%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB047+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:29:45 AM UTC 2025
% Result : Theorem 0.56s 0.76s
% Output : Proof 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 68
% Syntax : Number of formulae : 167 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 2019 ( 272 equ)
% Maximal formula atoms : 40 ( 12 avg)
% Number of connectives : 3644 (1856 ~;1353 |; 184 &)
% ( 242 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 64 ( 64 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 732 ( 700 !; 0 ?; 732 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(tptp_fun_X2_115_type,type,
tptp_fun_X2_115: $i > $i ).
tff(uri_ex_p2_type,type,
uri_ex_p2: $i ).
tff(tptp_fun_Y_114_type,type,
tptp_fun_Y_114: $i > $i ).
tff(uri_ex_p1_type,type,
uri_ex_p1: $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(uri_owl_inverseOf_type,type,
uri_owl_inverseOf: $i ).
tff(tptp_fun_X_108_type,type,
tptp_fun_X_108: ( $i * $i ) > $i ).
tff(tptp_fun_Y_107_type,type,
tptp_fun_Y_107: ( $i * $i ) > $i ).
tff(uri_owl_FunctionalProperty_type,type,
uri_owl_FunctionalProperty: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(tptp_fun_X1_116_type,type,
tptp_fun_X1_116: $i > $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(uri_owl_InverseFunctionalProperty_type,type,
uri_owl_InverseFunctionalProperty: $i ).
tff(tptp_fun_Y2_111_type,type,
tptp_fun_Y2_111: $i > $i ).
tff(tptp_fun_Y1_112_type,type,
tptp_fun_Y1_112: $i > $i ).
tff(tptp_fun_X_113_type,type,
tptp_fun_X_113: $i > $i ).
tff(1,plain,
^ [P1: $i,P2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ~ ( ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [P1: $i,P2: $i] :
refl(( ~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [P1: $i,P2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [P1: $i,P2: $i] :
trans(monotonicity(rewrite(( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
<=> ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) )),
trans(monotonicity(rewrite(( ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) )
<=> ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) )),
( ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) )
<=> ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )),
rewrite(( ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) )
<=> ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )),
( ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) )
<=> ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )),
( ( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) )),
rewrite(( ( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) )),
( ( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [P1: $i,P2: $i] :
rewrite(( ( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
<=> ! [P1: $i,P2: $i] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [P1: $i,P2: $i] :
rewrite(( ( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
<=> ( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
<=> ! [P1: $i,P2: $i] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [P1: $i,P2: $i] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_inv) ).
tff(16,plain,
! [P1: $i,P2: $i] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [P1: $i,P2: $i] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
& ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) )
| ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_inverseOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_108(P2,P1),tptp_fun_Y_107(P2,P1))
<=> iext(P2,tptp_fun_Y_107(P2,P1),tptp_fun_X_108(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_inverseOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ( iext(uri_ex_p2,tptp_fun_X_108(uri_ex_p1,uri_ex_p2),tptp_fun_Y_107(uri_ex_p1,uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_107(uri_ex_p1,uri_ex_p2),tptp_fun_X_108(uri_ex_p1,uri_ex_p2)) ) )
| ~ ( ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
~ ( ~ ( iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ( iext(uri_ex_p2,tptp_fun_X_108(uri_ex_p1,uri_ex_p2),tptp_fun_Y_107(uri_ex_p1,uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_107(uri_ex_p1,uri_ex_p2),tptp_fun_X_108(uri_ex_p1,uri_ex_p2)) ) )
| ~ ( ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ( iext(uri_ex_p2,tptp_fun_X_108(uri_ex_p1,uri_ex_p2),tptp_fun_Y_107(uri_ex_p1,uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_107(uri_ex_p1,uri_ex_p2),tptp_fun_X_108(uri_ex_p1,uri_ex_p2)) ) )
| ~ ( ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) )
| ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(26,plain,
( ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
<=> iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
( iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
& iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_rdfbased_sem_char_inversefunc_term) ).
