%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB016+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:29:35 AM UTC 2025
% Result : Theorem 0.55s 0.74s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 68
% Syntax : Number of formulae : 163 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 2098 ( 0 equ)
% Maximal formula atoms : 40 ( 12 avg)
% Number of connectives : 3913 (2031 ~;1460 |; 159 &)
% ( 251 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 53 ( 53 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 588 ( 540 !; 0 ?; 588 :)
% Comments :
%------------------------------------------------------------------------------
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(tptp_fun_X_61_type,type,
tptp_fun_X_61: ( $i * $i ) > $i ).
tff(tptp_fun_X_63_type,type,
tptp_fun_X_63: ( $i * $i ) > $i ).
tff(uri_owl_equivalentClass_type,type,
uri_owl_equivalentClass: $i ).
tff(uri_rdfs_subClassOf_type,type,
uri_rdfs_subClassOf: $i ).
tff(tptp_fun_Y_62_type,type,
tptp_fun_Y_62: ( $i * $i ) > $i ).
tff(ic_type,type,
ic: $i > $o ).
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(ip_type,type,
ip: $i > $o ).
tff(uri_rdfs_subPropertyOf_type,type,
uri_rdfs_subPropertyOf: $i ).
tff(uri_rdfs_Container_type,type,
uri_rdfs_Container: $i ).
tff(uri_rdf_Alt_type,type,
uri_rdf_Alt: $i ).
tff(tptp_fun_X_67_type,type,
tptp_fun_X_67: ( $i * $i ) > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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)],[3]) ).
tff(5,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(6,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)],[5]) ).
tff(7,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)],[6,4]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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(14,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)],[13]) ).
tff(15,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/sandbox/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subclassof) ).
tff(16,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)],[15,14]) ).
tff(17,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)],[16,12]) ).
tff(18,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)],[17]) ).
tff(19,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)],[18,11]) ).
tff(20,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)],[19,9]) ).
tff(21,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)],[20,7]) ).
tff(22,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)],[21,2]) ).
tff(23,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,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ) )
<=> ( ~ ! [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,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,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,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),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,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,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,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),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,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,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,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,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,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ! [X: $i] :
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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)],[37,35]) ).
tff(39,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(40,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)],[39]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,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)],[44]) ).
tff(46,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/sandbox/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subpropertyof) ).
tff(47,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)],[46,45]) ).
tff(48,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)],[47,43]) ).
tff(49,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)],[48]) ).
tff(50,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)],[49,42]) ).
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)) ) ) ),
inference(modus_ponens,[status(thm)],[50,40]) ).
tff(52,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)],[51,38]) ).
tff(53,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)],[52,33]) ).
tff(54,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_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) )
| ~ ip(uri_owl_equivalentClass) ) ) ) )
<=> ( ~ ! [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_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) )
| ~ ip(uri_owl_equivalentClass) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) ) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) )
| ~ ip(uri_owl_equivalentClass) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,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_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) ) ) ) ) )
<=> ( ~ ! [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_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) )
| ~ ip(uri_owl_equivalentClass) ) ) ) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,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_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) ) ) ) ) )
<=> ( ~ ! [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_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) )
| ~ ip(uri_owl_equivalentClass) ) ) ) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,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_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,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_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) )
| ~ ip(uri_owl_equivalentClass) ) ) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ ( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) )
| ~ ip(uri_owl_equivalentClass) ) ) ),
inference(unit_resolution,[status(thm)],[59,53]) ).
tff(61,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ( ~ ip(uri_rdfs_subClassOf)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| iext(uri_rdfs_subClassOf,X,Y) )
| ~ ip(uri_owl_equivalentClass) ) )
| iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(62,plain,
( iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container)
<=> iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_container_alt_sub) ).
tff(65,plain,
iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
^ [S: $i,P: $i,O: $i] :
refl(( ( ip(P)
| ~ iext(P,S,O) )
<=> ( ip(P)
| ~ iext(P,S,O) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
<=> ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
<=> ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
^ [S: $i,P: $i,O: $i] :
rewrite(( ( iext(P,S,O)
=> ip(P) )
<=> ( ip(P)
| ~ iext(P,S,O) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [S: $i,P: $i,O: $i] :
( iext(P,S,O)
=> ip(P) )
<=> ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [S: $i,P: $i,O: $i] :
( iext(P,S,O)
=> ip(P) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',simple_iext_property) ).
tff(72,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
| ip(uri_rdfs_subClassOf)
| ~ iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container) )
<=> ( ~ ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
| ip(uri_rdfs_subClassOf)
| ~ iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
| ip(uri_rdfs_subClassOf)
| ~ iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) )
| ip(uri_rdfs_subClassOf)
| ~ iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
ip(uri_rdfs_subClassOf),
inference(unit_resolution,[status(thm)],[78,75,65]) ).
tff(80,plain,
( ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
<=> ~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',testcase_conclusion_fullish_016_Reflective_Tautologies_II) ).
