0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.11/0.33	% Computer   : n005.cluster.edu
0.11/0.33	% Model      : x86_64 x86_64
0.11/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory     : 8042.1875MB
0.11/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit   : 960
0.11/0.33	% WCLimit    : 120
0.11/0.33	% DateTime   : Thu Jul  2 07:00:06 EDT 2020
0.11/0.33	% CPUTime    : 
80.85/10.59	% SZS status Theorem
80.85/10.59	
80.85/10.59	% SZS output start Proof
80.85/10.59	Take the following subset of the input axioms:
80.85/10.59	  fof(owl_eqdis_sameas, axiom, ![X, Y]: (iext(uri_owl_sameAs, X, Y) <=> Y=X)).
80.85/10.59	  fof(testcase_conclusion_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes, conjecture, iext(uri_owl_sameAs, uri_ex_u, uri_ex_w)).
80.85/10.59	  fof(testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes, axiom, ?[BNODE_x]: (iext(uri_owl_sameAs, BNODE_x, literal_plain(dat_str_abc)) & (iext(uri_owl_sameAs, BNODE_x, uri_ex_w) & iext(uri_owl_sameAs, uri_ex_u, literal_plain(dat_str_abc))))).
80.85/10.59	
80.85/10.59	Now clausify the problem and encode Horn clauses using encoding 3 of
80.85/10.59	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
80.85/10.59	We repeatedly replace C & s=t => u=v by the two clauses:
80.85/10.59	  fresh(y, y, x1...xn) = u
80.85/10.59	  C => fresh(s, t, x1...xn) = v
80.85/10.59	where fresh is a fresh function symbol and x1..xn are the free
80.85/10.59	variables of u and v.
80.85/10.59	A predicate p(X) is encoded as p(X)=true (this is sound, because the
80.85/10.59	input problem has no model of domain size 1).
80.85/10.59	
80.85/10.59	The encoding turns the above axioms into the following unit equations and goals:
80.85/10.59	
80.85/10.59	Axiom 1 (owl_eqdis_sameas_1): fresh(X, X, Y, Z) = Y.
80.85/10.59	Axiom 2 (owl_eqdis_sameas_1): fresh(iext(uri_owl_sameAs, X, Y), true2, X, Y) = Y.
80.85/10.59	Axiom 3 (owl_eqdis_sameas): iext(uri_owl_sameAs, X, X) = true2.
80.85/10.59	Axiom 4 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_2): iext(uri_owl_sameAs, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x, literal_plain(dat_str_abc)) = true2.
80.85/10.59	Axiom 5 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_1): iext(uri_owl_sameAs, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x, uri_ex_w) = true2.
80.85/10.59	Axiom 6 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes): iext(uri_owl_sameAs, uri_ex_u, literal_plain(dat_str_abc)) = true2.
80.85/10.59	
80.85/10.59	Goal 1 (testcase_conclusion_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes): iext(uri_owl_sameAs, uri_ex_u, uri_ex_w) = true2.
80.85/10.59	Proof:
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, uri_ex_w)
80.85/10.59	= { by axiom 2 (owl_eqdis_sameas_1) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, fresh(iext(uri_owl_sameAs, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x, uri_ex_w), true2, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x, uri_ex_w))
80.85/10.59	= { by axiom 5 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_1) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, fresh(true2, true2, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x, uri_ex_w))
80.85/10.59	= { by axiom 1 (owl_eqdis_sameas_1) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x)
80.85/10.59	= { by axiom 1 (owl_eqdis_sameas_1) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, fresh(true2, true2, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x, literal_plain(dat_str_abc)))
80.85/10.59	= { by axiom 4 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_2) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, fresh(iext(uri_owl_sameAs, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x, literal_plain(dat_str_abc)), true2, sK1_testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes_BNODE_x, literal_plain(dat_str_abc)))
80.85/10.59	= { by axiom 2 (owl_eqdis_sameas_1) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, literal_plain(dat_str_abc))
80.85/10.59	= { by axiom 2 (owl_eqdis_sameas_1) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, fresh(iext(uri_owl_sameAs, uri_ex_u, literal_plain(dat_str_abc)), true2, uri_ex_u, literal_plain(dat_str_abc)))
80.85/10.59	= { by axiom 6 (testcase_premise_fullish_006_Literal_Values_represented_by_URIs_and_Blank_Nodes) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, fresh(true2, true2, uri_ex_u, literal_plain(dat_str_abc)))
80.85/10.59	= { by axiom 1 (owl_eqdis_sameas_1) }
80.85/10.59	  iext(uri_owl_sameAs, uri_ex_u, uri_ex_u)
80.85/10.59	= { by axiom 3 (owl_eqdis_sameas) }
80.85/10.59	  true2
80.85/10.59	% SZS output end Proof
80.85/10.59	
80.85/10.59	RESULT: Theorem (the conjecture is true).
80.85/10.65	EOF