecture,
~ equidistant(v,x,v1,x1) ).
%--------------------------------------------------------------------------