## TPTP Problem File: SEV304^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV304^5 : TPTP v7.5.0. 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_1112 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.60 v7.4.0, 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v6.2.0
% Syntax   : Number of formulae    :    7 (   0 unit;   3 type;   3 defn)
%            Number of atoms       :   85 (  10 equality;  58 variable)
%            Maximal formula depth :   19 (   7 average)
%            Number of connectives :   69 (   8   ~;   1   |;  15   &;  41   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :   20 (   0 sgn;   6   !;   7   ?;   7   ^)
%                                         (  20   :;   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
% Bugfixes : v5.2.0 - Added missing type declarations.
%          : v6.2.0 - Reordered definitions.
%------------------------------------------------------------------------------
thf(cONE_type,type,(
cONE: ( \$i > \$o ) > \$o )).

thf(cSUCC_type,type,(
cSUCC: ( ( \$i > \$o ) > \$o ) > ( \$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(cSIXPEOPLE_pme,conjecture,(
! [K: \$i > \$i > \$o,S: \$i > \$o] :
( ( ? [Xs: \$i > \$i > \$o] :
( ! [Xx: \$i] :
( ( S @ Xx )
=> ( cSUCC @ ( cSUCC @ ( cSUCC @ ( cSUCC @ ( cSUCC @ cONE ) ) ) ) @ ( Xs @ Xx ) ) )
& ! [Xy: \$i > \$o] :
( ( cSUCC @ ( cSUCC @ ( cSUCC @ ( cSUCC @ ( cSUCC @ cONE ) ) ) ) @ Xy )
=> ? [Xy0: \$i] :
( ( ^ [Xx: \$i] :
( ( S @ Xx )
& ( Xy
= ( Xs @ Xx ) ) ) )
= ( ^ [Xx: \$i,Xy: \$i] : ( Xx = Xy )
@ Xy0 ) ) ) )
& ! [Xx: \$i,Xy: \$i] :
( ( K @ Xx @ Xy )
=> ( K @ Xy @ Xx ) ) )
=> ? [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( S @ Xx )
& ( S @ Xy )
& ( S @ Xz )
& ( Xx != Xy )
& ( Xy != Xz )
& ( Xz != Xx )
& ( ( ( K @ Xx @ Xy )
& ( K @ Xy @ Xz )
& ( K @ Xx @ Xz ) )
| ( ~ ( K @ Xx @ Xy )
& ~ ( K @ Xy @ Xz )
& ~ ( K @ Xx @ Xz ) ) ) ) ) )).

%------------------------------------------------------------------------------
```