%--------------------------------------------------------------------------
% File     : KRS003_10 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Knowledge Representation
% Problem  : Paramasivam problem T-Box 1c
% Version  : KRS003_1 with the conjecture removed
% English  : e and f exist.

% Refs     : [PP95]  Paramasivam & Plaisted (1995), Automated Deduction Tec
% Source   : [TPTP]
% Names    : 

% Status   : Satisfiable
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :   29 (   0 unt;  15 typ;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   19 (   1   ~;   3   |;   4   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   14 (  12   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   8 usr;   0 prp; 1-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :   18 (  18   !;   0   ?;  18   :)
% SPC      : TF0_SAT_NEQ_NAR

% Comments :
%--------------------------------------------------------------------------
tff(unreal_type,type,
    unreal: $tType ).

tff(real_type,type,
    real: $tType ).

tff(u1r1_type,type,
    u1r1: unreal > real ).

tff(u1r2_type,type,
    u1r2: unreal > real ).

tff(u3r1_type,type,
    u3r1: unreal > real ).

tff(u3r2_type,type,
    u3r2: unreal > real ).

tff(exist_type,type,
    exist: unreal ).

tff(f_type,type,
    f: unreal > $o ).

tff(d_type,type,
    d: unreal > $o ).

tff(e_type,type,
    e: unreal > $o ).

tff(s1most_type,type,
    s1most: unreal > $o ).

tff(s_type,type,
    s: ( unreal * real ) > $o ).

tff(c_type,type,
    c: unreal > $o ).

tff(equalish_type,type,
    equalish: ( real * real ) > $o ).

tff(s2least_type,type,
    s2least: unreal > $o ).

tff(clause_3,axiom,
    ! [X1: unreal] :
      ( c(X1)
     => s2least(X1) ) ).

tff(clause_4,axiom,
    ! [X1: unreal] :
      ( s2least(X1)
     => c(X1) ) ).

tff(clause_5,axiom,
    ! [X1: unreal] :
      ~ ( s2least(X1)
        & equalish(u1r2(X1),u1r1(X1)) ) ).

tff(clause_6,axiom,
    ! [X1: unreal] :
      ( s2least(X1)
     => s(X1,u1r1(X1)) ) ).

tff(clause_7,axiom,
    ! [X1: unreal] :
      ( s2least(X1)
     => s(X1,u1r2(X1)) ) ).

tff(clause_8,axiom,
    ! [X2: real,X3: real,X1: unreal] :
      ( ( s(X1,X3)
        & s(X1,X2) )
     => ( s2least(X1)
        | equalish(X3,X2) ) ) ).

tff(clause_9,axiom,
    ! [X1: unreal] :
      ( d(X1)
     => s1most(X1) ) ).

tff(clause_10,axiom,
    ! [X1: unreal] :
      ( s1most(X1)
     => d(X1) ) ).

tff(clause_11,axiom,
    ! [X2: real,X3: real,X1: unreal] :
      ( ( s1most(X1)
        & s(X1,X3)
        & s(X1,X2) )
     => equalish(X3,X2) ) ).

tff(clause_12,axiom,
    ! [X1: unreal] :
      ( equalish(u3r2(X1),u3r1(X1))
     => s1most(X1) ) ).

tff(clause_13,axiom,
    ! [X1: unreal] :
      ( s1most(X1)
      | s(X1,u3r1(X1)) ) ).

tff(clause_14,axiom,
    ! [X1: unreal] :
      ( s1most(X1)
      | s(X1,u3r2(X1)) ) ).

tff(clause_15,axiom,
    ! [X1: unreal] :
      ( e(X1)
     => c(X1) ) ).

tff(clause_16,axiom,
    ! [X1: unreal] :
      ( f(X1)
     => d(X1) ) ).

% tff(clause_1__clause_2,conjecture,
%     ( ~ e(exist)
%     | ~ f(exist) ) ).

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