TPTP Problem File: LCL082-1.p

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```%--------------------------------------------------------------------------
% File     : LCL082-1 : TPTP v8.1.2. Released v1.0.0.
% Domain   : Logic Calculi (Implicational propositional)
% Problem  : IC-2 depends on the 1st Lukasiewicz axiom
% Version  : [McC92] axioms.
% English  : Axiomatisations of the Implicational propositional calculus
%            are {IC-2,IC-3,IC-4} by Tarski-Bernays and single Lukasiewicz
%            axioms.Show that IC-2 depends on the first Lukasiewicz axiom.

% Refs     : [Luk48] Lukasiewicz (1948), The Shortest Axiom of the Implicat
%          : [Pfe88] Pfenning (1988), Single Axioms in the Implicational Pr
%          : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to
%          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92]
% Names    : S1 [Pfe88]
%          : IC-1.1 [WW+90]
%          : IC-65 [MW92]
%          : ls2 [SETHEO]

% 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 v2.6.0, 0.14 v2.5.0, 0.00 v2.1.0, 0.00 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    :    4 (   2 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 1-1 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   2 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

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

cnf(ic_JLukasiewicz,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))) ).

cnf(prove_ic_2,negated_conjecture,
~ is_a_theorem(implies(a,implies(b,a))) ).

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