%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB017+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:36 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 28
% Syntax : Number of formulae : 74 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 754 ( 28 equ)
% Maximal formula atoms : 40 ( 10 avg)
% Number of connectives : 1472 ( 818 ~; 499 |; 83 &)
% ( 72 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 26 ( 26 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 256 ( 240 !; 0 ?; 256 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_ex_c_type,type,
uri_ex_c: $i ).
tff(uri_ex_u_type,type,
uri_ex_u: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(uri_ex_w_type,type,
uri_ex_w: $i ).
tff(uri_owl_differentFrom_type,type,
uri_owl_differentFrom: $i ).
tff(uri_ex_notInstanceOf_type,type,
uri_ex_notInstanceOf: $i ).
tff(uri_owl_propertyDisjointWith_type,type,
uri_owl_propertyDisjointWith: $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: ( $i * $i ) > $i ).
tff(tptp_fun_X_1_type,type,
tptp_fun_X_1: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) )
<=> ~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) )
<=> ! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) )
<=> ! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [X: $i,Y: $i] :
trans(rewrite(( ( iext(uri_owl_differentFrom,X,Y)
<=> ( X != Y ) )
<=> ~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ) )),
rewrite(( ~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) )
<=> ~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ) )),
( ( iext(uri_owl_differentFrom,X,Y)
<=> ( X != Y ) )
<=> ~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_differentFrom,X,Y)
<=> ( X != Y ) )
<=> ! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_differentFrom,X,Y)
<=> ( X != Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',owl_eqdis_differentfrom) ).
tff(7,plain,
! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [X: $i,Y: $i] :
~ ( ( X = Y )
<=> iext(uri_owl_differentFrom,X,Y) )
| ~ ( ( uri_ex_w = uri_ex_u )
<=> iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ ( ( uri_ex_w = uri_ex_u )
<=> iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ~ iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u)
<=> ~ iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
~ iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',testcase_conclusion_fullish_017_Built_in_Based_Definitions) ).
tff(15,plain,
~ iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ( ( uri_ex_w = uri_ex_u )
<=> iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u) )
| ( uri_ex_w = uri_ex_u )
| iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ( ( uri_ex_w = uri_ex_u )
<=> iext(uri_owl_differentFrom,uri_ex_w,uri_ex_u) )
| ( uri_ex_w = uri_ex_u ) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
uri_ex_w = uri_ex_u,
inference(unit_resolution,[status(thm)],[17,12]) ).
tff(19,plain,
uri_ex_u = uri_ex_w,
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( iext(uri_rdf_type,uri_ex_u,uri_ex_c)
<=> iext(uri_rdf_type,uri_ex_w,uri_ex_c) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( iext(uri_rdf_type,uri_ex_w,uri_ex_c)
<=> iext(uri_rdf_type,uri_ex_u,uri_ex_c) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( iext(uri_rdf_type,uri_ex_w,uri_ex_c)
<=> iext(uri_rdf_type,uri_ex_w,uri_ex_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
& iext(uri_rdf_type,uri_ex_w,uri_ex_c)
& iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',testcase_premise_fullish_017_Built_in_Based_Definitions) ).
tff(24,plain,
( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
& iext(uri_rdf_type,uri_ex_w,uri_ex_c) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
iext(uri_rdf_type,uri_ex_w,uri_ex_c),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
iext(uri_rdf_type,uri_ex_w,uri_ex_c),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
iext(uri_rdf_type,uri_ex_u,uri_ex_c),
inference(modus_ponens,[status(thm)],[26,21]) ).
