%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB099+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:29:51 AM UTC 2025
% Result : Theorem 0.60s 0.78s
% Output : Proof 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 78
% Syntax : Number of formulae : 189 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 1968 ( 0 equ)
% Maximal formula atoms : 40 ( 10 avg)
% Number of connectives : 3767 (2056 ~;1402 |; 165 &)
% ( 118 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 68 ( 68 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-3 aty)
% Number of variables : 700 ( 645 !; 9 ?; 700 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(tptp_fun_Y_42_type,type,
tptp_fun_Y_42: ( $i * $i * $i ) > $i ).
tff(uri_ex_p1_type,type,
uri_ex_p1: $i ).
tff(uri_ex_c_type,type,
uri_ex_c: $i ).
tff(tptp_fun_X_61_type,type,
tptp_fun_X_61: ( $i * $i ) > $i ).
tff(uri_ex_x1_type,type,
uri_ex_x1: $i ).
tff(uri_ex_x2_type,type,
uri_ex_x2: $i ).
tff(uri_ex_p2_type,type,
uri_ex_p2: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(uri_owl_onProperty_type,type,
uri_owl_onProperty: $i ).
tff(uri_owl_someValuesFrom_type,type,
uri_owl_someValuesFrom: $i ).
tff(uri_rdfs_subPropertyOf_type,type,
uri_rdfs_subPropertyOf: $i ).
tff(ic_type,type,
ic: $i > $o ).
tff(uri_rdfs_subClassOf_type,type,
uri_rdfs_subClassOf: $i ).
tff(uri_owl_Restriction_type,type,
uri_owl_Restriction: $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(1,plain,
( iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
<=> iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
& iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_somevalues_cmp_prop) ).
tff(3,plain,
( iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
<=> iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c) ),
inference(and_elim,[status(thm)],[3]) ).
tff(8,plain,
iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
^ [Z: $i,P: $i,C: $i] :
rewrite(( ( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [Z: $i,P: $i,C: $i] :
refl(( ( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [Z: $i,P: $i,C: $i] :
rewrite(( ( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ) ),
inference(transitivity,[status(thm)],[15,13]) ).
tff(17,plain,
^ [Z: $i,P: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
<=> ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C) ) )),
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
<=> ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C) ) )),
rewrite(( ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C) ) )),
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C) ) )),
quant_intro(proof_bind(^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
<=> ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) ) )),
rewrite(( ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) )
<=> ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )),
( ( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ( ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )),
rewrite(( ( ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )),
( ( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ))),
( ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )),
( ( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ) )),
rewrite(( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ) )),
( ( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [Z: $i,P: $i,C: $i] :
rewrite(( ( ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Z: $i,P: $i,C: $i] :
( ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [Z: $i,P: $i,C: $i] :
( ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
=> ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_restrict_somevaluesfrom) ).
tff(23,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( icext(Z,X)
<=> ? [Y: $i] :
( iext(P,X,Y)
& icext(C,Y) ) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_someValuesFrom,Z,C)
& iext(uri_owl_onProperty,Z,P) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y_42(X,C,P))
& icext(C,tptp_fun_Y_42(X,C,P)) ) )
& ( icext(Z,X)
| ! [Y: $i] :
~ ( iext(P,X,Y)
& icext(C,Y) ) ) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) )
| ~ iext(uri_owl_someValuesFrom,Z,C) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,11]) ).
tff(29,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) )
| ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) ),
inference(unit_resolution,[status(thm)],[34,28,9,5]) ).
tff(36,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) )
<=> ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x1,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,X,Y) ) )
| ~ ( ~ icext(uri_ex_x1,X)
| ~ ( ~ iext(uri_ex_p1,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ ( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ),
inference(unit_resolution,[status(thm)],[41,35]) ).
tff(43,plain,
( ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) )
| ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(44,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,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(46,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)],[45]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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)],[50,48]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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(57,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(58,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)],[57]) ).
tff(59,axiom,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subclassof) ).
tff(60,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)],[59,58]) ).
tff(61,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)],[60,56]) ).
tff(62,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)],[61]) ).
tff(63,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)],[62,55]) ).
tff(64,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)],[63,53]) ).
tff(65,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)],[64,51]) ).
tff(66,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)],[65,46]) ).
tff(67,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,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) )
<=> ( ~ ! [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,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,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,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,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,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) )
<=> ( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,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,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,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,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) ) ),
inference(unit_resolution,[status(thm)],[72,66]) ).
tff(74,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2) ) )
| iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(75,plain,
( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
( iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
<=> iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2) ),
inference(and_elim,[status(thm)],[7]) ).
tff(78,plain,
iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c),
inference(and_elim,[status(thm)],[77]) ).
tff(79,plain,
iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c),
inference(modus_ponens,[status(thm)],[78,76]) ).
tff(80,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
<=> ( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
^ [X: $i,Y: $i] :
rewrite(( ( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) )
<=> ( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [X: $i,Y: $i] :
rewrite(( ( iext(uri_owl_someValuesFrom,X,Y)
=> ( icext(uri_owl_Restriction,X)
& ic(Y) ) )
<=> ( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_someValuesFrom,X,Y)
=> ( icext(uri_owl_Restriction,X)
& ic(Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_someValuesFrom,X,Y)
=> ( icext(uri_owl_Restriction,X)
& ic(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_prop_somevaluesfrom_ext) ).
tff(88,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ( icext(uri_owl_Restriction,X)
& ic(Y) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(modus_ponens,[status(thm)],[91,81]) ).
tff(93,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(unit_resolution,[status(thm)],[95,92,79]) ).
