TPTP Problem File: SEV029^5.p

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```%------------------------------------------------------------------------------
% File     : SEV029^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from EQUIVALENCE-RELATIONS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1124 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.20 v7.4.0, 0.25 v7.2.0, 0.00 v6.4.0, 0.33 v6.3.0, 0.00 v5.4.0, 0.67 v5.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   53 (   1 equality;  52 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   50 (   0   ~;   0   |;   9   &;  30   @)
%                                         (   5 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   23 (   0 sgn;  16   !;   7   ?;   0   ^)
%                                         (  23   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_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(a_type,type,(
a: \$tType )).

thf(cTHM260A_pme,conjecture,(
! [Xr: a > a > \$o,Xs: a > \$o] :
( ( ! [Xx: a] :
( ( Xs @ Xx )
=> ( Xr @ Xx @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( Xr @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xr @ Xx @ Xy )
& ( Xr @ Xy @ Xz ) )
=> ( Xr @ Xx @ Xz ) ) )
=> ( ! [Xa: a > \$o] :
( ? [Xx: a] :
! [Xx_1: a] :
( ( Xa @ Xx_1 )
<=> ( Xr @ Xx @ Xx_1 ) )
=> ? [Xx: a] :
( Xa @ Xx ) )
& ! [Xx: a] :
( ( Xs @ Xx )
<=> ? [S: a > \$o] :
( ? [Xx0: a] :
! [Xx_2: a] :
( ( S @ Xx_2 )
<=> ( Xr @ Xx0 @ Xx_2 ) )
& ( S @ Xx ) ) )
& ! [Xb: a > \$o,Xc: a > \$o] :
( ( ? [Xx: a] :
! [Xx_3: a] :
( ( Xb @ Xx_3 )
<=> ( Xr @ Xx @ Xx_3 ) )
& ? [Xx: a] :
! [Xx_4: a] :
( ( Xc @ Xx_4 )
<=> ( Xr @ Xx @ Xx_4 ) )
& ? [Xx: a] :
( ( Xb @ Xx )
& ( Xc @ Xx ) ) )
=> ( Xb = Xc ) ) ) ) )).

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