0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.11	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.11/0.32	% Computer   : n026.cluster.edu
0.11/0.32	% Model      : x86_64 x86_64
0.11/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory     : 8042.1875MB
0.11/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1200
0.11/0.32	% WCLimit    : 120
0.11/0.32	% DateTime   : Tue Jul 13 17:58:29 EDT 2021
0.11/0.32	% CPUTime    : 
87.16/11.34	% SZS status Theorem
87.16/11.34	
87.16/11.35	% SZS output start Proof
87.16/11.35	Take the following subset of the input axioms:
87.16/11.35	  fof(conclusion_rdfbased_sem_char_reflexive_ext, conjecture, iext(uri_rdf_type, uri_ex_p, uri_owl_ReflexiveProperty)).
87.16/11.35	  fof(owl_char_reflexive, axiom, ![P]: (icext(uri_owl_ReflexiveProperty, P) <=> (![X]: iext(P, X, X) & ip(P)))).
87.16/11.35	  fof(owl_eqdis_equivalentproperty, axiom, ![P1, P2]: ((![X, Y]: (iext(P2, X, Y) <=> iext(P1, X, Y)) & (ip(P2) & ip(P1))) <=> iext(uri_owl_equivalentProperty, P1, P2))).
87.16/11.35	  fof(owl_prop_topobjectproperty_ext, axiom, ![X, Y]: ((ir(X) & ir(Y)) <=> iext(uri_owl_topObjectProperty, X, Y))).
87.16/11.35	  fof(premise_rdfbased_sem_char_reflexive_ext, axiom, iext(uri_owl_equivalentProperty, uri_ex_p, uri_owl_topObjectProperty)).
87.16/11.35	  fof(rdfs_cext_def, axiom, ![X, C]: (iext(uri_rdf_type, X, C) <=> icext(C, X))).
87.16/11.35	  fof(simple_ir, axiom, ![X]: ir(X)).
87.16/11.35	
87.16/11.35	Now clausify the problem and encode Horn clauses using encoding 3 of
87.16/11.35	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
87.16/11.35	We repeatedly replace C & s=t => u=v by the two clauses:
87.16/11.35	  fresh(y, y, x1...xn) = u
87.16/11.35	  C => fresh(s, t, x1...xn) = v
87.16/11.35	where fresh is a fresh function symbol and x1..xn are the free
87.16/11.35	variables of u and v.
87.16/11.35	A predicate p(X) is encoded as p(X)=true (this is sound, because the
87.16/11.35	input problem has no model of domain size 1).
87.16/11.35	
87.16/11.35	The encoding turns the above axioms into the following unit equations and goals:
87.16/11.35	
87.16/11.35	Axiom 1 (simple_ir): ir(X) = true2.
87.16/11.35	Axiom 2 (premise_rdfbased_sem_char_reflexive_ext): iext(uri_owl_equivalentProperty, uri_ex_p, uri_owl_topObjectProperty) = true2.
87.16/11.35	Axiom 3 (owl_char_reflexive): fresh468(X, X, Y) = icext(uri_owl_ReflexiveProperty, Y).
87.16/11.35	Axiom 4 (owl_char_reflexive): fresh467(X, X, Y) = true2.
87.16/11.35	Axiom 5 (owl_eqdis_equivalentproperty_3): fresh310(X, X, Y) = true2.
87.16/11.35	Axiom 6 (owl_prop_topobjectproperty_ext_2): fresh133(X, X, Y, Z) = iext(uri_owl_topObjectProperty, Y, Z).
87.16/11.35	Axiom 7 (owl_prop_topobjectproperty_ext_2): fresh132(X, X, Y, Z) = true2.
87.16/11.35	Axiom 8 (rdfs_cext_def_1): fresh34(X, X, Y, Z) = true2.
87.16/11.35	Axiom 9 (owl_eqdis_equivalentproperty_2): fresh311(X, X, Y, Z, W) = true2.
87.16/11.35	Axiom 10 (owl_eqdis_equivalentproperty_3): fresh310(iext(uri_owl_equivalentProperty, X, Y), true2, X) = ip(X).
87.16/11.35	Axiom 11 (owl_prop_topobjectproperty_ext_2): fresh133(ir(X), true2, Y, X) = fresh132(ir(Y), true2, Y, X).
