0.03/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.14/0.35	% Computer   : n015.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
0.14/0.36	% CPULimit   : 180
0.14/0.36	% DateTime   : Thu Aug 29 15:49:07 EDT 2019
0.14/0.36	% CPUTime    : 
7.91/8.12	% SZS status Theorem
7.91/8.12	
7.91/8.12	% SZS output start Proof
7.91/8.12	Take the following subset of the input axioms:
7.91/8.13	  fof(fact_Lin__irrefl, axiom, ![V_L_2, V_ba_2, V_aa_2]: ((~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_ba_2), V_aa_2)), V_L_2)) <= hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_aa_2), V_ba_2)), V_L_2))) <= hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), V_L_2), c_Arrow__Order__Mirabelle_OLin)))).
7.91/8.13	  fof(fact_Nil2__notin__lex, axiom, ![T_a, V_xs_2, V_r_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), V_xs_2), c_List_Olist_ONil(T_a))), c_List_Olex(T_a, V_r_2)))).
7.91/8.13	  fof(fact_Nil__notin__lex, axiom, ![T_a, V_r_2, V_ys_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), c_List_Olist_ONil(T_a)), V_ys_2)), c_List_Olex(T_a, V_r_2)))).
7.91/8.13	  fof(fact_dropWhile__eq__Cons__conv, axiom, ![V_y_2, T_a, V_Pa_2, V_xs_2, V_ys_2]: (hAPP(hAPP(c_List_Olist_OCons(T_a), V_y_2), V_ys_2)=c_List_OdropWhile(T_a, V_Pa_2, V_xs_2) <=> (hAPP(hAPP(c_List_Oappend(T_a), c_List_OtakeWhile(T_a, V_Pa_2, V_xs_2)), hAPP(hAPP(c_List_Olist_OCons(T_a), V_y_2), V_ys_2))=V_xs_2 & ~hBOOL(hAPP(V_Pa_2, V_y_2))))).
7.91/8.13	  fof(fact_ext, axiom, ![V_g_2, V_f_2]: (![B_x]: hAPP(V_f_2, B_x)=hAPP(V_g_2, B_x) => V_f_2=V_g_2)).
7.91/8.13	  fof(fact_impossible__Cons, axiom, ![T_a, V_xs, V_x, V_ys]: (V_xs!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_ys) <= c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_Osize__class_Osize(tc_List_Olist(T_a), V_xs), c_Nat_Osize__class_Osize(tc_List_Olist(T_a), V_ys)))).
7.91/8.13	  fof(fact_in__measures_I1_J, axiom, ![V_y_2, V_x_2, T_a]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(T_a, T_a)), hAPP(hAPP(c_Product__Type_OPair(T_a, T_a), V_x_2), V_y_2)), c_List_Omeasures(T_a, c_List_Olist_ONil(tc_fun(T_a, tc_Nat_Onat)))))).
7.91/8.13	  fof(fact_in__mkbot, axiom, ![V_z_2, V_L_2, V_y_2, V_x_2]: ((V_z_2!=V_y_2 & ((V_x_2=V_z_2 => V_x_2!=V_y_2) & (V_x_2!=V_z_2 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2), V_y_2)), V_L_2))))) <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2), V_y_2)), c_Arrow__Order__Mirabelle_Omkbot(V_L_2, V_z_2))))).
7.91/8.13	  fof(fact_in__mktop, axiom, ![V_z_2, V_L_2, V_y_2, V_x_2]: (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2), V_y_2)), c_Arrow__Order__Mirabelle_Omktop(V_L_2, V_z_2))) <=> (V_x_2!=V_z_2 & ((V_y_2=V_z_2 => V_x_2!=V_y_2) & (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), V_x_2), V_y_2)), V_L_2)) <= V_z_2!=V_y_2))))).
7.91/8.13	  fof(fact_irrefl__def, axiom, ![T_a, V_r_2]: (c_Relation_Oirrefl(T_a, V_r_2) <=> ![B_x]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(T_a, T_a)), hAPP(hAPP(c_Product__Type_OPair(T_a, T_a), B_x), B_x)), V_r_2)))).
7.91/8.13	  fof(fact_leD, axiom, ![V_y, T_a, V_x]: ((~c_Orderings_Oord__class_Oless(T_a, V_x, V_y) <= c_Orderings_Oord__class_Oless__eq(T_a, V_y, V_x)) <= class_Orderings_Olinorder(T_a))).
