TSTP Solution File: SWB027+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWB027+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 : 600s
% DateTime : Tue Jul 19 19:15:29 EDT 2022
% Result : Theorem 2.66s 2.90s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 25 unt; 0 def)
% Number of atoms : 378 ( 35 equ)
% Maximal formula atoms : 53 ( 3 avg)
% Number of connectives : 487 ( 206 ~; 209 |; 51 &)
% ( 18 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 170 ( 1 sgn 85 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdfs_cext_def,axiom,
! [X,C] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ).
fof(owl_eqdis_sameas,axiom,
! [X,Y] :
( iext(uri_owl_sameAs,X,Y)
<=> X = Y ) ).
fof(owl_chain_002,axiom,
! [P,S1,P1,S2,P2] :
( ( iext(uri_rdf_first,S1,P1)
& iext(uri_rdf_rest,S1,S2)
& iext(uri_rdf_first,S2,P2)
& iext(uri_rdf_rest,S2,uri_rdf_nil) )
=> ( iext(uri_owl_propertyChainAxiom,P,S1)
<=> ( ip(P)
& ip(P1)
& ip(P2)
& ! [Y0,Y1,Y2] :
( ( iext(P1,Y0,Y1)
& iext(P2,Y1,Y2) )
=> iext(P,Y0,Y2) ) ) ) ) ).
fof(owl_char_inversefunctional,axiom,
! [P] :
( icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ip(P)
& ! [X1,X2,Y] :
( ( iext(P,X1,Y)
& iext(P,X2,Y) )
=> X1 = X2 ) ) ) ).
fof(owl_inv,axiom,
! [P1,P2] :
( iext(uri_owl_inverseOf,P1,P2)
<=> ( ip(P1)
& ip(P2)
& ! [X,Y] :
( iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ) ).
fof(testcase_conclusion_fullish_027_Inferred_Property_Characteristics_II,conjecture,
iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty) ).
fof(testcase_premise_fullish_027_Inferred_Property_Characteristics_II,axiom,
? [BNODE_l1,BNODE_l2,BNODE_v] :
( iext(uri_owl_propertyChainAxiom,uri_owl_sameAs,BNODE_l1)
& iext(uri_rdf_first,BNODE_l1,uri_ex_p)
& iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_first,BNODE_l2,BNODE_v)
& iext(uri_rdf_rest,BNODE_l2,uri_rdf_nil)
& iext(uri_owl_inverseOf,BNODE_v,uri_ex_p) ) ).
fof(subgoal_0,plain,
iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty),
inference(strip,[],[testcase_conclusion_fullish_027_Inferred_Property_Characteristics_II]) ).
fof(negate_0_0,plain,
~ iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [C,X] :
( ~ icext(C,X)
<=> ~ iext(uri_rdf_type,X,C) ),
inference(canonicalize,[],[rdfs_cext_def]) ).
fof(normalize_0_1,plain,
! [C,X] :
( ~ icext(C,X)
<=> ~ iext(uri_rdf_type,X,C) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [C,X] :
( ( ~ icext(C,X)
| iext(uri_rdf_type,X,C) )
& ( ~ iext(uri_rdf_type,X,C)
| icext(C,X) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [C,X] :
( ~ icext(C,X)
| iext(uri_rdf_type,X,C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [P] :
( ~ icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ~ ip(P)
| ? [X1,X2,Y] :
( X1 != X2
& iext(P,X1,Y)
& iext(P,X2,Y) ) ) ),
inference(canonicalize,[],[owl_char_inversefunctional]) ).
