%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB087+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.55s 0.75s
% Output : Proof 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 53 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 268 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 302 ( 105 ~; 86 |; 19 &)
% ( 89 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 155 ( 138 !; 0 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_ex_w_type,type,
uri_ex_w: $i ).
tff(uri_ex_p_type,type,
uri_ex_p: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(uri_ex_z_type,type,
uri_ex_z: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
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(1,plain,
^ [X: $i,C: $i] :
refl(( ( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).
tff(5,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ iext(uri_rdf_type,uri_ex_w,uri_ex_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_restrict_hasself_inst_subj) ).
tff(12,plain,
~ iext(uri_rdf_type,uri_ex_w,uri_ex_z),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ~ ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) )
| iext(uri_rdf_type,uri_ex_w,uri_ex_z)
| ~ icext(uri_ex_z,uri_ex_w) ),
inference(tautology,[status(thm)],[]) ).
tff(14,plain,
( ~ ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) )
| ~ icext(uri_ex_z,uri_ex_w) ),
inference(unit_resolution,[status(thm)],[13,12]) ).
tff(15,plain,
~ icext(uri_ex_z,uri_ex_w),
inference(unit_resolution,[status(thm)],[14,9]) ).
tff(16,plain,
( iext(uri_ex_p,uri_ex_w,uri_ex_w)
<=> iext(uri_ex_p,uri_ex_w,uri_ex_w) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
( iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
& iext(uri_ex_p,uri_ex_w,uri_ex_w) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_hasself_inst_subj) ).
tff(18,plain,
iext(uri_ex_p,uri_ex_w,uri_ex_w),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
iext(uri_ex_p,uri_ex_w,uri_ex_w),
inference(modus_ponens,[status(thm)],[18,16]) ).
tff(20,plain,
( ~ ( icext(uri_ex_z,uri_ex_w)
<=> iext(uri_ex_p,uri_ex_w,uri_ex_w) )
| icext(uri_ex_z,uri_ex_w)
| ~ iext(uri_ex_p,uri_ex_w,uri_ex_w) ),
inference(tautology,[status(thm)],[]) ).
tff(21,plain,
~ ( icext(uri_ex_z,uri_ex_w)
<=> iext(uri_ex_p,uri_ex_w,uri_ex_w) ),
inference(unit_resolution,[status(thm)],[20,19,15]) ).
tff(22,plain,
( iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
<=> iext(uri_owl_onProperty,uri_ex_z,uri_ex_p) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p) ),
inference(and_elim,[status(thm)],[17]) ).
tff(24,plain,
iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
inference(modus_ponens,[status(thm)],[24,22]) ).
tff(26,plain,
( iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean))
<=> iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean)) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean)),
inference(and_elim,[status(thm)],[23]) ).
tff(28,plain,
iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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)],[34,32]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,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(40,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)],[39]) ).
tff(41,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(42,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)],[41,40]) ).
tff(43,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)],[42,38]) ).
tff(44,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)],[43]) ).
tff(45,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)],[44,37]) ).
tff(46,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)],[45,35]) ).
tff(47,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)],[46,30]) ).
tff(48,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_z,uri_ex_p)
| ~ iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_z,X)
<=> iext(uri_ex_p,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_z,uri_ex_p)
| ~ iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_z,X)
<=> iext(uri_ex_p,X,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,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_z,uri_ex_p)
| ~ iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_z,X)
<=> iext(uri_ex_p,X,X) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,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_z,uri_ex_p)
| ~ iext(uri_owl_hasSelf,uri_ex_z,literal_typed(dat_str_true,uri_xsd_boolean))
| ! [X: $i] :
( icext(uri_ex_z,X)
<=> iext(uri_ex_p,X,X) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X: $i] :
( icext(uri_ex_z,X)
<=> iext(uri_ex_p,X,X) ),
inference(unit_resolution,[status(thm)],[50,47,28,25]) ).
tff(52,plain,
( ~ ! [X: $i] :
( icext(uri_ex_z,X)
<=> iext(uri_ex_p,X,X) )
| ( icext(uri_ex_z,uri_ex_w)
<=> iext(uri_ex_p,uri_ex_w,uri_ex_w) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,51,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWB087+1 : TPTP v9.0.0. Released v5.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 : Fri Jun 20 07:58:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.55/0.75 % SZS status Theorem
% 0.55/0.75 % SZS output start Proof
% See solution above
% 0.60/0.78 % E exiting
%------------------------------------------------------------------------------