%------------------------------------------------------------------------------
% File     : LCL433-2 : TPTP v9.0.0. Released v3.2.0.
% Domain   : Logic Calculi (Propositional)
% Problem  : Problem about propositional logic
% Version  : [Pau06] axioms : Reduced > Especial.
% English  :

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

% Status   : Unsatisfiable
% Rating   : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v3.2.0
% Syntax   : Number of clauses     :    8 (   3 unt;   0 nHn;   6 RR)
%            Number of literals    :   14 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 3-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-3 aty)
%            Number of variables   :   19 (   2 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.
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
    c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a) ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) ).

cnf(cls_conjecture_4,negated_conjecture,
    ( c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a))
    | ~ c_PropLog_Osat(v_F,V_U,t_a) ) ).

cnf(cls_PropLog_Osat__imp_0,axiom,
    ( ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a)
    | c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a) ) ).

cnf(cls_PropLog_Othms_OH_0,axiom,
    ( ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a))
    | c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ).

cnf(cls_PropLog_Othms_OMP_0,axiom,
    ( ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
    | ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
    | c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ) ).

cnf(cls_PropLog_Oweaken__left__insert_0,axiom,
    ( ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a))
    | c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a)) ) ).

cnf(cls_Set_OinsertCI_1,axiom,
    c_in(V_x,c_insert(V_x,V_B,T_a),T_a) ).

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