fof(normalize_0_5,plain,
! [P] :
( ~ icext(uri_owl_InverseFunctionalProperty,P)
<=> ( ~ ip(P)
| ? [X1,X2,Y] :
( X1 != X2
& iext(P,X1,Y)
& iext(P,X2,Y) ) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,X1,X2,Y] :
( ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ip(P) )
& ( skolemFOFtoCNF_X1(P) != skolemFOFtoCNF_X2(P)
| ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P) )
& ( ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P)
| iext(P,skolemFOFtoCNF_X1(P),skolemFOFtoCNF_Y(P)) )
& ( ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P)
| iext(P,skolemFOFtoCNF_X2(P),skolemFOFtoCNF_Y(P)) )
& ( ~ icext(uri_owl_InverseFunctionalProperty,P)
| ~ iext(P,X1,Y)
| ~ iext(P,X2,Y)
| X1 = X2 ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [P] :
( skolemFOFtoCNF_X1(P) != skolemFOFtoCNF_X2(P)
| ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( X != Y
<=> ~ iext(uri_owl_sameAs,X,Y) ),
inference(canonicalize,[],[owl_eqdis_sameas]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( X != Y
<=> ~ iext(uri_owl_sameAs,X,Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( X != Y
| iext(uri_owl_sameAs,X,Y) )
& ( ~ iext(uri_owl_sameAs,X,Y)
| X = Y ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ iext(uri_owl_sameAs,X,Y)
| X = Y ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
? [BNODE_l1,BNODE_l2,BNODE_v] :
( iext(uri_owl_inverseOf,BNODE_v,uri_ex_p)
& iext(uri_owl_propertyChainAxiom,uri_owl_sameAs,BNODE_l1)
& iext(uri_rdf_first,BNODE_l1,uri_ex_p)
& iext(uri_rdf_first,BNODE_l2,BNODE_v)
& iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_rest,BNODE_l2,uri_rdf_nil) ),
inference(canonicalize,[],[testcase_premise_fullish_027_Inferred_Property_Characteristics_II]) ).
fof(normalize_0_13,plain,
( iext(uri_owl_inverseOf,skolemFOFtoCNF_BNODE_v,uri_ex_p)
& iext(uri_owl_propertyChainAxiom,uri_owl_sameAs,skolemFOFtoCNF_BNODE_l1)
& iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l1,uri_ex_p)
& iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l2,skolemFOFtoCNF_BNODE_v)
& iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l1,skolemFOFtoCNF_BNODE_l2)
& iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l2,uri_rdf_nil) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
iext(uri_owl_propertyChainAxiom,uri_owl_sameAs,skolemFOFtoCNF_BNODE_l1),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l1,skolemFOFtoCNF_BNODE_l2),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_16,plain,
iext(uri_owl_inverseOf,skolemFOFtoCNF_BNODE_v,uri_ex_p),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_17,plain,
! [P1,P2] :
( ~ iext(uri_owl_inverseOf,P1,P2)
<=> ( ~ ip(P1)
| ~ ip(P2)
| ? [X,Y] :
( ~ iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ),
inference(canonicalize,[],[owl_inv]) ).
fof(normalize_0_18,plain,
! [P1,P2] :
( ~ iext(uri_owl_inverseOf,P1,P2)
<=> ( ~ ip(P1)
| ~ ip(P2)
| ? [X,Y] :
( ~ iext(P1,X,Y)
<=> iext(P2,Y,X) ) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [P1,P2,X,Y] :
( ( ~ iext(uri_owl_inverseOf,P1,P2)
| ip(P1) )
& ( ~ iext(uri_owl_inverseOf,P1,P2)
| ip(P2) )
& ( ~ iext(P1,X,Y)
| ~ iext(uri_owl_inverseOf,P1,P2)
| iext(P2,Y,X) )
& ( ~ iext(P2,Y,X)
| ~ iext(uri_owl_inverseOf,P1,P2)
| iext(P1,X,Y) )
& ( ~ iext(P1,skolemFOFtoCNF_X(P1,P2),skolemFOFtoCNF_Y_1(P1,P2))
| ~ iext(P2,skolemFOFtoCNF_Y_1(P1,P2),skolemFOFtoCNF_X(P1,P2))
| ~ ip(P1)
| ~ ip(P2)
| iext(uri_owl_inverseOf,P1,P2) )
& ( ~ ip(P1)