7.91/8.13	  fof(fact_less__fun__def, axiom, ![T_a, V_g_2, V_f_2, T_b]: (class_Orderings_Oord(T_b) => (c_Orderings_Oord__class_Oless(tc_fun(T_a, T_b), V_f_2, V_g_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_fun(T_a, T_b), V_f_2, V_g_2) & ~c_Orderings_Oord__class_Oless__eq(tc_fun(T_a, T_b), V_g_2, V_f_2))))).
7.91/8.13	  fof(fact_less__imp__neq, axiom, ![V_y, T_a, V_x]: (class_Orderings_Oorder(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_x, V_y) => V_x!=V_y))).
7.91/8.13	  fof(fact_less__irrefl__nat, axiom, ![V_n]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_n)).
7.91/8.13	  fof(fact_less__le__not__le, axiom, ![V_y_2, V_x_2, T_a]: (class_Orderings_Opreorder(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2) <=> (~c_Orderings_Oord__class_Oless__eq(T_a, V_y_2, V_x_2) & c_Orderings_Oord__class_Oless__eq(T_a, V_x_2, V_y_2))))).
7.91/8.13	  fof(fact_less__not__refl, axiom, ![V_n]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_n)).
7.91/8.13	  fof(fact_less__not__refl2, axiom, ![V_n, V_m]: (V_m!=V_n <= c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m))).
7.91/8.13	  fof(fact_less__not__refl3, axiom, ![V_s, V_t]: (V_t!=V_s <= c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_s, V_t))).
7.91/8.13	  fof(fact_lexord__Nil__right, axiom, ![V_x_2, T_a, V_r_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), V_x_2), c_List_Olist_ONil(T_a))), c_List_Olexord(T_a, V_r_2)))).
7.91/8.13	  fof(fact_linorder__antisym__conv2, axiom, ![V_y_2, V_x_2, T_a]: (class_Orderings_Olinorder(T_a) => (c_Orderings_Oord__class_Oless__eq(T_a, V_x_2, V_y_2) => (V_y_2=V_x_2 <=> ~c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2))))).
7.91/8.13	  fof(fact_linorder__neq__iff, axiom, ![V_y_2, V_x_2, T_a]: (class_Orderings_Olinorder(T_a) => ((c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2) | c_Orderings_Oord__class_Oless(T_a, V_y_2, V_x_2)) <=> V_x_2!=V_y_2))).
7.91/8.13	  fof(fact_linorder__not__le, axiom, ![V_y_2, V_x_2, T_a]: (class_Orderings_Olinorder(T_a) => (~c_Orderings_Oord__class_Oless__eq(T_a, V_x_2, V_y_2) <=> c_Orderings_Oord__class_Oless(T_a, V_y_2, V_x_2)))).
7.91/8.13	  fof(fact_linorder__not__less, axiom, ![V_y_2, V_x_2, T_a]: ((~c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2) <=> c_Orderings_Oord__class_Oless__eq(T_a, V_y_2, V_x_2)) <= class_Orderings_Olinorder(T_a))).
7.91/8.13	  fof(fact_list_Osimps_I2_J, axiom, ![T_a, V_list_H, V_a_H]: c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_a_H), V_list_H)).
7.91/8.13	  fof(fact_list_Osimps_I3_J, axiom, ![T_a, V_list_H, V_a_H]: c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_a_H), V_list_H)).
7.91/8.13	  fof(fact_nat__less__cases, axiom, ![V_m_2, V_Pa_2, V_n_2]: ((((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2) => hBOOL(hAPP(hAPP(V_Pa_2, V_n_2), V_m_2))) => hBOOL(hAPP(hAPP(V_Pa_2, V_n_2), V_m_2))) <= (hBOOL(hAPP(hAPP(V_Pa_2, V_n_2), V_m_2)) <= V_n_2=V_m_2)) <= (hBOOL(hAPP(hAPP(V_Pa_2, V_n_2), V_m_2)) <= c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)))).
7.91/8.13	  fof(fact_nat__less__le, axiom, ![V_m_2, V_n_2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m_2, V_n_2) & V_n_2!=V_m_2))).
7.91/8.13	  fof(fact_nat__neq__iff, axiom, ![V_m_2, V_n_2]: ((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) <=> V_n_2!=V_m_2)).
7.91/8.13	  fof(fact_not__Cons__self, axiom, ![T_a, V_xs, V_x]: hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_xs)!=V_xs).
7.91/8.13	  fof(fact_not__Cons__self2, axiom, ![T_a, V_xs, V_x]: V_xs!=hAPP(hAPP(c_List_Olist_OCons(T_a), V_x), V_xs)).