tff(29,plain,
iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1),
inference(modus_ponens,[status(thm)],[29,27]) ).
tff(31,plain,
( ~ ( ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) )
| ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(32,plain,
( ~ ( ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) )
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ) ),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ),
inference(unit_resolution,[status(thm)],[32,26]) ).
tff(34,plain,
( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) )
| ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ) ),
inference(tautology,[status(thm)],[]) ).
tff(35,plain,
! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) ),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
( ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) )
| ( iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
^ [P: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )
<=> ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )
<=> ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
^ [P: $i] :
refl(( ~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
^ [P: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
^ [P: $i] :
trans(monotonicity(rewrite(( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
<=> ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )),
trans(monotonicity(rewrite(( ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) )
<=> ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )),
( ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) )
<=> ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )),
rewrite(( ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
<=> ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )),
( ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) )
<=> ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )),
( ( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) )
<=> ( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) )),
rewrite(( ( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) )),
( ( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [P: $i] :
( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
^ [P: $i] :
rewrite(( ( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) )
<=> ( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [P: $i] :
( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) )
<=> ! [P: $i] :
( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [P: $i] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
<=> ! [P: $i] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
^ [P: $i] :
rewrite(( ( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ( iext(P,X1,Y)
& iext(P,X2,Y) )
=> ( X1 = X2 ) ) ) )
<=> ( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [P: $i] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ( iext(P,X1,Y)
& iext(P,X2,Y) )
=> ( X1 = X2 ) ) ) )
<=> ! [P: $i] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [P: $i] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ( iext(P,X1,Y)
& iext(P,X2,Y) )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_char_inversefunctional) ).
tff(53,plain,
! [P: $i] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [P: $i] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [P: $i] :
( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [P: $i] :
( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ( ip(P)
& ! [X1: $i,X2: $i,Y: $i] :
( ~ ( iext(P,X1,Y)
& iext(P,X2,Y) )
| ( X1 = X2 ) ) ) )
& ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
& iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) )
| ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) ) ) ) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ),
inference(modus_ponens,[status(thm)],[56,46]) ).
tff(58,plain,
! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) )
| ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) ) ),
inference(modus_ponens,[status(thm)],[57,44]) ).
tff(59,plain,
! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[58,39]) ).
tff(60,plain,
( ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )
| ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) )
<=> ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )
| ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) )
<=> ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )
| ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) )
<=> ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )
| ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )
| ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) )
<=> ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )
| ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )
| ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_X1_116(P) = tptp_fun_X2_115(P) )
| ~ iext(P,tptp_fun_X1_116(P),tptp_fun_Y_114(P))
| ~ iext(P,tptp_fun_X2_115(P),tptp_fun_Y_114(P)) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(P,X2,Y)
| ~ iext(P,X1,Y) ) ) ) )
| ~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
~ ( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[65,59]) ).
tff(67,plain,
( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ! [X1: $i,X2: $i,Y: $i] :
( ( X1 = X2 )
| ~ iext(uri_ex_p2,X2,Y)
| ~ iext(uri_ex_p2,X1,Y) ) ) )
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(68,plain,
( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
<=> ( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) )
<=> ( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
^ [X: $i,Y: $i] :
rewrite(( ( iext(uri_owl_inverseOf,X,Y)
=> ( ip(X)
& ip(Y) ) )
<=> ( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_inverseOf,X,Y)
=> ( ip(X)
& ip(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_inverseOf,X,Y)
=> ( ip(X)
& ip(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_prop_inverseof_ext) ).
tff(77,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ),
inference(modus_ponens,[status(thm)],[80,70]) ).
tff(82,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
| ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
| ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
| ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
| ~ iext(uri_owl_inverseOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2) ),
inference(unit_resolution,[status(thm)],[84,81,30]) ).
tff(86,plain,
( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ip(uri_ex_p2) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
ip(uri_ex_p2),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
^ [X: $i,C: $i] :
refl(( ( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).