87.16/11.35	Axiom 12 (rdfs_cext_def_1): fresh34(icext(X, Y), true2, Y, X) = iext(uri_rdf_type, Y, X).
87.16/11.35	Axiom 13 (owl_eqdis_equivalentproperty_2): fresh312(X, X, Y, Z, W, V) = iext(Y, W, V).
87.16/11.35	Axiom 14 (owl_char_reflexive): fresh468(ip(X), true2, X) = fresh467(iext(X, x22(X), x22(X)), true2, X).
87.16/11.35	Axiom 15 (owl_eqdis_equivalentproperty_2): fresh312(iext(uri_owl_equivalentProperty, X, Y), true2, X, Y, Z, W) = fresh311(iext(Y, Z, W), true2, X, Z, W).
87.16/11.35	
87.16/11.35	Goal 1 (conclusion_rdfbased_sem_char_reflexive_ext): iext(uri_rdf_type, uri_ex_p, uri_owl_ReflexiveProperty) = true2.
87.16/11.35	Proof:
87.16/11.35	  iext(uri_rdf_type, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 12 (rdfs_cext_def_1) R->L }
87.16/11.35	  fresh34(icext(uri_owl_ReflexiveProperty, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 3 (owl_char_reflexive) R->L }
87.16/11.35	  fresh34(fresh468(true2, true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 5 (owl_eqdis_equivalentproperty_3) R->L }
87.16/11.35	  fresh34(fresh468(fresh310(true2, true2, uri_ex_p), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 2 (premise_rdfbased_sem_char_reflexive_ext) R->L }
87.16/11.35	  fresh34(fresh468(fresh310(iext(uri_owl_equivalentProperty, uri_ex_p, uri_owl_topObjectProperty), true2, uri_ex_p), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 10 (owl_eqdis_equivalentproperty_3) }
87.16/11.35	  fresh34(fresh468(ip(uri_ex_p), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 14 (owl_char_reflexive) }
87.16/11.35	  fresh34(fresh467(iext(uri_ex_p, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 13 (owl_eqdis_equivalentproperty_2) R->L }
87.16/11.35	  fresh34(fresh467(fresh312(true2, true2, uri_ex_p, uri_owl_topObjectProperty, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 2 (premise_rdfbased_sem_char_reflexive_ext) R->L }
87.16/11.35	  fresh34(fresh467(fresh312(iext(uri_owl_equivalentProperty, uri_ex_p, uri_owl_topObjectProperty), true2, uri_ex_p, uri_owl_topObjectProperty, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 15 (owl_eqdis_equivalentproperty_2) }
87.16/11.35	  fresh34(fresh467(fresh311(iext(uri_owl_topObjectProperty, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 6 (owl_prop_topobjectproperty_ext_2) R->L }
87.16/11.35	  fresh34(fresh467(fresh311(fresh133(true2, true2, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 1 (simple_ir) R->L }
87.16/11.35	  fresh34(fresh467(fresh311(fresh133(ir(x22(uri_ex_p)), true2, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 11 (owl_prop_topobjectproperty_ext_2) }
87.16/11.35	  fresh34(fresh467(fresh311(fresh132(ir(x22(uri_ex_p)), true2, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 1 (simple_ir) }
87.16/11.35	  fresh34(fresh467(fresh311(fresh132(true2, true2, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 7 (owl_prop_topobjectproperty_ext_2) }
87.16/11.35	  fresh34(fresh467(fresh311(true2, true2, uri_ex_p, x22(uri_ex_p), x22(uri_ex_p)), true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 9 (owl_eqdis_equivalentproperty_2) }
87.16/11.35	  fresh34(fresh467(true2, true2, uri_ex_p), true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 4 (owl_char_reflexive) }
87.16/11.35	  fresh34(true2, true2, uri_ex_p, uri_owl_ReflexiveProperty)
87.16/11.35	= { by axiom 8 (rdfs_cext_def_1) }
87.16/11.35	  true2
87.16/11.35	% SZS output end Proof
87.16/11.35	
87.16/11.35	RESULT: Theorem (the conjecture is true).
87.16/11.42	EOF