0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n003.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 11:56:02 EDT 2019
0.12/0.33	% CPUTime    : 
19.53/19.68	% SZS status Unsatisfiable
19.53/19.68	
19.53/19.68	% SZS output start Proof
19.53/19.68	Take the following subset of the input axioms:
19.53/19.68	  fof(ax2_4304, axiom, genls(c_tptpcol_16_130924, c_tptpcol_15_130923)=true).
19.53/19.68	  fof(goal, negated_conjecture, b!=a).
19.53/19.68	  fof(ifeq_axiom_001, axiom, ![A, B, C]: ifeq3(A, A, B, C)=B).
19.53/19.68	  fof(query172_1, negated_conjecture, ifeq3(genls(c_tptpcol_16_130924, c_tptpcol_15_130923), true, a, b)=b).
19.53/19.68	
19.53/19.68	Now clausify the problem and encode Horn clauses using encoding 3 of
19.53/19.68	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
19.53/19.68	We repeatedly replace C & s=t => u=v by the two clauses:
19.53/19.68	  fresh(y, y, x1...xn) = u
19.53/19.68	  C => fresh(s, t, x1...xn) = v
19.53/19.68	where fresh is a fresh function symbol and x1..xn are the free
19.53/19.68	variables of u and v.
19.53/19.68	A predicate p(X) is encoded as p(X)=true (this is sound, because the
19.53/19.68	input problem has no model of domain size 1).
19.53/19.68	
19.53/19.68	The encoding turns the above axioms into the following unit equations and goals:
19.53/19.68	
19.53/19.68	Axiom 1 (ifeq_axiom_001): ifeq3(X, X, Y, Z) = Y.
19.53/19.68	Axiom 2 (ax2_4304): genls(c_tptpcol_16_130924, c_tptpcol_15_130923) = true.
19.53/19.68	Axiom 3 (query172_1): ifeq3(genls(c_tptpcol_16_130924, c_tptpcol_15_130923), true, a, b) = b.
19.53/19.68	
19.53/19.68	Goal 1 (goal): b = a.
19.53/19.68	Proof:
19.53/19.68	  b
19.53/19.68	= { by axiom 3 (query172_1) }
19.53/19.68	  ifeq3(genls(c_tptpcol_16_130924, c_tptpcol_15_130923), true, a, b)
19.53/19.68	= { by axiom 2 (ax2_4304) }
19.53/19.68	  ifeq3(true, true, a, b)
19.53/19.68	= { by axiom 1 (ifeq_axiom_001) }
19.53/19.68	  a
19.53/19.68	% SZS output end Proof
19.53/19.68	
19.53/19.68	RESULT: Unsatisfiable (the axioms are contradictory).
19.53/19.75	EOF