0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n016.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   : 180
0.12/0.33	% DateTime   : Thu Aug 29 09:39:08 EDT 2019
0.12/0.33	% CPUTime    : 
0.18/0.42	% SZS status Theorem
0.18/0.42	
0.18/0.42	% SZS output start Proof
0.18/0.42	Take the following subset of the input axioms:
0.18/0.43	  fof(complement, axiom, ![X, Z]: (member(Z, complement(X)) <=> (~member(Z, X) & member(Z, universal_class)))).
0.18/0.43	  fof(disjoint_defn, axiom, ![X, Y]: (disjoint(X, Y) <=> ![U]: ~(member(U, X) & member(U, Y)))).
0.18/0.43	  fof(domain_of, axiom, ![X, Z]: ((member(Z, universal_class) & null_class!=restrict(X, singleton(Z), universal_class)) <=> member(Z, domain_of(X)))).
0.18/0.43	  fof(existence_of_null_class, conjecture, ?[X]: ![Z]: ~member(Z, X)).
0.18/0.43	  fof(null_class_defn, axiom, ![X]: ~member(X, null_class)).
0.18/0.43	
0.18/0.43	Now clausify the problem and encode Horn clauses using encoding 3 of
0.18/0.43	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.18/0.43	We repeatedly replace C & s=t => u=v by the two clauses:
0.18/0.43	  fresh(y, y, x1...xn) = u
0.18/0.43	  C => fresh(s, t, x1...xn) = v
0.18/0.43	where fresh is a fresh function symbol and x1..xn are the free
0.18/0.43	variables of u and v.
0.18/0.43	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.18/0.43	input problem has no model of domain size 1).
0.18/0.43	
0.18/0.43	The encoding turns the above axioms into the following unit equations and goals:
0.18/0.43	
0.18/0.43	Axiom 1 (existence_of_null_class): member(sK1_existence_of_null_class_Z(X), X) = true2.
0.18/0.43	
0.18/0.43	Goal 1 (null_class_defn): member(X, null_class) = true2.
0.18/0.43	The goal is true when:
0.18/0.43	  X = sK1_existence_of_null_class_Z(null_class)
0.18/0.43	
0.18/0.43	Proof:
0.18/0.43	  member(sK1_existence_of_null_class_Z(null_class), null_class)
0.18/0.43	= { by axiom 1 (existence_of_null_class) }
0.18/0.43	  true2
0.18/0.43	% SZS output end Proof
0.18/0.43	
0.18/0.43	RESULT: Theorem (the conjecture is true).
0.18/0.43	EOF