%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB049+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:29:45 AM UTC 2025
% Result : Theorem 0.61s 0.77s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 56
% Syntax : Number of formulae : 136 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 1090 ( 0 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 1778 ( 874 ~; 540 |; 96 &)
% ( 265 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 50 ( 50 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 358 ( 328 !; 0 ?; 358 :)
% Comments :
%------------------------------------------------------------------------------
tff(ir_type,type,
ir: $i > $o ).
tff(tptp_fun_X_118_type,type,
tptp_fun_X_118: $i > $i ).
tff(uri_ex_p_type,type,
uri_ex_p: $i ).
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_owl_topObjectProperty_type,type,
uri_owl_topObjectProperty: $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(uri_owl_equivalentProperty_type,type,
uri_owl_equivalentProperty: $i ).
tff(tptp_fun_Y_68_type,type,
tptp_fun_Y_68: ( $i * $i ) > $i ).
tff(tptp_fun_X_69_type,type,
tptp_fun_X_69: ( $i * $i ) > $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(uri_owl_ReflexiveProperty_type,type,
uri_owl_ReflexiveProperty: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
<=> ~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
<=> ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i,Y: $i] :
trans(trans(monotonicity(rewrite(( ( ir(X)
& ir(Y) )
<=> ~ ( ~ ir(X)
| ~ ir(Y) ) )),
( ( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) )
<=> ( iext(uri_owl_topObjectProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ ir(Y) ) ) )),
rewrite(( ( iext(uri_owl_topObjectProperty,X,Y)
<=> ~ ( ~ ir(X)
| ~ ir(Y) ) )
<=> ~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ) )),
( ( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) )
<=> ~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ) )),
rewrite(( ~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
<=> ~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ) )),
( ( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) )
<=> ~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) )
<=> ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) )
<=> ! [X: $i,Y: $i] :
( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_topobjectproperty_ext) ).
tff(7,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i,Y: $i] :
( iext(uri_owl_topObjectProperty,X,Y)
<=> ( ir(X)
& ir(Y) ) ),
inference(skolemize,[status(sab)],[7]) ).
tff(9,plain,
! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ),
inference(modus_ponens,[status(thm)],[8,4]) ).
tff(10,plain,
! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
<=> ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
<=> ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
( ( ~ ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
<=> ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> ~ ir(tptp_fun_X_118(uri_ex_p)) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
<=> ( ~ ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
<=> ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
<=> ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(transitivity,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
<=> ~ ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ~ ( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
<=> ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(transitivity,[status(thm)],[19,12]) ).
tff(21,plain,
( ( ~ ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ~ ( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( ( ~ ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ~ ( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ) ),
inference(transitivity,[status(thm)],[21,11]) ).
tff(23,plain,
( ~ ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ~ ( ( ~ ir(tptp_fun_X_118(uri_ex_p))
| ~ ir(tptp_fun_X_118(uri_ex_p)) )
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [X: $i,Y: $i] :
~ ( ( ~ ir(X)
| ~ ir(Y) )
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[24,10]) ).
tff(26,plain,
^ [P1: $i,P2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ~ ( ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [P1: $i,P2: $i] :
refl(( ~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [P1: $i,P2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
^ [P1: $i,P2: $i] :
trans(monotonicity(rewrite(( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
<=> ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ) )),
trans(monotonicity(rewrite(( ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) )
<=> ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) )),
( ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) )
<=> ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )),
rewrite(( ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) )
<=> ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )),
( ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) )
<=> ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )),
( ( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) )),
rewrite(( ( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) )),
( ( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
^ [P1: $i,P2: $i] :
rewrite(( ( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_owl_equivalentProperty,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
<=> ! [P1: $i,P2: $i] :
( iext(uri_owl_equivalentProperty,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [P1: $i,P2: $i] :
rewrite(( ( iext(uri_owl_equivalentProperty,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
<=> ( iext(uri_owl_equivalentProperty,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_owl_equivalentProperty,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
<=> ! [P1: $i,P2: $i] :
( iext(uri_owl_equivalentProperty,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [P1: $i,P2: $i] :
( iext(uri_owl_equivalentProperty,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_eqdis_equivalentproperty) ).
tff(41,plain,
! [P1: $i,P2: $i] :
( iext(uri_owl_equivalentProperty,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [P1: $i,P2: $i] :
( iext(uri_owl_equivalentProperty,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
& ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[44,34]) ).
tff(46,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[45,32]) ).
tff(47,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[46,27]) ).
