%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB086+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:49 AM UTC 2025
% Result : Theorem 0.59s 0.78s
% Output : Proof 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 68
% Syntax : Number of formulae : 166 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 1377 ( 0 equ)
% Maximal formula atoms : 40 ( 8 avg)
% Number of connectives : 2282 (1126 ~; 844 |; 131 &)
% ( 155 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 55 ( 55 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 528 ( 483 !; 0 ?; 528 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(tptp_fun_X_61_type,type,
tptp_fun_X_61: ( $i * $i ) > $i ).
tff(uri_ex_x1_type,type,
uri_ex_x1: $i ).
tff(uri_ex_x2_type,type,
uri_ex_x2: $i ).
tff(uri_ex_p1_type,type,
uri_ex_p1: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(uri_owl_onProperty_type,type,
uri_owl_onProperty: $i ).
tff(literal_typed_type,type,
literal_typed: ( $i * $i ) > $i ).
tff(uri_xsd_boolean_type,type,
uri_xsd_boolean: $i ).
tff(dat_str_true_type,type,
dat_str_true: $i ).
tff(uri_owl_hasSelf_type,type,
uri_owl_hasSelf: $i ).
tff(uri_ex_p2_type,type,
uri_ex_p2: $i ).
tff(uri_rdfs_subPropertyOf_type,type,
uri_rdfs_subPropertyOf: $i ).
tff(ic_type,type,
ic: $i > $o ).
tff(uri_rdfs_subClassOf_type,type,
uri_rdfs_subClassOf: $i ).
tff(uri_owl_Restriction_type,type,
uri_owl_Restriction: $i ).
tff(ir_type,type,
ir: $i > $o ).
tff(ip_type,type,
ip: $i > $o ).
tff(1,plain,
( iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
<=> iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
& iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_hasself_cmp_prop) ).
tff(3,plain,
( iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
<=> iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean)) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean)) ),
inference(and_elim,[status(thm)],[3]) ).
tff(8,plain,
iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean)),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean)),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
^ [Z: $i,P: $i,V: $i] :
rewrite(( ( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) )
<=> ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [Z: $i,P: $i,V: $i] :
refl(( ( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) )
<=> ( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) )
<=> ! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [Z: $i,P: $i,V: $i] :
rewrite(( ( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) )
<=> ( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) )
<=> ! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) )
<=> ! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,plain,
^ [Z: $i,P: $i,V: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
<=> ~ ( ~ iext(uri_owl_hasSelf,Z,V)
| ~ iext(uri_owl_onProperty,Z,P) ) )),
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
<=> ~ ~ ( ~ iext(uri_owl_hasSelf,Z,V)
| ~ iext(uri_owl_onProperty,Z,P) ) )),
rewrite(( ~ ~ ( ~ iext(uri_owl_hasSelf,Z,V)
| ~ iext(uri_owl_onProperty,Z,P) )
<=> ( ~ iext(uri_owl_hasSelf,Z,V)
| ~ iext(uri_owl_onProperty,Z,P) ) )),
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
<=> ( ~ iext(uri_owl_hasSelf,Z,V)
| ~ iext(uri_owl_onProperty,Z,P) ) )),
( ( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
<=> ( ~ iext(uri_owl_hasSelf,Z,V)
| ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ) )),
rewrite(( ( ~ iext(uri_owl_hasSelf,Z,V)
| ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
<=> ( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ) )),
( ( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
<=> ( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [Z: $i,P: $i,V: $i] :
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
<=> ! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [Z: $i,P: $i,V: $i] :
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
<=> ! [Z: $i,P: $i,V: $i] :
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [Z: $i,P: $i,V: $i] :
rewrite(( ( ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
=> ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
<=> ( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Z: $i,P: $i,V: $i] :
( ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
=> ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
<=> ! [Z: $i,P: $i,V: $i] :
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [Z: $i,P: $i,V: $i] :
( ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
=> ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_restrict_hasself) ).
tff(23,plain,
! [Z: $i,P: $i,V: $i] :
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Z: $i,P: $i,V: $i] :
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [Z: $i,P: $i,V: $i] :
( ~ ( iext(uri_owl_hasSelf,Z,V)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [Z: $i,P: $i,V: $i] :
( ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) ),
inference(modus_ponens,[status(thm)],[27,11]) ).
tff(29,plain,
( ( ~ ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_x1,X)
<=> iext(uri_ex_p1,X,X) ) )
<=> ( ~ ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_x1,X)
<=> iext(uri_ex_p1,X,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_x1,X)
<=> iext(uri_ex_p1,X,X) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_x1,X)
<=> iext(uri_ex_p1,X,X) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [X: $i] :
( icext(uri_ex_x1,X)
<=> iext(uri_ex_p1,X,X) ),
inference(unit_resolution,[status(thm)],[31,28,9,5]) ).
tff(33,plain,
( ~ ! [X: $i] :
( icext(uri_ex_x1,X)
<=> iext(uri_ex_p1,X,X) )
| ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
<=> iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
<=> iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
^ [C1: $i,C2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
^ [C1: $i,C2: $i] :
refl(( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [C1: $i,C2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
^ [C1: $i,C2: $i] :
trans(monotonicity(rewrite(( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )),
rewrite(( ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
<=> ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )),
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
rewrite(( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
^ [C1: $i,C2: $i] :
rewrite(( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [C1: $i,C2: $i] :
rewrite(( ( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) )
<=> ( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subclassof) ).
tff(50,plain,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[53,43]) ).
tff(55,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[54,41]) ).
tff(56,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(modus_ponens,[status(thm)],[55,36]) ).
tff(57,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ),
inference(unit_resolution,[status(thm)],[62,56]) ).
