## TPTP Problem File: LDA008-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : LDA008-1 : TPTP v7.5.0. Bugfixed v2.6.0.
% Domain   : LD-Algebras (Embedding algebras)
% Problem  : Let g = cr(t) = cr(T). If Ta < Tsg, then ta < tsg
% Version  : [Jec93] axioms : Incomplete.
% English  :

% Refs     : [Jec93] Jech (1993), LD-Algebras
% Source   : [Jec93]
% Names    : Problem 9 [Jec93]

% Status   : Unsatisfiable
% Rating   : 1.00 v2.6.0
% Syntax   : Number of clauses     :   19 (   2 non-Horn;  14 unit;  13 RR)
%            Number of atoms       :   26 (  13 equality)
%            Maximal clause size   :    3 (   1 average)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :   14 (  11 constant; 0-2 arity)
%            Number of variables   :   21 (   0 singleton)
%            Maximal term depth    :    3 (   2 average)
% SPC      : CNF_UNS_RFO_SEQ_NHN

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

cnf(clause_2,axiom,
( bts = f(bt,s) )).

cnf(clause_3,axiom,
( ta = f(t,aconst) )).

cnf(clause_4,axiom,
( bta = f(bt,aconst) )).

cnf(clause_5,axiom,
( k = critical_point(t) )).

cnf(clause_6,axiom,
( critical_point(bt) = k )).

cnf(clause_7,axiom,
( tsk = f(ts,k) )).

cnf(clause_8,axiom,
( btsk = f(bts,k) )).

cnf(clause_9,axiom,
( less(bta,btsk) )).

%----ta<tsk,  assuming Ta<Tsk and k=crit(t)=crit(T)
cnf(prove_equation,negated_conjecture,
( ~ less(ta,tsk) )).

%--------------------------------------------------------------------------
```