## TPTP Problem File: SEV217^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV217^5 : 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_1257 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    9 (   0 unit;   8 type;   0 defn)
%            Number of atoms       :  600 (  78 equality; 418 variable)
%            Maximal formula depth :   39 (   7 average)
%            Number of connectives :  445 (   2   ~;  24   |; 111   &; 274   @)
%                                         (   1 <=>;  33  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   37 (  37   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8   :;   0   =)
%            Number of variables   :  139 (   0 sgn;  75   !;  64   ?;   0   ^)
%                                         ( 139   :;   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(cL,type,(
cL: c > c )).

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

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

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

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

thf(cS_T_DUC_MONOTONE_LEM_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 ) ) ) )
=> ( ! [R0: c > iS > \$o] :
( ! [Xc: c] :
( ( R0 @ Xc @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( R0 @ Xc @ Xy )
& ! [R1: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xy ) ) )
=> ( R0 @ Xc @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( R0 @ Xc @ Xx )
& ( R0 @ Xc @ Xy )
& ! [R1: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xz ) ) )
=> ( R0 @ Xc @ Xz ) ) )
=> ! [Xc: c] :
( ( ( c0 = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( c0
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) )
& ! [Xx: iS,Xy: iS] :
( ( ( ( Xy = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xy
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) )
& ! [R1: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xy ) ) )
=> ( ( Xx = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xx
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( ( Xx = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xx
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) )
& ( ( Xy = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xy
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) )
& ! [R1: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xz ) ) )
=> ( ( Xz = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xz
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) ) ) ) )
& ! [R0: c > iS > \$o,S: c > iS > \$o] :
( ( ! [Xc: c] :
( ( R0 @ Xc @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( R0 @ Xc @ Xy )
& ! [R1: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xy ) ) )
=> ( R0 @ Xc @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( R0 @ Xc @ Xx )
& ( R0 @ Xc @ Xy )
& ! [R1: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xz ) ) )
=> ( R0 @ Xc @ Xz ) ) )
& ! [Xc: c] :
( ( S @ Xc @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( S @ Xc @ Xy )
& ! [R1: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xy ) ) )
=> ( S @ Xc @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( S @ Xc @ Xx )
& ( S @ Xc @ Xy )
& ! [R1: iS > iS > iS > \$o] :
( ( \$true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xz ) ) )
=> ( S @ Xc @ Xz ) ) )
& ! [Xa: c,Xb: iS] :
( ( R0 @ Xa @ Xb )
=> ( S @ Xa @ Xb ) ) )
=> ! [Xa: c,Xb: iS] :
( ( ( Xb = c0 )
| ( ( cX1 @ Xa )
& ? [Xu1: iS,Xu2: iS] :
( ( Xb
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xa ) @ Xu1 )
& ( R0 @ ( cR @ Xa ) @ Xu2 ) ) ) )
=> ( ( Xb = c0 )
| ( ( cX1 @ Xa )
& ? [Xu1: iS,Xu2: iS] :
( ( Xb
= ( cP @ Xu1 @ Xu2 ) )
& ( S @ ( cL @ Xa ) @ Xu1 )
& ( S @ ( cR @ Xa ) @ Xu2 ) ) ) ) ) ) ) )).

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