TSTP Solution File: SWW473+5 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n018.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 : Fri Sep 1 00:55:09 EDT 2023
% Result : Theorem 15.16s 2.31s
% Output : Proof 15.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 20:36:16 EDT 2023
% 0.14/0.36 % CPUTime :
% 15.16/2.31 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 15.16/2.31
% 15.16/2.31 % SZS status Theorem
% 15.16/2.31
% 15.16/2.34 % SZS output start Proof
% 15.16/2.34 Take the following subset of the input axioms:
% 15.16/2.34 fof(conj_1, hypothesis, hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))).
% 15.16/2.34 fof(conj_4, hypothesis, hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u))).
% 15.16/2.34 fof(conj_6, conjecture, hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))).
% 15.16/2.34 fof(fact_61_insert__code, axiom, ![X_b, A_1, X_2, Y_2]: (hBOOL(hAPP(X_b, bool, hAPP(fun(X_b, bool), fun(X_b, bool), hAPP(X_b, fun(fun(X_b, bool), fun(X_b, bool)), insert(X_b), Y_2), A_1), X_2)) <=> (ti(X_b, Y_2)=ti(X_b, X_2) | hBOOL(hAPP(X_b, bool, A_1, X_2))))).
% 15.16/2.34 fof(fact_64_insert__absorb, axiom, ![A_2, X_b2, A_1_2]: (hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(X_b2, fun(fun(X_b2, bool), bool), member(X_b2), A_2), A_1_2)) => hAPP(fun(X_b2, bool), fun(X_b2, bool), hAPP(X_b2, fun(fun(X_b2, bool), fun(X_b2, bool)), insert(X_b2), A_2), A_1_2)=ti(fun(X_b2, bool), A_1_2))).
% 15.16/2.34 fof(fact_75_mem__def, axiom, ![X_b2, A_1_2, X_2_2]: (hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(X_b2, fun(fun(X_b2, bool), bool), member(X_b2), X_2_2), A_1_2)) <=> hBOOL(hAPP(X_b2, bool, A_1_2, X_2_2)))).
% 15.16/2.34 fof(fact_84_insert__subset, axiom, ![B, X_b2, A_1_2, X_2_2]: (hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(fun(X_b2, bool), fun(fun(X_b2, bool), bool), ord_less_eq(fun(X_b2, bool)), hAPP(fun(X_b2, bool), fun(X_b2, bool), hAPP(X_b2, fun(fun(X_b2, bool), fun(X_b2, bool)), insert(X_b2), X_2_2), A_1_2)), B)) <=> (hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(X_b2, fun(fun(X_b2, bool), bool), member(X_b2), X_2_2), B)) & hBOOL(hAPP(fun(X_b2, bool), bool, hAPP(fun(X_b2, bool), fun(fun(X_b2, bool), bool), ord_less_eq(fun(X_b2, bool)), A_1_2), B))))).
% 15.16/2.34 fof(fact_88_image__insert, axiom, ![X_c, F, X_b2, A_2_2, B2]: hAPP(fun(X_c, bool), fun(X_b2, bool), hAPP(fun(X_c, X_b2), fun(fun(X_c, bool), fun(X_b2, bool)), image(X_c, X_b2), F), hAPP(fun(X_c, bool), fun(X_c, bool), hAPP(X_c, fun(fun(X_c, bool), fun(X_c, bool)), insert(X_c), A_2_2), B2))=hAPP(fun(X_b2, bool), fun(X_b2, bool), hAPP(X_b2, fun(fun(X_b2, bool), fun(X_b2, bool)), insert(X_b2), hAPP(X_c, X_b2, F, A_2_2)), hAPP(fun(X_c, bool), fun(X_b2, bool), hAPP(fun(X_c, X_b2), fun(fun(X_c, bool), fun(X_b2, bool)), image(X_c, X_b2), F), B2))).
% 15.16/2.34 fof(tsy_v_U_res, hypothesis, ti(fun(pname, bool), u)=u).
% 15.16/2.34
% 15.16/2.34 Now clausify the problem and encode Horn clauses using encoding 3 of
% 15.16/2.34 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 15.16/2.34 We repeatedly replace C & s=t => u=v by the two clauses:
% 15.16/2.34 fresh(y, y, x1...xn) = u
% 15.16/2.34 C => fresh(s, t, x1...xn) = v
% 15.16/2.34 where fresh is a fresh function symbol and x1..xn are the free
% 15.16/2.34 variables of u and v.