| ~ ip(P2)
| iext(P1,skolemFOFtoCNF_X(P1,P2),skolemFOFtoCNF_Y_1(P1,P2))
| iext(P2,skolemFOFtoCNF_Y_1(P1,P2),skolemFOFtoCNF_X(P1,P2))
| iext(uri_owl_inverseOf,P1,P2) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [P1,P2] :
( ~ iext(uri_owl_inverseOf,P1,P2)
| ip(P2) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [P] :
( ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P)
| iext(P,skolemFOFtoCNF_X1(P),skolemFOFtoCNF_Y(P)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_22,plain,
! [P] :
( ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P)
| iext(P,skolemFOFtoCNF_X2(P),skolemFOFtoCNF_Y(P)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_23,plain,
! [P1,P2,X,Y] :
( ~ iext(P2,Y,X)
| ~ iext(uri_owl_inverseOf,P1,P2)
| iext(P1,X,Y) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_24,plain,
iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l2,uri_rdf_nil),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_25,plain,
! [P,P1,P2,S1,S2] :
( ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ( ~ iext(uri_owl_propertyChainAxiom,P,S1)
<=> ( ~ ip(P)
| ~ ip(P1)
| ~ ip(P2)
| ? [Y0,Y1,Y2] :
( ~ iext(P,Y0,Y2)
& iext(P1,Y0,Y1)
& iext(P2,Y1,Y2) ) ) ) ),
inference(canonicalize,[],[owl_chain_002]) ).
fof(normalize_0_26,plain,
! [P,P1,P2,S1,S2] :
( ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ( ~ iext(uri_owl_propertyChainAxiom,P,S1)
<=> ( ~ ip(P)
| ~ ip(P1)
| ~ ip(P2)
| ? [Y0,Y1,Y2] :
( ~ iext(P,Y0,Y2)
& iext(P1,Y0,Y1)
& iext(P2,Y1,Y2) ) ) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [P,P1,P2,S1,S2,Y0,Y1,Y2] :
( ( ~ iext(uri_owl_propertyChainAxiom,P,S1)
| ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ip(P) )
& ( ~ iext(uri_owl_propertyChainAxiom,P,S1)
| ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ip(P1) )
& ( ~ iext(uri_owl_propertyChainAxiom,P,S1)
| ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ip(P2) )
& ( ~ iext(P1,Y0,Y1)
| ~ iext(P2,Y1,Y2)
| ~ iext(uri_owl_propertyChainAxiom,P,S1)
| ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| iext(P,Y0,Y2) )
& ( ~ iext(P,skolemFOFtoCNF_Y0(P,P1,P2),skolemFOFtoCNF_Y2(P,P1,P2))
| ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ~ ip(P)
| ~ ip(P1)
| ~ ip(P2)
| iext(uri_owl_propertyChainAxiom,P,S1) )
& ( ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ~ ip(P)
| ~ ip(P1)
| ~ ip(P2)
| iext(P1,skolemFOFtoCNF_Y0(P,P1,P2),skolemFOFtoCNF_Y1(P,P1,P2))
| iext(uri_owl_propertyChainAxiom,P,S1) )
& ( ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| ~ ip(P)
| ~ ip(P1)
| ~ ip(P2)
| iext(P2,skolemFOFtoCNF_Y1(P,P1,P2),skolemFOFtoCNF_Y2(P,P1,P2))
| iext(uri_owl_propertyChainAxiom,P,S1) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [P,P1,P2,S1,S2,Y0,Y1,Y2] :
( ~ iext(P1,Y0,Y1)
| ~ iext(P2,Y1,Y2)
| ~ iext(uri_owl_propertyChainAxiom,P,S1)
| ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| iext(P,Y0,Y2) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l2,skolemFOFtoCNF_BNODE_v),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_30,plain,
iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l1,uri_ex_p),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_31,plain,
~ iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
( ~ icext(C,X)
| iext(uri_rdf_type,X,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty) ),
inference(subst,[],[refute_0_0:[bind(C,$fot(uri_owl_InverseFunctionalProperty)),bind(X,$fot(uri_ex_p))]]) ).
