TPTP Problem File: SEV183^5.p
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% File : SEV183^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem from SET-TOP-ACS-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1240 [Bro09]
% Status : Theorem
% Rating : 1.00 v6.2.0, 0.86 v6.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% Number of atoms : 37 ( 5 equ; 0 cnn)
% Maximal formula atoms : 36 ( 37 avg)
% Number of connectives : 172 ( 0 ~; 4 |; 32 &; 92 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 24 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 10 ^; 45 !; 8 ?; 63 :)
% 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(f,type,
f: ( a > $o ) > b > $o ).
thf(cA,type,
cA: ( a > $o ) > $o ).
thf(cB,type,
cB: ( a > $o ) > $o ).
thf(cC,type,
cC: ( b > $o ) > $o ).
thf(cDOMTHM7_pme,conjecture,
( ( ! [Xx: a > $o] :
( ( cA @ Xx )
=> ( cB @ Xx ) )
& ! [X: ( b > $o ) > $o] :
( ! [Xx: b > $o] :
( ( X @ Xx )
=> ( cC @ Xx ) )
=> ( cC
@ ^ [Xx: b] :
! [S: b > $o] :
( ( X @ S )
=> ( S @ Xx ) ) ) )
& ! [D: ( b > $o ) > $o] :
( ( ! [Xx: b > $o] :
( ( D @ Xx )
=> ( cC @ Xx ) )
& ? [Xy: b > $o] : ( D @ Xy )
& ! [Xy: b > $o,Xz: b > $o] :
? [Xw: b > $o] :
( ! [Xx: b] :
( ( Xy @ Xx )
=> ( Xw @ Xx ) )
& ! [Xx: b] :
( ( Xz @ Xx )
=> ( Xw @ Xx ) ) ) )
=> ( cC
@ ^ [Xx: b] :
? [S: b > $o] :
( ( D @ S )
& ( S @ Xx ) ) ) )
& ! [Xx: a > $o] :
( ( cA @ Xx )
=> ( cC @ ( 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] :
( ( cC @ 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 ) ) ) ) ) ) ) ) )
=> ? [Xg: ( a > $o ) > b > $o] :
( ! [Xx: a > $o] :
( ( cB @ Xx )
=> ( cC @ ( Xg @ 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] :
( ( cC @ S )
& ( S @ Xx ) ) ) )
=> ( ! [Xx: a > $o] :
( ( ( cB @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xg @ Xx @ Xx0 ) ) )
=> ( cB @ Xx ) )
& ! [Xx: a > $o] :
( ( ( cB @ Xx )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xg @ 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] :
( ( ( cB @ Xy )
& ! [Xx0: a] :
( ( Xe0 @ Xx0 )
=> ( Xy @ Xx0 ) ) )
=> ( ( cB @ Xy )
& ! [Xx0: b] :
( ( Xe @ Xx0 )
=> ( Xg @ Xy @ Xx0 ) ) ) ) ) ) ) )
& ! [Xx: a > $o] :
( ( cA @ Xx )
=> ( ( f @ Xx )
= ( Xg @ Xx ) ) ) ) ) ).
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