%------------------------------------------------------------------------------
% File     : LCL928-1 : TPTP v9.0.0. Released v6.4.0.
% Domain   : Logic Calculi (Postive sential logic)
% Problem  : AxTO in BCK-> [AxL] + (Resid)
% Version  : [Sla02] axioms.
% English  :

% Refs     : [Sla02] Slaney (2002), More Proofs of an Axiom of Lukasiewicz
% Source   : [Sla02]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.93 v9.0.0, 0.91 v8.2.0, 0.86 v8.1.0, 0.75 v7.4.0, 0.83 v7.3.0, 0.75 v6.4.0
% Syntax   : Number of clauses     :    7 (   4 unt;   0 nHn;   4 RR)
%            Number of literals    :   11 (   0 equ;   5 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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

% Comments :
%------------------------------------------------------------------------------
cnf(modus_ponens,axiom,
    ( ~ p(i(A,B))
    | ~ p(A)
    | p(B) ) ).

cnf(resid1,axiom,
    ( ~ p(i(f(A,B),C))
    | p(i(A,i(B,C))) ) ).

cnf(resid2,axiom,
    ( p(i(f(A,B),C))
    | ~ p(i(A,i(B,C))) ) ).

cnf(axBp,axiom,
    p(i(i(A,B),i(i(B,C),i(A,C)))) ).

cnf(axL,axiom,
    p(i(i(i(A,B),B),i(i(B,A),A))) ).

cnf(axC,axiom,
    p(i(i(A,i(B,C)),i(B,i(A,C)))) ).

cnf(axTO,negated_conjecture,
    ~ p(i(i(i(c1,c2),i(c2,c1)),i(c2,c1))) ).

%------------------------------------------------------------------------------