cnf(refute_0_2,plain,
( skolemFOFtoCNF_X1(P) != skolemFOFtoCNF_X2(P)
| ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( skolemFOFtoCNF_X1(uri_ex_p) != skolemFOFtoCNF_X2(uri_ex_p)
| ~ ip(uri_ex_p)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p) ),
inference(subst,[],[refute_0_2:[bind(P,$fot(uri_ex_p))]]) ).
cnf(refute_0_4,plain,
( ~ iext(uri_owl_sameAs,X,Y)
| X = Y ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ iext(uri_owl_sameAs,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p))
| skolemFOFtoCNF_X1(uri_ex_p) = skolemFOFtoCNF_X2(uri_ex_p) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X1(uri_ex_p))),bind(Y,$fot(skolemFOFtoCNF_X2(uri_ex_p)))]]) ).
cnf(refute_0_6,plain,
iext(uri_owl_propertyChainAxiom,uri_owl_sameAs,skolemFOFtoCNF_BNODE_l1),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l1,skolemFOFtoCNF_BNODE_l2),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_8,plain,
iext(uri_owl_inverseOf,skolemFOFtoCNF_BNODE_v,uri_ex_p),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_9,plain,
( ~ iext(uri_owl_inverseOf,P1,P2)
| ip(P2) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_10,plain,
( ~ iext(uri_owl_inverseOf,skolemFOFtoCNF_BNODE_v,uri_ex_p)
| ip(uri_ex_p) ),
inference(subst,[],[refute_0_9:[bind(P1,$fot(skolemFOFtoCNF_BNODE_v)),bind(P2,$fot(uri_ex_p))]]) ).
cnf(refute_0_11,plain,
ip(uri_ex_p),
inference(resolve,[$cnf( iext(uri_owl_inverseOf,skolemFOFtoCNF_BNODE_v,uri_ex_p) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P)
| iext(P,skolemFOFtoCNF_X1(P),skolemFOFtoCNF_Y(P)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_13,plain,
( ~ ip(uri_ex_p)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(uri_ex_p,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_Y(uri_ex_p)) ),
inference(subst,[],[refute_0_12:[bind(P,$fot(uri_ex_p))]]) ).
cnf(refute_0_14,plain,
( icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(uri_ex_p,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_Y(uri_ex_p)) ),
inference(resolve,[$cnf( ip(uri_ex_p) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ ip(P)
| icext(uri_owl_InverseFunctionalProperty,P)
| iext(P,skolemFOFtoCNF_X2(P),skolemFOFtoCNF_Y(P)) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_16,plain,
( ~ ip(uri_ex_p)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(uri_ex_p,skolemFOFtoCNF_X2(uri_ex_p),skolemFOFtoCNF_Y(uri_ex_p)) ),
inference(subst,[],[refute_0_15:[bind(P,$fot(uri_ex_p))]]) ).
cnf(refute_0_17,plain,
( icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(uri_ex_p,skolemFOFtoCNF_X2(uri_ex_p),skolemFOFtoCNF_Y(uri_ex_p)) ),
inference(resolve,[$cnf( ip(uri_ex_p) )],[refute_0_11,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ iext(P2,Y,X)
| ~ iext(uri_owl_inverseOf,P1,P2)
| iext(P1,X,Y) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_19,plain,
( ~ iext(uri_ex_p,X_45,X_44)
| ~ iext(uri_owl_inverseOf,skolemFOFtoCNF_BNODE_v,uri_ex_p)
| iext(skolemFOFtoCNF_BNODE_v,X_44,X_45) ),
inference(subst,[],[refute_0_18:[bind(P1,$fot(skolemFOFtoCNF_BNODE_v)),bind(P2,$fot(uri_ex_p)),bind(X,$fot(X_44)),bind(Y,$fot(X_45))]]) ).
