%------------------------------------------------------------------------------
% File : SEU880^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Finite sets)
% Problem : TPS problem from SET-TOPOLOGY-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1258 [Bro09]
% Status : CounterSatisfiable
% Rating : 0.67 v9.0.0, 1.00 v8.1.0, 0.80 v7.4.0, 0.75 v7.2.0, 0.67 v6.2.0, 0.33 v4.1.0, 0.00 v4.0.1, 0.50 v4.0.0
% Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% Number of atoms : 122 ( 24 equ; 0 cnn)
% Maximal formula atoms : 122 ( 122 avg)
% Number of connectives : 723 ( 0 ~; 22 |; 139 &; 362 @)
% ( 3 <=>; 197 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 41 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 207 ( 207 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 269 ( 44 ^; 197 !; 28 ?; 269 :)
% SPC : TH0_CSA_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(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(f,type,
f: ( a > $o ) > b > $o ).
thf(cA,type,
cA: ( a > $o ) > $o ).
thf(cB,type,
cB: ( b > $o ) > $o ).
thf(cDOMTHM5_pme,conjecture,
( ( ! [Xx: a > $o] :
( ( cA @ Xx )
=> ( cB @ ( f @ 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: a > $o] :
( ( ( cA @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( f @ Xx @ Xx0 ) ) )
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( ( ( cA @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( f @ Xx @ Xx0 ) ) )
=> ? [Xe0: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe0 @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe0 ) )
& ! [Xx0: a] :
( ( Xe0 @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cA @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( f @ Xy @ Xx0 ) ) ) ) ) ) ) ) )
<=> ( ! [Y: ( a > $o ) > $o] :
( ( ! [Xx: a > $o] :
( ( Y @ Xx )
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( ( Y @ Xx )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( Y @ Xy ) ) ) ) )
=> ! [Xx: a > $o] :
( ( Y @ Xx )
=> ( cA @ Xx ) ) )
& ! [Xx: a > $o] :
( ( cA @ Xx )
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( ( cA @ Xx )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( cA @ Xy ) ) ) )
& ! [Xx: a > $o] :
( $false
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( $false
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> $false ) ) )
& ! [K: ( ( a > $o ) > $o ) > $o] :
( ! [Xx: ( a > $o ) > $o] :
( ( K @ Xx )
=> ( ! [Xx0: a > $o] :
( ( Xx @ Xx0 )
=> ( cA @ Xx0 ) )
& ! [Xx0: a > $o] :
( ( Xx @ Xx0 )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx1: a > $o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx1: a] :
( ( Xe @ Xx1 )
=> ( Xx0 @ Xx1 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx1: a] :
( ( Xe @ Xx1 )
=> ( Xy @ Xx1 ) ) )
=> ( Xx @ Xy ) ) ) ) ) )
=> ( ! [Xx: a > $o] :
( ? [S: ( a > $o ) > $o] :
( ( K @ S )
& ( S @ Xx ) )
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( ? [S: ( a > $o ) > $o] :
( ( K @ S )
& ( S @ Xx ) )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ? [S: ( a > $o ) > $o] :
( ( K @ S )
& ( S @ Xy ) ) ) ) ) ) )
& ! [Y: ( a > $o ) > $o,Z: ( a > $o ) > $o] :
( ( ! [Xx: a > $o] :
( ( Y @ Xx )
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( ( Y @ Xx )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( Y @ Xy ) ) ) )
& ! [Xx: a > $o] :
( ( Z @ Xx )
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( ( Z @ Xx )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( Z @ Xy ) ) ) ) )
=> ( ! [Xx: a > $o] :
( ( ( Y @ Xx )
& ( Z @ Xx ) )
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( ( ( Y @ Xx )
& ( Z @ Xx ) )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( Y @ Xy )
& ( Z @ Xy ) ) ) ) ) ) )
& ! [Xx: a > $o] :
( ( cA @ Xx )
=> ! [Xy: a > $o] :
( ( cA @ Xy )
=> ( ! [Y: ( a > $o ) > $o] :
( ( ! [Xx0: a > $o] :
( ( Y @ Xx0 )
=> ( cA @ Xx0 ) )
& ! [Xx0: a > $o] :
( ( Y @ Xx0 )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy0: a] : $false )
& ! [Xx1: a > $o] :
( ( X @ Xx1 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx1: a] :
( ( Xe @ Xx1 )
