0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n004.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   : 960
0.12/0.33	% WCLimit    : 120
0.12/0.33	% DateTime   : Thu Jul  2 07:16:58 EDT 2020
0.12/0.34	% CPUTime    : 
2.22/0.67	% SZS status Theorem
2.22/0.67	
2.22/0.67	% SZS output start Proof
2.22/0.67	Take the following subset of the input axioms:
2.22/0.67	  fof(less_property, axiom, ![X, Y]: ((X!=Y & ~less(Y, X)) <=> less(X, Y))).
2.22/0.67	  fof(something_not_n12, conjecture, ?[X]: X!=n12).
2.22/0.67	
2.22/0.67	Now clausify the problem and encode Horn clauses using encoding 3 of
2.22/0.67	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
2.22/0.67	We repeatedly replace C & s=t => u=v by the two clauses:
2.22/0.67	  fresh(y, y, x1...xn) = u
2.22/0.67	  C => fresh(s, t, x1...xn) = v
2.22/0.67	where fresh is a fresh function symbol and x1..xn are the free
2.22/0.67	variables of u and v.
2.22/0.67	A predicate p(X) is encoded as p(X)=true (this is sound, because the
2.22/0.67	input problem has no model of domain size 1).
2.22/0.67	
2.22/0.67	The encoding turns the above axioms into the following unit equations and goals:
2.22/0.67	
2.22/0.67	Axiom 1 (something_not_n12): X = n12.
2.22/0.67	
2.22/0.67	Lemma 2: X = ?.
2.22/0.67	Proof:
2.22/0.67	  X
2.22/0.67	= { by axiom 1 (something_not_n12) }
2.22/0.67	  n12
2.22/0.67	= { by axiom 1 (something_not_n12) }
2.22/0.67	  ?
2.22/0.67	
2.22/0.67	Goal 1 (true_equals_false): true = false.
2.22/0.67	Proof:
2.22/0.67	  true
2.22/0.67	= { by lemma 2 }
2.22/0.67	  ?
2.22/0.67	= { by lemma 2 }
2.22/0.67	  false
2.22/0.67	% SZS output end Proof
2.22/0.67	
2.22/0.67	RESULT: Theorem (the conjecture is true).
2.22/0.68	EOF