%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB073+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:47 AM UTC 2025
% Result : Theorem 0.59s 0.75s
% Output : Proof 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 37
% Syntax : Number of formulae : 84 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 747 ( 0 equ)
% Maximal formula atoms : 40 ( 8 avg)
% Number of connectives : 1354 ( 709 ~; 528 |; 49 &)
% ( 62 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 251 ( 234 !; 0 ?; 251 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(tptp_fun_Y_62_type,type,
tptp_fun_Y_62: ( $i * $i ) > $i ).
tff(uri_owl_bottomDataProperty_type,type,
uri_owl_bottomDataProperty: $i ).
tff(uri_ex_p_type,type,
uri_ex_p: $i ).
tff(tptp_fun_X_63_type,type,
tptp_fun_X_63: ( $i * $i ) > $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(uri_rdfs_subPropertyOf_type,type,
uri_rdfs_subPropertyOf: $i ).
tff(iodp_type,type,
iodp: $i > $o ).
tff(uri_owl_DatatypeProperty_type,type,
uri_owl_DatatypeProperty: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(1,plain,
^ [P1: $i,P2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [P1: $i,P2: $i] :
refl(( ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [P1: $i,P2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [P1: $i,P2: $i] :
trans(monotonicity(rewrite(( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )),
rewrite(( ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
<=> ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )),
( ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
rewrite(( ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
( ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [P1: $i,P2: $i] :
rewrite(( ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
<=> ! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [P1: $i,P2: $i] :
rewrite(( ( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
=> iext(P2,X,Y) ) ) )
<=> ( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
=> iext(P2,X,Y) ) ) )
<=> ! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
=> iext(P2,X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subpropertyof) ).
tff(16,plain,
! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) )
<=> ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) )
<=> ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) )
<=> ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_bottomDataProperty,X,Y)
| iext(uri_ex_p,X,Y) ) ) )
| iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( iodp(uri_owl_bottomDataProperty)
<=> iodp(uri_owl_bottomDataProperty) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
iodp(uri_owl_bottomDataProperty),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_bottomdataproperty_type) ).
tff(34,plain,
iodp(uri_owl_bottomDataProperty),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
^ [X: $i] :
refl(( ( ip(X)
| ~ iodp(X) )
<=> ( ip(X)
| ~ iodp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i] :
( ip(X)
| ~ iodp(X) )
<=> ! [X: $i] :
( ip(X)
| ~ iodp(X) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [X: $i] :
( ip(X)
| ~ iodp(X) )
<=> ! [X: $i] :
( ip(X)
| ~ iodp(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [X: $i] :
rewrite(( ( iodp(X)
=> ip(X) )
<=> ( ip(X)
| ~ iodp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] :
( iodp(X)
=> ip(X) )
<=> ! [X: $i] :
( ip(X)
| ~ iodp(X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [X: $i] :
( iodp(X)
=> ip(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_parts_iodp_cond_set) ).
tff(41,plain,
! [X: $i] :
( ip(X)
| ~ iodp(X) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X: $i] :
( ip(X)
| ~ iodp(X) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [X: $i] :
( ip(X)
| ~ iodp(X) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] :
( ip(X)
| ~ iodp(X) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_owl_bottomDataProperty)
| ~ iodp(uri_owl_bottomDataProperty) )
<=> ( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_owl_bottomDataProperty)
| ~ iodp(uri_owl_bottomDataProperty) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_owl_bottomDataProperty)
| ~ iodp(uri_owl_bottomDataProperty) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_owl_bottomDataProperty)
| ~ iodp(uri_owl_bottomDataProperty) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
ip(uri_owl_bottomDataProperty),
inference(unit_resolution,[status(thm)],[47,44,34]) ).
tff(49,plain,
^ [X: $i] :
refl(( ( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) )
<=> ( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) )
<=> ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) )
<=> ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_parts_iodp_def) ).
tff(53,plain,
! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) )
| ( iodp(uri_ex_p)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( iodp(uri_ex_p)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_prop_bottomdataproperty_term) ).
tff(60,plain,
iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ( iodp(uri_ex_p)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) )
| iodp(uri_ex_p)
| ~ iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) ),
inference(tautology,[status(thm)],[]) ).
tff(62,plain,
( ~ ( iodp(uri_ex_p)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) )
| iodp(uri_ex_p) ),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
iodp(uri_ex_p),
inference(unit_resolution,[status(thm)],[62,57]) ).
tff(64,plain,
( ( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_ex_p)
| ~ iodp(uri_ex_p) )
<=> ( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_ex_p)
| ~ iodp(uri_ex_p) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_ex_p)
| ~ iodp(uri_ex_p) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_ex_p)
| ~ iodp(uri_ex_p) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
ip(uri_ex_p),
inference(unit_resolution,[status(thm)],[66,44,63]) ).
tff(68,plain,
( ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
<=> ~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_prop_bottomdataproperty_term) ).
tff(70,plain,
~ iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(72,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_bottomDataProperty,uri_ex_p)
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) )
| ~ ip(uri_owl_bottomDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ) ),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
~ ( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ),
inference(unit_resolution,[status(thm)],[72,67,48,31]) ).
tff(74,plain,
( ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_ex_p,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty))
| iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ),
inference(tautology,[status(thm)],[]) ).
tff(75,plain,
iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
^ [X: $i,Y: $i] :
refl(( ~ iext(uri_owl_bottomDataProperty,X,Y)
<=> ~ iext(uri_owl_bottomDataProperty,X,Y) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y)
<=> ! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y)
<=> ! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_bottomdataproperty_ext) ).
tff(80,plain,
! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [X: $i,Y: $i] : ~ iext(uri_owl_bottomDataProperty,X,Y)
| ~ iext(uri_owl_bottomDataProperty,tptp_fun_X_63(uri_ex_p,uri_owl_bottomDataProperty),tptp_fun_Y_62(uri_ex_p,uri_owl_bottomDataProperty)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
$false,
inference(unit_resolution,[status(thm)],[83,82,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWB073+1 : TPTP v9.0.0. Released v5.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:56:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.59/0.75 % SZS status Theorem
% 0.59/0.75 % SZS output start Proof
% See solution above
% 0.59/0.79 % E exiting
%------------------------------------------------------------------------------