0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.33	% Computer   : n028.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   : 1200
0.12/0.33	% WCLimit    : 120
0.12/0.33	% DateTime   : Wed Jul 14 17:22:33 EDT 2021
0.12/0.33	% CPUTime    : 
279.86/35.48	% SZS status Theorem
279.86/35.48	
279.86/35.50	% SZS output start Proof
279.86/35.50	Take the following subset of the input axioms:
279.86/35.50	  fof(conj_0, hypothesis, hBOOL(hoare_1883395792gleton)).
279.86/35.50	  fof(conj_1, hypothesis, hBOOL(wT_bodies)).
279.86/35.50	  fof(conj_5, hypothesis, hAPP(com, option(com), some(com), y)=hAPP(pname, option(com), body, pn)).
279.86/35.50	  fof(conj_7, conjecture, hBOOL(hAPP(fun(hoare_509422987triple(state), bool), bool, hAPP(fun(hoare_509422987triple(state), bool), fun(fun(hoare_509422987triple(state), bool), bool), hoare_122391849derivs(state), hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body))), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool)))))).
279.86/35.50	  fof(fact_0_empty, axiom, ![X_a, G]: hBOOL(hAPP(fun(hoare_509422987triple(X_a), bool), bool, hAPP(fun(hoare_509422987triple(X_a), bool), fun(fun(hoare_509422987triple(X_a), bool), bool), hoare_122391849derivs(X_a), G), bot_bot(fun(hoare_509422987triple(X_a), bool))))).
279.86/35.50	  fof(fact_19_MGF, axiom, ![C_1]: (hBOOL(hoare_1883395792gleton) => (hBOOL(wT_bodies) => (hBOOL(hAPP(com, bool, wt, C_1)) => hBOOL(hAPP(fun(hoare_509422987triple(state), bool), bool, hAPP(fun(hoare_509422987triple(state), bool), fun(fun(hoare_509422987triple(state), bool), bool), hoare_122391849derivs(state), bot_bot(fun(hoare_509422987triple(state), bool))), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, C_1)), bot_bot(fun(hoare_509422987triple(state), bool))))))))).
279.86/35.50	  fof(fact_4_cut, axiom, ![X_a, Ts, G, G_2]: ((hBOOL(hAPP(fun(hoare_509422987triple(X_a), bool), bool, hAPP(fun(hoare_509422987triple(X_a), bool), fun(fun(hoare_509422987triple(X_a), bool), bool), hoare_122391849derivs(X_a), G), Ts)) <= hBOOL(hAPP(fun(hoare_509422987triple(X_a), bool), bool, hAPP(fun(hoare_509422987triple(X_a), bool), fun(fun(hoare_509422987triple(X_a), bool), bool), hoare_122391849derivs(X_a), G), G_2))) <= hBOOL(hAPP(fun(hoare_509422987triple(X_a), bool), bool, hAPP(fun(hoare_509422987triple(X_a), bool), fun(fun(hoare_509422987triple(X_a), bool), bool), hoare_122391849derivs(X_a), G_2), Ts)))).
279.86/35.50	  fof(fact_92_WT__bodiesD, axiom, ![Pn, B_2]: (hBOOL(wT_bodies) => (hAPP(pname, option(com), body, Pn)=hAPP(com, option(com), some(com), B_2) => hBOOL(hAPP(com, bool, wt, B_2))))).
279.86/35.50	
279.86/35.50	Now clausify the problem and encode Horn clauses using encoding 3 of
279.86/35.50	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
279.86/35.50	We repeatedly replace C & s=t => u=v by the two clauses:
279.86/35.50	  fresh(y, y, x1...xn) = u
279.86/35.50	  C => fresh(s, t, x1...xn) = v
279.86/35.50	where fresh is a fresh function symbol and x1..xn are the free
279.86/35.50	variables of u and v.
279.86/35.50	A predicate p(X) is encoded as p(X)=true (this is sound, because the
279.86/35.50	input problem has no model of domain size 1).
279.86/35.50	
279.86/35.50	The encoding turns the above axioms into the following unit equations and goals:
279.86/35.50	
279.86/35.50	Axiom 1 (conj_0): hBOOL(hoare_1883395792gleton) = true2.
