TPTP Problem File: LDA009-1.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : LDA009-1 : TPTP v8.2.0. Bugfixed v2.6.0.
% Domain : LD-Algebras (Embedding algebras)
% Problem : Let g = cr(t). If g < sg, then st(ts)g < stt(sg)
% Version : [Jec93] axioms : Incomplete.
% English :
% Refs : [Jec93] Jech (1993), LD-Algebras
% Source : [Jec93]
% Names : Problem 10 [Jec93]
% Status : Unsatisfiable
% Rating : 1.00 v2.6.0
% Syntax : Number of clauses : 21 ( 16 unt; 2 nHn; 15 RR)
% Number of literals : 28 ( 15 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 : 15 ( 15 usr; 12 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,
st = f(s,t) ).
cnf(clause_2,axiom,
stt = f(st,t) ).
cnf(clause_3,axiom,
sttt = f(stt,t) ).
cnf(clause_4,axiom,
stts = f(stt,s) ).
cnf(clause_5,axiom,
ts = f(t,s) ).
cnf(clause_6,axiom,
sts = f(st,s) ).
cnf(clause_7,axiom,
st_ts = f(st,ts) ).
cnf(clause_8,axiom,
k = critical_point(t) ).
cnf(clause_9,axiom,
sk = f(s,k) ).
cnf(clause_10,axiom,
stk = f(st,k) ).
cnf(clause_11,hypothesis,
less(k,sk) ).
%----st(ts)k < stt(sk) if crit(t)=k < sk
cnf(prove_equation,negated_conjecture,
~ less(f(st_ts,k),f(stt,sk)) ).
%--------------------------------------------------------------------------