TPTP Problem File: LDA008-2.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : LDA008-2 : TPTP v8.2.0. 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 > Reduced & Augmented > Incomplete.
% English :
% Refs : [Jec93] Jech (1993), LD-Algebras
% Source : [TPTP]
% Names :
% Status : Unsatisfiable
% Rating : 1.00 v4.1.0, 0.92 v4.0.1, 0.91 v3.7.0, 1.00 v3.4.0, 0.92 v3.3.0, 1.00 v2.6.0
% Syntax : Number of clauses : 19 ( 13 unt; 2 nHn; 12 RR)
% Number of literals : 26 ( 14 equ; 7 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 : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 24 ( 1 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').
%--------------------------------------------------------------------------
%----A1 x(yz)=(xy)(xz)
cnf(a1,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ).
%----A1a a(x,a(y,z)) = a(x*y,a(x,z))
cnf(a1a,axiom,
a(X,a(Y,Z)) = a(f(X,Y),a(X,Z)) ).
%----A2 cr(u*v) = a(u,cr(v))
cnf(a2,axiom,
critical_point(f(U,V)) = a(U,critical_point(V)) ).
%----B1 -(x<x)
cnf(b1,axiom,
~ less(X,X) ).
%----B3 transitive
cnf(b3,axiom,
( ~ less(X,Y)
| ~ less(Y,Z)
| less(X,Z) ) ).
%----B4 if x<y then ux<uy
cnf(b4,axiom,
( ~ less(X,Y)
| less(a(U,X),a(U,Y)) ) ).
%----C1 x=a(u,x) | (x<a(u,x)) (from C2, C3)
cnf(c1,axiom,
( X = a(U,X)
| less(X,a(U,X)) ) ).
%----C2 if x<crit(u) then ux=x
cnf(c2,axiom,
( ~ less(X,critical_point(U))
| a(U,X) = X ) ).
%----C3 x<crit(u) or x<ux
cnf(c3,axiom,
( less(X,critical_point(U))
| less(X,a(U,X)) ) ).
%----D2 a(u,x)!=x | a(v*u,x)=x (from B1, C3, C1, A2, B3, C2)
cnf(d2,axiom,
( a(U,X) != X
| a(f(V,U),X) = X ) ).
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) ).
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