%------------------------------------------------------------------------------
% File : SEU916^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory
% Problem : TPS problem from SET-TOP-CATEGORY-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1256 [Bro09]
% Status : Theorem
% Rating : 1.00 v6.2.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v4.0.0
% Syntax : Number of formulae : 9 ( 0 unt; 8 typ; 0 def)
% Number of atoms : 90 ( 30 equ; 0 cnn)
% Maximal formula atoms : 90 ( 90 avg)
% Number of connectives : 429 ( 0 ~; 18 |; 79 &; 220 @)
% ( 8 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 33 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 167 ( 167 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 171 ( 36 ^; 113 !; 22 ?; 171 :)
% 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/
%------------------------------------------------------------------------------
thf(c_type,type,
c: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(g,type,
g: ( c > $o ) > b > $o ).
thf(f,type,
f: ( c > $o ) > a > $o ).
thf(cC,type,
cC: ( c > $o ) > $o ).
thf(cB,type,
cB: ( b > $o ) > $o ).
thf(cA,type,
cA: ( a > $o ) > $o ).
thf(cDOMTHM12_pme,conjecture,
( ( ! [Xx: c > $o] :
( ( cC @ Xx )
=> ( cA @ ( f @ Xx ) ) )
& ! [Xe: a > $o] :
( ( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx: a > $o] :
( ( X @ Xx )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: a] :
( ( Xe @ Xx )
=> ? [S: a > $o] :
( ( cA @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: c > $o] :
( ( ( cC @ Xx )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( f @ Xx @ Xx0 ) ) )
=> ( cC @ Xx ) )
& ! [Xx: c > $o] :
( ( ( cC @ Xx )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( f @ Xx @ Xx0 ) ) )
=> ? [Xe0: c > $o] :
( ! [X: ( c > $o ) > $o] :
( ( ( X
@ ^ [Xy: c] : $false )
& ! [Xx0: c > $o] :
( ( X @ Xx0 )
=> ! [Xt: c] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: c] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: c > $o] :
( ( ( cC @ Xy )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cC @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( f @ Xy @ Xx0 ) ) ) ) ) ) ) )
& ! [Xx: c > $o] :
( ( cC @ Xx )
=> ( cB @ ( g @ Xx ) ) )
& ! [Xe: b > $o] :
( ( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx: b > $o] :
( ( X @ Xx )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: b] :
( ( Xe @ Xx )
=> ? [S: b > $o] :
( ( cB @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: c > $o] :
( ( ( cC @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( g @ Xx @ Xx0 ) ) )
=> ( cC @ Xx ) )
& ! [Xx: c > $o] :
( ( ( cC @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( g @ Xx @ Xx0 ) ) )
=> ? [Xe0: c > $o] :
( ! [X: ( c > $o ) > $o] :
( ( ( X
@ ^ [Xy: c] : $false )
& ! [Xx0: c > $o] :
( ( X @ Xx0 )
=> ! [Xt: c] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: c] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: c > $o] :
( ( ( cC @ Xy )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cC @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( g @ Xy @ Xx0 ) ) ) ) ) ) ) ) )
=> ( ! [Xx: c > $o] :
( ( cC @ Xx )
=> ? [Xx0: a > $o] :
( ( cA @ Xx0 )
& ? [Xy: b > $o] :
( ( cB @ Xy )
& ! [Xr: ( a > $o ) > ( b > $o ) > $o] :
( ? [Xd: a > $o,Xe: b > $o] :
( ( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy0: a] : $false )
& ! [Xx1: a > $o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( f @ Xx @ Xx1 ) )
& ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy0: b] : $false )
& ! [Xx1: b > $o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx1: b] :
( ( Xe @ Xx1 )
=> ( g @ Xx @ Xx1 ) ) )
=> ! [Xu: a > $o,Xv: b > $o] :
( ( Xr @ Xu @ Xv )
<=> ( ( Xu = Xd )
& ( Xv = Xe ) ) ) )