tff(97,plain,
( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x2)
| icext(uri_owl_Restriction,uri_ex_x2) ),
inference(tautology,[status(thm)],[]) ).
tff(98,plain,
icext(uri_owl_Restriction,uri_ex_x2),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
^ [X: $i] :
refl(( ( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ( ic(X)
| ~ icext(uri_owl_Restriction,X) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
^ [X: $i] :
rewrite(( ( icext(uri_owl_Restriction,X)
=> ic(X) )
<=> ( ic(X)
| ~ icext(uri_owl_Restriction,X) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [X: $i] :
( icext(uri_owl_Restriction,X)
=> ic(X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [X: $i] :
( icext(uri_owl_Restriction,X)
=> ic(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_class_restriction_ext) ).
tff(105,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
( ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) )
<=> ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
ic(uri_ex_x2),
inference(unit_resolution,[status(thm)],[111,108,98]) ).
tff(113,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_someValuesFrom,X,Y)
| ~ ( ~ ic(Y)
| ~ icext(uri_owl_Restriction,X) ) )
| ~ iext(uri_owl_someValuesFrom,uri_ex_x1,uri_ex_c)
| ~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
~ ( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(unit_resolution,[status(thm)],[115,92,9]) ).
tff(117,plain,
( ~ ic(uri_ex_c)
| ~ icext(uri_owl_Restriction,uri_ex_x1)
| icext(uri_owl_Restriction,uri_ex_x1) ),
inference(tautology,[status(thm)],[]) ).
tff(118,plain,
icext(uri_owl_Restriction,uri_ex_x1),
inference(unit_resolution,[status(thm)],[117,116]) ).
tff(119,plain,
( ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) )
<=> ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
ic(uri_ex_x1),
inference(unit_resolution,[status(thm)],[121,108,118]) ).
tff(123,plain,
( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
<=> ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,axiom,
~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_rdfbased_sem_restrict_somevalues_cmp_prop) ).
tff(125,plain,
~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(127,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ic(uri_ex_x1)
| ~ ic(uri_ex_x2)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(unit_resolution,[status(thm)],[127,122,112,75]) ).
tff(129,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],[]) ).
tff(130,plain,
icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) )
| ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(132,plain,
( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) )
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ),
inference(unit_resolution,[status(thm)],[132,44]) ).
tff(134,plain,
( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ),
inference(tautology,[status(thm)],[]) ).
tff(135,plain,
iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
( iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
<=> iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,plain,
iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2),
inference(and_elim,[status(thm)],[2]) ).
tff(138,plain,
iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
^ [P: $i,Q: $i] :
refl(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
^ [P: $i,Q: $i] :
rewrite(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
^ [P: $i,Q: $i] :
rewrite(( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
^ [P: $i,Q: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [X: $i,Y: $i] :
rewrite(( ( iext(P,X,Y)
=> iext(Q,X,Y) )
<=> ( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ))),
( ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) )),
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
rewrite(( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
rewrite(( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [P: $i,Q: $i] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [P: $i,Q: $i] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_subpropertyof_main) ).
tff(150,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[153,143]) ).
tff(155,plain,
( ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p1,uri_ex_p2)
| ~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
~ ( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ),
inference(unit_resolution,[status(thm)],[157,154,138]) ).
tff(159,plain,
( ~ ip(uri_ex_p2)
| ~ ip(uri_ex_p1)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(160,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) ),
inference(unit_resolution,[status(thm)],[159,158]) ).
tff(161,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p1,X,Y)
| iext(uri_ex_p2,X,Y) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)),
inference(unit_resolution,[status(thm)],[163,160,135]) ).
tff(165,plain,
( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ),
inference(tautology,[status(thm)],[]) ).
tff(166,plain,
icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)),
inference(unit_resolution,[status(thm)],[165,133]) ).
tff(167,plain,
( iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
<=> iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,plain,
iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2),
inference(and_elim,[status(thm)],[77]) ).
tff(169,plain,
iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(transitivity,[status(thm)],[172,170]) ).
tff(174,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) )
| ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
| ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
| ~ ( icext(Z,X)
| ! [Y: $i] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_someValuesFrom,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) ) ) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) ) ),
inference(unit_resolution,[status(thm)],[175,28,79,169]) ).
tff(177,plain,
( ~ ! [X: $i] :
~ ( ~ ( icext(uri_ex_x2,X)
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,X,Y) ) )
| ~ ( ~ icext(uri_ex_x2,X)
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p2)) ) ) )
| ~ ( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
~ ( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ) ),
inference(unit_resolution,[status(thm)],[177,176]) ).
tff(179,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) )
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(180,plain,
( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) ),
inference(unit_resolution,[status(thm)],[179,178]) ).
tff(181,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],[]) ).
tff(182,plain,
~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[181,128]) ).
tff(183,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(184,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) )
| ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ) ),
inference(unit_resolution,[status(thm)],[183,182]) ).
tff(185,plain,
! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) ),
inference(unit_resolution,[status(thm)],[184,180]) ).
tff(186,plain,
( ( ~ ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) )
| ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) )
<=> ( ~ ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) )
| ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ~ ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) )
| ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
( ~ ! [Y: $i] :
( ~ icext(uri_ex_c,Y)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y) )
| ~ icext(uri_ex_c,tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y_42(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
$false,
inference(unit_resolution,[status(thm)],[188,185,166,164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWB099+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.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 07:58:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.60/0.78 % SZS status Theorem
% 0.60/0.78 % SZS output start Proof
% See solution above
% 0.65/0.83 % E exiting
%------------------------------------------------------------------------------