%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB097+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:29:51 AM UTC 2025
% Result : Theorem 0.61s 0.78s
% Output : Proof 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 77 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 753 ( 0 equ)
% Maximal formula atoms : 36 ( 9 avg)
% Number of connectives : 1340 ( 701 ~; 465 |; 92 &)
% ( 76 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 262 ( 233 !; 13 ?; 262 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_ex_w_type,type,
uri_ex_w: $i ).
tff(uri_ex_p_type,type,
uri_ex_p: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(uri_ex_c_type,type,
uri_ex_c: $i ).
tff(uri_ex_z_type,type,
uri_ex_z: $i ).
tff(tptp_fun_Y_42_type,type,
tptp_fun_Y_42: ( $i * $i * $i ) > $i ).
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_ex_x_type,type,
uri_ex_x: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(1,plain,
( iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
<=> iext(uri_owl_onClass,uri_ex_z,uri_ex_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
& iext(uri_rdf_type,uri_ex_x,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,uri_ex_x) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_minqcr_inst_subj_one) ).
tff(3,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
& iext(uri_rdf_type,uri_ex_x,uri_ex_c) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_z,uri_ex_c) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
iext(uri_owl_onClass,uri_ex_z,uri_ex_c),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
iext(uri_owl_onClass,uri_ex_z,uri_ex_c),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
<=> iext(uri_owl_onProperty,uri_ex_z,uri_ex_p) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p) ),
inference(and_elim,[status(thm)],[4]) ).
tff(9,plain,
iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
inference(and_elim,[status(thm)],[8]) ).
tff(10,plain,
iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
inference(modus_ponens,[status(thm)],[9,7]) ).
tff(11,plain,
( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
<=> iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(and_elim,[status(thm)],[8]) ).
tff(13,plain,
iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(modus_ponens,[status(thm)],[12,11]) ).
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_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,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_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) ) )
<=> ~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,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_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,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_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,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_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,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_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,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_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,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_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) ),
inference(unit_resolution,[status(thm)],[39,29,13,10,6]) ).
tff(41,plain,
( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_z,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,X,Y) ) )
| ~ ( ~ icext(uri_ex_z,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) )
| ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
~ ( ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) )
| ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) )
| ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) )
| icext(uri_ex_z,uri_ex_w)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(44,plain,
( icext(uri_ex_z,uri_ex_w)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) ),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
^ [X: $i,C: $i] :
refl(( ( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).
tff(49,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
~ iext(uri_rdf_type,uri_ex_w,uri_ex_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_restrict_minqcr_inst_subj_one) ).
tff(56,plain,
~ iext(uri_rdf_type,uri_ex_w,uri_ex_z),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) )
| iext(uri_rdf_type,uri_ex_w,uri_ex_z)
| ~ icext(uri_ex_z,uri_ex_w) ),
inference(tautology,[status(thm)],[]) ).
tff(58,plain,
( ~ ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) )
| ~ icext(uri_ex_z,uri_ex_w) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
~ icext(uri_ex_z,uri_ex_w),
inference(unit_resolution,[status(thm)],[58,53]) ).
tff(60,plain,
( ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) )
| icext(uri_ex_z,uri_ex_w)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(61,plain,
( ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) )
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) ),
inference(unit_resolution,[status(thm)],[61,44]) ).
tff(63,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
<=> icext(uri_ex_c,uri_ex_x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
<=> icext(uri_ex_c,uri_ex_x) ),
inference(unit_resolution,[status(thm)],[63,51]) ).
tff(65,plain,
( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
<=> iext(uri_rdf_type,uri_ex_x,uri_ex_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
iext(uri_rdf_type,uri_ex_x,uri_ex_c),
inference(and_elim,[status(thm)],[3]) ).
tff(67,plain,
iext(uri_rdf_type,uri_ex_x,uri_ex_c),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ ( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
<=> icext(uri_ex_c,uri_ex_x) )
| ~ iext(uri_rdf_type,uri_ex_x,uri_ex_c)
| icext(uri_ex_c,uri_ex_x) ),
inference(tautology,[status(thm)],[]) ).
tff(69,plain,
( ~ ( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
<=> icext(uri_ex_c,uri_ex_x) )
| icext(uri_ex_c,uri_ex_x) ),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
icext(uri_ex_c,uri_ex_x),
inference(unit_resolution,[status(thm)],[69,64]) ).
tff(71,plain,
( iext(uri_ex_p,uri_ex_w,uri_ex_x)
<=> iext(uri_ex_p,uri_ex_w,uri_ex_x) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
iext(uri_ex_p,uri_ex_w,uri_ex_x),
inference(and_elim,[status(thm)],[2]) ).
tff(73,plain,
iext(uri_ex_p,uri_ex_w,uri_ex_x),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( ~ ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) )
| ~ icext(uri_ex_c,uri_ex_x)
| ~ iext(uri_ex_p,uri_ex_w,uri_ex_x) )
<=> ( ~ ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) )
| ~ icext(uri_ex_c,uri_ex_x)
| ~ iext(uri_ex_p,uri_ex_w,uri_ex_x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) )
| ~ icext(uri_ex_c,uri_ex_x)
| ~ iext(uri_ex_p,uri_ex_w,uri_ex_x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p,uri_ex_w,Y) )
| ~ icext(uri_ex_c,uri_ex_x)
| ~ iext(uri_ex_p,uri_ex_w,uri_ex_x) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
$false,
inference(unit_resolution,[status(thm)],[76,73,70,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB097+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.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 08:00:12 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.61/0.78 % SZS status Theorem
% 0.61/0.78 % SZS output start Proof
% See solution above
% 0.65/0.82 % E exiting
%------------------------------------------------------------------------------