TPTP Problem File: SEV217^5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SEV217^5 : TPTP v8.2.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem from S-T-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1257 [Bro09]
% Status : Unknown
% Rating : 1.00 v4.0.0
% Syntax : Number of formulae : 9 ( 0 unt; 8 typ; 0 def)
% Number of atoms : 97 ( 78 equ; 0 cnn)
% Maximal formula atoms : 97 ( 97 avg)
% Number of connectives : 445 ( 2 ~; 24 |; 111 &; 274 @)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 39 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 139 ( 0 ^; 75 !; 64 ?; 139 :)
% 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(c_type,type,
c: $tType ).
thf(iS_type,type,
iS: $tType ).
thf(cR,type,
cR: c > c ).
thf(cL,type,
cL: c > c ).
thf(cP,type,
cP: iS > iS > iS ).
thf(cX1,type,
cX1: c > $o ).
thf(c0,type,
c0: iS ).
thf(cX0,type,
cX0: c > $o ).
thf(cS_T_DUC_MONOTONE_LEM_pme,conjecture,
( ( ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 )
& ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xx = Xy )
& ( Xu = Xv ) ) )
& ! [X: iS > $o] :
( ( ( X @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( X @ Xx )
& ( X @ Xy ) )
=> ( X @ ( cP @ Xx @ Xy ) ) ) )
=> ! [Xx: iS] : ( X @ Xx ) )
& ! [Xz: c] :
( ( cX0 @ Xz )
<=> ~ ( cX1 @ Xz ) )
& ! [Xz: c] :
( ( cX0 @ Xz )
=> ( ( ( cL @ Xz )
= Xz )
& ( ( cR @ Xz )
= Xz ) ) ) )
=> ( ! [R0: c > iS > $o] :
( ! [Xc: c] :
( ( R0 @ Xc @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( R0 @ Xc @ Xy )
& ! [R1: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xy ) ) )
=> ( R0 @ Xc @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( R0 @ Xc @ Xx )
& ( R0 @ Xc @ Xy )
& ! [R1: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xz ) ) )
=> ( R0 @ Xc @ Xz ) ) )
=> ! [Xc: c] :
( ( ( c0 = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( c0
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) )
& ! [Xx: iS,Xy: iS] :
( ( ( ( Xy = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xy
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) )
& ! [R1: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xy ) ) )
=> ( ( Xx = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xx
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( ( Xx = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xx
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) )
& ( ( Xy = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xy
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) )
& ! [R1: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xz ) ) )
=> ( ( Xz = c0 )
| ( ( cX1 @ Xc )
& ? [Xu1: iS,Xu2: iS] :
( ( Xz
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xc ) @ Xu1 )
& ( R0 @ ( cR @ Xc ) @ Xu2 ) ) ) ) ) ) )
& ! [R0: c > iS > $o,S: c > iS > $o] :
( ( ! [Xc: c] :
( ( R0 @ Xc @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( R0 @ Xc @ Xy )
& ! [R1: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xy ) ) )
=> ( R0 @ Xc @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( R0 @ Xc @ Xx )
& ( R0 @ Xc @ Xy )
& ! [R1: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xz ) ) )
=> ( R0 @ Xc @ Xz ) ) )
& ! [Xc: c] :
( ( S @ Xc @ c0 )
& ! [Xx: iS,Xy: iS] :
( ( ( S @ Xc @ Xy )
& ! [R1: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xy ) ) )
=> ( S @ Xc @ Xx ) )
& ! [Xx: iS,Xy: iS,Xz: iS] :
( ( ( S @ Xc @ Xx )
& ( S @ Xc @ Xy )
& ! [R1: iS > iS > iS > $o] :
( ( $true
& ! [Xa: iS,Xb: iS,Xc0: iS] :
( ( ( ( Xa = c0 )
& ( Xb = Xc0 ) )
| ( ( Xb = c0 )
& ( Xa = Xc0 ) )
| ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc0
= ( cP @ Xz1 @ Xz2 ) )
& ( R1 @ Xx1 @ Xy1 @ Xz1 )
& ( R1 @ Xx2 @ Xy2 @ Xz2 ) ) )
=> ( R1 @ Xa @ Xb @ Xc0 ) ) )
=> ( R1 @ Xx @ Xy @ Xz ) ) )
=> ( S @ Xc @ Xz ) ) )
& ! [Xa: c,Xb: iS] :
( ( R0 @ Xa @ Xb )
=> ( S @ Xa @ Xb ) ) )
=> ! [Xa: c,Xb: iS] :
( ( ( Xb = c0 )
| ( ( cX1 @ Xa )
& ? [Xu1: iS,Xu2: iS] :
( ( Xb
= ( cP @ Xu1 @ Xu2 ) )
& ( R0 @ ( cL @ Xa ) @ Xu1 )
& ( R0 @ ( cR @ Xa ) @ Xu2 ) ) ) )
=> ( ( Xb = c0 )
| ( ( cX1 @ Xa )
& ? [Xu1: iS,Xu2: iS] :
( ( Xb
= ( cP @ Xu1 @ Xu2 ) )
& ( S @ ( cL @ Xa ) @ Xu1 )
& ( S @ ( cR @ Xa ) @ Xu2 ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------