0.00/0.04	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command    : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn
0.03/0.29	% Computer   : n133.star.cs.uiowa.edu
0.03/0.29	% Model      : x86_64 x86_64
0.03/0.29	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.29	% Memory     : 32218.625MB
0.03/0.29	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.29	% CPULimit   : 300
0.03/0.29	% DateTime   : Fri Jul 13 14:52:42 CDT 2018
0.03/0.29	% CPUTime    : 
0.34/0.60	% SZS status Theorem
0.34/0.60	
0.34/0.60	% SZS output start Proof
0.34/0.60	Take the following subset of the input axioms:
0.34/0.60	  fof(less_property, axiom,
0.34/0.60	      ![X, Y]: (less(X, Y) <=> (X!=Y & ~less(Y, X)))).
0.34/0.60	  fof(something_not_n12, conjecture, ?[X]: X!=n12).
0.34/0.60	
0.34/0.60	Now clausify the problem and encode Horn clauses using encoding 3 of
0.34/0.60	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.34/0.60	We repeatedly replace C & s=t => u=v by the two clauses:
0.34/0.60	  $$fresh(y, y, x1...xn) = u
0.34/0.60	  C => $$fresh(s, t, x1...xn) = v
0.34/0.60	where $$fresh is a fresh function symbol and x1..xn are the free
0.34/0.60	variables of u and v.
0.34/0.60	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
0.34/0.60	input problem has no model of domain size 1).
0.34/0.60	
0.34/0.60	The encoding turns the above axioms into the following unit equations and goals:
0.34/0.60	
0.34/0.60	Axiom 472 (something_not_n12): X = n12.
0.34/0.60	
0.34/0.60	Lemma 473: X = ?.
0.34/0.60	Proof:
0.34/0.60	  X
0.34/0.60	= { by axiom 472 (something_not_n12) }
0.34/0.60	  n12
0.34/0.60	= { by axiom 472 (something_not_n12) }
0.34/0.60	  ?
0.34/0.60	
0.34/0.60	Goal 1 (true_equals_false): $$true = $$false.
0.34/0.60	Proof:
0.34/0.60	  $$true
0.34/0.60	= { by lemma 473 }
0.34/0.60	  ?
0.34/0.60	= { by lemma 473 }
0.34/0.60	  $$false
0.34/0.60	% SZS output end Proof
0.34/0.60	
0.34/0.60	RESULT: Theorem (the conjecture is true).
0.34/0.61	EOF