TPTP Problem File: SEV038^5.p
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% File : SEV038^5 : 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_1210 [Bro09]
% Status : Unknown
% Rating : 1.00 v4.0.0
% Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% Number of atoms : 7 ( 7 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 101 ( 2 ~; 0 |; 27 &; 57 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 19 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% Number of variables : 38 ( 0 ^; 28 !; 10 ?; 38 :)
% 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
% license: http://creativecommons.org/licenses/by-sa/3.0/
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thf(a_type,type,
a: $tType ).
thf(cTHM266_pme,conjecture,
? [F: ( ( a > $o ) > $o ) > a > a > $o] :
( ! [P: ( a > $o ) > $o] :
( ( ! [Xp: a > $o] :
( ( P @ Xp )
=> ? [Xz: a] : ( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > $o] :
( ( P @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > $o] :
( ( ( P @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) ) )
=> ( ! [Xx: a] : ( F @ P @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( F @ P @ Xx @ Xy )
=> ( F @ P @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( F @ P @ Xx @ Xy )
& ( F @ P @ Xy @ Xz ) )
=> ( F @ P @ Xx @ Xz ) ) ) )
& ! [R: a > a > $o] :
( ( ! [Xx: a] : ( R @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( R @ Xx @ Xy )
=> ( R @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) )
=> ? [P: ( a > $o ) > $o] :
( ! [Xp: a > $o] :
( ( P @ Xp )
=> ? [Xz: a] : ( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > $o] :
( ( P @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > $o] :
( ( ( P @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) )
& ( R
= ( F @ P ) ) ) )
& ! [T: ( a > $o ) > $o,U: ( a > $o ) > $o] :
( ( ( T != U )
& ! [Xp: a > $o] :
( ( T @ Xp )
=> ? [Xz: a] : ( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > $o] :
( ( T @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > $o] :
( ( ( T @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) )
& ! [Xp: a > $o] :
( ( U @ Xp )
=> ? [Xz: a] : ( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > $o] :
( ( U @ Xp )
& ( Xp @ Xx )
& ! [Xq: a > $o] :
( ( ( U @ Xq )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) ) )
=> ( ( F @ T )
!= ( F @ U ) ) ) ) ).
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