## TPTP Problem File: LCL124-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : LCL124-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% Domain   : Logic Calculi (Right group)
% Problem  : LG-5 depends on LG-2
% Version  : [McC92b] axioms.
% English  : Kalman's axiomatisation of the right group calculus
%            is {LG-1,LG-2,LG-3,LG-4,LG-5}. McCune has shown that LG-2
%            is a single axiom. Other axiomatisations by McCune are
%            {Q-2,Q-3}, {Q-3,Q-4}, S-2, S-3, S-4, P-4, S-6. Show that LG-5
%            depends on LG-2.

% Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92a] McCune (1992), Automated Discovery of New Axiomatisat
%          : [McC92b] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92b]
% Names    : RG-105 [MW92]

% Status   : Unsatisfiable
% Rating   : 0.43 v8.1.0, 0.50 v6.2.0, 0.67 v6.1.0, 0.86 v6.0.0, 0.89 v5.5.0, 0.94 v5.4.0, 1.00 v4.1.0, 0.93 v4.0.1, 0.86 v4.0.0, 0.71 v3.4.0, 0.60 v3.3.0, 0.33 v3.1.0, 0.50 v2.7.0, 0.75 v2.6.0, 0.57 v2.4.0, 0.75 v2.3.0
% Syntax   : Number of clauses     :    3 (   2 unt;   0 nHn;   2 RR)
%            Number of literals    :    5 (   0 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 1-1 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

% Bugfixes : v2.3.0 - Clause prove_lg_5 fixed.
%--------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).

cnf(lg_2,axiom,
is_a_theorem(equivalent(X,equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Y,U),equivalent(Z,U)))))) ).

cnf(prove_lg_5,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(a,equivalent(b,equivalent(c,equivalent(e,f)))),equivalent(equivalent(a,equivalent(f,c)),equivalent(equivalent(b,equivalent(f,e)),f)))) ).

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