## TPTP Problem File: LCL107-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : LCL107-1 : TPTP v8.1.2. Released v1.0.0.
% Domain   : Logic Calculi (Left group)
% Problem  : P-1 depends on the single McCune axiom
% Version  : [McC92b] axioms.
% English  : Axiomatisations of the left group calculus are {LG-1,
%            LG-2,LG-3,LG-4,LG-5} by Kalman, {LG-2,LG-3}, {LG-2,P-1},
%            {LG-2,P-4}, {LG-2,Q-1,Q-2}, {P-1,Q-3}, {P-4,Q-3}, {Q-1,
%            Q-2,Q-3}, {Q-1,Q-3,Q-4}, {LG-27-1690} all by McCune. Show
%            that P-1 depends on the single McCune axiom.

% 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    : LG-100 [MW92]

% Status   : Unsatisfiable
% Rating   : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.07 v4.0.1, 0.00 v2.2.1, 0.11 v2.1.0, 0.13 v2.0.0
% 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    :    7 (   2 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 1-1 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    9 (   0 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

%--------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ) ).

cnf(lg_27_1690,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),equivalent(equivalent(U,V),equivalent(equivalent(equivalent(W,V),equivalent(W,U)),V6))),equivalent(Z,equivalent(equivalent(Y,X),V6)))) ).

cnf(prove_p_1,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) ).

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