7.91/8.13	  fof(fact_not__Nil__listrel1, axiom, ![T_a, V_xs_2, V_r_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), c_List_Olist_ONil(T_a)), V_xs_2)), c_List_Olistrel1(T_a, V_r_2)))).
7.91/8.13	  fof(fact_not__less__iff__gr__or__eq, axiom, ![V_y_2, V_x_2, T_a]: ((~c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2) <=> (c_Orderings_Oord__class_Oless(T_a, V_y_2, V_x_2) | V_x_2=V_y_2)) <= class_Orderings_Olinorder(T_a))).
7.91/8.13	  fof(fact_not__listrel1__Nil, axiom, ![T_a, V_xs_2, V_r_2]: ~hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a), tc_List_Olist(T_a))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a), tc_List_Olist(T_a)), V_xs_2), c_List_Olist_ONil(T_a))), c_List_Olistrel1(T_a, V_r_2)))).
7.91/8.13	  fof(fact_nth__length__takeWhile, axiom, ![T_a, V_Pa_2, V_xs_2]: (~hBOOL(hAPP(V_Pa_2, c_List_Onth(T_a, V_xs_2, c_Nat_Osize__class_Osize(tc_List_Olist(T_a), c_List_OtakeWhile(T_a, V_Pa_2, V_xs_2))))) <= c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_Osize__class_Osize(tc_List_Olist(T_a), c_List_OtakeWhile(T_a, V_Pa_2, V_xs_2)), c_Nat_Osize__class_Osize(tc_List_Olist(T_a), V_xs_2)))).
7.91/8.13	  fof(fact_order__less__asym, axiom, ![V_y, T_a, V_x]: (class_Orderings_Opreorder(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_x, V_y) => ~c_Orderings_Oord__class_Oless(T_a, V_y, V_x)))).
7.91/8.13	  fof(fact_order__less__asym_H, axiom, ![T_a, V_b, V_a]: (class_Orderings_Opreorder(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_a, V_b) => ~c_Orderings_Oord__class_Oless(T_a, V_b, V_a)))).
7.91/8.13	  fof(fact_order__less__imp__not__eq, axiom, ![V_y, T_a, V_x]: (class_Orderings_Oorder(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_x, V_y) => V_y!=V_x))).
7.91/8.13	  fof(fact_order__less__imp__not__eq2, axiom, ![V_y, T_a, V_x]: (class_Orderings_Oorder(T_a) => (V_x!=V_y <= c_Orderings_Oord__class_Oless(T_a, V_x, V_y)))).
7.91/8.13	  fof(fact_order__less__imp__not__less, axiom, ![V_y, T_a, V_x]: (class_Orderings_Opreorder(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_x, V_y) => ~c_Orderings_Oord__class_Oless(T_a, V_y, V_x)))).
7.91/8.13	  fof(fact_order__less__irrefl, axiom, ![T_a, V_x]: (~c_Orderings_Oord__class_Oless(T_a, V_x, V_x) <= class_Orderings_Opreorder(T_a))).
7.91/8.13	  fof(fact_order__less__le, axiom, ![V_y_2, V_x_2, T_a]: (((c_Orderings_Oord__class_Oless__eq(T_a, V_x_2, V_y_2) & V_x_2!=V_y_2) <=> c_Orderings_Oord__class_Oless(T_a, V_x_2, V_y_2)) <= class_Orderings_Oorder(T_a))).
7.91/8.13	  fof(fact_order__less__not__sym, axiom, ![V_y, T_a, V_x]: ((~c_Orderings_Oord__class_Oless(T_a, V_y, V_x) <= c_Orderings_Oord__class_Oless(T_a, V_x, V_y)) <= class_Orderings_Opreorder(T_a))).
7.91/8.13	  fof(fact_psubset__eq, axiom, ![T_a, V_A_2, V_B_2]: ((V_B_2!=V_A_2 & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a, tc_HOL_Obool), V_A_2, V_B_2)) <=> c_Orderings_Oord__class_Oless(tc_fun(T_a, tc_HOL_Obool), V_A_2, V_B_2))).
7.91/8.13	  fof(fact_snoc__eq__iff__butlast, axiom, ![V_x_2, T_a, V_xs_2, V_ys_2]: (hAPP(hAPP(c_List_Oappend(T_a), V_xs_2), hAPP(hAPP(c_List_Olist_OCons(T_a), V_x_2), c_List_Olist_ONil(T_a)))=V_ys_2 <=> (c_List_Olist_ONil(T_a)!=V_ys_2 & (V_x_2=c_List_Olast(T_a, V_ys_2) & V_xs_2=c_List_Obutlast(T_a, V_ys_2))))).
