%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB094+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:29:50 AM UTC 2025
% Result : Theorem 0.60s 0.78s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 79
% Syntax : Number of formulae : 197 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 2081 ( 0 equ)
% Maximal formula atoms : 40 ( 10 avg)
% Number of connectives : 3887 (2078 ~;1443 |; 208 &)
% ( 129 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 75 ( 75 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 13 con; 0-3 aty)
% Number of variables : 638 ( 581 !; 13 ?; 638 :)
% Comments :
%------------------------------------------------------------------------------
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(tptp_fun_Y_42_type,type,
tptp_fun_Y_42: ( $i * $i * $i ) > $i ).
tff(uri_ex_p_type,type,
uri_ex_p: $i ).
tff(uri_ex_c1_type,type,
uri_ex_c1: $i ).
tff(tptp_fun_X_61_type,type,
tptp_fun_X_61: ( $i * $i ) > $i ).
tff(uri_ex_x1_type,type,
uri_ex_x1: $i ).
tff(uri_ex_x2_type,type,
uri_ex_x2: $i ).
tff(uri_ex_c2_type,type,
uri_ex_c2: $i ).
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_owl_onClass_type,type,
uri_owl_onClass: $i ).
tff(uri_owl_onProperty_type,type,
uri_owl_onProperty: $i ).
tff(literal_typed_type,type,
literal_typed: ( $i * $i ) > $i ).
tff(uri_xsd_nonNegativeInteger_type,type,
uri_xsd_nonNegativeInteger: $i ).
tff(dat_str_1_type,type,
dat_str_1: $i ).
tff(uri_owl_minQualifiedCardinality_type,type,
uri_owl_minQualifiedCardinality: $i ).
tff(uri_rdfs_subClassOf_type,type,
uri_rdfs_subClassOf: $i ).
tff(ic_type,type,
ic: $i > $o ).
tff(uri_owl_Restriction_type,type,
uri_owl_Restriction: $i ).
tff(uri_xml_nonNegativeInteger_type,type,
uri_xml_nonNegativeInteger: $i ).
tff(1,plain,
( iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
<=> iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
& iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
& iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_minqcr_cmp_class) ).
tff(3,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
& iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
<=> iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
& iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p) ),
inference(and_elim,[status(thm)],[3]) ).
tff(8,plain,
iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
<=> iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
& iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(and_elim,[status(thm)],[7]) ).
tff(12,plain,
iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
^ [Z: $i,P: $i,C: $i] :
refl(( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [Z: $i,P: $i,C: $i] :
rewrite(( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[17,15]) ).
tff(19,plain,
^ [Z: $i,P: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
rewrite(( ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
quant_intro(proof_bind(^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
<=> ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) ) )),
rewrite(( ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) )
<=> ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )),
( ( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ( ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )),
rewrite(( ( ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )),
( ( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ))),
( ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )),
( ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) )),
rewrite(( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) )),
( ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
^ [Z: $i,P: $i,C: $i] :
trans(monotonicity(rewrite(( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) ) )),
( ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) )),
rewrite(( ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) )),
( ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [Z: $i,P: $i,C: $i] :
( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [Z: $i,P: $i,C: $i] :
( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_restrict_minqcr_object_001) ).
tff(25,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) ) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,18]) ).
tff(30,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) ) )
<=> ~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) ) ),
inference(transitivity,[status(thm)],[34,31]) ).
tff(36,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) ) ),
inference(transitivity,[status(thm)],[36,30]) ).
tff(38,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c1)
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) ),
inference(unit_resolution,[status(thm)],[39,29,13,9,5]) ).
tff(41,plain,
( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c1,uri_ex_p)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c1,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) )
| ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(44,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) ),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
^ [C1: $i,C2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
^ [C1: $i,C2: $i] :
refl(( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
^ [C1: $i,C2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
^ [C1: $i,C2: $i] :
trans(monotonicity(rewrite(( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )),
rewrite(( ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
<=> ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )),
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
rewrite(( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [C1: $i,C2: $i] :
rewrite(( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
^ [C1: $i,C2: $i] :
rewrite(( ( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) )
<=> ( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,axiom,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subclassof) ).