tff(48,plain,
( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_equivalentProperty,P1,P2)
| ~ ip(P2)
| ~ ip(P1)
| ~ ( iext(P1,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1))
<=> iext(P2,tptp_fun_X_69(P2,P1),tptp_fun_Y_68(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_equivalentProperty,P1,P2)
| ~ ( ~ ip(P2)
| ~ ip(P1)
| ~ ! [X: $i,Y: $i] :
( iext(P1,X,Y)
<=> iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ( iext(uri_ex_p,tptp_fun_X_69(uri_owl_topObjectProperty,uri_ex_p),tptp_fun_Y_68(uri_owl_topObjectProperty,uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_69(uri_owl_topObjectProperty,uri_ex_p),tptp_fun_Y_68(uri_owl_topObjectProperty,uri_ex_p)) ) )
| ~ ( ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
~ ( ~ ( iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ( iext(uri_ex_p,tptp_fun_X_69(uri_owl_topObjectProperty,uri_ex_p),tptp_fun_Y_68(uri_owl_topObjectProperty,uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_69(uri_owl_topObjectProperty,uri_ex_p),tptp_fun_Y_68(uri_owl_topObjectProperty,uri_ex_p)) ) )
| ~ ( ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ ( iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ( iext(uri_ex_p,tptp_fun_X_69(uri_owl_topObjectProperty,uri_ex_p),tptp_fun_Y_68(uri_owl_topObjectProperty,uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_69(uri_owl_topObjectProperty,uri_ex_p),tptp_fun_Y_68(uri_owl_topObjectProperty,uri_ex_p)) ) )
| ~ ( ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) )
| ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
( ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
<=> iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_char_reflexive_ext) ).
tff(54,plain,
iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ( ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) )
| ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
( ~ ( ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) )
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ),
inference(unit_resolution,[status(thm)],[56,51]) ).
tff(58,plain,
( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(59,plain,
! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ ! [X: $i,Y: $i] :
( iext(uri_ex_p,X,Y)
<=> iext(uri_owl_topObjectProperty,X,Y) )
| ( iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
^ [P: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ~ ( ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) )
| ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ! [P: $i] :
~ ( ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) )
| ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
^ [P: $i] :
refl(( ~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
^ [P: $i] :
rewrite(( ~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
^ [P: $i] :
trans(monotonicity(rewrite(( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
<=> ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) ) )),
rewrite(( ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) )
<=> ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )),
( ( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) )),
rewrite(( ( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) )),
( ( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [P: $i] :
( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
^ [P: $i] :
rewrite(( ( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [P: $i] :
( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) )
<=> ! [P: $i] :
( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [P: $i] :
( icext(uri_owl_ReflexiveProperty,P)
<=> ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
<=> ! [P: $i] :
( icext(uri_owl_ReflexiveProperty,P)
<=> ( ip(P)
& ! [X: $i] : iext(P,X,X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
! [P: $i] :
( icext(uri_owl_ReflexiveProperty,P)
<=> ( ip(P)
& ! [X: $i] : iext(P,X,X) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_char_reflexive) ).
tff(75,plain,
! [P: $i] :
( icext(uri_owl_ReflexiveProperty,P)
<=> ( ip(P)
& ! [X: $i] : iext(P,X,X) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [P: $i] :
( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [P: $i] :
( ( ~ icext(uri_owl_ReflexiveProperty,P)
| ( ip(P)
& ! [X: $i] : iext(P,X,X) ) )
& ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
! [P: $i] :
~ ( ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) )
| ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) ) ),
inference(modus_ponens,[status(thm)],[78,68]) ).
tff(80,plain,
! [P: $i] :
~ ( ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) )
| ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) ) ),
inference(modus_ponens,[status(thm)],[79,63]) ).
tff(81,plain,
( ~ ! [P: $i] :
~ ( ~ ( icext(uri_owl_ReflexiveProperty,P)
| ~ ip(P)
| ~ iext(P,tptp_fun_X_118(P),tptp_fun_X_118(P)) )
| ~ ( ~ icext(uri_owl_ReflexiveProperty,P)
| ~ ( ~ ip(P)
| ~ ! [X: $i] : iext(P,X,X) ) ) )
| ~ ( ~ ( icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| ~ ( ~ icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ! [X: $i] : iext(uri_ex_p,X,X) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
~ ( ~ ( icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| ~ ( ~ icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ! [X: $i] : iext(uri_ex_p,X,X) ) ) ),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( ~ ( icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| ~ ( ~ icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ( ~ ip(uri_ex_p)
| ~ ! [X: $i] : iext(uri_ex_p,X,X) ) )
| icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(tautology,[status(thm)],[]) ).