% 15.16/2.34 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 15.16/2.34 input problem has no model of domain size 1).
% 15.16/2.34
% 15.16/2.34 The encoding turns the above axioms into the following unit equations and goals:
% 15.16/2.34
% 15.16/2.34 Axiom 1 (tsy_v_U_res): ti(fun(pname, bool), u) = u.
% 15.16/2.34 Axiom 2 (fact_64_insert__absorb): fresh58(X, X, Y, Z, W) = ti(fun(Y, bool), W).
% 15.16/2.34 Axiom 3 (fact_75_mem__def): fresh39(X, X, Y, Z, W) = true2.
% 15.16/2.34 Axiom 4 (fact_84_insert__subset): fresh119(X, X, Y, Z, W, V) = true2.
% 15.16/2.34 Axiom 5 (fact_61_insert__code): fresh61(X, X, Y, Z, W, V) = true2.
% 15.16/2.34 Axiom 6 (fact_75_mem__def): fresh39(hBOOL(hAPP(X, bool, Y, Z)), true2, X, Z, Y) = hBOOL(hAPP(fun(X, bool), bool, hAPP(X, fun(fun(X, bool), bool), member(X), Z), Y)).
% 15.16/2.34 Axiom 7 (conj_4): hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u)) = true2.
% 15.16/2.34 Axiom 8 (fact_89_insert__image): fresh29(X, X, Y, Z, W, V, U) = hAPP(fun(Z, bool), fun(Y, bool), hAPP(fun(Z, Y), fun(fun(Z, bool), fun(Y, bool)), image(Z, Y), W), U).
% 15.16/2.34 Axiom 9 (fact_72_subset__trans): fresh44(X, X, Y, Z, W, V) = hBOOL(hAPP(fun(Y, bool), bool, hAPP(fun(Y, bool), fun(fun(Y, bool), bool), ord_less_eq(fun(Y, bool)), W), Z)).
% 15.16/2.34 Axiom 10 (fact_64_insert__absorb): fresh58(hBOOL(hAPP(fun(X, bool), bool, hAPP(X, fun(fun(X, bool), bool), member(X), Y), Z)), true2, X, Y, Z) = hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), Y), Z).
% 15.16/2.34 Axiom 11 (fact_61_insert__code): fresh61(ti(X, Y), ti(X, Z), X, Y, W, Z) = hBOOL(hAPP(X, bool, hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), Y), W), Z)).
% 15.16/2.34 Axiom 12 (fact_84_insert__subset): fresh118(X, X, Y, Z, W, V) = fresh119(hBOOL(hAPP(fun(Y, bool), bool, hAPP(Y, fun(fun(Y, bool), bool), member(Y), Z), V)), true2, Y, Z, W, V).
% 15.16/2.34 Axiom 13 (fact_84_insert__subset): fresh118(hBOOL(hAPP(fun(X, bool), bool, hAPP(fun(X, bool), fun(fun(X, bool), bool), ord_less_eq(fun(X, bool)), Y), Z)), true2, X, W, Y, Z) = hBOOL(hAPP(fun(X, bool), bool, hAPP(fun(X, bool), fun(fun(X, bool), bool), ord_less_eq(fun(X, bool)), hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), W), Y)), Z)).
% 15.16/2.34 Axiom 14 (conj_1): hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))) = true2.
% 15.16/2.34 Axiom 15 (fact_88_image__insert): hAPP(fun(X, bool), fun(Y, bool), hAPP(fun(X, Y), fun(fun(X, bool), fun(Y, bool)), image(X, Y), Z), hAPP(fun(X, bool), fun(X, bool), hAPP(X, fun(fun(X, bool), fun(X, bool)), insert(X), W), V)) = hAPP(fun(Y, bool), fun(Y, bool), hAPP(Y, fun(fun(Y, bool), fun(Y, bool)), insert(Y), hAPP(X, Y, Z, W)), hAPP(fun(X, bool), fun(Y, bool), hAPP(fun(X, Y), fun(fun(X, bool), fun(Y, bool)), image(X, Y), Z), V)).
% 15.16/2.34
% 15.16/2.34 Goal 1 (conj_6): hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))) = true2.
