TPTP Problem File: LDA004-1.p
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%--------------------------------------------------------------------------
% File : LDA004-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : LD-Algebras (Left segments)
% Problem : Show that 3*2(U2) is a left segment of U1(U3)
% Version : [Jec93] axioms.
% English :
% Refs : [Jec93] Jech (1993), LD-Algebras
% Source : [Jec93]
% Names : Problem 4 [Jec93]
% Status : Unsatisfiable
% Rating : 0.46 v9.0.0, 0.44 v8.2.0, 0.58 v8.1.0, 0.56 v7.5.0, 0.50 v7.4.0, 0.44 v7.2.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.43 v6.3.0, 0.33 v6.1.0, 0.40 v6.0.0, 0.56 v5.5.0, 0.81 v5.4.0, 0.87 v5.3.0, 0.92 v5.2.0, 0.75 v5.1.0, 0.43 v4.1.0, 0.44 v4.0.1, 0.33 v4.0.0, 0.50 v3.5.0, 0.33 v3.4.0, 0.50 v3.3.0, 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.50 v2.6.0, 0.43 v2.5.0, 0.40 v2.4.0, 0.67 v2.3.0, 0.83 v2.2.1, 1.00 v2.0.0
% Syntax : Number of clauses : 12 ( 11 unt; 0 nHn; 10 RR)
% Number of literals : 14 ( 9 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 8 ( 1 sgn)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments :
%--------------------------------------------------------------------------
%----A1: x(yz)=xy(xz)
cnf(a1,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ).
%----x is a left segment of xy
cnf(a2,axiom,
left(X,f(X,Y)) ).
%----transitive
cnf(a3,axiom,
( ~ left(X,Y)
| ~ left(Y,Z)
| left(X,Z) ) ).
cnf(clause_4,axiom,
n2 = f(n1,n1) ).
cnf(clause_5,axiom,
n3 = f(n2,n1) ).
cnf(clause_6,axiom,
u = f(n2,n2) ).
cnf(clause_7,axiom,
u1 = f(u,n1) ).
cnf(clause_8,axiom,
u2 = f(u,n2) ).
cnf(clause_9,axiom,
u3 = f(u,n3) ).
cnf(clause_10,axiom,
a = f(f(n3,n2),u2) ).
cnf(clause_11,axiom,
b = f(u1,u3) ).
%----3*2*U2 is a left segment of U1*U3
cnf(prove_equation,negated_conjecture,
~ left(a,b) ).
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