## TPTP Problem File: SEV209^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV209^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from S-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1218 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :  160 (  29 equality; 108 variable)
%            Maximal formula depth :   39 (  12 average)
%            Number of connectives :  101 (   0   ~;   8   |;  27   &;  60   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3   :;   0   =)
%            Number of variables   :   42 (   0 sgn;  12   !;  24   ?;   6   ^)
%                                         (  42   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cP,type,(
cP: a > a > a )).

thf(c0,type,(
c0: a )).

thf(cS_JOIN_FPPROP_pme,conjecture,
( ( ^ [Xa: a,Xb: a,Xc: a] :
! [R: a > a > a > \$o] :
( ( \$true
& ! [Xa0: a,Xb0: a,Xc0: a] :
( ( ( ( Xa0 = c0 )
& ( Xb0 = Xc0 ) )
| ( ( Xb0 = c0 )
& ( Xa0 = Xc0 ) )
| ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa0
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R @ Xa0 @ Xb0 @ Xc0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
= ( ^ [Xx: a,Xy: a,Xz: a] :
( ( ( Xx = c0 )
& ( Xy = Xz ) )
| ( ( Xy = c0 )
& ( Xx = Xz ) )
| ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xx
= ( cP @ Xx1 @ Xx2 ) )
& ( Xy
= ( cP @ Xy1 @ Xy2 ) )
& ( Xz
= ( cP @ Xz1 @ Xz2 ) )
& ! [R: a > a > a > \$o] :
( ( \$true
& ! [Xa: a,Xb: a,Xc: a] :
( ( ( ( Xa = c0 )
& ( Xb = Xc ) )
| ( ( Xb = c0 )
& ( Xa = Xc ) )
| ? [Xx10: a,Xx20: a,Xy10: a,Xy20: a,Xz10: a,Xz20: a] :
( ( Xa
= ( cP @ Xx10 @ Xx20 ) )
& ( Xb
= ( cP @ Xy10 @ Xy20 ) )
& ( Xc
= ( cP @ Xz10 @ Xz20 ) )
& ( R @ Xx10 @ Xy10 @ Xz10 )
& ( R @ Xx20 @ Xy20 @ Xz20 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ Xx1 @ Xy1 @ Xz1 ) )
& ! [R: a > a > a > \$o] :
( ( \$true
& ! [Xa: a,Xb: a,Xc: a] :
( ( ( ( Xa = c0 )
& ( Xb = Xc ) )
| ( ( Xb = c0 )
& ( Xa = Xc ) )
| ? [Xx10: a,Xx20: a,Xy10: a,Xy20: a,Xz10: a,Xz20: a] :
( ( Xa
= ( cP @ Xx10 @ Xx20 ) )
& ( Xb
= ( cP @ Xy10 @ Xy20 ) )
& ( Xc
= ( cP @ Xz10 @ Xz20 ) )
& ( R @ Xx10 @ Xy10 @ Xz10 )
& ( R @ Xx20 @ Xy20 @ Xz20 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ Xx2 @ Xy2 @ Xz2 ) ) ) ) ) )).

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