TSTP Solution File: SWB075+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB075+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 08:32:12 EDT 2022
% Result : Theorem 0.69s 0.75s
% Output : Proof 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 60
% Syntax : Number of formulae : 123 ( 27 unt; 12 typ; 0 def)
% Number of atoms : 847 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 1415 ( 711 ~; 514 |; 76 &)
% ( 96 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 331 ( 306 !; 0 ?; 331 :)
% Comments :
%------------------------------------------------------------------------------
tff(lv_type,type,
lv: $i > $o ).
tff(tptp_fun_Y_62_type,type,
tptp_fun_Y_62: ( $i * $i ) > $i ).
tff(uri_ex_p_type,type,
uri_ex_p: $i ).
tff(uri_owl_topDataProperty_type,type,
uri_owl_topDataProperty: $i ).
tff(ir_type,type,
ir: $i > $o ).
tff(tptp_fun_X_63_type,type,
tptp_fun_X_63: ( $i * $i ) > $i ).
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(iodp_type,type,
iodp: $i > $o ).
tff(uri_owl_DatatypeProperty_type,type,
uri_owl_DatatypeProperty: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(uri_rdfs_subPropertyOf_type,type,
uri_rdfs_subPropertyOf: $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(
( ( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) )
<=> ( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) )
<=> ! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( iext(uri_owl_topDataProperty,X,Y)
<=> ( ir(X)
& lv(Y) ) )
<=> ( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ( ir(X)
& lv(Y) ) )
<=> ! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ( ir(X)
& lv(Y) ) )
<=> ! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ( ir(X)
& lv(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ( ir(X)
& lv(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_topdataproperty_ext) ).
tff(7,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ( ir(X)
& lv(Y) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ( ir(X)
& lv(Y) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i,Y: $i] :
( iext(uri_owl_topDataProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ lv(Y) ) )
| ( iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
<=> ~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(12,plain,
( iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
<=> ~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(
( ( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) )
<=> ( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) )
<=> ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) )
<=> ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_parts_iodp_def) ).
tff(17,plain,
! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [X: $i] :
( iodp(X)
<=> iext(uri_rdf_type,X,uri_owl_DatatypeProperty) )
| ( iodp(uri_ex_p)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
( iodp(uri_ex_p)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) ),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_prop_topdataproperty_term) ).
tff(24,plain,
iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( iodp(uri_ex_p)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) )
| iodp(uri_ex_p)
| ~ iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) ),
inference(tautology,[status(thm)],]) ).
tff(26,plain,
( ~ ( iodp(uri_ex_p)
<=> iext(uri_rdf_type,uri_ex_p,uri_owl_DatatypeProperty) )
| iodp(uri_ex_p) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
iodp(uri_ex_p),
inference(unit_resolution,[status(thm)],[26,21]) ).
tff(28,plain,
^ [X: $i] :
refl(
( ( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
<=> ( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
<=> ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [X: $i] :
rewrite(
( ( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
<=> ( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
<=> ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
<=> ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
^ [X: $i] :
rewrite(
( ( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) )
<=> ( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) )
<=> ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) )
<=> ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [X: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i,Z: $i] :
rewrite(
( ( iext(X,Y,Z)
=> ( ir(Y)
& lv(Z) ) )
<=> ( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ))),
( ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& lv(Z) ) )
<=> ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) )),
( ( iodp(X)
=> ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& lv(Z) ) ) )
<=> ( iodp(X)
=> ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ) )),
rewrite(
( ( iodp(X)
=> ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) )
<=> ( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ) )),
( ( iodp(X)
=> ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& lv(Z) ) ) )
<=> ( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X: $i] :
( iodp(X)
=> ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& lv(Z) ) ) )
<=> ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [X: $i] :
( iodp(X)
=> ! [Y: $i,Z: $i] :
( iext(X,Y,Z)
=> ( ir(Y)
& lv(Z) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_parts_iodp_cond_inst) ).
tff(39,plain,
! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ( ir(Y)
& lv(Z) ) ) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ),
inference(modus_ponens,[status(thm)],[42,32]) ).
tff(44,plain,
( ( ~ ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
| ~ iodp(uri_ex_p)
| ! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
<=> ( ~ ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
| ~ iodp(uri_ex_p)
| ! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
| ~ iodp(uri_ex_p)
| ! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [X: $i] :
( ~ iodp(X)
| ! [Y: $i,Z: $i] :
( ~ iext(X,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) )
| ~ iodp(uri_ex_p)
| ! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) ),
inference(unit_resolution,[status(thm)],[46,43,27]) ).
tff(48,plain,
^ [P1: $i,P2: $i] :
rewrite(
( ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [P1: $i,P2: $i] :
refl(
( ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
^ [P1: $i,P2: $i] :
rewrite(
( ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
^ [P1: $i,P2: $i] :
trans(
monotonicity(
rewrite(
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )),
rewrite(
( ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
<=> ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )),
( ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
rewrite(
( ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
( ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [P1: $i,P2: $i] :
rewrite(
( ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
<=> ! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
^ [P1: $i,P2: $i] :
rewrite(
( ( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
=> iext(P2,X,Y) ) ) )
<=> ( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
=> iext(P2,X,Y) ) ) )
<=> ! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
=> iext(P2,X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subpropertyof) ).
