TPTP Problem File: COL121-2.p

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%------------------------------------------------------------------------------
% File     : COL121-2 : TPTP v9.0.0. Released v3.2.0.
% Domain   : Combinatory Logic
% Problem  : Problem about combinators
% Version  : [Pau06] axioms : Reduced > Especial.
% English  :

% Refs     : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source   : [Pau06]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.07 v9.0.0, 0.00 v7.4.0, 0.17 v7.3.0, 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 v3.2.0
% Syntax   : Number of clauses     :   10 (   3 unt;   0 nHn;  10 RR)
%            Number of literals    :   22 (   0 equ;  13 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 2-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-4 aty)
%            Number of variables   :   21 (   0 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

% Comments : The problems in the [Pau06] collection each have very many axioms,
%            of which only a small selection are required for the refutation.
%            The mission is to find those few axioms, after which a refutation
%            can be quite easily found. This version has only the necessary
%            axioms.
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cnf(cls_Comb_Odiamond__strip__lemmaE_0,axiom,
    ( ~ c_Comb_Odiamond(V_r,T_a)
    | ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
    | ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
    | c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).

cnf(cls_Comb_Odiamond__strip__lemmaE_1,axiom,
    ( ~ c_Comb_Odiamond(V_r,T_a)
    | ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
    | ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
    | c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ).

cnf(cls_Transitive__Closure_Or__into__rtrancl_0,axiom,
    ( ~ c_in(V_p,V_r,tc_prod(T_a,T_a))
    | c_in(V_p,c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).

cnf(cls_Transitive__Closure_Ortrancl__trans_0,axiom,
    ( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
    | ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
    | c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_Comb_Odiamond(v_r,t_a) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_in(c_Pair(v_ya,v_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).

cnf(cls_conjecture_3,negated_conjecture,
    c_in(c_Pair(v_y,v_xaa,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ).

cnf(cls_conjecture_4,negated_conjecture,
    ( c_in(c_Pair(v_ya,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ).

cnf(cls_conjecture_5,negated_conjecture,
    ( c_in(c_Pair(V_U,v_x(V_U),t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ).

cnf(cls_conjecture_6,negated_conjecture,
    ( ~ c_in(c_Pair(v_xaa,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_z,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ).

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