0.00/0.04	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn
0.03/0.25	% Computer   : n131.star.cs.uiowa.edu
0.03/0.25	% Model      : x86_64 x86_64
0.03/0.25	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.25	% Memory     : 32218.625MB
0.03/0.25	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.25	% CPULimit   : 300
0.03/0.25	% DateTime   : Sat Jul 14 04:18:40 CDT 2018
0.03/0.25	% CPUTime    : 
0.49/0.72	% SZS status Theorem
0.49/0.72	
0.49/0.72	% SZS output start Proof
0.49/0.72	Take the following subset of the input axioms:
0.49/0.72	  fof(eqv, axiom,
0.49/0.72	      ![Ax, C]:
0.49/0.72	        (status(Ax, C, eqv)
0.49/0.72	           <=> (![I2]: (model(I2, Ax) <=> model(I2, C))
0.49/0.72	                  & ?[I1]: model(I1, Ax)))).
0.49/0.72	  fof(mighta, axiom,
0.49/0.72	      ![S1, S2]:
0.49/0.72	        (?[Ax, C]: (status(Ax, C, S1) & status(Ax, C, S2))
0.49/0.72	           <=> mighta(S1, S2))).
0.49/0.72	  fof(mighta_eqv_thm, conjecture, mighta(eqv, thm)).
0.49/0.72	  fof(tautology, axiom, ?[F]: ![I]: model(I, F)).
0.49/0.72	  fof(thm, axiom,
0.49/0.72	      ![Ax, C]:
0.49/0.72	        (![I1]: (model(I1, Ax) => model(I1, C)) <=> status(Ax, C, thm))).
0.49/0.72	
0.49/0.72	Now clausify the problem and encode Horn clauses using encoding 3 of
0.49/0.72	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.49/0.72	We repeatedly replace C & s=t => u=v by the two clauses:
0.49/0.72	  $$fresh(y, y, x1...xn) = u
0.49/0.72	  C => $$fresh(s, t, x1...xn) = v
0.49/0.72	where $$fresh is a fresh function symbol and x1..xn are the free
0.49/0.72	variables of u and v.
0.49/0.72	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
0.49/0.72	input problem has no model of domain size 1).
0.49/0.72	
0.49/0.72	The encoding turns the above axioms into the following unit equations and goals:
0.49/0.72	
0.49/0.72	Axiom 10 (eqv_4): $$fresh63(X, X, Y, Z, W) = status(Y, Z, eqv).
0.49/0.72	Axiom 11 (eqv_4): $$fresh73(X, X, Y, Z) = $$true2.
0.49/0.72	Axiom 12 (eqv_4): $$fresh74(X, X, Y, Z, W) = $$fresh73(model(W, Y), $$true2, Y, Z).
0.49/0.72	Axiom 27 (mighta): $$fresh48(X, X, Y, Z, W, V) = mighta(Y, Z).
0.49/0.72	Axiom 28 (mighta): $$fresh47(X, X, Y, Z) = $$true2.
0.49/0.72	Axiom 60 (thm_2): $$fresh19(X, X, Y, Z) = $$true2.
0.49/0.72	Axiom 88 (thm_2): $$fresh19(model(sK48_thm_I1(X, Y), Y), $$true2, X, Y) = status(X, Y, thm).
0.49/0.72	Axiom 122 (eqv_4): $$fresh74(model(sK26_eqv_I2(X, Y), Y), $$true2, X, Y, Z) = $$fresh63(model(sK26_eqv_I2(X, Y), X), $$true2, X, Y, Z).
0.49/0.72	Axiom 139 (mighta): $$fresh48(status(X, Y, Z), $$true2, W, Z, X, Y) = $$fresh47(status(X, Y, W), $$true2, W, Z).
0.49/0.72	Axiom 140 (tautology): model(X, sK1_tautology_F) = $$true2.
0.49/0.72	
0.49/0.72	Goal 1 (mighta_eqv_thm): mighta(eqv, thm) = $$true2.
0.49/0.72	Proof:
0.49/0.72	  mighta(eqv, thm)
0.49/0.72	= { by axiom 27 (mighta) }
0.49/0.72	  $$fresh48($$true2, $$true2, eqv, thm, sK1_tautology_F, sK1_tautology_F)
0.49/0.72	= { by axiom 60 (thm_2) }
0.49/0.72	  $$fresh48($$fresh19($$true2, $$true2, sK1_tautology_F, sK1_tautology_F), $$true2, eqv, thm, sK1_tautology_F, sK1_tautology_F)
0.49/0.72	= { by axiom 140 (tautology) }
0.49/0.72	  $$fresh48($$fresh19(model(sK48_thm_I1(sK1_tautology_F, sK1_tautology_F), sK1_tautology_F), $$true2, sK1_tautology_F, sK1_tautology_F), $$true2, eqv, thm, sK1_tautology_F, sK1_tautology_F)
0.49/0.72	= { by axiom 88 (thm_2) }
0.49/0.72	  $$fresh48(status(sK1_tautology_F, sK1_tautology_F, thm), $$true2, eqv, thm, sK1_tautology_F, sK1_tautology_F)
0.49/0.72	= { by axiom 139 (mighta) }
0.49/0.72	  $$fresh47(status(sK1_tautology_F, sK1_tautology_F, eqv), $$true2, eqv, thm)
0.49/0.72	= { by axiom 10 (eqv_4) }
0.49/0.72	  $$fresh47($$fresh63($$true2, $$true2, sK1_tautology_F, sK1_tautology_F, ?), $$true2, eqv, thm)
0.49/0.72	= { by axiom 140 (tautology) }
0.49/0.72	  $$fresh47($$fresh63(model(sK26_eqv_I2(sK1_tautology_F, sK1_tautology_F), sK1_tautology_F), $$true2, sK1_tautology_F, sK1_tautology_F, ?), $$true2, eqv, thm)
0.49/0.72	= { by axiom 122 (eqv_4) }
0.49/0.72	  $$fresh47($$fresh74(model(sK26_eqv_I2(sK1_tautology_F, sK1_tautology_F), sK1_tautology_F), $$true2, sK1_tautology_F, sK1_tautology_F, ?), $$true2, eqv, thm)
0.49/0.72	= { by axiom 140 (tautology) }
0.49/0.72	  $$fresh47($$fresh74($$true2, $$true2, sK1_tautology_F, sK1_tautology_F, ?), $$true2, eqv, thm)
0.49/0.72	= { by axiom 12 (eqv_4) }
0.49/0.72	  $$fresh47($$fresh73(model(?, sK1_tautology_F), $$true2, sK1_tautology_F, sK1_tautology_F), $$true2, eqv, thm)
0.49/0.72	= { by axiom 140 (tautology) }
0.49/0.72	  $$fresh47($$fresh73($$true2, $$true2, sK1_tautology_F, sK1_tautology_F), $$true2, eqv, thm)
0.49/0.72	= { by axiom 11 (eqv_4) }
0.49/0.72	  $$fresh47($$true2, $$true2, eqv, thm)
0.49/0.72	= { by axiom 28 (mighta) }
0.49/0.72	  $$true2
0.49/0.72	% SZS output end Proof
0.49/0.72	
0.49/0.72	RESULT: Theorem (the conjecture is true).
0.49/0.72	EOF