## TPTP Problem File: SYO326^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO326^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1004 [Bro09]

% Status   : Theorem
% Rating   : 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v6.2.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   34 (   0 equality;  26 variable)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :   33 (   0   ~;   0   |;   5   &;  22   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :   10 (   0 sgn;   9   !;   1   ?;   0   ^)
%                                         (  10   :;   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(cC,type,(
cC: \$i > \$o )).

thf(f,type,(
f: \$i > \$i )).

thf(cB,type,(
cB: \$i > \$i > \$o )).

thf(cA,type,(
cA: \$i > \$o )).

thf(cSV8,conjecture,(
? [Xu: \$i > \$i > \$o] :
( ! [Xw: \$i,Xz: \$i] :
( ( ( cA @ Xw )
& ( cB @ Xz @ Xw ) )
=> ( Xu @ ( f @ Xw ) @ Xz ) )
& ! [Xz: \$i] :
( ( cC @ Xz )
=> ( Xu @ Xz @ Xz ) )
& ! [Xv: \$i > \$i > \$o] :
( ( ! [Xw: \$i,Xz: \$i] :
( ( ( cA @ Xw )
& ( cB @ Xz @ Xw ) )
=> ( Xv @ ( f @ Xw ) @ Xz ) )
& ! [Xz: \$i] :
( ( cC @ Xz )
=> ( Xv @ Xz @ Xz ) ) )
=> ! [Xx: \$i,Xy: \$i] :
( ( Xu @ Xx @ Xy )
=> ( Xv @ Xx @ Xy ) ) ) ) )).

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