tff(60,plain,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[62,55]) ).
tff(64,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[63,53]) ).
tff(65,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[64,51]) ).
tff(66,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(modus_ponens,[status(thm)],[65,46]) ).
tff(67,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ),
inference(unit_resolution,[status(thm)],[72,66]) ).
tff(74,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) )
| iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(75,plain,
( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
<=> iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2) ),
inference(and_elim,[status(thm)],[11]) ).
tff(78,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p) ),
inference(and_elim,[status(thm)],[77]) ).
tff(79,plain,
iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(and_elim,[status(thm)],[78]) ).
tff(80,plain,
iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(modus_ponens,[status(thm)],[79,76]) ).
tff(81,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
^ [X: $i,Y: $i] :
rewrite(( ( iext(uri_owl_minQualifiedCardinality,X,Y)
=> ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_minQualifiedCardinality,X,Y)
=> ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_minQualifiedCardinality,X,Y)
=> ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_minqualifiedcardinality_ext) ).
tff(89,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(modus_ponens,[status(thm)],[92,82]) ).
tff(94,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(unit_resolution,[status(thm)],[96,93,80]) ).
tff(98,plain,
( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| icext(uri_owl_Restriction,uri_ex_x2) ),
inference(tautology,[status(thm)],[]) ).
tff(99,plain,
icext(uri_owl_Restriction,uri_ex_x2),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
^ [X: $i] :
refl(( ( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ( ic(X)
| ~ icext(uri_owl_Restriction,X) ) )),
inference(bind,[status(th)],[]) ).
tff(101,plain,
( ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,plain,
^ [X: $i] :
rewrite(( ( icext(uri_owl_Restriction,X)
=> ic(X) )
<=> ( ic(X)
| ~ icext(uri_owl_Restriction,X) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [X: $i] :
( icext(uri_owl_Restriction,X)
=> ic(X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [X: $i] :
( icext(uri_owl_Restriction,X)
=> ic(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_class_restriction_ext) ).
tff(106,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
( ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) )
<=> ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
ic(uri_ex_x2),
inference(unit_resolution,[status(thm)],[112,109,99]) ).
tff(114,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_minQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(unit_resolution,[status(thm)],[116,93,13]) ).
tff(118,plain,
( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| icext(uri_owl_Restriction,uri_ex_x1) ),
inference(tautology,[status(thm)],[]) ).
tff(119,plain,
icext(uri_owl_Restriction,uri_ex_x1),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
( ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) )
<=> ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
ic(uri_ex_x1),
inference(unit_resolution,[status(thm)],[122,109,119]) ).
tff(124,plain,
( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
<=> ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_restrict_minqcr_cmp_class) ).
tff(126,plain,
~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(128,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(unit_resolution,[status(thm)],[128,123,113,75]) ).
tff(130,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],[]) ).
tff(131,plain,
icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,plain,
( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) )
| ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(133,plain,
( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) )
| ~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) ),
inference(unit_resolution,[status(thm)],[132,131]) ).
tff(134,plain,
~ ( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[133,44]) ).
tff(135,plain,
( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ),
inference(tautology,[status(thm)],[]) ).
tff(136,plain,
iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
( iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
<=> iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2),
inference(and_elim,[status(thm)],[77]) ).
tff(139,plain,
iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
<=> iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p),
inference(and_elim,[status(thm)],[78]) ).
tff(142,plain,
iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(145,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) ) )
<=> ~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) ) ),
inference(transitivity,[status(thm)],[147,144]) ).
tff(149,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) ) ),
inference(transitivity,[status(thm)],[149,143]) ).
tff(151,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c2)
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) ),
inference(unit_resolution,[status(thm)],[152,29,80,142,139]) ).
tff(154,plain,
( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c2,uri_ex_p)) ) ) )
| ~ ( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c2,uri_ex_p)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
~ ( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c2,uri_ex_p)) ) ) ),
inference(unit_resolution,[status(thm)],[154,153]) ).
tff(156,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c2,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c2,uri_ex_p)) ) )
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(157,plain,
( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) ),
inference(unit_resolution,[status(thm)],[156,155]) ).
tff(158,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],[]) ).
