## TPTP Problem File: SEV203^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV203^5 : 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_1156 [Bro09]

% Status   : Theorem
% Rating   : 0.73 v7.5.0, 0.71 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    6 (   0 unit;   5 type;   0 defn)
%            Number of atoms       :   80 (  11 equality;  48 variable)
%            Maximal formula depth :   24 (   6 average)
%            Number of connectives :   58 (   1   ~;   2   |;  12   &;  37   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5   :;   0   =)
%            Number of variables   :   20 (   0 sgn;  14   !;   6   ?;   0   ^)
%                                         (  20   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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/
%------------------------------------------------------------------------------
thf(iS_type,type,(
iS: \$tType )).

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

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

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

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

thf(cS_INCL_LEM5_pme,conjecture,
( ( ! [Xx0: iS,Xy0: iS] :
( ( cP @ Xx0 @ Xy0 )
!= c0 )
& ! [Xx0: iS,Xy0: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx0 @ Xu )
= ( cP @ Xy0 @ Xv ) )
=> ( ( Xx0 = Xy0 )
& ( Xu = Xv ) ) )
& ! [X: iS > \$o] :
( ( ( X @ c0 )
& ! [Xx0: iS,Xy0: iS] :
( ( ( X @ Xx0 )
& ( X @ Xy0 ) )
=> ( X @ ( cP @ Xx0 @ Xy0 ) ) ) )
=> ! [Xx0: iS] :
( X @ Xx0 ) ) )
=> ! [R: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc ) )
| ( ( Xb = c0 )
& ( Xa = Xc ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) )).

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