## TPTP Problem File: LDA005-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : LDA005-1 : TPTP v7.5.0. 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 (   2 non-Horn;  13 unit;  12 RR)
%            Number of atoms       :   25 (  13 equality)
%            Maximal clause size   :    3 (   1 average)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :   13 (  10 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,
( 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)) )).

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