tff(159,plain,
~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[158,129]) ).
tff(160,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(161,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) ),
inference(unit_resolution,[status(thm)],[160,159]) ).
tff(162,plain,
! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ),
inference(unit_resolution,[status(thm)],[161,157]) ).
tff(163,plain,
( ( ~ ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) )
| ~ icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) )
<=> ( ~ ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) )
| ~ icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) )
| ~ icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [Y: $i] :
( ~ icext(uri_ex_c2,Y)
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) )
| ~ icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
~ icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)),
inference(unit_resolution,[status(thm)],[165,162,136]) ).
tff(167,plain,
( ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| ~ iext(uri_ex_p,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ),
inference(tautology,[status(thm)],[]) ).
tff(168,plain,
icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)),
inference(unit_resolution,[status(thm)],[167,134]) ).
tff(169,plain,
( iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
<=> iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,plain,
iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2),
inference(and_elim,[status(thm)],[2]) ).
tff(171,plain,
iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
^ [C: $i,D: $i] :
refl(( ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(173,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,plain,
^ [C: $i,D: $i] :
rewrite(( ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(175,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(quant_intro,[status(thm)],[174]) ).
tff(176,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(transitivity,[status(thm)],[175,173]) ).
tff(177,plain,
^ [C: $i,D: $i] :
rewrite(( ( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(178,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(quant_intro,[status(thm)],[177]) ).
tff(179,plain,
( ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,plain,
^ [C: $i,D: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [X: $i] :
rewrite(( ( icext(C,X)
=> icext(D,X) )
<=> ( ~ icext(C,X)
| icext(D,X) ) ))),
( ! [X: $i] :
( icext(C,X)
=> icext(D,X) )
<=> ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) )),
( ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) )
<=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )),
rewrite(( ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) )
<=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )),
( ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) )
<=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )),
( ( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) ) )
<=> ( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
rewrite(( ( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
( ( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(181,plain,
( ! [C: $i,D: $i] :
( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) ) )
<=> ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ) ),
inference(quant_intro,[status(thm)],[180]) ).
tff(182,axiom,
! [C: $i,D: $i] :
( iext(uri_rdfs_subClassOf,C,D)
=> ( ic(C)
& ic(D)
& ! [X: $i] :
( icext(C,X)
=> icext(D,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_subclassof_main) ).
tff(183,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(modus_ponens,[status(thm)],[183,179]) ).
tff(185,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ( ic(C)
& ic(D)
& ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(skolemize,[status(sab)],[184]) ).
tff(186,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(modus_ponens,[status(thm)],[185,178]) ).
tff(187,plain,
! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) ),
inference(modus_ponens,[status(thm)],[186,176]) ).
tff(188,plain,
( ( ~ ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
| ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ) )
<=> ( ~ ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
| ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ~ ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
| ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
( ~ ! [C: $i,D: $i] :
( ~ iext(uri_rdfs_subClassOf,C,D)
| ~ ( ~ ic(D)
| ~ ic(C)
| ~ ! [X: $i] :
( ~ icext(C,X)
| icext(D,X) ) ) )
| ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
| ~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
~ ( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ),
inference(unit_resolution,[status(thm)],[190,187,171]) ).
tff(192,plain,
( ~ ic(uri_ex_c2)
| ~ ic(uri_ex_c1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ) ),
inference(tautology,[status(thm)],[]) ).
tff(193,plain,
! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) ),
inference(unit_resolution,[status(thm)],[192,191]) ).
tff(194,plain,
( ( ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) )
<=> ( ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(195,plain,
( ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(196,plain,
( ~ ! [X: $i] :
( ~ icext(uri_ex_c1,X)
| icext(uri_ex_c2,X) )
| ~ icext(uri_ex_c1,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p))
| icext(uri_ex_c2,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c1,uri_ex_p)) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
$false,
inference(unit_resolution,[status(thm)],[196,193,168,166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWB094+1 : TPTP v9.0.0. Released v5.2.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:58:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.60/0.78 % SZS status Theorem
% 0.60/0.78 % SZS output start Proof
% See solution above
% 0.60/0.83 % E exiting
%------------------------------------------------------------------------------