0.00/0.05	% 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
0.02/0.31	% Computer   : n025.star.cs.uiowa.edu
0.02/0.31	% Model      : x86_64 x86_64
0.02/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.31	% Memory     : 32218.625MB
0.02/0.31	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.31	% CPULimit   : 300
0.02/0.31	% DateTime   : Sat Jul 14 04:22:40 CDT 2018
0.02/0.31	% CPUTime    : 
0.08/0.52	% SZS status Theorem
0.08/0.52	
0.08/0.52	% SZS output start Proof
0.08/0.52	Take the following subset of the input axioms:
0.08/0.52	  fof(mighta, axiom,
0.08/0.52	      ![S1, S2]:
0.08/0.52	        (?[Ax, C]: (status(Ax, C, S1) & status(Ax, C, S2))
0.08/0.52	           <=> mighta(S1, S2))).
0.08/0.52	  fof(mighta_tac_thm, conjecture, mighta(tac, thm)).
0.08/0.52	  fof(non_thm_spt, axiom,
0.08/0.52	      ?[Ax, C, I1]:
0.08/0.52	        (~model(I1, C) & (?[I2]: model(I2, C) & model(I1, Ax)))).
0.08/0.52	  fof(tac, axiom,
0.08/0.52	      ![Ax, C]:
0.08/0.52	        (status(Ax, C, tac)
0.08/0.52	           <=> (?[I1]: model(I1, Ax) & ![I2]: model(I2, C)))).
0.08/0.52	  fof(tautology, axiom, ?[F]: ![I]: model(I, F)).
0.08/0.52	  fof(thm, axiom,
0.08/0.52	      ![Ax, C]:
0.08/0.52	        (![I1]: (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))).
0.08/0.52	
0.08/0.52	Now clausify the problem and encode Horn clauses using encoding 3 of
0.08/0.52	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.08/0.52	We repeatedly replace C & s=t => u=v by the two clauses:
0.08/0.52	  $$fresh(y, y, x1...xn) = u
0.08/0.52	  C => $$fresh(s, t, x1...xn) = v
0.08/0.52	where $$fresh is a fresh function symbol and x1..xn are the free
0.08/0.52	variables of u and v.
0.08/0.52	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
0.08/0.52	input problem has no model of domain size 1).
0.08/0.52	
0.08/0.52	The encoding turns the above axioms into the following unit equations and goals:
0.08/0.52	
0.08/0.52	Axiom 27 (mighta): $$fresh48(X, X, Y, Z, W, V) = mighta(Y, Z).
0.08/0.52	Axiom 28 (mighta): $$fresh47(X, X, Y, Z) = $$true2.
0.08/0.52	Axiom 51 (tac_2): $$fresh28(X, X, Y, Z, W) = status(Y, Z, tac).
0.08/0.52	Axiom 52 (tac_2): $$fresh27(X, X, Y, Z) = $$true2.
0.08/0.52	Axiom 60 (thm_2): $$fresh19(X, X, Y, Z) = $$true2.
0.08/0.52	Axiom 88 (thm_2): $$fresh19(model(sK48_thm_I1(X, Y), Y), $$true2, X, Y) = status(X, Y, thm).
0.08/0.52	Axiom 108 (tac_2): $$fresh28(model(sK34_tac_I2(X), X), $$true2, Y, X, Z) = $$fresh27(model(Z, Y), $$true2, Y, X).
0.08/0.52	Axiom 126 (non_thm_spt_1): model(sK22_non_thm_spt_I2, sK25_non_thm_spt_C) = $$true2.
0.08/0.52	Axiom 139 (mighta): $$fresh48(status(X, Y, Z), $$true2, W, Z, X, Y) = $$fresh47(status(X, Y, W), $$true2, W, Z).
0.08/0.52	Axiom 140 (tautology): model(X, sK1_tautology_F) = $$true2.
0.08/0.52	
0.08/0.52	Goal 1 (mighta_tac_thm): mighta(tac, thm) = $$true2.
0.08/0.52	Proof:
0.08/0.52	  mighta(tac, thm)
0.08/0.52	= { by axiom 27 (mighta) }
0.08/0.52	  $$fresh48($$true2, $$true2, tac, thm, sK25_non_thm_spt_C, sK1_tautology_F)
0.08/0.52	= { by axiom 60 (thm_2) }
0.08/0.52	  $$fresh48($$fresh19($$true2, $$true2, sK25_non_thm_spt_C, sK1_tautology_F), $$true2, tac, thm, sK25_non_thm_spt_C, sK1_tautology_F)
0.08/0.52	= { by axiom 140 (tautology) }
0.08/0.52	  $$fresh48($$fresh19(model(sK48_thm_I1(sK25_non_thm_spt_C, sK1_tautology_F), sK1_tautology_F), $$true2, sK25_non_thm_spt_C, sK1_tautology_F), $$true2, tac, thm, sK25_non_thm_spt_C, sK1_tautology_F)
0.08/0.52	= { by axiom 88 (thm_2) }
0.08/0.52	  $$fresh48(status(sK25_non_thm_spt_C, sK1_tautology_F, thm), $$true2, tac, thm, sK25_non_thm_spt_C, sK1_tautology_F)
0.08/0.52	= { by axiom 139 (mighta) }
0.08/0.52	  $$fresh47(status(sK25_non_thm_spt_C, sK1_tautology_F, tac), $$true2, tac, thm)
0.08/0.52	= { by axiom 51 (tac_2) }
0.08/0.52	  $$fresh47($$fresh28($$true2, $$true2, sK25_non_thm_spt_C, sK1_tautology_F, sK22_non_thm_spt_I2), $$true2, tac, thm)
0.08/0.52	= { by axiom 140 (tautology) }
0.08/0.52	  $$fresh47($$fresh28(model(sK34_tac_I2(sK1_tautology_F), sK1_tautology_F), $$true2, sK25_non_thm_spt_C, sK1_tautology_F, sK22_non_thm_spt_I2), $$true2, tac, thm)
0.08/0.52	= { by axiom 108 (tac_2) }
0.08/0.52	  $$fresh47($$fresh27(model(sK22_non_thm_spt_I2, sK25_non_thm_spt_C), $$true2, sK25_non_thm_spt_C, sK1_tautology_F), $$true2, tac, thm)
0.08/0.52	= { by axiom 126 (non_thm_spt_1) }
0.08/0.52	  $$fresh47($$fresh27($$true2, $$true2, sK25_non_thm_spt_C, sK1_tautology_F), $$true2, tac, thm)
0.08/0.52	= { by axiom 52 (tac_2) }
0.08/0.52	  $$fresh47($$true2, $$true2, tac, thm)
0.08/0.52	= { by axiom 28 (mighta) }
0.08/0.52	  $$true2
0.08/0.52	% SZS output end Proof
0.08/0.52	
0.08/0.52	RESULT: Theorem (the conjecture is true).
0.08/0.56	EOF