TSTP Solution File: SWB047+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB047+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 : Tue Sep 20 08:32:06 EDT 2022
% Result : Theorem 1.21s 1.05s
% Output : Proof 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 84
% Syntax : Number of formulae : 182 ( 37 unt; 17 typ; 0 def)
% Number of atoms : 1862 ( 250 equ)
% Maximal formula atoms : 40 ( 11 avg)
% Number of connectives : 3290 (1651 ~;1214 |; 184 &)
% ( 232 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 58 ( 58 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 11 >; 5 *; 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 : 689 ( 657 !; 0 ?; 689 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(tptp_fun_X1_116_type,type,
tptp_fun_X1_116: $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_X2_115_type,type,
tptp_fun_X2_115: $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_X_113_type,type,
tptp_fun_X_113: $i > $i ).
tff(tptp_fun_Y1_112_type,type,
tptp_fun_Y1_112: $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) ) ) ) )),
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(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/sandbox2/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/sandbox2/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_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(37,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)],[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/sandbox2/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)
| ~ ( ( 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(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) ) ) ) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,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)
| ~ ( ( 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)) ) ),
inference(tautology,[status(thm)],]) ).
tff(63,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)) ) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,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)],[66]) ).
tff(68,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(69,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(70,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)],[69]) ).
tff(71,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_inverseOf,X,Y)
=> ( ip(X)
& ip(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_inverseof_ext) ).
tff(72,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_inverseOf,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ),
inference(modus_ponens,[status(thm)],[75,65]) ).
tff(77,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(78,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(79,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)],[78,77]) ).
tff(80,plain,
~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2) ),
inference(unit_resolution,[status(thm)],[79,76,30]) ).
tff(81,plain,
( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ip(uri_ex_p2) ),
inference(tautology,[status(thm)],]) ).
tff(82,plain,
ip(uri_ex_p2),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).
tff(87,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,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(91,plain,
( iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty)
<=> icext(uri_owl_InverseFunctionalProperty,uri_ex_p2) ),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,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(93,axiom,
~ iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_char_inversefunc_term) ).
tff(94,plain,
~ iext(uri_rdf_type,uri_ex_p2,uri_owl_InverseFunctionalProperty),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,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(96,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)],[95,94]) ).
tff(97,plain,
~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p2),
inference(unit_resolution,[status(thm)],[96,91]) ).
tff(98,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)
| ~ ( ( 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)) ) ),
inference(tautology,[status(thm)],]) ).
tff(99,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)) ) )
| ~ ( ( 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)) ) ),
inference(unit_resolution,[status(thm)],[98,97,82]) ).
tff(100,plain,
~ ( ( 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)) ),
inference(unit_resolution,[status(thm)],[99,63]) ).
tff(101,plain,
( ( 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))
| iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)) ),
inference(tautology,[status(thm)],]) ).
tff(102,plain,
iext(uri_ex_p2,tptp_fun_X1_116(uri_ex_p2),tptp_fun_Y_114(uri_ex_p2)),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,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(104,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)],[103,102]) ).
tff(105,plain,
iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)),
inference(unit_resolution,[status(thm)],[104,37]) ).
tff(106,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(107,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)],[106,35]) ).
tff(108,plain,
( ( 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))
| iext(uri_ex_p2,tptp_fun_X2_115(uri_ex_p2),tptp_fun_Y_114(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)),
inference(unit_resolution,[status(thm)],[108,100]) ).
tff(110,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(111,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)],[110,109]) ).
tff(112,plain,
iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X2_115(uri_ex_p2)),
inference(unit_resolution,[status(thm)],[111,107]) ).
tff(113,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(114,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)],[113]) ).
tff(115,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(116,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)],[115]) ).
tff(117,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(118,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)],[117]) ).
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)
| ~ ! [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)],[118,116]) ).
tff(120,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(121,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)],[120]) ).
tff(122,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(123,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)],[122]) ).
tff(124,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(125,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(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 ) ) ) )
<=> ! [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)],[125]) ).
tff(127,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/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_char_functional) ).
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 ) ) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
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 ) ) ) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,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)],[129]) ).
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 ) ) ) )
& ( 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)],[130,123]) ).
tff(132,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)],[131,121]) ).
tff(133,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)],[132,119]) ).
tff(134,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)],[133,114]) ).
tff(135,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)
| ~ ( ( 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)
| ~ ( ( 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(rewrite,[status(thm)],]) ).
tff(136,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)
| ~ ( ( 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(rewrite,[status(thm)],]) ).
tff(137,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)
| ~ ( ( 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(monotonicity,[status(thm)],[136]) ).
tff(138,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)
| ~ ( ( 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(transitivity,[status(thm)],[137,135]) ).
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) ) ) ) )
| ~ ( ~ ( 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(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)
| ~ ( ( 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(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
~ ( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,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(unit_resolution,[status(thm)],[140,134]) ).
tff(142,plain,
( ~ ( ~ ip(uri_ex_p1)
| icext(uri_owl_FunctionalProperty,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) ) ) )
| ~ 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(143,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)],[142,141]) ).
tff(144,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(145,plain,
( iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty)
<=> icext(uri_owl_FunctionalProperty,uri_ex_p1) ),
inference(unit_resolution,[status(thm)],[144,89]) ).
tff(146,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(147,plain,
iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty),
inference(and_elim,[status(thm)],[28]) ).
tff(148,plain,
iext(uri_rdf_type,uri_ex_p1,uri_owl_FunctionalProperty),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,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(150,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)],[149,148]) ).
tff(151,plain,
icext(uri_owl_FunctionalProperty,uri_ex_p1),
inference(unit_resolution,[status(thm)],[150,145]) ).
tff(152,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(153,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)],[152,151]) ).
tff(154,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)],[153,143]) ).
tff(155,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(156,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)],[155,154]) ).
tff(157,plain,
( ( 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))
| ( tptp_fun_X1_116(uri_ex_p2) != tptp_fun_X2_115(uri_ex_p2) ) ),
inference(tautology,[status(thm)],]) ).
tff(158,plain,
tptp_fun_X1_116(uri_ex_p2) != tptp_fun_X2_115(uri_ex_p2),
inference(unit_resolution,[status(thm)],[157,100]) ).
tff(159,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_X2_115(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(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_X2_115(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ( ( 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)) )
<=> ( ( 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_X2_115(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ) ),
inference(rewrite,[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) )
| ( 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_X2_115(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ) ),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,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_X2_115(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ) ),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,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(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_X2_115(uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_Y_114(uri_ex_p2),tptp_fun_X1_116(uri_ex_p2)) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
$false,
inference(unit_resolution,[status(thm)],[164,158,156,112,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB047+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 20:03:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.21/1.05 % SZS status Theorem
% 1.21/1.05 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------