TPTP Problem File: SEV035^5.p

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% File     : SEV035^5 : 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_1195 [Bro09]
%          : tps_1196 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :  108 (  18 equality;  90 variable)
%            Maximal formula depth :   18 (  10 average)
%            Number of connectives :   71 (   0   ~;   0   |;  15   &;  42   @)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   48 (   0 sgn;  18   !;  12   ?;  18   ^)
%                                         (  48   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cEQP1_1_pme,conjecture,
( ! [Xx: a > \$o] :
? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xx @ Xx0 )
=> ( Xx @ ( Xs @ Xx0 ) ) )
& ! [Xy: a] :
( ( Xx @ Xy )
=> ? [Xy_20: a] :
( ( ^ [Xx0: a] :
( ( Xx @ Xx0 )
& ( Xy
= ( Xs @ Xx0 ) ) ) )
= ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
@ Xy_20 ) ) ) )
& ! [Xx: a > \$o,Xy: a > \$o] :
( ? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xx @ Xx0 )
=> ( Xy @ ( Xs @ Xx0 ) ) )
& ! [Xy0: a] :
( ( Xy @ Xy0 )
=> ? [Xy_21: a] :
( ( ^ [Xx0: a] :
( ( Xx @ Xx0 )
& ( Xy0
= ( Xs @ Xx0 ) ) ) )
= ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
@ Xy_21 ) ) ) )
=> ? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xy @ Xx0 )
=> ( Xx @ ( Xs @ Xx0 ) ) )
& ! [Xy0: a] :
( ( Xx @ Xy0 )
=> ? [Xy_22: a] :
( ( ^ [Xx0: a] :
( ( Xy @ Xx0 )
& ( Xy0
= ( Xs @ Xx0 ) ) ) )
= ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
@ Xy_22 ) ) ) ) )
& ! [Xx: a > \$o,Xy: a > \$o,Xz: a > \$o] :
( ( ? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xx @ Xx0 )
=> ( Xy @ ( Xs @ Xx0 ) ) )
& ! [Xy0: a] :
( ( Xy @ Xy0 )
=> ? [Xy_23: a] :
( ( ^ [Xx0: a] :
( ( Xx @ Xx0 )
& ( Xy0
= ( Xs @ Xx0 ) ) ) )
= ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
@ Xy_23 ) ) ) )
& ? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xy @ Xx0 )
=> ( Xz @ ( Xs @ Xx0 ) ) )
& ! [Xy0: a] :
( ( Xz @ Xy0 )
=> ? [Xy_24: a] :
( ( ^ [Xx0: a] :
( ( Xy @ Xx0 )
& ( Xy0
= ( Xs @ Xx0 ) ) ) )
= ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
@ Xy_24 ) ) ) ) )
=> ? [Xs: a > a] :
( ! [Xx0: a] :
( ( Xx @ Xx0 )
=> ( Xz @ ( Xs @ Xx0 ) ) )
& ! [Xy0: a] :
( ( Xz @ Xy0 )
=> ? [Xy_25: a] :
( ( ^ [Xx0: a] :
( ( Xx @ Xx0 )
& ( Xy0
= ( Xs @ Xx0 ) ) ) )
= ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
@ Xy_25 ) ) ) ) ) )).

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