## TPTP Problem File: SYO173^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO173^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-FO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1028 [Bro09]

% Status   : Theorem
% Rating   : 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.40 v5.4.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   44 (   0 equality;  20 variable)
%            Maximal formula depth :   14 (   6 average)
%            Number of connectives :   47 (   4   ~;   2   |;   4   &;  37   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   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(nt,type,(
nt: \$i > \$i )).

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

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

thf(cLCL077_1,conjecture,(
~ ( ! [Xp: \$i,Xq: \$i] :
( ~ ( cT @ ( imp @ Xp @ Xq ) )
| ~ ( cT @ Xp )
| ( cT @ Xq ) )
& ! [Xp: \$i,Xq: \$i] :
( cT @ ( imp @ Xp @ ( imp @ Xq @ Xp ) ) )
& ! [Xp: \$i,Xq: \$i,Xr: \$i] :
( cT @ ( imp @ ( imp @ Xp @ ( imp @ Xq @ Xr ) ) @ ( imp @ ( imp @ Xp @ Xq ) @ ( imp @ Xp @ Xr ) ) ) )
& ! [Xp: \$i,Xq: \$i] :
( cT @ ( imp @ ( imp @ ( nt @ Xp ) @ ( nt @ Xq ) ) @ ( imp @ Xq @ Xp ) ) )
& ? [Xa: \$i] :
~ ( cT @ ( imp @ ( nt @ ( nt @ Xa ) ) @ Xa ) ) ) )).

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