0.06/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.33	% Computer   : n025.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1200
0.12/0.33	% WCLimit    : 120
0.12/0.33	% DateTime   : Tue Jul 13 17:29:42 EDT 2021
0.12/0.33	% CPUTime    : 
328.50/41.76	% SZS status Theorem
328.50/41.76	
328.50/41.77	% SZS output start Proof
328.50/41.77	Take the following subset of the input axioms:
328.50/41.77	  fof(owl_char_inversefunctional, axiom, ![P]: (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![Y, X1, X2]: ((iext(P, X2, Y) & iext(P, X1, Y)) => X2=X1)))).
328.50/41.77	  fof(owl_eqdis_sameas, axiom, ![X, Y]: (X=Y <=> iext(uri_owl_sameAs, X, Y))).
328.50/41.77	  fof(rdfs_cext_def, axiom, ![X, C]: (iext(uri_rdf_type, X, C) <=> icext(C, X))).
328.50/41.77	  fof(testcase_conclusion_fullish_008_Inverse_Functional_Data_Properties, conjecture, iext(uri_owl_sameAs, uri_ex_bob, uri_ex_robert)).
328.50/41.77	  fof(testcase_premise_fullish_008_Inverse_Functional_Data_Properties, axiom, iext(uri_rdf_type, uri_foaf_mbox_sha1sum, uri_owl_DatatypeProperty) & (iext(uri_rdf_type, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty) & (iext(uri_foaf_mbox_sha1sum, uri_ex_robert, literal_plain(dat_str_xyz)) & iext(uri_foaf_mbox_sha1sum, uri_ex_bob, literal_plain(dat_str_xyz))))).
328.50/41.77	
328.50/41.77	Now clausify the problem and encode Horn clauses using encoding 3 of
328.50/41.77	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
328.50/41.77	We repeatedly replace C & s=t => u=v by the two clauses:
328.50/41.77	  fresh(y, y, x1...xn) = u
328.50/41.77	  C => fresh(s, t, x1...xn) = v
328.50/41.77	where fresh is a fresh function symbol and x1..xn are the free
328.50/41.77	variables of u and v.
328.50/41.77	A predicate p(X) is encoded as p(X)=true (this is sound, because the
328.50/41.77	input problem has no model of domain size 1).
328.50/41.77	
328.50/41.77	The encoding turns the above axioms into the following unit equations and goals:
328.50/41.77	
328.50/41.77	Axiom 1 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_1): iext(uri_rdf_type, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty) = true2.
328.50/41.77	Axiom 2 (owl_eqdis_sameas): iext(uri_owl_sameAs, X, X) = true2.
328.50/41.77	Axiom 3 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_2): iext(uri_foaf_mbox_sha1sum, uri_ex_robert, literal_plain(dat_str_xyz)) = true2.
328.50/41.77	Axiom 4 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_3): iext(uri_foaf_mbox_sha1sum, uri_ex_bob, literal_plain(dat_str_xyz)) = true2.
328.50/41.77	Axiom 5 (owl_char_inversefunctional_1): fresh1275(X, X, Y, Z) = Y.
328.50/41.77	Axiom 6 (rdfs_cext_def): fresh35(X, X, Y, Z) = true2.
328.50/41.77	Axiom 7 (owl_char_inversefunctional_1): fresh3(X, X, Y, Z, W, V) = W.
328.50/41.77	Axiom 8 (owl_char_inversefunctional_1): fresh1274(X, X, Y, Z, W, V) = fresh1275(iext(Y, Z, V), true2, Z, W).
328.50/41.77	Axiom 9 (rdfs_cext_def): fresh35(iext(uri_rdf_type, X, Y), true2, X, Y) = icext(Y, X).
328.50/41.77	Axiom 10 (owl_char_inversefunctional_1): fresh1274(icext(uri_owl_InverseFunctionalProperty, X), true2, X, Y, Z, W) = fresh3(iext(X, Z, W), true2, X, Y, Z, W).
328.50/41.77	
328.50/41.77	Goal 1 (testcase_conclusion_fullish_008_Inverse_Functional_Data_Properties): iext(uri_owl_sameAs, uri_ex_bob, uri_ex_robert) = true2.
328.50/41.77	Proof:
328.50/41.77	  iext(uri_owl_sameAs, uri_ex_bob, uri_ex_robert)
328.50/41.77	= { by axiom 5 (owl_char_inversefunctional_1) R->L }
328.50/41.77	  iext(uri_owl_sameAs, fresh1275(true2, true2, uri_ex_bob, uri_ex_robert), uri_ex_robert)
328.50/41.77	= { by axiom 4 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_3) R->L }
328.50/41.77	  iext(uri_owl_sameAs, fresh1275(iext(uri_foaf_mbox_sha1sum, uri_ex_bob, literal_plain(dat_str_xyz)), true2, uri_ex_bob, uri_ex_robert), uri_ex_robert)
328.50/41.77	= { by axiom 8 (owl_char_inversefunctional_1) R->L }
328.50/41.77	  iext(uri_owl_sameAs, fresh1274(true2, true2, uri_foaf_mbox_sha1sum, uri_ex_bob, uri_ex_robert, literal_plain(dat_str_xyz)), uri_ex_robert)
328.50/41.77	= { by axiom 6 (rdfs_cext_def) R->L }
328.50/41.77	  iext(uri_owl_sameAs, fresh1274(fresh35(true2, true2, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty), true2, uri_foaf_mbox_sha1sum, uri_ex_bob, uri_ex_robert, literal_plain(dat_str_xyz)), uri_ex_robert)
328.50/41.77	= { by axiom 1 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_1) R->L }
328.50/41.77	  iext(uri_owl_sameAs, fresh1274(fresh35(iext(uri_rdf_type, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty), true2, uri_foaf_mbox_sha1sum, uri_owl_InverseFunctionalProperty), true2, uri_foaf_mbox_sha1sum, uri_ex_bob, uri_ex_robert, literal_plain(dat_str_xyz)), uri_ex_robert)
328.50/41.77	= { by axiom 9 (rdfs_cext_def) }
328.50/41.77	  iext(uri_owl_sameAs, fresh1274(icext(uri_owl_InverseFunctionalProperty, uri_foaf_mbox_sha1sum), true2, uri_foaf_mbox_sha1sum, uri_ex_bob, uri_ex_robert, literal_plain(dat_str_xyz)), uri_ex_robert)
328.50/41.77	= { by axiom 10 (owl_char_inversefunctional_1) }
328.50/41.77	  iext(uri_owl_sameAs, fresh3(iext(uri_foaf_mbox_sha1sum, uri_ex_robert, literal_plain(dat_str_xyz)), true2, uri_foaf_mbox_sha1sum, uri_ex_bob, uri_ex_robert, literal_plain(dat_str_xyz)), uri_ex_robert)
328.50/41.77	= { by axiom 3 (testcase_premise_fullish_008_Inverse_Functional_Data_Properties_2) }
328.50/41.77	  iext(uri_owl_sameAs, fresh3(true2, true2, uri_foaf_mbox_sha1sum, uri_ex_bob, uri_ex_robert, literal_plain(dat_str_xyz)), uri_ex_robert)
328.50/41.77	= { by axiom 7 (owl_char_inversefunctional_1) }
328.50/41.77	  iext(uri_owl_sameAs, uri_ex_robert, uri_ex_robert)
328.50/41.77	= { by axiom 2 (owl_eqdis_sameas) }
328.50/41.77	  true2
328.50/41.77	% SZS output end Proof
328.50/41.77	
328.50/41.77	RESULT: Theorem (the conjecture is true).
328.50/41.83	EOF