TSTP Solution File: SWB096+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB096+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:32:18 EDT 2022
% Result : Theorem 0.76s 0.75s
% Output : Proof 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 48
% Syntax : Number of formulae : 104 ( 21 unt; 14 typ; 0 def)
% Number of atoms : 772 ( 0 equ)
% Maximal formula atoms : 36 ( 8 avg)
% Number of connectives : 1332 ( 697 ~; 443 |; 105 &)
% ( 81 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 4 >; 6 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-3 aty)
% Number of variables : 264 ( 223 !; 23 ?; 264 :)
% 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_c_type,type,
uri_ex_c: $i ).
tff(uri_ex_w_type,type,
uri_ex_w: $i ).
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(uri_ex_z_type,type,
uri_ex_z: $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(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).
tff(5,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
<=> icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
( iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
<=> icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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_w,uri_ex_z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_minqcr_inst_obj_one) ).
tff(12,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)],[11]) ).
tff(13,plain,
iext(uri_owl_onClass,uri_ex_z,uri_ex_c),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
iext(uri_owl_onClass,uri_ex_z,uri_ex_c),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,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(16,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)],[12]) ).
tff(17,plain,
iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
inference(modus_ponens,[status(thm)],[17,15]) ).
tff(19,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(20,plain,
iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(and_elim,[status(thm)],[16]) ).
tff(21,plain,
iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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)],[25,23]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,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)],[30]) ).
tff(32,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/sandbox/benchmark/Axioms/SWB001+0.ax',owl_restrict_minqcr_object_001) ).
tff(33,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)],[32,31]) ).
tff(34,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)],[33,29]) ).
tff(35,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)],[34]) ).
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) ) ) ) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
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) ) ) ) ),
inference(modus_ponens,[status(thm)],[36,26]) ).
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_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)
| ! [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_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [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(rewrite,[status(thm)],]) ).
tff(39,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_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [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(rewrite,[status(thm)],]) ).
tff(40,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_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [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(monotonicity,[status(thm)],[39]) ).
tff(41,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_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [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(transitivity,[status(thm)],[40,38]) ).
tff(42,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(43,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_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [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(modus_ponens,[status(thm)],[42,41]) ).
tff(44,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) ) ) ),
inference(unit_resolution,[status(thm)],[43,37,21,18,14]) ).
tff(45,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) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,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(quant_inst,[status(thm)],]) ).
tff(46,plain,
~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,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(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,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) ) )
| ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(tautology,[status(thm)],]) ).
tff(48,plain,
( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,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(50,plain,
( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) ),
inference(unit_resolution,[status(thm)],[49,7]) ).
tff(51,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(52,plain,
iext(uri_rdf_type,uri_ex_w,uri_ex_z),
inference(and_elim,[status(thm)],[11]) ).
tff(53,plain,
iext(uri_rdf_type,uri_ex_w,uri_ex_z),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,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(55,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)],[54,53]) ).
tff(56,plain,
icext(uri_ex_z,uri_ex_w),
inference(unit_resolution,[status(thm)],[55,50]) ).
tff(57,plain,
( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) )
| ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(tautology,[status(thm)],]) ).
tff(58,plain,
( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ 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_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[58,48]) ).
tff(60,plain,
( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ 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(tautology,[status(thm)],]) ).
tff(61,plain,
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)],[60,59]) ).
tff(62,plain,
^ [X0: $i] :
refl(
( ( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
<=> ( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
<=> ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
^ [X0: $i] :
trans(
monotonicity(
rewrite(
( ( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) )
<=> ~ ( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ) )),
( ~ ( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) )
<=> ~ ~ ( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ) )),
rewrite(
( ~ ~ ( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
<=> ( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ) )),
( ~ ( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) )
<=> ( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [X0: $i] :
~ ( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) )
<=> ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) )
<=> ~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_rdfbased_sem_restrict_minqcr_inst_obj_one) ).
tff(68,plain,
~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[68,66]) ).
tff(70,plain,
~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[69,66]) ).
tff(71,plain,
~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[71,66]) ).
tff(73,plain,
~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[72,66]) ).
tff(74,plain,
~ ? [X0: $i] :
( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
^ [X0: $i] :
refl(
$oeq(
~ ( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
~ ( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ))),
inference(bind,[status(th)],]) ).
tff(76,plain,
! [X0: $i] :
~ ( iext(uri_rdf_type,X0,uri_ex_c)
& iext(uri_ex_p,uri_ex_w,X0) ),
inference(nnf-neg,[status(sab)],[74,75]) ).
tff(77,plain,
! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[76,65]) ).
tff(78,plain,
! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) ),
inference(modus_ponens,[status(thm)],[77,63]) ).
tff(79,plain,
( ( ~ ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c) )
<=> ( ~ ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,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))
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( ~ ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) )
<=> ( ~ ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) )
<=> ( ~ ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
( ~ ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
| ~ 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(84,plain,
( ~ ! [X0: $i] :
( ~ iext(uri_rdf_type,X0,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_w,X0) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c),
inference(unit_resolution,[status(thm)],[84,78,61]) ).
tff(86,plain,
( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
| icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(87,plain,
icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)),
inference(unit_resolution,[status(thm)],[86,59]) ).
tff(88,plain,
( ~ ( iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
<=> icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) )
| iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
| ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(89,plain,
( ~ ( iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c)
<=> icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) )
| iext(uri_rdf_type,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p),uri_ex_c) ),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
$false,
inference(unit_resolution,[status(thm)],[89,85,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB096+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 20:48:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.76/0.75 % SZS status Theorem
% 0.76/0.75 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------