279.86/35.50	Axiom 2 (conj_1): hBOOL(wT_bodies) = true2.
279.86/35.50	Axiom 3 (fact_19_MGF): fresh143(X, X, Y) = true2.
279.86/35.50	Axiom 4 (fact_92_WT__bodiesD): fresh27(X, X, Y) = true2.
279.86/35.50	Axiom 5 (fact_19_MGF): fresh141(X, X, Y) = fresh142(hBOOL(hoare_1883395792gleton), true2, Y).
279.86/35.50	Axiom 6 (fact_95_WTs__elim__cases_I7_J): fresh22(X, X, Y) = hAPP(pname, option(com), body, Y).
279.86/35.50	Axiom 7 (fact_92_WT__bodiesD): fresh28(X, X, Y, Z) = hBOOL(hAPP(com, bool, wt, Z)).
279.86/35.50	Axiom 8 (fact_4_cut): fresh75(X, X, Y, Z, W) = true2.
279.86/35.50	Axiom 9 (conj_5): hAPP(com, option(com), some(com), y) = hAPP(pname, option(com), body, pn).
279.86/35.50	Axiom 10 (fact_19_MGF): fresh142(X, X, Y) = fresh143(hBOOL(hAPP(com, bool, wt, Y)), true2, Y).
279.86/35.50	Axiom 11 (fact_92_WT__bodiesD): fresh28(hBOOL(wT_bodies), true2, X, Y) = fresh27(hAPP(pname, option(com), body, X), hAPP(com, option(com), some(com), Y), Y).
279.86/35.50	Axiom 12 (fact_4_cut): fresh76(X, X, Y, Z, W, V) = hBOOL(hAPP(fun(hoare_509422987triple(Y), bool), bool, hAPP(fun(hoare_509422987triple(Y), bool), fun(fun(hoare_509422987triple(Y), bool), bool), hoare_122391849derivs(Y), Z), V)).
279.86/35.50	Axiom 13 (fact_0_empty): hBOOL(hAPP(fun(hoare_509422987triple(X), bool), bool, hAPP(fun(hoare_509422987triple(X), bool), fun(fun(hoare_509422987triple(X), bool), bool), hoare_122391849derivs(X), Y), bot_bot(fun(hoare_509422987triple(X), bool)))) = true2.
279.86/35.50	Axiom 14 (fact_4_cut): fresh76(hBOOL(hAPP(fun(hoare_509422987triple(X), bool), bool, hAPP(fun(hoare_509422987triple(X), bool), fun(fun(hoare_509422987triple(X), bool), bool), hoare_122391849derivs(X), Y), Z)), true2, X, W, Y, Z) = fresh75(hBOOL(hAPP(fun(hoare_509422987triple(X), bool), bool, hAPP(fun(hoare_509422987triple(X), bool), fun(fun(hoare_509422987triple(X), bool), bool), hoare_122391849derivs(X), W), Y)), true2, X, W, Z).
279.86/35.50	Axiom 15 (fact_19_MGF): fresh141(hBOOL(wT_bodies), true2, X) = hBOOL(hAPP(fun(hoare_509422987triple(state), bool), bool, hAPP(fun(hoare_509422987triple(state), bool), fun(fun(hoare_509422987triple(state), bool), bool), hoare_122391849derivs(state), bot_bot(fun(hoare_509422987triple(state), bool))), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, X)), bot_bot(fun(hoare_509422987triple(state), bool))))).
279.86/35.50	
279.86/35.50	Goal 1 (conj_7): hBOOL(hAPP(fun(hoare_509422987triple(state), bool), bool, hAPP(fun(hoare_509422987triple(state), bool), fun(fun(hoare_509422987triple(state), bool), bool), hoare_122391849derivs(state), hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body))), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))) = true2.
