TSTP Solution File: SWW474+5 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : SWW474+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:27:10 EDT 2024
% Result : Timeout 293.02s 37.20s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW474+5 : TPTP v8.2.0. Released v5.3.0.
% 0.03/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n016.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 : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 09:45:38 EDT 2024
% 0.12/0.33 % CPUTime :
% 293.02/37.20 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 293.02/37.20
% 293.02/37.20 % SZS status Theorem
% 293.02/37.20
% 293.64/37.22 % SZS output start Proof
% 293.64/37.22 Take the following subset of the input axioms:
% 293.64/37.22 fof(conj_0, hypothesis, hBOOL(hoare_1883395792gleton)).
% 293.64/37.22 fof(conj_1, hypothesis, hBOOL(wT_bodies)).
% 293.64/37.22 fof(conj_5, hypothesis, hAPP(pname, option(com), body, pn)=hAPP(com, option(com), some(com), y)).
% 293.64/37.22 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)))))).
% 293.64/37.22 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))))).
% 293.64/37.22 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))))))))).
% 293.64/37.22 fof(fact_4_cut, axiom, ![Ts, G_2, X_a2, G2]: (hBOOL(hAPP(fun(hoare_509422987triple(X_a2), bool), bool, hAPP(fun(hoare_509422987triple(X_a2), bool), fun(fun(hoare_509422987triple(X_a2), bool), bool), hoare_122391849derivs(X_a2), G_2), Ts)) => (hBOOL(hAPP(fun(hoare_509422987triple(X_a2), bool), bool, hAPP(fun(hoare_509422987triple(X_a2), bool), fun(fun(hoare_509422987triple(X_a2), bool), bool), hoare_122391849derivs(X_a2), G2), G_2)) => hBOOL(hAPP(fun(hoare_509422987triple(X_a2), bool), bool, hAPP(fun(hoare_509422987triple(X_a2), bool), fun(fun(hoare_509422987triple(X_a2), bool), bool), hoare_122391849derivs(X_a2), G2), Ts))))).
% 293.64/37.22 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))))).
% 293.64/37.22
% 293.64/37.22 Now clausify the problem and encode Horn clauses using encoding 3 of
% 293.64/37.22 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 293.64/37.22 We repeatedly replace C & s=t => u=v by the two clauses:
% 293.64/37.22 fresh(y, y, x1...xn) = u
% 293.64/37.22 C => fresh(s, t, x1...xn) = v
% 293.64/37.22 where fresh is a fresh function symbol and x1..xn are the free
% 293.64/37.22 variables of u and v.
% 293.64/37.22 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 293.64/37.22 input problem has no model of domain size 1).
% 293.64/37.22
% 293.64/37.22 The encoding turns the above axioms into the following unit equations and goals:
% 293.64/37.22
% 293.64/37.22 Axiom 1 (conj_1): hBOOL(wT_bodies) = true2.
% 293.64/37.22 Axiom 2 (conj_0): hBOOL(hoare_1883395792gleton) = true2.
% 293.64/37.22 Axiom 3 (fact_19_MGF): fresh145(X, X, Y) = true2.
% 293.64/37.22 Axiom 4 (fact_92_WT__bodiesD): fresh22(X, X, Y) = true2.
% 293.64/37.22 Axiom 5 (fact_19_MGF): fresh144(X, X, Y) = fresh145(hBOOL(wT_bodies), true2, Y).
% 293.64/37.22 Axiom 6 (fact_19_MGF): fresh143(X, X, Y) = fresh144(hBOOL(hoare_1883395792gleton), true2, Y).
% 293.64/37.22 Axiom 7 (fact_95_WTs__elim__cases_I7_J): fresh18(X, X, Y) = hAPP(pname, option(com), body, Y).
% 293.64/37.22 Axiom 8 (fact_92_WT__bodiesD): fresh23(X, X, Y, Z) = hBOOL(hAPP(com, bool, wt, Z)).
% 293.64/37.22 Axiom 9 (fact_4_cut): fresh70(X, X, Y, Z, W) = true2.
% 293.64/37.22 Axiom 10 (conj_5): hAPP(pname, option(com), body, pn) = hAPP(com, option(com), some(com), y).
% 293.64/37.22 Axiom 11 (fact_92_WT__bodiesD): fresh23(hBOOL(wT_bodies), true2, X, Y) = fresh22(hAPP(pname, option(com), body, X), hAPP(com, option(com), some(com), Y), Y).
% 293.64/37.22 Axiom 12 (fact_4_cut): fresh71(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)).
% 293.64/37.22 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.
% 293.64/37.22 Axiom 14 (fact_4_cut): fresh71(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) = fresh70(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).
% 293.64/37.22 Axiom 15 (fact_19_MGF): fresh143(hBOOL(hAPP(com, bool, wt, X)), 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))))).
% 293.64/37.22
% 293.64/37.22 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.
% 293.64/37.22 Proof:
% 293.64/37.22 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)))))
% 293.64/37.22 = { by axiom 12 (fact_4_cut) R->L }
% 293.64/37.22 fresh71(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))))
% 293.64/37.22 = { by axiom 3 (fact_19_MGF) R->L }
% 293.64/37.22 fresh71(fresh145(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))))
% 293.64/37.22 = { by axiom 1 (conj_1) R->L }
% 293.64/37.23 fresh71(fresh145(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))))
% 293.64/37.23 = { by axiom 5 (fact_19_MGF) R->L }
% 293.64/37.23 fresh71(fresh144(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))))
% 293.64/37.23 = { by axiom 2 (conj_0) R->L }
% 293.64/37.23 fresh71(fresh144(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))))
% 293.64/37.23 = { by axiom 6 (fact_19_MGF) R->L }
% 293.64/37.23 fresh71(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))))
% 293.64/37.23 = { by axiom 4 (fact_92_WT__bodiesD) R->L }
% 293.64/37.23 fresh71(fresh143(fresh22(fresh18(X, X, pn), fresh18(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))))
% 293.64/37.23 = { by axiom 7 (fact_95_WTs__elim__cases_I7_J) }
% 293.64/37.23 fresh71(fresh143(fresh22(fresh18(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))))
% 293.64/37.23 = { by axiom 10 (conj_5) }
% 293.64/37.23 fresh71(fresh143(fresh22(fresh18(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))))
% 293.64/37.23 = { by axiom 7 (fact_95_WTs__elim__cases_I7_J) }
% 293.64/37.23 fresh71(fresh143(fresh22(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))))
% 293.64/37.23 = { by axiom 11 (fact_92_WT__bodiesD) R->L }
% 293.64/37.23 fresh71(fresh143(fresh23(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))))
% 293.64/37.23 = { by axiom 1 (conj_1) }
% 293.64/37.23 fresh71(fresh143(fresh23(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))))
% 293.64/37.23 = { by axiom 8 (fact_92_WT__bodiesD) }
% 293.64/37.23 fresh71(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))))
% 293.64/37.23 = { by axiom 15 (fact_19_MGF) }
% 293.64/37.23 fresh71(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))))
% 293.64/37.23 = { by axiom 14 (fact_4_cut) }
% 293.64/37.23 fresh70(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))))
% 293.64/37.23 = { by axiom 13 (fact_0_empty) }
% 293.64/37.23 fresh70(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))))
% 293.64/37.23 = { by axiom 9 (fact_4_cut) }
% 293.64/37.23 true2
% 293.64/37.23 % SZS output end Proof
% 293.64/37.23
% 293.64/37.23 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------