=> ( Xx0 @ Xx1 ) )
& ! [Xy0: a > $o] :
( ( ( cA @ Xy0 )
& ! [Xx1: a] :
( ( Xe @ Xx1 )
=> ( Xy0 @ Xx1 ) ) )
=> ( Y @ Xy0 ) ) ) ) )
=> ( ( Y @ Xx )
<=> ( Y @ Xy ) ) )
=> ( Xx = Xy ) ) ) )
& ! [Y: ( b > $o ) > $o] :
( ( ! [Xx: b > $o] :
( ( Y @ Xx )
=> ( cB @ Xx ) )
& ! [Xx: b > $o] :
( ( Y @ Xx )
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx0: b > $o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( Y @ Xy ) ) ) ) )
=> ! [Xx: b > $o] :
( ( Y @ Xx )
=> ( cB @ Xx ) ) )
& ! [Xx: b > $o] :
( ( cB @ Xx )
=> ( cB @ Xx ) )
& ! [Xx: b > $o] :
( ( cB @ Xx )
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx0: b > $o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( cB @ Xy ) ) ) )
& ! [Xx: b > $o] :
( $false
=> ( cB @ Xx ) )
& ! [Xx: b > $o] :
( $false
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx0: b > $o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> $false ) ) )
& ! [K: ( ( b > $o ) > $o ) > $o] :
( ! [Xx: ( b > $o ) > $o] :
( ( K @ Xx )
=> ( ! [Xx0: b > $o] :
( ( Xx @ Xx0 )
=> ( cB @ Xx0 ) )
& ! [Xx0: b > $o] :
( ( Xx @ Xx0 )
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx1: b > $o] :
( ( X @ Xx1 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx1 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx1: b] :
( ( Xe @ Xx1 )
=> ( Xx0 @ Xx1 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx1: b] :
( ( Xe @ Xx1 )
=> ( Xy @ Xx1 ) ) )
=> ( Xx @ Xy ) ) ) ) ) )
=> ( ! [Xx: b > $o] :
( ? [S: ( b > $o ) > $o] :
( ( K @ S )
& ( S @ Xx ) )
=> ( cB @ Xx ) )
& ! [Xx: b > $o] :
( ? [S: ( b > $o ) > $o] :
( ( K @ S )
& ( S @ Xx ) )
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx0: b > $o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ? [S: ( b > $o ) > $o] :
( ( K @ S )
& ( S @ Xy ) ) ) ) ) ) )
& ! [Y: ( b > $o ) > $o,Z: ( b > $o ) > $o] :
( ( ! [Xx: b > $o] :
( ( Y @ Xx )
=> ( cB @ Xx ) )
& ! [Xx: b > $o] :
( ( Y @ Xx )
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx0: b > $o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( Y @ Xy ) ) ) )
& ! [Xx: b > $o] :
( ( Z @ Xx )
=> ( cB @ Xx ) )
& ! [Xx: b > $o] :
( ( Z @ Xx )
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx0: b > $o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( Z @ Xy ) ) ) ) )
=> ( ! [Xx: b > $o] :
( ( ( Y @ Xx )
& ( Z @ Xx ) )
=> ( cB @ Xx ) )
& ! [Xx: b > $o] :
( ( ( Y @ Xx )
& ( Z @ Xx ) )
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx0: b > $o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( Y @ Xy )
& ( Z @ Xy ) ) ) ) ) ) )
& ! [Xx: b > $o] :
( ( cB @ Xx )
=> ! [Xy: b > $o] :
( ( cB @ Xy )
=> ( ! [Y: ( b > $o ) > $o] :
( ( ! [Xx0: b > $o] :
( ( Y @ Xx0 )
=> ( cB @ Xx0 ) )
& ! [Xx0: b > $o] :
( ( Y @ Xx0 )
=> ? [Xe: b > $o] :
( ! [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 )
=> ( Xx0 @ Xx1 ) )
& ! [Xy0: b > $o] :
( ( ( cB @ Xy0 )
& ! [Xx1: b] :
( ( Xe @ Xx1 )
=> ( Xy0 @ Xx1 ) ) )
=> ( Y @ Xy0 ) ) ) ) )
=> ( ( Y @ Xx )
<=> ( Y @ Xy ) ) )
=> ( Xx = Xy ) ) ) )
& ! [Xx: a > $o] :
( ( cA @ Xx )
=> ( cB @ ( f @ Xx ) ) )
& ! [W: ( b > $o ) > $o] :
( ( ! [Xx: b > $o] :
( ( W @ Xx )
=> ( cB @ Xx ) )
& ! [Xx: b > $o] :
( ( W @ Xx )
=> ? [Xe: b > $o] :
( ! [X: ( b > $o ) > $o] :
( ( ( X
@ ^ [Xy: b] : $false )
& ! [Xx0: b > $o] :
( ( X @ Xx0 )
=> ! [Xt: b] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: b] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: b > $o] :
( ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( W @ Xy ) ) ) ) )
=> ( ! [Xx: a > $o] :
( ( W @ ( f @ Xx ) )
=> ( cA @ Xx ) )
& ! [Xx: a > $o] :
( ( W @ ( f @ Xx ) )
=> ? [Xe: a > $o] :
( ! [X: ( a > $o ) > $o] :
( ( ( X
@ ^ [Xy: a] : $false )
& ! [Xx0: a > $o] :
( ( X @ Xx0 )
=> ! [Xt: a] :
( ( Xe @ Xt )
=> ( X
@ ^ [Xz: a] :
( ( Xx0 @ Xz )
| ( Xt = Xz ) ) ) ) ) )
=> ( X @ Xe ) )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xx @ Xx0 ) )
& ! [Xy: a > $o] :
( ( ( cA @ Xy )
& ! [Xx0: a] :
( ( Xe @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( W @ ( f @ Xy ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------