tff(63,plain,
! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
& ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) )
| ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[67,54]) ).
tff(69,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[68,49]) ).
tff(70,plain,
( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( ~ iext(P1,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1))
| iext(P2,tptp_fun_X_63(P2,P1),tptp_fun_Y_62(P2,P1)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ( ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p,X,Y)
| iext(uri_owl_topDataProperty,X,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ( ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p,X,Y)
| iext(uri_owl_topDataProperty,X,Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ( ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p,X,Y)
| iext(uri_owl_topDataProperty,X,Y) ) ) )
| iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ),
inference(tautology,[status(thm)],]) ).
tff(73,plain,
( iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( iodp(uri_owl_topDataProperty)
<=> iodp(uri_owl_topDataProperty) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
iodp(uri_owl_topDataProperty),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_topdataproperty_type) ).
tff(76,plain,
iodp(uri_owl_topDataProperty),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
^ [X: $i] :
refl(
( ( ip(X)
| ~ iodp(X) )
<=> ( ip(X)
| ~ iodp(X) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [X: $i] :
( ip(X)
| ~ iodp(X) )
<=> ! [X: $i] :
( ip(X)
| ~ iodp(X) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [X: $i] :
( ip(X)
| ~ iodp(X) )
<=> ! [X: $i] :
( ip(X)
| ~ iodp(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
^ [X: $i] :
rewrite(
( ( iodp(X)
=> ip(X) )
<=> ( ip(X)
| ~ iodp(X) ) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [X: $i] :
( iodp(X)
=> ip(X) )
<=> ! [X: $i] :
( ip(X)
| ~ iodp(X) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,axiom,
! [X: $i] :
( iodp(X)
=> ip(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_parts_iodp_cond_set) ).
tff(83,plain,
! [X: $i] :
( ip(X)
| ~ iodp(X) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [X: $i] :
( ip(X)
| ~ iodp(X) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
! [X: $i] :
( ip(X)
| ~ iodp(X) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [X: $i] :
( ip(X)
| ~ iodp(X) ),
inference(modus_ponens,[status(thm)],[85,78]) ).
tff(87,plain,
( ( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_owl_topDataProperty)
| ~ iodp(uri_owl_topDataProperty) )
<=> ( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_owl_topDataProperty)
| ~ iodp(uri_owl_topDataProperty) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_owl_topDataProperty)
| ~ iodp(uri_owl_topDataProperty) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_owl_topDataProperty)
| ~ iodp(uri_owl_topDataProperty) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
ip(uri_owl_topDataProperty),
inference(unit_resolution,[status(thm)],[89,86,76]) ).
tff(91,plain,
( ( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_ex_p)
| ~ iodp(uri_ex_p) )
<=> ( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_ex_p)
| ~ iodp(uri_ex_p) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_ex_p)
| ~ iodp(uri_ex_p) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [X: $i] :
( ip(X)
| ~ iodp(X) )
| ip(uri_ex_p)
| ~ iodp(uri_ex_p) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
ip(uri_ex_p),
inference(unit_resolution,[status(thm)],[93,86,27]) ).
tff(95,plain,
( ~ iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
<=> ~ iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
~ iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_prop_topdataproperty_term) ).
tff(97,plain,
~ iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) )
| iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ),
inference(tautology,[status(thm)],]) ).
tff(99,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_ex_p,uri_owl_topDataProperty)
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) )
| ~ ip(uri_owl_topDataProperty)
| ~ ip(uri_ex_p)
| ~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
~ ( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[99,94,90,73]) ).
tff(101,plain,
( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(102,plain,
iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
( ( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) )
| ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| ~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) )
<=> ( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) )
| ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| ~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) )
| ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| ~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
( ~ ! [Y: $i,Z: $i] :
( ~ iext(uri_ex_p,Y,Z)
| ~ ( ~ ir(Y)
| ~ lv(Z) ) )
| ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| ~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[105,102,47]) ).
tff(107,plain,
( ~ iext(uri_ex_p,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| ~ iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(108,plain,
~ iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)),
inference(unit_resolution,[status(thm)],[107,100]) ).
tff(109,plain,
( ~ ( iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
<=> ~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) )
| iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
| ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(110,plain,
( ~ ( iext(uri_owl_topDataProperty,tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p),tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p))
<=> ~ ( ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ) )
| ~ ir(tptp_fun_X_63(uri_owl_topDataProperty,uri_ex_p))
| ~ lv(tptp_fun_Y_62(uri_owl_topDataProperty,uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
$false,
inference(unit_resolution,[status(thm)],[110,106,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWB075+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n002.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 20:30:02 EDT 2022
% 0.12/0.33 % 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.
% 0.69/0.75 % SZS status Theorem
% 0.69/0.75 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------