TPTP Problem File: SEV296^5.p

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%------------------------------------------------------------------------------
% File     : SEV296^5 : TPTP v7.0.0. Bugfixed v6.2.0.
% Domain   : Set Theory
% Problem  : TPS problem from TTTP-NATS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0652 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.67 v6.2.0
% Syntax   : Number of formulae    :   15 (   0 unit;   8 type;   6 defn)
%            Number of atoms       :   64 (  12 equality;  21 variable)
%            Maximal formula depth :   11 (   5 average)
%            Number of connectives :   35 (   2   ~;   0   |;   5   &;  27   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8   :;   0   =)
%            Number of variables   :   12 (   0 sgn;   6   !;   2   ?;   4   ^)
%                                         (  12   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%          : 
% Bugfixes : v5.2.0 - Added missing type declarations.
%          : v6.2.0 - Reordered definitions.
%------------------------------------------------------------------------------
thf(c_plus_type,type,(
    c_plus: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > ( $i > $o ) > $o )).

thf(c_star_type,type,(
    c_star: ( ( $i > $o ) > $o ) > ( ( $i > $o ) > $o ) > ( $i > $o ) > $o )).

thf(cONE_type,type,(
    cONE: ( $i > $o ) > $o )).

thf(cPLUS_AXIOMS_type,type,(
    cPLUS_AXIOMS: $o )).

thf(cSUCC_type,type,(
    cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o )).

thf(cTIMES_AXIOMS_type,type,(
    cTIMES_AXIOMS: $o )).

thf(cTWO_type,type,(
    cTWO: ( $i > $o ) > $o )).

thf(cZERO_type,type,(
    cZERO: ( $i > $o ) > $o )).

thf(cZERO_def,definition,
    ( cZERO
    = ( ^ [Xp: $i > $o] :
          ~ ( ? [Xx: $i] :
                ( Xp @ Xx ) ) ) )).

thf(cSUCC_def,definition,
    ( cSUCC
    = ( ^ [Xn: ( $i > $o ) > $o,Xp: $i > $o] :
        ? [Xx: $i] :
          ( ( Xp @ Xx )
          & ( Xn
            @ ^ [Xt: $i] :
                ( ( Xt != Xx )
                & ( Xp @ Xt ) ) ) ) ) )).

thf(cONE_def,definition,
    ( cONE
    = ( cSUCC @ cZERO ) )).

thf(cTWO_def,definition,
    ( cTWO
    = ( cSUCC @ cONE ) )).

thf(cPLUS_AXIOMS_def,definition,
    ( cPLUS_AXIOMS
    = ( ! [X: ( $i > $o ) > $o] :
          ( ( c_plus @ X @ cZERO )
          = X )
      & ! [X: ( $i > $o ) > $o,Y: ( $i > $o ) > $o] :
          ( ( c_plus @ X @ ( cSUCC @ Y ) )
          = ( cSUCC @ ( c_plus @ X @ Y ) ) ) ) )).

thf(cTIMES_AXIOMS_def,definition,
    ( cTIMES_AXIOMS
    = ( ! [X: ( $i > $o ) > $o] :
          ( ( c_star @ X @ cZERO )
          = cZERO )
      & ! [X: ( $i > $o ) > $o,Y: ( $i > $o ) > $o] :
          ( ( c_star @ X @ ( cSUCC @ Y ) )
          = ( c_plus @ ( c_star @ X @ Y ) @ Y ) ) ) )).

thf(cFOUR_THEOREM_B,conjecture,
    ( ( cPLUS_AXIOMS
      & cTIMES_AXIOMS )
   => ( ( c_star @ cTWO @ cTWO )
      = ( c_plus @ cTWO @ cTWO ) ) )).

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