0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.33	% Computer   : n010.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 1200
0.13/0.33	% WCLimit    : 120
0.13/0.33	% DateTime   : Tue Jul 13 17:17:21 EDT 2021
0.13/0.33	% CPUTime    : 
590.38/74.61	% SZS status Theorem
590.38/74.61	
590.38/74.61	% SZS output start Proof
590.38/74.61	Take the following subset of the input axioms:
590.38/74.61	  fof(owl_eqdis_sameas, axiom, ![X, Y]: (X=Y <=> iext(uri_owl_sameAs, X, Y))).
590.38/74.61	  fof(owl_rdfsext_domain, axiom, ![P, C]: ((ip(P) & (![X, Y]: (icext(C, X) <= iext(P, X, Y)) & ic(C))) <=> iext(uri_rdfs_domain, P, C))).
590.38/74.61	  fof(rdfs_cext_def, axiom, ![X, C]: (iext(uri_rdf_type, X, C) <=> icext(C, X))).
590.38/74.61	  fof(testcase_conclusion_fullish_018_Modified_Logical_Vocabulary_Semantics, conjecture, iext(uri_rdf_type, uri_ex_u, uri_ex_Person)).
590.38/74.61	  fof(testcase_premise_fullish_018_Modified_Logical_Vocabulary_Semantics, axiom, iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) & iext(uri_rdfs_domain, uri_owl_sameAs, uri_ex_Person)).
590.38/74.61	
590.38/74.61	Now clausify the problem and encode Horn clauses using encoding 3 of
590.38/74.61	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
590.38/74.61	We repeatedly replace C & s=t => u=v by the two clauses:
590.38/74.61	  fresh(y, y, x1...xn) = u
590.38/74.61	  C => fresh(s, t, x1...xn) = v
590.38/74.61	where fresh is a fresh function symbol and x1..xn are the free
590.38/74.61	variables of u and v.
590.38/74.61	A predicate p(X) is encoded as p(X)=true (this is sound, because the
590.38/74.61	input problem has no model of domain size 1).
590.38/74.61	
590.38/74.61	The encoding turns the above axioms into the following unit equations and goals:
590.38/74.61	
590.38/74.61	Axiom 1 (testcase_premise_fullish_018_Modified_Logical_Vocabulary_Semantics): iext(uri_rdfs_domain, uri_owl_sameAs, uri_ex_Person) = true2.
590.38/74.61	Axiom 2 (owl_eqdis_sameas): iext(uri_owl_sameAs, X, X) = true2.
590.38/74.61	Axiom 3 (owl_rdfsext_domain): fresh122(X, X, Y, Z) = true2.
590.38/74.61	Axiom 4 (rdfs_cext_def_1): fresh34(X, X, Y, Z) = true2.
590.38/74.61	Axiom 5 (rdfs_cext_def_1): fresh34(icext(X, Y), true2, Y, X) = iext(uri_rdf_type, Y, X).
590.38/74.61	Axiom 6 (owl_rdfsext_domain): fresh123(X, X, Y, Z, W, V) = icext(Z, W).
590.38/74.61	Axiom 7 (owl_rdfsext_domain): fresh123(iext(uri_rdfs_domain, X, Y), true2, X, Y, Z, W) = fresh122(iext(X, Z, W), true2, Y, Z).
590.38/74.61	
590.38/74.61	Goal 1 (testcase_conclusion_fullish_018_Modified_Logical_Vocabulary_Semantics): iext(uri_rdf_type, uri_ex_u, uri_ex_Person) = true2.
590.38/74.61	Proof:
590.38/74.61	  iext(uri_rdf_type, uri_ex_u, uri_ex_Person)
590.38/74.61	= { by axiom 5 (rdfs_cext_def_1) R->L }
590.38/74.61	  fresh34(icext(uri_ex_Person, uri_ex_u), true2, uri_ex_u, uri_ex_Person)
590.38/74.61	= { by axiom 6 (owl_rdfsext_domain) R->L }
590.38/74.61	  fresh34(fresh123(true2, true2, uri_owl_sameAs, uri_ex_Person, uri_ex_u, uri_ex_u), true2, uri_ex_u, uri_ex_Person)
590.38/74.61	= { by axiom 1 (testcase_premise_fullish_018_Modified_Logical_Vocabulary_Semantics) R->L }
590.38/74.61	  fresh34(fresh123(iext(uri_rdfs_domain, uri_owl_sameAs, uri_ex_Person), true2, uri_owl_sameAs, uri_ex_Person, uri_ex_u, uri_ex_u), true2, uri_ex_u, uri_ex_Person)
590.38/74.61	= { by axiom 7 (owl_rdfsext_domain) }
590.38/74.61	  fresh34(fresh122(iext(uri_owl_sameAs, uri_ex_u, uri_ex_u), true2, uri_ex_Person, uri_ex_u), true2, uri_ex_u, uri_ex_Person)
590.38/74.61	= { by axiom 2 (owl_eqdis_sameas) }
590.38/74.61	  fresh34(fresh122(true2, true2, uri_ex_Person, uri_ex_u), true2, uri_ex_u, uri_ex_Person)
590.38/74.61	= { by axiom 3 (owl_rdfsext_domain) }
590.38/74.61	  fresh34(true2, true2, uri_ex_u, uri_ex_Person)
590.38/74.61	= { by axiom 4 (rdfs_cext_def_1) }
590.38/74.61	  true2
590.38/74.61	% SZS output end Proof
590.38/74.61	
590.38/74.61	RESULT: Theorem (the conjecture is true).
590.38/74.67	EOF