7.91/8.13	  fof(fact_xt1_I9_J, axiom, ![T_a, V_b, V_a]: (class_Orderings_Oorder(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_b, V_a) => ~c_Orderings_Oord__class_Oless(T_a, V_a, V_b)))).
7.91/8.13	  fof(help_c__COMBI__1, axiom, ![T_a, V_P]: V_P=hAPP(c_COMBI(T_a), V_P)).
7.91/8.13	  fof(help_c__COMBS__1, axiom, ![T_a, V_Pa_2, T_b, T_c, V_R_2, V_Q_2]: hAPP(hAPP(hAPP(c_COMBS(T_b, T_c, T_a), V_Pa_2), V_Q_2), V_R_2)=hAPP(hAPP(V_Pa_2, V_R_2), hAPP(V_Q_2, V_R_2))).
7.91/8.13	  fof(help_c__fNot__1, axiom, ![V_Pa_2]: (~hBOOL(V_Pa_2) | ~hBOOL(hAPP(c_fNot, V_Pa_2)))).
7.91/8.13	
7.91/8.13	Now clausify the problem and encode Horn clauses using encoding 3 of
7.91/8.13	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
7.91/8.13	We repeatedly replace C & s=t => u=v by the two clauses:
7.91/8.13	  fresh(y, y, x1...xn) = u
7.91/8.13	  C => fresh(s, t, x1...xn) = v
7.91/8.13	where fresh is a fresh function symbol and x1..xn are the free
7.91/8.13	variables of u and v.
7.91/8.13	A predicate p(X) is encoded as p(X)=true (this is sound, because the
7.91/8.13	input problem has no model of domain size 1).
7.91/8.13	
7.91/8.13	The encoding turns the above axioms into the following unit equations and goals:
7.91/8.13	
7.91/8.13	Axiom 1 (help_c__COMBI__1): X = hAPP(c_COMBI(Y), X).
7.91/8.13	Axiom 2 (fact_ext): fresh7(hAPP(X, sK38_fact_ext_B_x(Y, X)), hAPP(Y, sK38_fact_ext_B_x(Y, X)), Y, X) = X.
7.91/8.13	Axiom 3 (help_c__COMBS__1): hAPP(hAPP(hAPP(c_COMBS(X, Y, Z), W), V), U) = hAPP(hAPP(W, U), hAPP(V, U)).
7.91/8.13	
7.91/8.13	Lemma 4: fresh7(hAPP(X, sK38_fact_ext_B_x(c_COMBI(Y), X)), sK38_fact_ext_B_x(c_COMBI(Y), X), c_COMBI(Y), X) = X.
7.91/8.13	Proof:
7.91/8.13	  fresh7(hAPP(X, sK38_fact_ext_B_x(c_COMBI(Y), X)), sK38_fact_ext_B_x(c_COMBI(Y), X), c_COMBI(Y), X)
7.91/8.13	= { by axiom 1 (help_c__COMBI__1) }
7.91/8.13	  fresh7(hAPP(X, sK38_fact_ext_B_x(c_COMBI(Y), X)), hAPP(c_COMBI(Y), sK38_fact_ext_B_x(c_COMBI(Y), X)), c_COMBI(Y), X)
7.91/8.13	= { by axiom 2 (fact_ext) }
7.91/8.13	  X
7.91/8.13	
7.91/8.13	Goal 1 (fact_not__Cons__self): hAPP(hAPP(c_List_Olist_OCons(X), Y), Z) = Z.
7.91/8.13	The goal is true when:
7.91/8.13	  X = ?
7.91/8.13	  Y = hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))
7.91/8.13	  Z = hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)))
7.91/8.13	where "?" stands for an arbitrary term of your choice.
7.91/8.13	
7.91/8.13	Proof:
7.91/8.13	  hAPP(hAPP(c_List_Olist_OCons(?), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))), hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))))
7.91/8.13	= { by axiom 3 (help_c__COMBS__1) }
7.91/8.13	  hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)))
7.91/8.13	= { by axiom 1 (help_c__COMBI__1) }
7.91/8.13	  hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))), hAPP(c_COMBI(?), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?))))
7.91/8.13	= { by axiom 3 (help_c__COMBS__1) }
7.91/8.13	  hAPP(hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)), hAPP(hAPP(c_COMBS(?, ?, ?), hAPP(c_COMBS(?, ?, ?), c_List_Olist_OCons(?))), c_COMBI(?)))
7.91/8.13	% SZS output end Proof
7.91/8.13	
7.91/8.13	RESULT: Theorem (the conjecture is true).
7.91/8.14	EOF