tff(28,plain,
^ [P1: $i,P2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [P1: $i,P2: $i] :
refl(( ~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [P1: $i,P2: $i] :
rewrite(( ~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
^ [P1: $i,P2: $i] :
trans(monotonicity(rewrite(( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
<=> ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )),
trans(monotonicity(rewrite(( ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) )
<=> ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )),
( ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
<=> ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )),
rewrite(( ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
<=> ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )),
( ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
<=> ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )),
( ( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) )),
rewrite(( ( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) )),
( ( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
^ [P1: $i,P2: $i] :
rewrite(( ( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) )
<=> ! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_owl_propertyDisjointWith,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_propertyDisjointWith,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [P1: $i,P2: $i] :
rewrite(( ( iext(uri_owl_propertyDisjointWith,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
<=> ( iext(uri_owl_propertyDisjointWith,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [P1: $i,P2: $i] :
( iext(uri_owl_propertyDisjointWith,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_propertyDisjointWith,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [P1: $i,P2: $i] :
( iext(uri_owl_propertyDisjointWith,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',owl_eqdis_propertydisjointwith) ).
tff(43,plain,
! [P1: $i,P2: $i] :
( iext(uri_owl_propertyDisjointWith,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [P1: $i,P2: $i] :
( iext(uri_owl_propertyDisjointWith,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [P1: $i,P2: $i] :
( ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ( ip(P1)
& ip(P2)
& ! [X: $i,Y: $i] :
~ ( iext(P1,X,Y)
& iext(P2,X,Y) ) ) )
& ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ( iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
& iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[46,36]) ).
tff(48,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) )
| ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) ) ),
inference(modus_ponens,[status(thm)],[47,34]) ).
tff(49,plain,
! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[48,29]) ).
tff(50,plain,
( ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) )
<=> ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) )
<=> ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) )
<=> ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) )
<=> ( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [P1: $i,P2: $i] :
~ ( ~ ( iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ip(P1)
| ~ ip(P2)
| ~ ( ~ iext(P1,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1))
| ~ iext(P2,tptp_fun_X_1(P2,P1),tptp_fun_Y_0(P2,P1)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,P1,P2)
| ~ ( ~ ip(P1)
| ~ ip(P2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P1,X,Y)
| ~ iext(P2,X,Y) ) ) ) )
| ~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ ( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[55,49]) ).
tff(57,plain,
( ~ ( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ip(uri_rdf_type)
| ~ ip(uri_ex_notInstanceOf)
| ~ ( ~ iext(uri_ex_notInstanceOf,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf))
| ~ iext(uri_rdf_type,tptp_fun_X_1(uri_rdf_type,uri_ex_notInstanceOf),tptp_fun_Y_0(uri_rdf_type,uri_ex_notInstanceOf)) ) )
| ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) )
| ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(58,plain,
( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
<=> iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type),
inference(and_elim,[status(thm)],[24]) ).
tff(61,plain,
iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) )
| ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
( ~ ( ~ iext(uri_owl_propertyDisjointWith,uri_ex_notInstanceOf,uri_rdf_type)
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) )
| ~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
~ ( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ),
inference(unit_resolution,[status(thm)],[63,58]) ).
tff(65,plain,
( ~ ip(uri_ex_notInstanceOf)
| ~ ip(uri_rdf_type)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) )
| ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(66,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) ),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c)
<=> iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c),
inference(and_elim,[status(thm)],[23]) ).
tff(69,plain,
iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) )
| ~ iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c)
| ~ iext(uri_rdf_type,uri_ex_u,uri_ex_c) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) )
| ~ iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c)
| ~ iext(uri_rdf_type,uri_ex_u,uri_ex_c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) )
| ~ iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c)
| ~ iext(uri_rdf_type,uri_ex_u,uri_ex_c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_notInstanceOf,X,Y)
| ~ iext(uri_rdf_type,X,Y) )
| ~ iext(uri_ex_notInstanceOf,uri_ex_u,uri_ex_c)
| ~ iext(uri_rdf_type,uri_ex_u,uri_ex_c) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
~ iext(uri_rdf_type,uri_ex_u,uri_ex_c),
inference(unit_resolution,[status(thm)],[72,69,66]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB017+2 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.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 : Fri Jun 20 07:51:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------