tff(92,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty)
<=> icext(uri_owl_InverseFunctionalProperty,uri_ex_p2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty)
<=> icext(uri_owl_InverseFunctionalProperty,uri_ex_p2) ),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
( ~ iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty)
<=> ~ iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
~ iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_rdfbased_sem_char_inversefunc_term) ).
tff(99,plain,
~ iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ ( iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty)
<=> icext(uri_owl_InverseFunctionalProperty,uri_ex_p2) )
| iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty)
| ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2) ),
inference(tautology,[status(thm)],[]) ).
tff(101,plain,
( ~ ( iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty)
<=> icext(uri_owl_InverseFunctionalProperty,uri_ex_p2) )
| ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2) ),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2),
inference(unit_resolution,[status(thm)],[101,96]) ).
tff(103,plain,
( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
( ~ ( icext(uri_owl_InverseFunctionalProperty,uri_ex_p2)
| ~ ip(uri_ex_p2)
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) )
| ~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ) ),
inference(unit_resolution,[status(thm)],[103,102,87]) ).
tff(105,plain,
~ ( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) ) ),
inference(unit_resolution,[status(thm)],[104,68]) ).
tff(106,plain,
( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)) ),
inference(tautology,[status(thm)],[]) ).
tff(107,plain,
iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ ( iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) )
| ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) ),
inference(tautology,[status(thm)],[]) ).
tff(109,plain,
( ~ ( iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) )
| iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) ),
inference(unit_resolution,[status(thm)],[108,107]) ).
tff(110,plain,
iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)),
inference(unit_resolution,[status(thm)],[109,37]) ).
tff(111,plain,
( ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p2,X,Y)
<=> iext(uri_ex_p1,Y,X) )
| ( iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ),
inference(unit_resolution,[status(thm)],[111,35]) ).
tff(113,plain,
( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)) ),
inference(tautology,[status(thm)],[]) ).
tff(114,plain,
iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)),
inference(unit_resolution,[status(thm)],[113,105]) ).
tff(115,plain,
( ~ ( iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) )
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ),
inference(tautology,[status(thm)],[]) ).
tff(116,plain,
( ~ ( iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
<=> iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) )
| iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)),
inference(unit_resolution,[status(thm)],[116,112]) ).
tff(118,plain,
^ [P: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )
<=> ~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )
<=> ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
^ [P: $i] :
refl(( ~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [P: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
tff(125,plain,
^ [P: $i] :
trans(monotonicity(rewrite(( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
<=> ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )),
trans(monotonicity(rewrite(( ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) )
<=> ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )),
( ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) )
<=> ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )),
rewrite(( ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
<=> ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )),
( ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) )
<=> ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )),
( ( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) )
<=> ( ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) )),
rewrite(( ( ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) )),
( ( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [P: $i] :
( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
^ [P: $i] :
rewrite(( ( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) )
<=> ( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [P: $i] :
( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) )
<=> ! [P: $i] :
( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,plain,
( ! [P: $i] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
<=> ! [P: $i] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,plain,
^ [P: $i] :
rewrite(( ( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& iext(P,X,Y2) )
=> ( Y1 = Y2 ) ) ) )
<=> ( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [P: $i] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& iext(P,X,Y2) )
=> ( Y1 = Y2 ) ) ) )
<=> ! [P: $i] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,axiom,
! [P: $i] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& iext(P,X,Y2) )
=> ( Y1 = Y2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_char_functional) ).
tff(133,plain,
! [P: $i] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [P: $i] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
! [P: $i] :
( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [P: $i] :
( ( ~ icext(uri_owl_FunctionalProperty,P)
| ( ip(P)
& ! [X: $i,Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& iext(P,X,Y2) )
| ( Y1 = Y2 ) ) ) )
& ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ~ ( iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
& iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) )
| ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) ) ) ) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ),
inference(modus_ponens,[status(thm)],[136,126]) ).
tff(138,plain,
! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) )
| ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) ) ),
inference(modus_ponens,[status(thm)],[137,124]) ).