% 15.16/2.34 Proof:
% 15.16/2.34 hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)))
% 15.16/2.34 = { by axiom 8 (fact_89_insert__image) R->L }
% 15.16/2.34 hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), g)), fresh29(X, X, x_a, pname, mgt_call, Y, u)))
% 15.16/2.34 = { by axiom 13 (fact_84_insert__subset) R->L }
% 15.16/2.34 fresh118(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), fresh29(X, X, x_a, pname, mgt_call, Y, u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, fresh29(X, X, x_a, pname, mgt_call, Y, u))
% 15.16/2.34 = { by axiom 9 (fact_72_subset__trans) R->L }
% 15.16/2.34 fresh118(fresh44(Z, Z, x_a, fresh29(X, X, x_a, pname, mgt_call, Y, u), g, W), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, fresh29(X, X, x_a, pname, mgt_call, Y, u))
% 15.16/2.34 = { by axiom 8 (fact_89_insert__image) }
% 15.16/2.34 fresh118(fresh44(Z, Z, x_a, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u), g, W), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, fresh29(X, X, x_a, pname, mgt_call, Y, u))
% 15.16/2.34 = { by axiom 8 (fact_89_insert__image) }
% 15.16/2.34 fresh118(fresh44(Z, Z, x_a, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u), g, W), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.34 = { by axiom 9 (fact_72_subset__trans) }
% 15.16/2.34 fresh118(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(fun(x_a, bool), fun(fun(x_a, bool), bool), ord_less_eq(fun(x_a, bool)), g), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 14 (conj_1) }
% 15.16/2.35 fresh118(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 12 (fact_84_insert__subset) }
% 15.16/2.35 fresh119(hBOOL(hAPP(fun(x_a, bool), bool, hAPP(x_a, fun(fun(x_a, bool), bool), member(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 6 (fact_75_mem__def) R->L }
% 15.16/2.35 fresh119(fresh39(hBOOL(hAPP(x_a, bool, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u), hAPP(pname, x_a, mgt_call, pn))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 1 (tsy_v_U_res) R->L }
% 15.16/2.35 fresh119(fresh39(hBOOL(hAPP(x_a, bool, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), ti(fun(pname, bool), u)), hAPP(pname, x_a, mgt_call, pn))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 2 (fact_64_insert__absorb) R->L }
% 15.16/2.35 fresh119(fresh39(hBOOL(hAPP(x_a, bool, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), fresh58(true2, true2, pname, pn, u)), hAPP(pname, x_a, mgt_call, pn))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 7 (conj_4) R->L }
% 15.16/2.35 fresh119(fresh39(hBOOL(hAPP(x_a, bool, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), fresh58(hBOOL(hAPP(fun(pname, bool), bool, hAPP(pname, fun(fun(pname, bool), bool), member(pname), pn), u)), true2, pname, pn, u)), hAPP(pname, x_a, mgt_call, pn))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 10 (fact_64_insert__absorb) }
% 15.16/2.35 fresh119(fresh39(hBOOL(hAPP(x_a, bool, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), hAPP(fun(pname, bool), fun(pname, bool), hAPP(pname, fun(fun(pname, bool), fun(pname, bool)), insert(pname), pn), u)), hAPP(pname, x_a, mgt_call, pn))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 15 (fact_88_image__insert) }
% 15.16/2.35 fresh119(fresh39(hBOOL(hAPP(x_a, bool, hAPP(fun(x_a, bool), fun(x_a, bool), hAPP(x_a, fun(fun(x_a, bool), fun(x_a, bool)), insert(x_a), hAPP(pname, x_a, mgt_call, pn)), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), hAPP(pname, x_a, mgt_call, pn))), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 11 (fact_61_insert__code) R->L }
% 15.16/2.35 fresh119(fresh39(fresh61(ti(x_a, hAPP(pname, x_a, mgt_call, pn)), ti(x_a, hAPP(pname, x_a, mgt_call, pn)), x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u), hAPP(pname, x_a, mgt_call, pn)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 5 (fact_61_insert__code) }
% 15.16/2.35 fresh119(fresh39(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u)), true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 3 (fact_75_mem__def) }
% 15.16/2.35 fresh119(true2, true2, x_a, hAPP(pname, x_a, mgt_call, pn), g, hAPP(fun(pname, bool), fun(x_a, bool), hAPP(fun(pname, x_a), fun(fun(pname, bool), fun(x_a, bool)), image(pname, x_a), mgt_call), u))
% 15.16/2.35 = { by axiom 4 (fact_84_insert__subset) }
% 15.16/2.35 true2
% 15.16/2.35 % SZS output end Proof
% 15.16/2.35
% 15.16/2.35 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------