TPTP Problem File: SEV041^5.p
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% File : SEV041^5 : TPTP v8.2.0. 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_1215 [Bro09]
% Status : Theorem
% Rating : 0.70 v8.2.0, 0.69 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v5.1.0, 1.00 v5.0.0, 0.80 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% Number of atoms : 4 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 129 ( 0 ~; 0 |; 12 &; 97 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 21 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% Number of variables : 45 ( 4 ^; 41 !; 0 ?; 45 :)
% SPC : TH0_THM_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
% license: http://creativecommons.org/licenses/by-sa/3.0/
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thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(cTHM517_pme,conjecture,
! [Xp: a > a > $o,Xq: a > a > $o,Xr: a > b > b > $o,Xs: a > b > b > $o] :
( ( ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xp @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( Xp @ Xx @ Xy )
& ( Xp @ Xy @ Xz ) )
=> ( Xp @ Xx @ Xz ) )
& ( Xp = Xq ) )
=> ( ! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( ! [Xx0: b,Xy0: b] :
( ( Xr @ Xx @ Xx0 @ Xy0 )
=> ( Xr @ Xx @ Xy0 @ Xx0 ) )
& ! [Xx0: b,Xy0: b,Xz: b] :
( ( ( Xr @ Xx @ Xx0 @ Xy0 )
& ( Xr @ Xx @ Xy0 @ Xz ) )
=> ( Xr @ Xx @ Xx0 @ Xz ) )
& ( ( Xr @ Xx )
= ( Xr @ Xy ) ) ) )
=> ( ! [Xx: a] :
( ( Xp @ Xx @ Xx )
=> ( ! [Xx0: b,Xy: b] :
( ( Xr @ Xx @ Xx0 @ Xy )
=> ( Xr @ Xx @ Xy @ Xx0 ) )
& ! [Xx0: b,Xy: b,Xz: b] :
( ( ( Xr @ Xx @ Xx0 @ Xy )
& ( Xr @ Xx @ Xy @ Xz ) )
=> ( Xr @ Xx @ Xx0 @ Xz ) )
& ( ( Xr @ Xx )
= ( Xs @ Xx ) ) ) )
=> ( ! [Xx: a > b,Xy: a > b] :
( ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
=> ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xx @ Xy0 ) ) ) )
& ! [Xx: a > b,Xy: a > b,Xz: a > b] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xy @ Xy0 ) ) )
& ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xy @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
=> ! [Xx0: a,Xy0: a] :
( ( Xp @ Xx0 @ Xy0 )
=> ( Xr @ Xx0 @ ( Xx @ Xx0 ) @ ( Xz @ Xy0 ) ) ) )
& ( ( ^ [Xf: a > b,Xg: a > b] :
! [Xx: a,Xy: a] :
( ( Xp @ Xx @ Xy )
=> ( Xr @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) )
= ( ^ [Xf: a > b,Xg: a > b] :
! [Xx: a,Xy: a] :
( ( Xq @ Xx @ Xy )
=> ( Xs @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) ) ) ) ).
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