%--------------------------------------------------------------------------
% File     : COL098-1 : TPTP v8.2.0. Released v2.7.0.
% Domain   : Combinatory Logic
% Problem  : diamond_strip_lemmaD_2c1
% Version  : Reduced > Especial.
% English  : [rule_format]:[| diamond(r); <x, y> : r^+ |]

% Refs     : [Men03] Meng (2003), Email to G. Sutcliffe
% Source   : [Men03]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.00 v8.1.0, 0.11 v7.5.0, 0.10 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.00 v6.1.0, 0.20 v6.0.0, 0.11 v5.5.0, 0.12 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.29 v4.1.0, 0.22 v4.0.1, 0.17 v3.3.0, 0.14 v3.2.0, 0.00 v2.7.0
% Syntax   : Number of clauses     :   17 (   7 unt;   0 nHn;  16 RR)
%            Number of literals    :   32 (  10 equ;  19 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 1-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-3 aty)
%            Number of variables   :   33 (   9 sgn)
% SPC      : CNF_UNS_RFO_SEQ_HRN

% Comments : Problem coming out of an Isabelle proof.
%--------------------------------------------------------------------------
%----axioms from CombZF.thy.
%----free algebra for K, S, comb_app(P,Q).
cnf(k_s,axiom,
    combK != combS ).

cnf(k_app,axiom,
    combK != comb_app(P,Q) ).

cnf(s_app,axiom,
    combS != comb_app(P,Q) ).

cnf(app_app1,axiom,
    ( comb_app(P1,Q1) != comb_app(P2,Q2)
    | P1 = P2 ) ).

cnf(app_app2,axiom,
    ( comb_app(P1,Q1) != comb_app(P2,Q2)
    | Q1 = Q2 ) ).

cnf(app_app3,axiom,
    ( P1 != P2
    | Q1 != Q2
    | comb_app(P1,Q1) = comb_app(P2,Q2) ) ).

%----the following three axioms are only added in here(not in classical rules set).
cnf(r_into_trancl,axiom,
    ( ~ member(pair(A,B),R)
    | member(pair(A,B),trancl(R)) ) ).

cnf(trans_trancl,axiom,
    trans(trancl(R)) ).

cnf(transD,axiom,
    ( ~ trans(R)
    | ~ member(pair(A,B),R)
    | ~ member(pair(B,C),R)
    | member(pair(A,C),R) ) ).

cnf(diamond_strip_lemmaD_2h1,hypothesis,
    ( ~ member(pair(X,Y),r)
    | ~ member(pair(X,YP),r)
    | member(pair(Y,sk1(X,Y,YP)),r) ) ).

cnf(diamond_strip_lemmaD_2h2,hypothesis,
    ( ~ member(pair(X,Y),r)
    | ~ member(pair(X,YP),r)
    | member(pair(YP,sk1(X,Y,YP)),r) ) ).

cnf(diamond_strip_lemmaD_2h3,hypothesis,
    member(pair(x,y),trancl(r)) ).

cnf(diamond_strip_lemmaD_2h4,hypothesis,
    member(pair(y,z),r) ).

cnf(diamond_strip_lemmaD_2h5,hypothesis,
    ( ~ member(pair(x,YP),r)
    | member(pair(YP,sk2(YP)),trancl(r)) ) ).

cnf(diamond_strip_lemmaD_2h6,hypothesis,
    ( ~ member(pair(x,YP),r)
    | member(pair(y,sk2(YP)),r) ) ).

cnf(diamond_strip_lemmaD_2c1,negated_conjecture,
    member(pair(x,sk3),r) ).

cnf(diamond_strip_lemmaD_2c2,negated_conjecture,
    ( ~ member(pair(sk3,ZA),trancl(r))
    | ~ member(pair(z,ZA),r) ) ).

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