0.00/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.09/0.10	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.09/0.30	% Computer   : n015.cluster.edu
0.09/0.30	% Model      : x86_64 x86_64
0.09/0.30	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.30	% Memory     : 8042.1875MB
0.09/0.30	% OS         : Linux 3.10.0-693.el7.x86_64
0.09/0.30	% CPULimit   : 960
0.09/0.30	% WCLimit    : 120
0.09/0.30	% DateTime   : Thu Jul  2 06:41:30 EDT 2020
0.09/0.30	% CPUTime    : 
0.13/0.58	% SZS status Theorem
0.13/0.58	
0.13/0.58	% SZS output start Proof
0.13/0.58	Take the following subset of the input axioms:
0.13/0.58	  fof(mighta, axiom, ![S1, S2]: (?[Ax, C]: (status(Ax, C, S1) & status(Ax, C, S2)) <=> mighta(S1, S2))).
0.13/0.58	  fof(mighta_tac_thm, conjecture, mighta(tac, thm)).
0.13/0.58	  fof(non_thm_spt, axiom, ?[Ax, C, I1]: (model(I1, Ax) & (?[I2]: model(I2, C) & ~model(I1, C)))).
0.13/0.58	  fof(tac, axiom, ![Ax, C]: ((![I2]: model(I2, C) & ?[I1]: model(I1, Ax)) <=> status(Ax, C, tac))).
0.13/0.58	  fof(tautology, axiom, ?[F]: ![I]: model(I, F)).
0.13/0.58	  fof(thm, axiom, ![Ax, C]: (status(Ax, C, thm) <=> ![I1]: (model(I1, C) <= model(I1, Ax)))).
0.13/0.58	
0.13/0.58	Now clausify the problem and encode Horn clauses using encoding 3 of
0.13/0.58	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.13/0.58	We repeatedly replace C & s=t => u=v by the two clauses:
0.13/0.58	  fresh(y, y, x1...xn) = u
0.13/0.58	  C => fresh(s, t, x1...xn) = v
0.13/0.58	where fresh is a fresh function symbol and x1..xn are the free
0.13/0.58	variables of u and v.
0.13/0.58	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.13/0.58	input problem has no model of domain size 1).
0.13/0.58	
0.13/0.58	The encoding turns the above axioms into the following unit equations and goals:
0.13/0.58	
0.13/0.58	Axiom 1 (mighta): fresh48(X, X, Y, Z, W, V) = mighta(Y, Z).
0.13/0.58	Axiom 2 (mighta): fresh47(X, X, Y, Z) = true2.
0.13/0.58	Axiom 3 (tac): fresh30(X, X, Y, Z, W) = status(Y, Z, tac).
0.13/0.59	Axiom 4 (tac): fresh29(X, X, Y, Z) = true2.
0.13/0.59	Axiom 5 (thm_2): fresh19(X, X, Y, Z) = true2.
0.13/0.59	Axiom 6 (tac): fresh30(model(sK49_tac_I2(X), X), true2, Y, X, Z) = fresh29(model(Z, Y), true2, Y, X).
0.13/0.59	Axiom 7 (thm_2): fresh19(model(sK45_thm_I1(X, Y), Y), true2, X, Y) = status(X, Y, thm).
0.13/0.59	Axiom 8 (non_thm_spt_1): model(sK21_non_thm_spt_I2, sK24_non_thm_spt_C) = true2.
0.13/0.59	Axiom 9 (mighta): fresh48(status(X, Y, Z), true2, W, Z, X, Y) = fresh47(status(X, Y, W), true2, W, Z).
0.13/0.59	Axiom 10 (tautology): model(X, sK13_tautology_F) = true2.
0.13/0.59	
0.13/0.59	Goal 1 (mighta_tac_thm): mighta(tac, thm) = true2.
0.13/0.59	Proof:
0.13/0.59	  mighta(tac, thm)
0.13/0.59	= { by axiom 1 (mighta) }
0.13/0.59	  fresh48(true2, true2, tac, thm, sK24_non_thm_spt_C, sK13_tautology_F)
0.13/0.59	= { by axiom 5 (thm_2) }
0.13/0.59	  fresh48(fresh19(true2, true2, sK24_non_thm_spt_C, sK13_tautology_F), true2, tac, thm, sK24_non_thm_spt_C, sK13_tautology_F)
0.13/0.59	= { by axiom 10 (tautology) }
0.13/0.59	  fresh48(fresh19(model(sK45_thm_I1(sK24_non_thm_spt_C, sK13_tautology_F), sK13_tautology_F), true2, sK24_non_thm_spt_C, sK13_tautology_F), true2, tac, thm, sK24_non_thm_spt_C, sK13_tautology_F)
0.13/0.59	= { by axiom 7 (thm_2) }
0.13/0.59	  fresh48(status(sK24_non_thm_spt_C, sK13_tautology_F, thm), true2, tac, thm, sK24_non_thm_spt_C, sK13_tautology_F)
0.13/0.59	= { by axiom 9 (mighta) }
0.13/0.59	  fresh47(status(sK24_non_thm_spt_C, sK13_tautology_F, tac), true2, tac, thm)
0.13/0.59	= { by axiom 3 (tac) }
0.13/0.59	  fresh47(fresh30(true2, true2, sK24_non_thm_spt_C, sK13_tautology_F, sK21_non_thm_spt_I2), true2, tac, thm)
0.13/0.59	= { by axiom 10 (tautology) }
0.13/0.59	  fresh47(fresh30(model(sK49_tac_I2(sK13_tautology_F), sK13_tautology_F), true2, sK24_non_thm_spt_C, sK13_tautology_F, sK21_non_thm_spt_I2), true2, tac, thm)
0.13/0.59	= { by axiom 6 (tac) }
0.13/0.59	  fresh47(fresh29(model(sK21_non_thm_spt_I2, sK24_non_thm_spt_C), true2, sK24_non_thm_spt_C, sK13_tautology_F), true2, tac, thm)
0.13/0.59	= { by axiom 8 (non_thm_spt_1) }
0.13/0.59	  fresh47(fresh29(true2, true2, sK24_non_thm_spt_C, sK13_tautology_F), true2, tac, thm)
0.13/0.59	= { by axiom 4 (tac) }
0.13/0.59	  fresh47(true2, true2, tac, thm)
0.13/0.59	= { by axiom 2 (mighta) }
0.13/0.59	  true2
0.13/0.59	% SZS output end Proof
0.13/0.59	
0.13/0.59	RESULT: Theorem (the conjecture is true).
0.13/0.59	EOF