tff(64,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) )
| iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(65,plain,
( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
<=> iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean)) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2) ),
inference(and_elim,[status(thm)],[7]) ).
tff(68,plain,
iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean)),
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean)),
inference(modus_ponens,[status(thm)],[68,66]) ).
tff(70,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
<=> ( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) )
<=> ( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [X: $i,Y: $i] :
rewrite(( ( iext(uri_owl_hasSelf,X,Y)
=> ( icext(uri_owl_Restriction,X)
& ir(Y) ) )
<=> ( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_hasSelf,X,Y)
=> ( icext(uri_owl_Restriction,X)
& ir(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_hasSelf,X,Y)
=> ( icext(uri_owl_Restriction,X)
& ir(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_hasself_ext) ).
tff(78,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ( icext(uri_owl_Restriction,X)
& ir(Y) ) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(modus_ponens,[status(thm)],[81,71]) ).
tff(83,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
| ~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
| ~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
| ~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
| ~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(unit_resolution,[status(thm)],[85,82,69]) ).
tff(87,plain,
( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x2)
| icext(uri_owl_Restriction,uri_ex_x2) ),
inference(tautology,[status(thm)],[]) ).
tff(88,plain,
icext(uri_owl_Restriction,uri_ex_x2),
inference(unit_resolution,[status(thm)],[87,86]) ).
tff(89,plain,
^ [X: $i] :
refl(( ( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ( ic(X)
| ~ icext(uri_owl_Restriction,X) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [X: $i] :
rewrite(( ( icext(uri_owl_Restriction,X)
=> ic(X) )
<=> ( ic(X)
| ~ icext(uri_owl_Restriction,X) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [X: $i] :
( icext(uri_owl_Restriction,X)
=> ic(X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [X: $i] :
( icext(uri_owl_Restriction,X)
=> ic(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_class_restriction_ext) ).
tff(95,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) )
<=> ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
ic(uri_ex_x2),
inference(unit_resolution,[status(thm)],[101,98,88]) ).
tff(103,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
| ~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
| ~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
| ~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_hasSelf,X,Y)
| ~ ( ~ ir(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_hasSelf,uri_ex_x1,literal_typed(dat_str_true,uri_xsd_boolean))
| ~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
~ ( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(unit_resolution,[status(thm)],[105,82,9]) ).
tff(107,plain,
( ~ ir(literal_typed(dat_str_true,uri_xsd_boolean))
| ~ icext(uri_owl_Restriction,uri_ex_x1)
| icext(uri_owl_Restriction,uri_ex_x1) ),
inference(tautology,[status(thm)],[]) ).
tff(108,plain,
icext(uri_owl_Restriction,uri_ex_x1),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
( ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) )
<=> ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
ic(uri_ex_x1),
inference(unit_resolution,[status(thm)],[111,98,108]) ).
tff(113,plain,
( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
<=> ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,axiom,
~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_restrict_hasself_cmp_prop) ).
tff(115,plain,
~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(117,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(unit_resolution,[status(thm)],[117,112,102,65]) ).
tff(119,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],[]) ).
tff(120,plain,
icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[119,118]) ).
tff(121,plain,
( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
<=> iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) )
| ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],[]) ).
tff(122,plain,
( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
<=> iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) )
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[122,34]) ).
tff(124,plain,
( iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
<=> iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2),
inference(and_elim,[status(thm)],[67]) ).
tff(126,plain,
iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( ( ~ ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_x2,X)
<=> iext(uri_ex_p2,X,X) ) )
<=> ( ~ ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_x2,X)
<=> iext(uri_ex_p2,X,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_x2,X)
<=> iext(uri_ex_p2,X,X) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
( ~ ! [Z: $i,P: $i,V: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_hasSelf,Z,V)
| ! [X: $i] :
( icext(Z,X)
<=> iext(P,X,X) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_hasSelf,uri_ex_x2,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_x2,X)
<=> iext(uri_ex_p2,X,X) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [X: $i] :
( icext(uri_ex_x2,X)
<=> iext(uri_ex_p2,X,X) ),
inference(unit_resolution,[status(thm)],[129,28,69,126]) ).
tff(131,plain,
( ~ ! [X: $i] :
( icext(uri_ex_x2,X)
<=> iext(uri_ex_p2,X,X) )
| ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
<=> iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
<=> iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],[]) ).
tff(134,plain,
~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[133,118]) ).
tff(135,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
<=> iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) )
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],[]) ).
tff(136,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
<=> iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[136,132]) ).
tff(138,plain,
( iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
<=> iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2),
inference(and_elim,[status(thm)],[2]) ).
tff(140,plain,
iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
^ [P: $i,Q: $i] :
refl(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
^ [P: $i,Q: $i] :
rewrite(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(144,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[144,142]) ).
tff(146,plain,
^ [P: $i,Q: $i] :
rewrite(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,plain,
^ [P: $i,Q: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [X: $i,Y: $i] :
rewrite(( ( iext(P,X,Y)
=> iext(Q,X,Y) )
<=> ( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ))),
( ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) )),
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
rewrite(( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
rewrite(( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(150,plain,
( ! [P: $i,Q: $i] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,axiom,
! [P: $i,Q: $i] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_subpropertyof_main) ).
tff(152,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(skolemize,[status(sab)],[153]) ).
tff(155,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[154,147]) ).
tff(156,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[155,145]) ).
tff(157,plain,
( ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ),
inference(unit_resolution,[status(thm)],[159,156,140]) ).
tff(161,plain,
( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(162,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ),
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
$false,
inference(unit_resolution,[status(thm)],[165,162,137,123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWB086+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:58:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.59/0.78 % SZS status Theorem
% 0.59/0.78 % SZS output start Proof
% See solution above
% 0.59/0.83 % E exiting
%------------------------------------------------------------------------------