%--------------------------------------------------------------------------
% File     : LDA005-1 : TPTP v8.2.0. Bugfixed v2.6.0.
% Domain   : LD-Algebras (Embedding algebras)
% Problem  : Let g=cr(t). Show that tt(tsg) < t(tsg) (for any s)
% Version  : [Jec93] axioms : Incomplete.
% English  :

% Refs     : [Jec93] Jech (1993), LD-Algebras
% Source   : [Jec93]
% Names    : Problem 5 [Jec93]

% Status   : Unsatisfiable
% Rating   : 1.00 v2.6.0
% Syntax   : Number of clauses     :   18 (  13 unt;   2 nHn;  12 RR)
%            Number of literals    :   25 (  13 equ;   6 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    :   13 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :   21 (   0 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
% Bugfixes : v2.6.0 - Bugfix in LDA001-0.ax
%--------------------------------------------------------------------------
%----Include Embedding algebra axioms
include('Axioms/LDA001-0.ax').
%--------------------------------------------------------------------------
cnf(clause_1,axiom,
    tt = f(t,t) ).

cnf(clause_2,axiom,
    st = f(s,t) ).

cnf(clause_3,axiom,
    ts = f(t,s) ).

cnf(clause_4,axiom,
    k = critical_point(t) ).

cnf(clause_5,axiom,
    sk = f(s,k) ).

cnf(clause_6,axiom,
    tk = f(t,k) ).

cnf(clause_7,axiom,
    stk = f(st,k) ).

cnf(clause_8,axiom,
    tsk = f(ts,k) ).

%----tt(tsk) < t(tsk), where k=crit(t)
cnf(prove_equation,negated_conjecture,
    ~ less(f(tt,tsk),f(t,tsk)) ).

%--------------------------------------------------------------------------