TSTP Solution File: SWB016+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB016+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:31:47 EDT 2022
% Result : Theorem 0.79s 0.77s
% Output : Proof 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 74
% Syntax : Number of formulae : 158 ( 37 unt; 13 typ; 0 def)
% Number of atoms : 1561 ( 0 equ)
% Maximal formula atoms : 20 ( 10 avg)
% Number of connectives : 2729 (1360 ~;1003 |; 159 &)
% ( 195 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 474 ( 426 !; 0 ?; 474 :)
% 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/sandbox2/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_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(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) ) ) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,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_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))) ) ),
inference(tautology,[status(thm)],]) ).
tff(26,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))) ) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,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)],[31]) ).
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)
| ~ ! [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)],[32,30]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,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(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) ) ) )
<=> ! [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)],[39]) ).
tff(41,axiom,
! [P1: $i,P2: $i] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
=> iext(P2,X,Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subpropertyof) ).
tff(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) ) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
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) ) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,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)],[43]) ).
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) ) ) )
& ( 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)],[44,37]) ).
tff(46,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)],[45,35]) ).
tff(47,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)],[46,33]) ).
tff(48,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)],[47,28]) ).
tff(49,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(50,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) ) ) ) ),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,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)) ) ),
inference(tautology,[status(thm)],]) ).
tff(52,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)],[51,50]) ).
tff(53,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(54,axiom,
iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_container_alt_sub) ).
tff(55,plain,
iext(uri_rdfs_subClassOf,uri_rdf_Alt,uri_rdfs_Container),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,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(60,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)],[59]) ).
tff(61,axiom,
! [S: $i,P: $i,O: $i] :
( iext(P,S,O)
=> ip(P) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',simple_iext_property) ).
tff(62,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [S: $i,P: $i,O: $i] :
( ip(P)
| ~ iext(P,S,O) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,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(67,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(68,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)],[67,66]) ).
tff(69,plain,
ip(uri_rdfs_subClassOf),
inference(unit_resolution,[status(thm)],[68,65,55]) ).
tff(70,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(71,axiom,
~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',testcase_conclusion_fullish_016_Reflective_Tautologies_II) ).
tff(72,plain,
~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( ip(uri_owl_equivalentClass)
<=> ip(uri_owl_equivalentClass) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
ip(uri_owl_equivalentClass),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_equivalentclass_type) ).
tff(75,plain,
ip(uri_owl_equivalentClass),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,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(77,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)],[76,75,72,69]) ).
tff(78,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)],[77,52]) ).
tff(79,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(80,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)],[79,78]) ).
tff(81,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(82,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)],[81]) ).
tff(83,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(84,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)],[83]) ).
tff(85,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(86,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(87,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)],[86]) ).
tff(88,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_equivalentClass,X,Y)
=> ( ic(X)
& ic(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_equivalentclass_ext) ).
tff(89,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ( ic(X)
& ic(Y) ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentClass,X,Y)
| ~ ( ~ ic(Y)
| ~ ic(X) ) ),
inference(modus_ponens,[status(thm)],[92,82]) ).
tff(94,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_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,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(96,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(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
~ ( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ),
inference(unit_resolution,[status(thm)],[96,93,80]) ).
tff(98,plain,
( ~ ic(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(tautology,[status(thm)],]) ).
tff(99,plain,
ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass)),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ ic(tptp_fun_Y_62(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ~ ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass))
| ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)) ),
inference(tautology,[status(thm)],]) ).
tff(101,plain,
ic(tptp_fun_X_63(uri_rdfs_subClassOf,uri_owl_equivalentClass)),
inference(unit_resolution,[status(thm)],[100,97]) ).
tff(102,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(103,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)],[102,78]) ).
tff(104,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))
| ~ ( ~ 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(105,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))) ) )
| ~ 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))) ) ),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,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)],[105,101,99,26]) ).
tff(107,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(108,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)],[107,106]) ).
tff(109,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(110,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)],[109,106]) ).
tff(111,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(112,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)],[111,110,108]) ).
tff(113,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(114,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)],[113]) ).
tff(115,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(116,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)],[115]) ).
tff(117,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(118,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)],[117]) ).
tff(119,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)],[118,116]) ).
tff(120,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) ) ) ) )),
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(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(121,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)],[120]) ).
tff(122,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(123,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)],[122]) ).
tff(124,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(125,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(126,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)],[125]) ).
tff(127,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/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_eqdis_equivalentclass) ).
tff(128,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)],[127,126]) ).
tff(129,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)],[128,124]) ).
tff(130,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)],[129]) ).
tff(131,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)],[130,123]) ).
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)) ) ) ),
inference(modus_ponens,[status(thm)],[131,121]) ).
tff(133,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)],[132,119]) ).
tff(134,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)],[133,114]) ).
tff(135,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(136,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) ) ) ) ),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,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_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(tautology,[status(thm)],]) ).
tff(138,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))
| ~ ! [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)],[137,136]) ).
tff(139,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))
| ~ ! [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_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(tautology,[status(thm)],]) ).
tff(140,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))
| ~ ! [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_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(unit_resolution,[status(thm)],[139,80]) ).
tff(141,plain,
~ ( ~ 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(unit_resolution,[status(thm)],[140,138]) ).
tff(142,plain,
( ~ 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) )
| ! [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(143,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)],[142,141]) ).
tff(144,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(145,plain,
$false,
inference(unit_resolution,[status(thm)],[144,143,112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWB016+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 19:34:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.79/0.77 % SZS status Theorem
% 0.79/0.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------