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% COMMAND-LINE: --uf-ho --finite-model-find
% EXPECT: % SZS status GaveUp for soundness_fmf_SYO362^5-delta
%------------------------------------------------------------------------------
% File : SYO362^5 : TPTP v7.2.0. Released v4.0.0.
% Domain : Syntactic
% Problem : TPS problem THM631A
% Version : Especial.
% English : If a set function preserves unions, then it is monotone.
% Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source : [Bro09]
% Names : tps_0419 [Bro09]
% : THM631 [TPS]
% : THM631A [TPS]
% Status : Theorem
% Rating : 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0, 1.00 v4.0.0
% Syntax : Number of formulae : 2 ( 0 unit; 1 type; 0 defn)
% Number of atoms : 22 ( 1 equality; 16 variable)
% Maximal formula depth : 9 ( 6 average)
% Number of connectives : 19 ( 0 ~; 2 |; 0 &; 13 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% ( 0 ~|; 0 ~&)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 :; 0 =)
% Number of variables : 8 ( 0 sgn; 6 !; 0 ?; 2 ^)
% ( 8 :; 0 !>; 0 ?*)
% ( 0 @-; 0 @+)
% 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/
% : Polymorphic definitions expanded.
% :
%------------------------------------------------------------------------------
thf(cK,type,(
cK: ( $i > $o ) > $i > $o )).
thf(cTHM631A_pme,conjecture,
( ! [X: $i > $o,Y: $i > $o] :
( ( cK
@ ^ [Xz: $i] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xw: $i] :
( ( cK @ X @ Xw )
| ( cK @ Y @ Xw ) ) ) )
=> ! [X: $i > $o,Y: $i > $o] :
( ! [Xx: $i] :
( ( X @ Xx )
=> ( Y @ Xx ) )
=> ! [Xx: $i] :
( ( cK @ X @ Xx )
=> ( cK @ Y @ Xx ) ) ) )).
%------------------------------------------------------------------------------
%% soundness issue (since resolved) was due to wrong lambda
%% lifting. Free variables in lambda body not being carried out to
%% quantified formula standing for lambda lifting
|