cnf(refute_0_20,plain,
( ~ iext(uri_ex_p,X_45,X_44)
| iext(skolemFOFtoCNF_BNODE_v,X_44,X_45) ),
inference(resolve,[$cnf( iext(uri_owl_inverseOf,skolemFOFtoCNF_BNODE_v,uri_ex_p) )],[refute_0_8,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ iext(uri_ex_p,skolemFOFtoCNF_X2(uri_ex_p),skolemFOFtoCNF_Y(uri_ex_p))
| iext(skolemFOFtoCNF_BNODE_v,skolemFOFtoCNF_Y(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(subst,[],[refute_0_20:[bind(X_44,$fot(skolemFOFtoCNF_Y(uri_ex_p))),bind(X_45,$fot(skolemFOFtoCNF_X2(uri_ex_p)))]]) ).
cnf(refute_0_22,plain,
( icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(skolemFOFtoCNF_BNODE_v,skolemFOFtoCNF_Y(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(resolve,[$cnf( iext(uri_ex_p,skolemFOFtoCNF_X2(uri_ex_p),skolemFOFtoCNF_Y(uri_ex_p)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l2,uri_rdf_nil),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_24,plain,
( ~ iext(P1,Y0,Y1)
| ~ iext(P2,Y1,Y2)
| ~ iext(uri_owl_propertyChainAxiom,P,S1)
| ~ iext(uri_rdf_first,S1,P1)
| ~ iext(uri_rdf_first,S2,P2)
| ~ iext(uri_rdf_rest,S1,S2)
| ~ iext(uri_rdf_rest,S2,uri_rdf_nil)
| iext(P,Y0,Y2) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_25,plain,
( ~ iext(X_2146,X_2150,X_2151)
| ~ iext(X_2147,X_2151,X_2152)
| ~ iext(uri_owl_propertyChainAxiom,X_2145,X_2148)
| ~ iext(uri_rdf_first,X_2148,X_2146)
| ~ iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l2,X_2147)
| ~ iext(uri_rdf_rest,X_2148,skolemFOFtoCNF_BNODE_l2)
| ~ iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l2,uri_rdf_nil)
| iext(X_2145,X_2150,X_2152) ),
inference(subst,[],[refute_0_24:[bind(P,$fot(X_2145)),bind(P1,$fot(X_2146)),bind(P2,$fot(X_2147)),bind(S1,$fot(X_2148)),bind(S2,$fot(skolemFOFtoCNF_BNODE_l2)),bind(Y0,$fot(X_2150)),bind(Y1,$fot(X_2151)),bind(Y2,$fot(X_2152))]]) ).
cnf(refute_0_26,plain,
( ~ iext(X_2146,X_2150,X_2151)
| ~ iext(X_2147,X_2151,X_2152)
| ~ iext(uri_owl_propertyChainAxiom,X_2145,X_2148)
| ~ iext(uri_rdf_first,X_2148,X_2146)
| ~ iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l2,X_2147)
| ~ iext(uri_rdf_rest,X_2148,skolemFOFtoCNF_BNODE_l2)
| iext(X_2145,X_2150,X_2152) ),
inference(resolve,[$cnf( iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l2,uri_rdf_nil) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ iext(X_2990,X_2993,skolemFOFtoCNF_Y(uri_ex_p))
| ~ iext(skolemFOFtoCNF_BNODE_v,skolemFOFtoCNF_Y(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p))
| ~ iext(uri_owl_propertyChainAxiom,X_2989,X_2992)
| ~ iext(uri_rdf_first,X_2992,X_2990)
| ~ iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l2,skolemFOFtoCNF_BNODE_v)
| ~ iext(uri_rdf_rest,X_2992,skolemFOFtoCNF_BNODE_l2)
| iext(X_2989,X_2993,skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(subst,[],[refute_0_26:[bind(X_2145,$fot(X_2989)),bind(X_2146,$fot(X_2990)),bind(X_2147,$fot(skolemFOFtoCNF_BNODE_v)),bind(X_2148,$fot(X_2992)),bind(X_2150,$fot(X_2993)),bind(X_2151,$fot(skolemFOFtoCNF_Y(uri_ex_p))),bind(X_2152,$fot(skolemFOFtoCNF_X2(uri_ex_p)))]]) ).
