TPTP Problem File: SEV211^5.p
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% File : SEV211^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem from S-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1223 [Bro09]
% Status : Unknown
% Rating : 1.00 v4.0.0
% Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% Number of atoms : 29 ( 26 equ; 0 cnn)
% Maximal formula atoms : 29 ( 29 avg)
% Number of connectives : 117 ( 1 ~; 6 |; 28 &; 71 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 29 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 22 !; 20 ?; 42 :)
% 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(y,type,
y: a ).
thf(cP,type,
cP: a > a > a ).
thf(cZ,type,
cZ: a ).
thf(x,type,
x: a ).
thf(z,type,
z: a ).
thf(cS_LEM1F_pme,conjecture,
( ( ! [Xx0: a,Xy0: a] :
( ( cP @ Xx0 @ Xy0 )
!= cZ )
& ! [Xx0: a,Xy0: a,Xu: a,Xv: a] :
( ( ( cP @ Xx0 @ Xu )
= ( cP @ Xy0 @ Xv ) )
=> ( ( Xx0 = Xy0 )
& ( Xu = Xv ) ) )
& ! [X: a > $o] :
( ( ( X @ cZ )
& ! [Xx0: a,Xy0: a] :
( ( ( X @ Xx0 )
& ( X @ Xy0 ) )
=> ( X @ ( cP @ Xx0 @ Xy0 ) ) ) )
=> ! [Xx0: a] : ( X @ Xx0 ) ) )
=> ( ! [R: a > a > a > $o] :
( ( $true
& ! [Xa: a,Xb: a,Xc: a] :
( ( ( ( Xa = cZ )
& ( Xb = Xc ) )
| ( ( Xb = cZ )
& ( Xa = Xc ) )
| ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ ( cP @ x @ y ) @ z @ z ) )
=> ? [Xu: a,Xv: a] :
( ( z
= ( cP @ Xu @ Xv ) )
& ! [R: a > a > a > $o] :
( ( $true
& ! [Xa: a,Xb: a,Xc: a] :
( ( ( ( Xa = cZ )
& ( Xb = Xc ) )
| ( ( Xb = cZ )
& ( Xa = Xc ) )
| ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ x @ Xu @ Xu ) )
& ! [R: a > a > a > $o] :
( ( $true
& ! [Xa: a,Xb: a,Xc: a] :
( ( ( ( Xa = cZ )
& ( Xb = Xc ) )
| ( ( Xb = cZ )
& ( Xa = Xc ) )
| ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R @ Xa @ Xb @ Xc ) ) )
=> ( R @ y @ Xv @ Xv ) ) ) ) ) ).
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