tff(84,plain,
( icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
<=> ( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) )
<=> ( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
^ [X: $i,Y: $i] :
rewrite(( ( iext(uri_owl_equivalentProperty,X,Y)
=> ( ip(X)
& ip(Y) ) )
<=> ( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_equivalentProperty,X,Y)
=> ( ip(X)
& ip(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_equivalentProperty,X,Y)
=> ( ip(X)
& ip(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_prop_equivalentproperty_ext) ).
tff(93,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ( ip(X)
& ip(Y) ) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) ),
inference(modus_ponens,[status(thm)],[96,86]) ).
tff(98,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
| ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
| ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
| ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_equivalentProperty,X,Y)
| ~ ( ~ ip(Y)
| ~ ip(X) ) )
| ~ iext(uri_owl_equivalentProperty,uri_ex_p,uri_owl_topObjectProperty)
| ~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p) ) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
~ ( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p) ),
inference(unit_resolution,[status(thm)],[100,97,54]) ).
tff(102,plain,
( ~ ip(uri_owl_topObjectProperty)
| ~ ip(uri_ex_p)
| ip(uri_ex_p) ),
inference(tautology,[status(thm)],[]) ).
tff(103,plain,
ip(uri_ex_p),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,plain,
^ [X: $i,C: $i] :
refl(( ( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).
tff(108,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty)
<=> icext(uri_owl_ReflexiveProperty,uri_ex_p) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty)
<=> icext(uri_owl_ReflexiveProperty,uri_ex_p) ),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty)
<=> ~ iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,axiom,
~ iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_char_reflexive_ext) ).
tff(115,plain,
~ iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ ( iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty)
<=> icext(uri_owl_ReflexiveProperty,uri_ex_p) )
| iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty)
| ~ icext(uri_owl_ReflexiveProperty,uri_ex_p) ),
inference(tautology,[status(thm)],[]) ).
tff(117,plain,
( ~ ( iext(uri_rdf_type,uri_ex_p,uri_owl_ReflexiveProperty)
<=> icext(uri_owl_ReflexiveProperty,uri_ex_p) )
| ~ icext(uri_owl_ReflexiveProperty,uri_ex_p) ),
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
~ icext(uri_owl_ReflexiveProperty,uri_ex_p),
inference(unit_resolution,[status(thm)],[117,112]) ).
tff(119,plain,
( ~ ( icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(tautology,[status(thm)],[]) ).
tff(120,plain,
( ~ ( icext(uri_owl_ReflexiveProperty,uri_ex_p)
| ~ ip(uri_ex_p)
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| ~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[119,118,103]) ).
tff(121,plain,
~ iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)),
inference(unit_resolution,[status(thm)],[120,84]) ).
tff(122,plain,
( ~ ( iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p))
| ~ iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(tautology,[status(thm)],[]) ).
tff(123,plain,
( ~ ( iext(uri_ex_p,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| ~ iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[122,121]) ).
tff(124,plain,
~ iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)),
inference(unit_resolution,[status(thm)],[123,61]) ).
tff(125,plain,
( ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| ~ ir(tptp_fun_X_118(uri_ex_p))
| iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) ),
inference(tautology,[status(thm)],[]) ).
tff(126,plain,
( ~ ( ir(tptp_fun_X_118(uri_ex_p))
<=> iext(uri_owl_topObjectProperty,tptp_fun_X_118(uri_ex_p),tptp_fun_X_118(uri_ex_p)) )
| ~ ir(tptp_fun_X_118(uri_ex_p)) ),
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
~ ir(tptp_fun_X_118(uri_ex_p)),
inference(unit_resolution,[status(thm)],[126,25]) ).
tff(128,plain,
^ [X: $i] :
refl(( ir(X)
<=> ir(X) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [X: $i] : ir(X)
<=> ! [X: $i] : ir(X) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [X: $i] : ir(X)
<=> ! [X: $i] : ir(X) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,axiom,
! [X: $i] : ir(X),
file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',simple_ir) ).
tff(132,plain,
! [X: $i] : ir(X),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [X: $i] : ir(X),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [X: $i] : ir(X),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
( ~ ! [X: $i] : ir(X)
| ir(tptp_fun_X_118(uri_ex_p)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
$false,
inference(unit_resolution,[status(thm)],[135,134,127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB049+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:54:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.61/0.77 % SZS status Theorem
% 0.61/0.77 % SZS output start Proof
% See solution above
% 0.61/0.80 % E exiting
%------------------------------------------------------------------------------