tff(82,plain,
~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( ip(uri_owl_equivalentClass)
<=> ip(uri_owl_equivalentClass) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,axiom,
ip(uri_owl_equivalentClass),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_prop_equivalentclass_type) ).
tff(85,plain,
ip(uri_owl_equivalentClass),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
( ~ ( iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf)
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass)
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ),
inference(unit_resolution,[status(thm)],[86,85,82,79]) ).
tff(88,plain,
~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ),
inference(unit_resolution,[status(thm)],[87,62]) ).
tff(89,plain,
( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ),
inference(tautology,[status(thm)],[]) ).
tff(90,plain,
iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
<=> ( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) )
<=> ( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [X: $i,Y: $i] :
rewrite(( ( iext(uri_owl_equivalentClass,X,Y)
=> ( ic(X)
& ic(Y) ) )
<=> ( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_equivalentClass,X,Y)
=> ( ic(X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_equivalentClass,X,Y)
=> ( ic(X)
& ic(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_prop_equivalentclass_ext) ).
tff(99,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ),
inference(modus_ponens,[status(thm)],[102,92]) ).
tff(104,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
<=> ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ),
inference(unit_resolution,[status(thm)],[109,103,90]) ).
tff(111,plain,
( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ),
inference(tautology,[status(thm)],[]) ).
tff(114,plain,
ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)),
inference(unit_resolution,[status(thm)],[113,110]) ).
tff(115,plain,
( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ),
inference(tautology,[status(thm)],[]) ).
tff(116,plain,
~ iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)),
inference(unit_resolution,[status(thm)],[115,88]) ).
tff(117,plain,
( ~ ( iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(118,plain,
( ~ ( iext(uri_rdfs_subClassOf,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) ),
inference(unit_resolution,[status(thm)],[117,116]) ).
tff(119,plain,
~ ( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ),
inference(unit_resolution,[status(thm)],[118,114,112,31]) ).
tff(120,plain,
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| ~ icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ),
inference(tautology,[status(thm)],[]) ).
tff(121,plain,
~ icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))),
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
( ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ),
inference(tautology,[status(thm)],[]) ).
tff(123,plain,
icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))),
inference(unit_resolution,[status(thm)],[122,119]) ).
tff(124,plain,
( ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) )
| ~ icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
| icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ),
inference(tautology,[status(thm)],[]) ).
tff(125,plain,
~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ),
inference(unit_resolution,[status(thm)],[124,123,121]) ).
tff(126,plain,
^ [C1: $i,C2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(127,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
^ [C1: $i,C2: $i] :
refl(( ~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
^ [C1: $i,C2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(131,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
^ [C1: $i,C2: $i] :
trans(monotonicity(rewrite(( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
<=> ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )),
trans(monotonicity(rewrite(( ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) )
<=> ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )),
( ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
<=> ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )),
rewrite(( ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
<=> ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )),
( ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
<=> ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )),
( ( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) )),
rewrite(( ( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) )),
( ( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(134,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,plain,
^ [C1: $i,C2: $i] :
rewrite(( ( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(136,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,plain,
^ [C1: $i,C2: $i] :
rewrite(( ( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
<=> ( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,axiom,
! [C1: $i,C2: $i] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_eqdis_equivalentclass) ).
tff(141,plain,
! [C1: $i,C2: $i] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
! [C1: $i,C2: $i] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[141,137]) ).
tff(143,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
& ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[143,136]) ).
tff(145,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[144,134]) ).
tff(146,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) )
| ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[145,132]) ).
tff(147,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) ),
inference(modus_ponens,[status(thm)],[146,127]) ).
tff(148,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,plain,
( ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) )
<=> ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[150,148]) ).
tff(152,plain,
( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_owl_equivalentClass,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( icext(C1,tptp_fun_X_67(C2,C1))
<=> icext(C2,tptp_fun_X_67(C2,C1)) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
~ ( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ) ),
inference(unit_resolution,[status(thm)],[153,147]) ).
tff(155,plain,
( ~ ( iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_67(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) )
| ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(156,plain,
( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ),
inference(unit_resolution,[status(thm)],[155,154]) ).
tff(157,plain,
( ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) )
| ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(158,plain,
( ~ ( ~ iext(uri_owl_equivalentClass,tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) )
| ~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ) ),
inference(unit_resolution,[status(thm)],[157,90]) ).
tff(159,plain,
~ ( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ),
inference(unit_resolution,[status(thm)],[158,156]) ).
tff(160,plain,
( ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ) ),
inference(tautology,[status(thm)],[]) ).
tff(161,plain,
! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) ),
inference(unit_resolution,[status(thm)],[160,159]) ).
tff(162,plain,
( ~ ! [X: $i] :
( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),X)
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),X) )
| ( icext(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)))
<=> icext(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_61(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass),tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
$false,
inference(unit_resolution,[status(thm)],[162,161,125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWB016+1 : TPTP v9.0.0. Released v5.2.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 07:47:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.55/0.74 % SZS status Theorem
% 0.55/0.74 % SZS output start Proof
% See solution above
% 0.62/0.80 % E exiting
%------------------------------------------------------------------------------