TPTP Problem File: SEV226^5.p
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% File : SEV226^5 : TPTP v9.0.0. Released v4.0.0.
% Domain : Set Theory (Sets of sets)
% Problem : TPS problem from REALS-THMS
% Version : Especial.
% English :
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_1194 [Bro09]
% Status : CounterSatisfiable
% Rating : 0.67 v9.0.0, 1.00 v8.1.0, 0.60 v7.4.0, 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v5.4.0, 1.00 v5.0.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% Number of atoms : 32 ( 5 equ; 0 cnn)
% Maximal formula atoms : 32 ( 32 avg)
% Number of connectives : 104 ( 3 ~; 6 |; 18 &; 66 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 17 !; 6 ?; 23 :)
% 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/
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thf(c_less_,type,
c_less_: $i > $i > $o ).
thf(b,type,
b: $i ).
thf(a,type,
a: $i ).
thf(cBLEDSOE_FENG_SV_IMV_SOL_2_pme,conjecture,
! [Xf: $i > $i,X0: $i] :
( ( ! [A: $i > $o] :
( ( ? [Xl: $i] : ( A @ Xl )
& ? [Xu: $i] :
! [Xx: $i] :
( ( A @ Xx )
=> ( ( c_less_ @ Xx @ Xu )
| ( Xx = Xu ) ) ) )
=> ? [Xl: $i] :
( ! [Xx: $i] :
( ( A @ Xx )
=> ( ( c_less_ @ Xx @ Xl )
| ( Xx = Xl ) ) )
& ! [Xy: $i] :
( ! [Xx: $i] :
( ( A @ Xx )
=> ( ( c_less_ @ Xx @ Xy )
| ( Xx = Xy ) ) )
=> ( ( c_less_ @ Xl @ Xy )
| ( Xl = Xy ) ) ) ) )
& ! [Xx: $i] :
( ( c_less_ @ X0 @ ( Xf @ Xx ) )
=> ? [Xt: $i] :
( ( c_less_ @ Xt @ Xx )
& ! [Xs: $i] :
( ( ( c_less_ @ Xt @ Xs )
& ( c_less_ @ Xs @ Xx ) )
=> ( c_less_ @ X0 @ ( Xf @ Xs ) ) ) ) )
& ! [Xx: $i] :
( ( c_less_ @ ( Xf @ Xx ) @ X0 )
=> ? [Xt: $i] :
( ( c_less_ @ Xx @ Xt )
& ! [Xs: $i] :
( ( ( c_less_ @ Xs @ Xt )
& ( c_less_ @ Xx @ Xs ) )
=> ( c_less_ @ ( Xf @ Xs ) @ X0 ) ) ) )
& ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( c_less_ @ Xx @ Xy )
& ( c_less_ @ Xy @ Xz ) )
=> ( c_less_ @ Xx @ Xz ) )
& ! [Xx: $i] :
~ ( c_less_ @ Xx @ Xx )
& ! [Xx: $i,Xy: $i] :
( ( c_less_ @ Xx @ Xy )
| ( c_less_ @ Xy @ Xx )
| ( Xx = Xy ) )
& ( c_less_ @ a @ b )
& ( c_less_ @ ( Xf @ a ) @ X0 )
& ( c_less_ @ X0 @ ( Xf @ b ) ) )
=> ? [Xx: $i] :
( ( c_less_ @ a @ Xx )
& ( c_less_ @ Xx @ b )
& ~ ( c_less_ @ ( Xf @ Xx ) @ X0 )
& ~ ( c_less_ @ X0 @ ( Xf @ Xx ) ) ) ) ).
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