%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB018+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:29:36 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 56 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 19 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 224 ( 84 ~; 65 |; 17 &)
% ( 55 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 124 ( 108 !; 0 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_ex_u_type,type,
uri_ex_u: $i ).
tff(uri_owl_sameAs_type,type,
uri_owl_sameAs: $i ).
tff(uri_ex_w_type,type,
uri_ex_w: $i ).
tff(uri_ex_Person_type,type,
uri_ex_Person: $i ).
tff(uri_rdfs_domain_type,type,
uri_rdfs_domain: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) )
<=> ( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) )
<=> ! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) )
<=> ! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',owl_eqdis_sameas) ).
tff(5,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i] :
( iext(uri_owl_sameAs,X,Y)
<=> ( X = Y ) )
| ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
<=> ( uri_ex_w = uri_ex_u ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
<=> ( uri_ex_w = uri_ex_u ) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
<=> iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
( iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
& iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',testcase_premise_fullish_018_Modified_Logical_Vocabulary_Semantics) ).
tff(12,plain,
iext(uri_owl_sameAs,uri_ex_w,uri_ex_u),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
iext(uri_owl_sameAs,uri_ex_w,uri_ex_u),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
( ~ ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
<=> ( uri_ex_w = uri_ex_u ) )
| ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
| ( uri_ex_w = uri_ex_u ) ),
inference(tautology,[status(thm)],[]) ).
tff(15,plain,
( ~ ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
<=> ( uri_ex_w = uri_ex_u ) )
| ( uri_ex_w = uri_ex_u ) ),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
uri_ex_w = uri_ex_u,
inference(unit_resolution,[status(thm)],[15,9]) ).
tff(17,plain,
uri_ex_u = uri_ex_w,
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( iext(uri_owl_sameAs,uri_ex_u,uri_ex_u)
<=> iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
<=> iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
iext(uri_owl_sameAs,uri_ex_u,uri_ex_u),
inference(modus_ponens,[status(thm)],[13,19]) ).
tff(21,plain,
^ [X: $i,C: $i] :
refl(( ( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdfs_cext_def) ).
tff(25,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
<=> icext(uri_ex_Person,uri_ex_u) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
<=> icext(uri_ex_Person,uri_ex_u) ),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
<=> ~ iext(uri_rdf_type,uri_ex_u,uri_ex_Person) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
~ iext(uri_rdf_type,uri_ex_u,uri_ex_Person),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',testcase_conclusion_fullish_018_Modified_Logical_Vocabulary_Semantics) ).
tff(32,plain,
~ iext(uri_rdf_type,uri_ex_u,uri_ex_Person),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ( iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
<=> icext(uri_ex_Person,uri_ex_u) )
| iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
| ~ icext(uri_ex_Person,uri_ex_u) ),
inference(tautology,[status(thm)],[]) ).
tff(34,plain,
( ~ ( iext(uri_rdf_type,uri_ex_u,uri_ex_Person)
<=> icext(uri_ex_Person,uri_ex_u) )
| ~ icext(uri_ex_Person,uri_ex_u) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
~ icext(uri_ex_Person,uri_ex_u),
inference(unit_resolution,[status(thm)],[34,29]) ).
tff(36,plain,
( iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
<=> iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person),
inference(and_elim,[status(thm)],[11]) ).
tff(38,plain,
iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
^ [P: $i,C: $i,X: $i,Y: $i] :
refl(( ( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) )
<=> ( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) )
<=> ! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
^ [P: $i,C: $i,X: $i,Y: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
<=> ~ ( ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) )),
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
<=> ~ ~ ( ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) )),
rewrite(( ~ ~ ( ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) )
<=> ( ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) )),
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
<=> ( ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) )),
( ( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) )
<=> ( ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y)
| icext(C,X) ) )),
rewrite(( ( ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y)
| icext(C,X) )
<=> ( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) )),
( ( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) )
<=> ( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [P: $i,C: $i,X: $i,Y: $i] :
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) )
<=> ! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [P: $i,C: $i,X: $i,Y: $i] :
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) )
<=> ! [P: $i,C: $i,X: $i,Y: $i] :
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [P: $i,C: $i,X: $i,Y: $i] :
rewrite(( ( ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
=> icext(C,X) )
<=> ( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [P: $i,C: $i,X: $i,Y: $i] :
( ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
=> icext(C,X) )
<=> ! [P: $i,C: $i,X: $i,Y: $i] :
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [P: $i,C: $i,X: $i,Y: $i] :
( ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
=> icext(C,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdfs_domain_main) ).
tff(47,plain,
! [P: $i,C: $i,X: $i,Y: $i] :
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [P: $i,C: $i,X: $i,Y: $i] :
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [P: $i,C: $i,X: $i,Y: $i] :
( ~ ( iext(uri_rdfs_domain,P,C)
& iext(P,X,Y) )
| icext(C,X) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) ),
inference(modus_ponens,[status(thm)],[50,40]) ).
tff(52,plain,
( ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) )
| icext(uri_ex_Person,uri_ex_u)
| ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
| ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) )
<=> ( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) )
| icext(uri_ex_Person,uri_ex_u)
| ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
| ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) )
| icext(uri_ex_Person,uri_ex_u)
| ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
| ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [P: $i,C: $i,X: $i,Y: $i] :
( icext(C,X)
| ~ iext(uri_rdfs_domain,P,C)
| ~ iext(P,X,Y) )
| icext(uri_ex_Person,uri_ex_u)
| ~ iext(uri_rdfs_domain,uri_owl_sameAs,uri_ex_Person)
| ~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ iext(uri_owl_sameAs,uri_ex_u,uri_ex_u),
inference(unit_resolution,[status(thm)],[54,51,38,35]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWB018+2 : TPTP v9.0.0. Released v5.2.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 07:49:46 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------