cnf(refute_0_28,plain,
( ~ iext(X_2990,X_2993,skolemFOFtoCNF_Y(uri_ex_p))
| ~ iext(uri_owl_propertyChainAxiom,X_2989,X_2992)
| ~ iext(uri_rdf_first,X_2992,X_2990)
| ~ iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l2,skolemFOFtoCNF_BNODE_v)
| ~ iext(uri_rdf_rest,X_2992,skolemFOFtoCNF_BNODE_l2)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(X_2989,X_2993,skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(resolve,[$cnf( iext(skolemFOFtoCNF_BNODE_v,skolemFOFtoCNF_Y(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) )],[refute_0_22,refute_0_27]) ).
cnf(refute_0_29,plain,
iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l2,skolemFOFtoCNF_BNODE_v),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_30,plain,
( ~ iext(X_2990,X_2993,skolemFOFtoCNF_Y(uri_ex_p))
| ~ iext(uri_owl_propertyChainAxiom,X_2989,X_2992)
| ~ iext(uri_rdf_first,X_2992,X_2990)
| ~ iext(uri_rdf_rest,X_2992,skolemFOFtoCNF_BNODE_l2)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(X_2989,X_2993,skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(resolve,[$cnf( iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l2,skolemFOFtoCNF_BNODE_v) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
( ~ iext(uri_ex_p,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_Y(uri_ex_p))
| ~ iext(uri_owl_propertyChainAxiom,X_3007,X_3009)
| ~ iext(uri_rdf_first,X_3009,uri_ex_p)
| ~ iext(uri_rdf_rest,X_3009,skolemFOFtoCNF_BNODE_l2)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(X_3007,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(subst,[],[refute_0_30:[bind(X_2989,$fot(X_3007)),bind(X_2990,$fot(uri_ex_p)),bind(X_2992,$fot(X_3009)),bind(X_2993,$fot(skolemFOFtoCNF_X1(uri_ex_p)))]]) ).
cnf(refute_0_32,plain,
( ~ iext(uri_owl_propertyChainAxiom,X_3007,X_3009)
| ~ iext(uri_rdf_first,X_3009,uri_ex_p)
| ~ iext(uri_rdf_rest,X_3009,skolemFOFtoCNF_BNODE_l2)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(X_3007,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(resolve,[$cnf( iext(uri_ex_p,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_Y(uri_ex_p)) )],[refute_0_14,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ iext(uri_owl_propertyChainAxiom,X_3014,skolemFOFtoCNF_BNODE_l1)
| ~ iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l1,uri_ex_p)
| ~ iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l1,skolemFOFtoCNF_BNODE_l2)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(X_3014,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(subst,[],[refute_0_32:[bind(X_3007,$fot(X_3014)),bind(X_3009,$fot(skolemFOFtoCNF_BNODE_l1))]]) ).
cnf(refute_0_34,plain,
( ~ iext(uri_owl_propertyChainAxiom,X_3014,skolemFOFtoCNF_BNODE_l1)
| ~ iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l1,uri_ex_p)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(X_3014,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(resolve,[$cnf( iext(uri_rdf_rest,skolemFOFtoCNF_BNODE_l1,skolemFOFtoCNF_BNODE_l2) )],[refute_0_7,refute_0_33]) ).
cnf(refute_0_35,plain,
iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l1,uri_ex_p),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_36,plain,
( ~ iext(uri_owl_propertyChainAxiom,X_3014,skolemFOFtoCNF_BNODE_l1)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(X_3014,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(resolve,[$cnf( iext(uri_rdf_first,skolemFOFtoCNF_BNODE_l1,uri_ex_p) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
( ~ iext(uri_owl_propertyChainAxiom,uri_owl_sameAs,skolemFOFtoCNF_BNODE_l1)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(uri_owl_sameAs,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(subst,[],[refute_0_36:[bind(X_3014,$fot(uri_owl_sameAs))]]) ).
