## TPTP Problem File: SEV215^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV215^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from S-T-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1248 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    9 (   0 unit;   8 type;   0 defn)
%            Number of atoms       :  323 (  47 equality; 223 variable)
%            Maximal formula depth :   40 (   7 average)
%            Number of connectives :  230 (   2   ~;  12   |;  53   &; 142   @)
%                                         (   3 <=>;  18  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8   :;   0   =)
%            Number of variables   :   80 (   0 sgn;  45   !;  29   ?;   6   ^)
%                                         (  80   :;   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(c_type,type,(
c: \$tType )).

thf(iS_type,type,(
iS: \$tType )).

thf(cR,type,(
cR: c > c )).

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

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

thf(cL,type,(
cL: c > c )).

thf(cX0,type,(
cX0: c > \$o )).

thf(cX1,type,(
cX1: c > \$o )).

thf(cTHM_S_CHAR_T_pme,conjecture,
( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 )
& ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) )
& ! [X: iS > \$o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] :
( X @ Xx ) )
& ! [Xz: c] :
( ( cX0 @ Xz )
<=> ~ ( cX1 @ Xz ) )
& ! [Xz: c] :
( ( cX0 @ Xz )
=> ( ( ( cL @ Xz )
= Xz )
& ( ( cR @ Xz )
= Xz ) ) ) )
=> ? [Xf: c > iS > \$o] :
( ! [Xb: c] :
( ( Xf @ Xb @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( Xf @ Xb @ Xy )
& ! [R0: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb0: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb0 = Xc ) )
| ( ( Xb0 = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R0 @ Xx1 @ Xy1 @ Xz1 )
& ( R0 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R0 @ Xa @ Xb0 @ Xc ) ) )
=> ( R0 @ Xx @ Xy @ Xy ) ) )
=> ( Xf @ Xb @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( Xf @ Xb @ Xx )
& ( Xf @ Xb @ Xy )
& ! [R0: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb0: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb0 = Xc ) )
| ( ( Xb0 = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R0 @ Xx1 @ Xy1 @ Xz1 )
& ( R0 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R0 @ Xa @ Xb0 @ Xc ) ) )
=> ( R0 @ Xx @ Xy @ Xz ) ) )
=> ( Xf @ Xb @ Xz ) ) )
& ! [Xc: c] :
( ( cX0 @ Xc )
<=> ( ( Xf @ Xc )
= ( ^ [Xy: iS] : ( c0 = Xy ) ) ) )
& ! [Xb: c] :
( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( Xf @ Xb @ ( cP @ Xx @ Xy ) ) ) )
= ( Xf @ ( cL @ Xb ) ) )
& ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( Xf @ Xb @ ( cP @ Xx @ Xy ) ) ) )
= ( Xf @ ( cR @ Xb ) ) ) )
& ! [Xg: c > iS > \$o] :
( ( ! [Xb: c] :
( ( Xg @ Xb @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( Xg @ Xb @ Xy )
& ! [R0: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb0: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb0 = Xc ) )
| ( ( Xb0 = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R0 @ Xx1 @ Xy1 @ Xz1 )
& ( R0 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R0 @ Xa @ Xb0 @ Xc ) ) )
=> ( R0 @ Xx @ Xy @ Xy ) ) )
=> ( Xg @ Xb @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( Xg @ Xb @ Xx )
& ( Xg @ Xb @ Xy )
& ! [R0: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb0: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb0 = Xc ) )
| ( ( Xb0 = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb0
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R0 @ Xx1 @ Xy1 @ Xz1 )
& ( R0 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R0 @ Xa @ Xb0 @ Xc ) ) )
=> ( R0 @ Xx @ Xy @ Xz ) ) )
=> ( Xg @ Xb @ Xz ) ) )
& ! [Xc: c] :
( ( cX0 @ Xc )
<=> ( ( Xg @ Xc )
= ( ^ [Xy: iS] : ( c0 = Xy ) ) ) )
& ! [Xb: c] :
( ( ( ^ [Xx: iS] :
( ( Xx = c0 )
| ? [Xy: iS] :
( Xg @ Xb @ ( cP @ Xx @ Xy ) ) ) )
= ( Xg @ ( cL @ Xb ) ) )
& ( ( ^ [Xy: iS] :
( ( Xy = c0 )
| ? [Xx: iS] :
( Xg @ Xb @ ( cP @ Xx @ Xy ) ) ) )
= ( Xg @ ( cR @ Xb ) ) ) ) )
=> ( Xf = Xg ) ) ) )).

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