%------------------------------------------------------------------------------
% File     : COL002-1 : TPTP v7.2.0. Released v3.2.0.
% Domain   : Combinatory Logic
% Axioms   : Combinators
% Version  : [Pau06] axioms.
% English  :

% Refs     : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source   : [Pau06]
% Names    : Comb2.ax [Pau06]

% Status   : Satisfiable
% Syntax   : Number of clauses     :   21 (   6 non-Horn;   3 unit;  16 RR)
%            Number of atoms       :   58 (  25 equality)
%            Maximal clause size   :    5 (   3 average)
%            Number of predicates  :    2 (   0 propositional; 2-3 arity)
%            Number of functors    :   17 (   5 constant; 0-4 arity)
%            Number of variables   :   53 (   1 singleton)
%            Maximal term depth    :    5 (   2 average)
% SPC      : 

% Comments : Requires MSC001-0.ax, MSC001-2.ax, COL002-0.ax
%------------------------------------------------------------------------------
cnf(cls_Comb_OAp__parcontractE_0,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p,V_q),V_r,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_r = c_Comb_Ocomb_Oop_A_D_D(V_p,V_q)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_r)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(V_p,V_q,V_r)),v_sko__uTG(V_p,V_q,V_r))
    | V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p,V_q,V_r),v_sko__uTH(V_p,V_q,V_r)) )).

cnf(cls_Comb_OAp__parcontractE_1,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p,V_q),V_r,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(V_q,v_sko__uTH(V_p,V_q,V_r),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_r = c_Comb_Ocomb_Oop_A_D_D(V_p,V_q)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_r)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(V_p,V_q,V_r)),v_sko__uTG(V_p,V_q,V_r)) )).

cnf(cls_Comb_OAp__parcontractE_2,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p,V_q),V_r,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(V_p,v_sko__uTI(V_p,V_q,V_r),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_r = c_Comb_Ocomb_Oop_A_D_D(V_p,V_q)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_r)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(V_p,V_q,V_r)),v_sko__uTG(V_p,V_q,V_r)) )).

cnf(cls_Comb_OAp__parcontractE_3,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p,V_q),V_r,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_r = c_Comb_Ocomb_Oop_A_D_D(V_p,V_q)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_r)
    | V_r = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_sko__uTF(V_p,V_q,V_r),V_q),c_Comb_Ocomb_Oop_A_D_D(v_sko__uTG(V_p,V_q,V_r),V_q))
    | V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p,V_q,V_r),v_sko__uTH(V_p,V_q,V_r)) )).

cnf(cls_Comb_OAp__parcontractE_4,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p,V_q),V_r,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(V_q,v_sko__uTH(V_p,V_q,V_r),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_r = c_Comb_Ocomb_Oop_A_D_D(V_p,V_q)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_r)
    | V_r = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_sko__uTF(V_p,V_q,V_r),V_q),c_Comb_Ocomb_Oop_A_D_D(v_sko__uTG(V_p,V_q,V_r),V_q)) )).

cnf(cls_Comb_OAp__parcontractE_5,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p,V_q),V_r,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(V_p,v_sko__uTI(V_p,V_q,V_r),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_r = c_Comb_Ocomb_Oop_A_D_D(V_p,V_q)
    | V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_r)
    | V_r = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_sko__uTF(V_p,V_q,V_r),V_q),c_Comb_Ocomb_Oop_A_D_D(v_sko__uTG(V_p,V_q,V_r),V_q)) )).

cnf(cls_Comb_OAp__reduce1_0,axiom,
    ( ~ c_in(c_Pair(V_x,V_y,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x,V_z),c_Comb_Ocomb_Oop_A_D_D(V_y,V_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_OAp__reduce2_0,axiom,
    ( ~ c_in(c_Pair(V_x,V_y,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_z,V_x),c_Comb_Ocomb_Oop_A_D_D(V_z,V_y),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Transitive__Closure_Ortrancl(c_Comb_Ocontract,tc_Comb_Ocomb),tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_OK1__parcontractD__dest_0,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_x),V_z,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(V_x,V_z)) )).

cnf(cls_Comb_OK1__parcontractD__dest_1,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_x),V_z,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(V_x,v_sko__uTE(V_x,V_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_OK__parcontractE_0,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_OK,V_r,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_r = c_Comb_Ocomb_OK )).

cnf(cls_Comb_OS1__parcontractD__dest_0,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,V_x),V_z,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTD(V_x,V_z)) )).

cnf(cls_Comb_OS1__parcontractD__dest_1,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,V_x),V_z,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(V_x,v_sko__uTD(V_x,V_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_OS2__parcontractD__dest_0,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,V_x),V_y),V_z,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTB(V_x,V_y,V_z)),v_sko__uTC(V_x,V_y,V_z)) )).

cnf(cls_Comb_OS2__parcontractD__dest_1,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,V_x),V_y),V_z,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(V_x,v_sko__uTB(V_x,V_y,V_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_OS2__parcontractD__dest_2,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,V_x),V_y),V_z,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(V_y,v_sko__uTC(V_x,V_y,V_z),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_OS__parcontractE_0,axiom,
    ( ~ c_in(c_Pair(c_Comb_Ocomb_OS,V_r,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | V_r = c_Comb_Ocomb_OS )).

cnf(cls_Comb_Oparcontract_Ointros__1_0,axiom,
    ( c_in(c_Pair(V_x,V_x,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_Oparcontract_Ointros__2_0,axiom,
    ( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,V_x),V_y),V_x,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_Oparcontract_Ointros__3_0,axiom,
    ( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,V_x),V_y),V_z),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(V_x,V_z),c_Comb_Ocomb_Oop_A_D_D(V_y,V_z)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

cnf(cls_Comb_Oparcontract_Ointros__4_0,axiom,
    ( ~ c_in(c_Pair(V_z,V_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | ~ c_in(c_Pair(V_x,V_y,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
    | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x,V_z),c_Comb_Ocomb_Oop_A_D_D(V_y,V_w),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) )).

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