cnf(refute_0_38,plain,
( icext(uri_owl_InverseFunctionalProperty,uri_ex_p)
| iext(uri_owl_sameAs,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),
inference(resolve,[$cnf( iext(uri_owl_propertyChainAxiom,uri_owl_sameAs,skolemFOFtoCNF_BNODE_l1) )],[refute_0_6,refute_0_37]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_X1(uri_ex_p) = skolemFOFtoCNF_X2(uri_ex_p)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p) ),
inference(resolve,[$cnf( iext(uri_owl_sameAs,skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) )],[refute_0_38,refute_0_5]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_X1(uri_ex_p) = skolemFOFtoCNF_X2(uri_ex_p)
| iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty) ),
inference(resolve,[$cnf( icext(uri_owl_InverseFunctionalProperty,uri_ex_p) )],[refute_0_39,refute_0_1]) ).
cnf(refute_0_41,plain,
~ iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_42,plain,
skolemFOFtoCNF_X1(uri_ex_p) = skolemFOFtoCNF_X2(uri_ex_p),
inference(resolve,[$cnf( iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_44,plain,
( X0 != X0
| X0 != Y3
| Y3 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y3)]]) ).
cnf(refute_0_45,plain,
( X0 != Y3
| Y3 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( skolemFOFtoCNF_X1(uri_ex_p) != skolemFOFtoCNF_X2(uri_ex_p)
| skolemFOFtoCNF_X2(uri_ex_p) = skolemFOFtoCNF_X1(uri_ex_p) ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(skolemFOFtoCNF_X1(uri_ex_p))),bind(Y3,$fot(skolemFOFtoCNF_X2(uri_ex_p)))]]) ).
cnf(refute_0_47,plain,
skolemFOFtoCNF_X2(uri_ex_p) = skolemFOFtoCNF_X1(uri_ex_p),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) )],[refute_0_42,refute_0_46]) ).
cnf(refute_0_48,plain,
( skolemFOFtoCNF_X1(uri_ex_p) != skolemFOFtoCNF_X1(uri_ex_p)
| skolemFOFtoCNF_X2(uri_ex_p) != skolemFOFtoCNF_X1(uri_ex_p)
| skolemFOFtoCNF_X1(uri_ex_p) = skolemFOFtoCNF_X2(uri_ex_p) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) ),[1],$fot(skolemFOFtoCNF_X1(uri_ex_p))]]) ).
cnf(refute_0_49,plain,
( skolemFOFtoCNF_X1(uri_ex_p) != skolemFOFtoCNF_X1(uri_ex_p)
| skolemFOFtoCNF_X1(uri_ex_p) = skolemFOFtoCNF_X2(uri_ex_p) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X2(uri_ex_p),skolemFOFtoCNF_X1(uri_ex_p)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( skolemFOFtoCNF_X1(uri_ex_p) != skolemFOFtoCNF_X1(uri_ex_p)
| ~ ip(uri_ex_p)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X2(uri_ex_p)) )],[refute_0_49,refute_0_3]) ).
cnf(refute_0_51,plain,
skolemFOFtoCNF_X1(uri_ex_p) = skolemFOFtoCNF_X1(uri_ex_p),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X1(uri_ex_p))]]) ).
cnf(refute_0_52,plain,
( ~ ip(uri_ex_p)
| icext(uri_owl_InverseFunctionalProperty,uri_ex_p) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(uri_ex_p),skolemFOFtoCNF_X1(uri_ex_p)) )],[refute_0_51,refute_0_50]) ).
cnf(refute_0_53,plain,
icext(uri_owl_InverseFunctionalProperty,uri_ex_p),
inference(resolve,[$cnf( ip(uri_ex_p) )],[refute_0_11,refute_0_52]) ).
cnf(refute_0_54,plain,
iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty),
inference(resolve,[$cnf( icext(uri_owl_InverseFunctionalProperty,uri_ex_p) )],[refute_0_53,refute_0_1]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( iext(uri_rdf_type,uri_ex_p,uri_owl_InverseFunctionalProperty) )],[refute_0_54,refute_0_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWB027+2 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 13:04:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.66/2.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.66/2.90
% 2.66/2.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.66/2.90
%------------------------------------------------------------------------------