279.86/35.50	Proof:
279.86/35.50	  hBOOL(hAPP(fun(hoare_509422987triple(state), bool), bool, hAPP(fun(hoare_509422987triple(state), bool), fun(fun(hoare_509422987triple(state), bool), bool), hoare_122391849derivs(state), hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body))), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool)))))
279.86/35.50	= { by axiom 12 (fact_4_cut) R->L }
279.86/35.50	  fresh76(true2, true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 3 (fact_19_MGF) R->L }
279.86/35.50	  fresh76(fresh143(true2, true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 4 (fact_92_WT__bodiesD) R->L }
279.86/35.50	  fresh76(fresh143(fresh27(fresh22(X, X, pn), fresh22(X, X, pn), y), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 6 (fact_95_WTs__elim__cases_I7_J) }
279.86/35.50	  fresh76(fresh143(fresh27(fresh22(X, X, pn), hAPP(pname, option(com), body, pn), y), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 9 (conj_5) R->L }
279.86/35.50	  fresh76(fresh143(fresh27(fresh22(X, X, pn), hAPP(com, option(com), some(com), y), y), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 6 (fact_95_WTs__elim__cases_I7_J) }
279.86/35.50	  fresh76(fresh143(fresh27(hAPP(pname, option(com), body, pn), hAPP(com, option(com), some(com), y), y), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 11 (fact_92_WT__bodiesD) R->L }
279.86/35.50	  fresh76(fresh143(fresh28(hBOOL(wT_bodies), true2, pn, y), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 2 (conj_1) }
279.86/35.50	  fresh76(fresh143(fresh28(true2, true2, pn, y), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 7 (fact_92_WT__bodiesD) }
279.86/35.50	  fresh76(fresh143(hBOOL(hAPP(com, bool, wt, y)), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 10 (fact_19_MGF) R->L }
279.86/35.50	  fresh76(fresh142(true2, true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 1 (conj_0) R->L }
279.86/35.50	  fresh76(fresh142(hBOOL(hoare_1883395792gleton), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.50	= { by axiom 5 (fact_19_MGF) R->L }
279.86/35.50	  fresh76(fresh141(true2, true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.51	= { by axiom 2 (conj_1) R->L }
279.86/35.51	  fresh76(fresh141(hBOOL(wT_bodies), true2, y), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.51	= { by axiom 15 (fact_19_MGF) }
279.86/35.51	  fresh76(hBOOL(hAPP(fun(hoare_509422987triple(state), bool), bool, hAPP(fun(hoare_509422987triple(state), bool), fun(fun(hoare_509422987triple(state), bool), bool), hoare_122391849derivs(state), bot_bot(fun(hoare_509422987triple(state), bool))), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), bot_bot(fun(hoare_509422987triple(state), bool)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.51	= { by axiom 14 (fact_4_cut) }
279.86/35.51	  fresh75(hBOOL(hAPP(fun(hoare_509422987triple(state), bool), bool, hAPP(fun(hoare_509422987triple(state), bool), fun(fun(hoare_509422987triple(state), bool), bool), hoare_122391849derivs(state), hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body))), bot_bot(fun(hoare_509422987triple(state), bool)))), true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.51	= { by axiom 13 (fact_0_empty) }
279.86/35.51	  fresh75(true2, true2, state, hAPP(fun(pname, bool), fun(hoare_509422987triple(state), bool), hAPP(fun(pname, hoare_509422987triple(state)), fun(fun(pname, bool), fun(hoare_509422987triple(state), bool)), image(pname, hoare_509422987triple(state)), hAPP(fun(pname, com), fun(pname, hoare_509422987triple(state)), hAPP(fun(com, hoare_509422987triple(state)), fun(fun(pname, com), fun(pname, hoare_509422987triple(state))), combb(com, hoare_509422987triple(state), pname), hoare_Mirabelle_MGT), body_1)), hAPP(fun(pname, option(com)), fun(pname, bool), dom(pname, com), body)), hAPP(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool), hAPP(hoare_509422987triple(state), fun(fun(hoare_509422987triple(state), bool), fun(hoare_509422987triple(state), bool)), insert(hoare_509422987triple(state)), hAPP(com, hoare_509422987triple(state), hoare_Mirabelle_MGT, y)), bot_bot(fun(hoare_509422987triple(state), bool))))
279.86/35.51	= { by axiom 8 (fact_4_cut) }
279.86/35.51	  true2
279.86/35.51	% SZS output end Proof
279.86/35.51	
279.86/35.51	RESULT: Theorem (the conjecture is true).
279.86/35.68	EOF