## TPTP Problem File: SEV109^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV109^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from RELN-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1164 [Bro09]
%          : tps_1165 [Bro09]
%          : tps_1166 [Bro09]
%          : tps_1167 [Bro09]
%          : tps_0501 [Bro09]
%          : THM250B [TPS]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   72 (   0 equality;  72 variable)
%            Maximal formula depth :   23 (  12 average)
%            Number of connectives :   71 (   0   ~;   2   |;   8   &;  48   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   28 (   0 sgn;  28   !;   0   ?;   0   ^)
%                                         (  28   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_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(cTHM251F_pme,conjecture,(
! [R: a > a > \$o,S: a > a > \$o,Xx: a,Xy: a] :
( ! [Xq1: a > a > \$o] :
( ( ! [Xs: a,Xt: a] :
( ( ( R @ Xs @ Xt )
| ( S @ Xs @ Xt ) )
=> ( Xq1 @ Xs @ Xt ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xq1 @ Xx0 @ Xy0 )
& ( Xq1 @ Xy0 @ Xz ) )
=> ( Xq1 @ Xx0 @ Xz ) ) )
=> ( Xq1 @ Xx @ Xy ) )
=> ! [Xp1: a > a > \$o] :
( ( ! [Xss: a,Xtt: a] :
( ( ! [Xq2: a > a > \$o] :
( ( ! [Xsss: a,Xttt: a] :
( ( R @ Xsss @ Xttt )
=> ( Xq2 @ Xsss @ Xttt ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xq2 @ Xx0 @ Xy0 )
& ( Xq2 @ Xy0 @ Xz ) )
=> ( Xq2 @ Xx0 @ Xz ) ) )
=> ( Xq2 @ Xss @ Xtt ) )
| ! [Xq3: a > a > \$o] :
( ( ! [Xssss: a,Xtttt: a] :
( ( S @ Xssss @ Xtttt )
=> ( Xq3 @ Xssss @ Xtttt ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xq3 @ Xx0 @ Xy0 )
& ( Xq3 @ Xy0 @ Xz ) )
=> ( Xq3 @ Xx0 @ Xz ) ) )
=> ( Xq3 @ Xss @ Xtt ) ) )
=> ( Xp1 @ Xss @ Xtt ) )
& ! [Xx0: a,Xy0: a,Xz: a] :
( ( ( Xp1 @ Xx0 @ Xy0 )
& ( Xp1 @ Xy0 @ Xz ) )
=> ( Xp1 @ Xx0 @ Xz ) ) )
=> ( Xp1 @ Xx @ Xy ) ) ) )).

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