tff(139,plain,
! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) ),
inference(modus_ponens,[status(thm)],[138,119]) ).
tff(140,plain,
( ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ ( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) ) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) )
<=> ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ ( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) ) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ~ ( ~ ( icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ip(uri_ex_p1)
| ~ ( ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) )
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) )
<=> ~ ( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) ) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ ( ~ ( icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ip(uri_ex_p1)
| ~ ( ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) )
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) )
<=> ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ ( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) ) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ ( ~ ( icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ip(uri_ex_p1)
| ~ ( ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) )
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) )
<=> ( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ ( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) ) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ ( ~ ( icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ip(uri_ex_p1)
| ~ ( ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) )
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_FunctionalProperty,P)
| ~ ip(P)
| ~ ( ( tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P) )
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y1_112(P))
| ~ iext(P,tptp_fun_X_113(P),tptp_fun_Y2_111(P)) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(P,X,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ ( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) ) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
~ ( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) ) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ) ),
inference(unit_resolution,[status(thm)],[145,139]) ).
tff(147,plain,
( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y2_111(uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_113(uri_ex_p1),tptp_fun_Y1_112(uri_ex_p1))
| ( tptp_fun_Y1_112(uri_ex_p1) = tptp_fun_Y2_111(uri_ex_p1) ) ) )
| ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) )
| ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(148,plain,
( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ),
inference(unit_resolution,[status(thm)],[147,146]) ).
tff(149,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty)
<=> icext(uri_owl_FunctionalProperty,uri_ex_p1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
( iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty)
<=> icext(uri_owl_FunctionalProperty,uri_ex_p1) ),
inference(unit_resolution,[status(thm)],[149,94]) ).
tff(151,plain,
( iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty)
<=> iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty),
inference(and_elim,[status(thm)],[28]) ).
tff(153,plain,
iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( ~ ( iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty)
<=> icext(uri_owl_FunctionalProperty,uri_ex_p1) )
| ~ iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty)
| icext(uri_owl_FunctionalProperty,uri_ex_p1) ),
inference(tautology,[status(thm)],[]) ).
tff(155,plain,
( ~ ( iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty)
<=> icext(uri_owl_FunctionalProperty,uri_ex_p1) )
| icext(uri_owl_FunctionalProperty,uri_ex_p1) ),
inference(unit_resolution,[status(thm)],[154,153]) ).
tff(156,plain,
icext(uri_owl_FunctionalProperty,uri_ex_p1),
inference(unit_resolution,[status(thm)],[155,150]) ).
tff(157,plain,
( ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) )
| ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(158,plain,
( ~ ( ~ icext(uri_owl_FunctionalProperty,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) )
| ~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ) ),
inference(unit_resolution,[status(thm)],[157,156]) ).
tff(159,plain,
~ ( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ),
inference(unit_resolution,[status(thm)],[158,148]) ).
tff(160,plain,
( ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) )
| ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) ),
inference(tautology,[status(thm)],[]) ).
tff(161,plain,
! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ),
inference(unit_resolution,[status(thm)],[160,159]) ).
tff(162,plain,
( ~ iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2))
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ( tptp_fun_X1_116(uri_ex_p2) != tptp_fun_X2_115(uri_ex_p2) ) ),
inference(tautology,[status(thm)],[]) ).
tff(163,plain,
tptp_fun_X1_116(uri_ex_p2) != tptp_fun_X2_115(uri_ex_p2),
inference(unit_resolution,[status(thm)],[162,105]) ).
tff(164,plain,
( ( ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) )
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) )
<=> ( ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) )
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) )
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [X: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) )
| ( tptp_fun_X1_116(uri_ex_p2) = tptp_fun_X2_115(uri_ex_p2) )
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
$false,
inference(unit_resolution,[status(thm)],[166,163,161,117,110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWB047+1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 07:54:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.56/0.76 % SZS status Theorem
% 0.56/0.76 % SZS output start Proof
% See solution above
% 0.63/0.81 % E exiting
%------------------------------------------------------------------------------