<=> ? [Xd: a > $o,Xe: b > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy0: a] : $false )
& ! [Xx1: a > $o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( Xx0 @ Xx1 ) )
& ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy0: b] : $false )
& ! [Xx1: b > $o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx1: b] :
( ( Xe @ Xx1 )
=> ( Xy @ Xx1 ) )
& ! [Xu: a > $o,Xv: b > $o] :
( ( Xr @ Xu @ Xv )
<=> ( ( Xd = Xu )
& ( Xe = Xv ) ) ) ) ) ) ) )
& ! [Xe: ( ( a > $o ) > ( b > $o ) > $o ) > $o] :
( ( ! [X: ( ( ( a > $o ) > ( b > $o ) > $o ) > $o ) > $o] :
( ( ( X
@ ^ [Xy: ( a > $o ) > ( b > $o ) > $o] : $false )
& ! [Xx: ( ( a > $o ) > ( b > $o ) > $o ) > $o] :
( ( X @ Xx )
=> ! [Xt: ( a > $o ) > ( b > $o ) > $o] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: ( a > $o ) > ( b > $o ) > $o] :
( ( Xx @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx: ( a > $o ) > ( b > $o ) > $o] :
( ( Xe @ Xx )
=> ? [S: ( ( a > $o ) > ( b > $o ) > $o ) > $o] :
( ? [Xx0: a > $o] :
( ( cA @ Xx0 )
& ? [Xy: b > $o] :
( ( cB @ Xy )
& ! [Xr: ( a > $o ) > ( b > $o ) > $o] :
( ( S @ Xr )
<=> ? [Xd: a > $o,Xe0: b > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy0: a] : $false )
& ! [Xx1: a > $o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( Xx0 @ Xx1 ) )
& ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy0: b] : $false )
& ! [Xx1: b > $o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx1: b] :
( ( Xe0 @ Xx1 )
=> ( Xy @ Xx1 ) )
& ! [Xu: a > $o,Xv: b > $o] :
( ( Xr @ Xu @ Xv )
<=> ( ( Xd = Xu )
& ( Xe0 = Xv ) ) ) ) ) ) )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: c > $o] :
( ( ( cC @ Xx )
& ! [Xx0: ( a > $o ) > ( b > $o ) > $o] :
( ( Xe @ Xx0 )
=> ? [Xd: a > $o,Xe0: b > $o] :
( ( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx1: a > $o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( f @ Xx @ Xx1 ) )
& ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx1: b > $o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx1: b] :
( ( Xe0 @ Xx1 )
=> ( g @ Xx @ Xx1 ) ) )
=> ! [Xu: a > $o,Xv: b > $o] :
( ( Xx0 @ Xu @ Xv )
<=> ( ( Xu = Xd )
& ( Xv = Xe0 ) ) ) ) ) )
=> ( cC @ Xx ) )
& ! [Xx: c > $o] :
( ( ( cC @ Xx )
& ! [Xx0: ( a > $o ) > ( b > $o ) > $o] :
( ( Xe @ Xx0 )
=> ? [Xd: a > $o,Xe0: b > $o] :
( ( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx1: a > $o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( f @ Xx @ Xx1 ) )
& ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx1: b > $o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx1: b] :
( ( Xe0 @ Xx1 )
=> ( g @ Xx @ Xx1 ) ) )
=> ! [Xu: a > $o,Xv: b > $o] :
( ( Xx0 @ Xu @ Xv )
<=> ( ( Xu = Xd )
& ( Xv = Xe0 ) ) ) ) ) )
=> ? [Xe0: c > $o] :
( ! [X: ( c > $o ) > $o] :
( ( ( X
@ ^ [Xy: c] : $false )
& ! [Xx0: c > $o] :
( ( X @ Xx0 )
=> ! [Xt: c] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: c] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: c > $o] :
( ( ( cC @ Xy )
& ! [Xx0: c] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cC @ Xy )
& ! [Xx0: ( a > $o ) > ( b > $o ) > $o] :
( ( Xe @ Xx0 )
=> ? [Xd: a > $o,Xe1: b > $o] :
( ( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy0: a] : $false )
& ! [Xx1: a > $o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xd @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xd ) )
& ! [Xx1: a] :
( ( Xd @ Xx1 )
=> ( f @ Xy @ Xx1 ) )
& ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy0: b] : $false )
& ! [Xx1: b > $o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe1 @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe1 ) )
& ! [Xx1: b] :
( ( Xe1 @ Xx1 )
=> ( g @ Xy @ Xx1 ) ) )
=> ! [Xu: a > $o,Xv: b > $o] :
( ( Xx0 @ Xu @ Xv )
<=> ( ( Xu = Xd )
& ( Xv = Xe1 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------