TPTP Problem File: SYO388^5.p
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% File : SYO388^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Syntactic
% Problem : TPS problem THM409-5
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0579 [Bro09]
% : THM409-5 [TPS]
% Status : Theorem
% Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% Syntax : Number of formulae : 17 ( 0 unt; 16 typ; 0 def)
% Number of atoms : 57 ( 0 equ; 0 cnn)
% Maximal formula atoms : 57 ( 57 avg)
% Number of connectives : 229 ( 27 ~; 25 |; 31 &; 146 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 47 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% 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
% Mellon University. Distributed under the Creative Commons copyleft
% license: http://creativecommons.org/licenses/by-sa/3.0/
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thf(cQ_6,type,
cQ_6: $i > $i > $i > $o ).
thf(f,type,
f: $i > $i ).
thf(cP_5,type,
cP_5: $i > $i > $o ).
thf(cQ_5,type,
cQ_5: $i > $i > $i > $o ).
thf(d,type,
d: $i ).
thf(c,type,
c: $i ).
thf(b,type,
b: $i ).
thf(a,type,
a: $i ).
thf(cP_4,type,
cP_4: $i > $i > $o ).
thf(cQ_4,type,
cQ_4: $i > $i > $i > $o ).
thf(cP_3,type,
cP_3: $i > $i > $o ).
thf(cQ_3,type,
cQ_3: $i > $i > $i > $o ).
thf(cP_2,type,
cP_2: $i > $i > $o ).
thf(cQ_2,type,
cQ_2: $i > $i > $i > $o ).
thf(cP_1,type,
cP_1: $i > $i > $o ).
thf(cQ_1,type,
cQ_1: $i > $i > $i > $o ).
thf(cTHM409_5,conjecture,
~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [Xx: $i] : ( cP_1 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_1 @ Xx @ Xy )
| ( cP_1 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_1 @ Xx @ Xy @ Xz )
| ~ ( cP_1 @ ( f @ Xx ) @ Xu )
| ~ ( cP_1 @ ( f @ Xy ) @ Xv )
| ~ ( cP_1 @ ( f @ Xz ) @ Xw )
| ( cQ_2 @ Xu @ Xv @ Xw ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [Xx: $i] : ( cP_2 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_2 @ Xx @ Xy )
| ( cP_2 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_2 @ Xx @ Xy @ Xz )
| ~ ( cP_2 @ ( f @ Xx ) @ Xu )
| ~ ( cP_2 @ ( f @ Xy ) @ Xv )
| ~ ( cP_2 @ ( f @ Xz ) @ Xw )
| ( cQ_3 @ Xu @ Xv @ Xw ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [Xx: $i] : ( cP_3 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_3 @ Xx @ Xy )
| ( cP_3 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_3 @ Xx @ Xy @ Xz )
| ~ ( cP_3 @ ( f @ Xx ) @ Xu )
| ~ ( cP_3 @ ( f @ Xy ) @ Xv )
| ~ ( cP_3 @ ( f @ Xz ) @ Xw )
| ( cQ_4 @ Xu @ Xv @ Xw ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [Xx: $i] : ( cP_4 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_4 @ Xx @ Xy )
| ( cP_4 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_4 @ Xx @ Xy @ Xz )
| ~ ( cP_4 @ ( f @ Xx ) @ Xu )
| ~ ( cP_4 @ ( f @ Xy ) @ Xv )
| ~ ( cP_4 @ ( f @ Xz ) @ Xw )
| ( cQ_5 @ Xu @ Xv @ Xw ) )
& ( cP_5 @ a @ a )
& ( cP_5 @ b @ b )
& ( cP_5 @ c @ c )
& ! [Xx: $i] : ( cP_5 @ d @ Xx )
& ! [Xx: $i,Xy: $i] :
( ~ ( cP_5 @ Xx @ Xy )
| ( cP_5 @ ( f @ Xx ) @ Xy ) )
& ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i,Xv: $i,Xw: $i] :
( ~ ( cQ_5 @ Xx @ Xy @ Xz )
| ~ ( cP_5 @ ( f @ Xx ) @ Xu )
| ~ ( cP_5 @ ( f @ Xy ) @ Xv )
| ~ ( cP_5 @ ( f @ Xz ) @ Xw )
| ( cQ_6 @ Xu @ Xv @ Xw ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
~ ( cQ_6 @ Xx @ Xy @ Xz ) ) ).
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