## TPTP Problem File: LCL097-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : LCL097-1 : TPTP v8.1.2. Released v1.0.0.
% Domain   : Logic Calculi (Left group)
% Problem  : LG-4 depends on LG-2, LG-3
% Version  : [McC92b] axioms : Reduced > Complete.
% 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 LG-4 depends on a part of the Kalman system.

% Refs     : [LM92]  Lusk & McCune (1992), Experiments with ROO, a Parallel
%          : [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    : CD-90 [LM92]
%          : LG-90 [MW92]

% Status   : Unsatisfiable
% Rating   : 0.00 v5.5.0, 0.06 v5.4.0, 0.11 v5.3.0, 0.15 v5.1.0, 0.12 v5.0.0, 0.13 v4.1.0, 0.07 v4.0.1, 0.00 v2.4.0, 0.14 v2.3.0, 0.14 v2.2.1, 0.22 v2.2.0, 0.33 v2.1.0, 0.25 v2.0.0
% Syntax   : Number of clauses     :    4 (   3 unt;   0 nHn;   2 RR)
%            Number of literals    :    6 (   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    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   11 (   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_2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)) ).

cnf(lg_3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)) ).

cnf(prove_lg_4,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))) ).

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