TPTP Axioms File: LAT006-2.ax


%------------------------------------------------------------------------------
% File     : LAT006-2 : TPTP v7.5.0. Released v3.2.0.
% Domain   : Lattice Theory
% Axioms   : Tarski's fixed point theorem L (equality) axioms
% Version  : [Pau06] (equality) axioms.
% English  :

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

% Status   : Satisfiable
% Syntax   : Number of clauses     :   15 (   5 non-Horn;   1 unit;  12 RR)
%            Number of atoms       :   51 (   4 equality)
%            Maximal clause size   :    5 (   3 average)
%            Number of predicates  :    7 (   0 propositional; 2-4 arity)
%            Number of functors    :   17 (   7 constant; 0-4 arity)
%            Number of variables   :   51 (   6 singleton)
%            Maximal term depth    :    3 (   1 average)
% SPC      : 

% Comments :
%------------------------------------------------------------------------------
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
    ( ~ c_lessequals(V_S,V_A,tc_set(t_a))
    | c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
    | c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
    | V_S = c_emptyset )).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
    ( ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_lessequals(V_S,V_A,tc_set(t_a))
    | c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
    | V_S = c_emptyset )).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2,axiom,
    ( ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_lessequals(V_S,V_A,tc_set(t_a))
    | c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
    | V_S = c_emptyset )).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3,axiom,
    ( ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | ~ c_lessequals(V_S,V_A,tc_set(t_a))
    | c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | V_S = c_emptyset )).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
    ( ~ c_in(V_x,V_S,T_a)
    | ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
    | c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) )).

cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
    ( ~ c_in(V_x,V_S,T_a)
    | ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
    | c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) )).

cnf(cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0,axiom,
    ( ~ c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
    | ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
    | c_in(V_x,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),T_a) )).

cnf(cls_Tarski_O_91_124_Aa1_A_58_AA_59_Ab1_A_58_AA_59_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_A_124_93_A_61_61_62_AS1_A_60_61_AA_A_61_61_ATrue_0,axiom,
    ( ~ c_in(V_b,v_A,t_a)
    | ~ c_in(V_a,v_A,t_a)
    | ~ c_lessequals(V_S,c_Tarski_Ointerval(v_r,V_a,V_b,t_a),tc_set(t_a))
    | c_lessequals(V_S,v_A,tc_set(t_a)) )).

cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
    ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
    | ~ c_in(V_y,V_S,t_a)
    | c_in(c_Pair(V_y,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )).

cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
    ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
    | ~ c_in(V_z,v_A,t_a)
    | c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a) )).

cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
    ( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
    | ~ c_in(V_z,v_A,t_a)
    | ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
    | c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) )).

cnf(cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Aantisym_A_Iorder_Acl1_J_A_61_61_ATrue_0,axiom,
    ( ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
    | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),T_a) )).

cnf(cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Arefl_A_Ipset_Acl1_J_A_Iorder_Acl1_J_A_61_61_ATrue_0,axiom,
    ( ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
    | c_Relation_Orefl(c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),T_a) )).

cnf(cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0,axiom,
    ( ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
    | c_Relation_Otrans(c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),T_a) )).

cnf(cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0,axiom,
    ( c_in(v_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )).

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