TSTP Solution File: LCL835-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL835-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n011.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 : Thu Aug 31 08:20:54 EDT 2023
% Result : Unsatisfiable 97.72s 12.91s
% Output : Proof 98.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL835-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 19:23:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 97.72/12.91 Command-line arguments: --flatten
% 97.72/12.91
% 97.72/12.91 % SZS status Unsatisfiable
% 97.72/12.91
% 98.45/12.93 % SZS output start Proof
% 98.45/12.93 Take the following subset of the input axioms:
% 98.45/12.93 fof(cls_Beta_I1_J_0, axiom, hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)))).
% 98.45/12.93 fof(cls_Beta_I6_J_0, axiom, hBOOL(hAPP(c_InductTermi_OIT, v_ua______))).
% 98.45/12.93 fof(cls_CHAINED_0, axiom, hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)))).
% 98.45/12.93 fof(cls_T_0, axiom, c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)).
% 98.45/12.93 fof(cls_conjecture_0, negated_conjecture, ~c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)).
% 98.45/12.93 fof(cls_r__into__rtranclp_0, axiom, ![T_a, V_r, V_x, V_y]: (hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r, T_a), V_x), V_y)) | ~hBOOL(hAPP(hAPP(V_r, V_x), V_y)))).
% 98.45/12.93 fof(cls_subject__reduction_H_0, axiom, ![V_t, V_t_H, V_e, V_T]: (c_Type_Otyping(V_e, V_t_H, V_T) | (~c_Type_Otyping(V_e, V_t, V_T) | ~hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), V_t), V_t_H))))).
% 98.45/12.93 fof(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, axiom, class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)).
% 98.45/12.93 fof(clsarity_nat__OrderedGroup_Omonoid__add, axiom, class_OrderedGroup_Omonoid__add(tc_nat)).
% 98.45/12.93 fof(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, axiom, class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)).
% 98.45/12.93 fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_nat)).
% 98.45/12.93
% 98.45/12.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 98.45/12.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 98.45/12.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 98.45/12.93 fresh(y, y, x1...xn) = u
% 98.45/12.93 C => fresh(s, t, x1...xn) = v
% 98.45/12.93 where fresh is a fresh function symbol and x1..xn are the free
% 98.45/12.93 variables of u and v.
% 98.45/12.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 98.45/12.93 input problem has no model of domain size 1).
% 98.45/12.93
% 98.45/12.93 The encoding turns the above axioms into the following unit equations and goals:
% 98.45/12.93
% 98.45/12.93 Axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add): class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) = true2.
% 98.45/12.93 Axiom 2 (clsarity_nat__OrderedGroup_Opordered__comm__monoid__add): class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) = true2.
% 98.45/12.93 Axiom 3 (clsarity_nat__OrderedGroup_Omonoid__add): class_OrderedGroup_Omonoid__add(tc_nat) = true2.
% 98.45/12.93 Axiom 4 (clsarity_nat__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_nat) = true2.
% 98.45/12.93 Axiom 5 (cls_Beta_I6_J_0): hBOOL(hAPP(c_InductTermi_OIT, v_ua______)) = true2.
% 98.45/12.93 Axiom 6 (cls_subject__reduction_H_0): fresh114(X, X, Y, Z, W) = true2.
% 98.45/12.93 Axiom 7 (cls_r__into__rtranclp_0): fresh131(X, X, Y, Z, W, V) = true2.
% 98.45/12.93 Axiom 8 (cls_subject__reduction_H_0): fresh115(X, X, Y, Z, W, V) = c_Type_Otyping(Y, Z, W).
% 98.45/12.93 Axiom 9 (cls_converse__rtranclp__into__rtranclp_0): fresh245(X, X, Y, Z, W, V, U) = hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(Y, Z), W), V)).
% 98.45/12.93 Axiom 10 (cls_r__into__rtranclp_0): fresh131(hBOOL(hAPP(hAPP(X, Y), Z)), true2, X, W, Y, Z) = hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X, W), Y), Z)).
% 98.45/12.93 Axiom 11 (cls_subject__reduction_H_0): fresh115(c_Type_Otyping(X, Y, Z), true2, X, W, Z, Y) = fresh114(hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), Y), W)), true2, X, W, Z).
% 98.45/12.93 Axiom 12 (cls_Beta_I1_J_0): hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))) = true2.
% 98.45/12.93 Axiom 13 (cls_T_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____) = true2.
% 98.45/12.93 Axiom 14 (cls_CHAINED_0): hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))) = true2.
% 98.45/12.93
% 98.45/12.93 Lemma 15: class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) = class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 98.45/12.93 Proof:
% 98.45/12.93 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 98.45/12.93 = { by axiom 2 (clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) }
% 98.45/12.93 true2
% 98.45/12.93 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.93 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
% 98.45/12.93
% 98.45/12.93 Lemma 16: class_OrderedGroup_Omonoid__add(tc_nat) = class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 98.45/12.93 Proof:
% 98.45/12.93 class_OrderedGroup_Omonoid__add(tc_nat)
% 98.45/12.93 = { by axiom 3 (clsarity_nat__OrderedGroup_Omonoid__add) }
% 98.45/12.93 true2
% 98.45/12.93 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.93 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
% 98.45/12.93 = { by lemma 15 R->L }
% 98.45/12.93 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 98.45/12.93
% 98.45/12.93 Lemma 17: class_Ring__and__Field_Ocomm__semiring__1(tc_nat) = class_OrderedGroup_Omonoid__add(tc_nat).
% 98.45/12.93 Proof:
% 98.45/12.93 class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
% 98.45/12.93 = { by axiom 4 (clsarity_nat__Ring__and__Field_Ocomm__semiring__1) }
% 98.45/12.93 true2
% 98.45/12.93 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.93 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
% 98.45/12.93 = { by lemma 15 R->L }
% 98.45/12.93 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 98.45/12.93 = { by lemma 16 R->L }
% 98.45/12.93 class_OrderedGroup_Omonoid__add(tc_nat)
% 98.45/12.93
% 98.45/12.93 Lemma 18: hBOOL(hAPP(c_InductTermi_OIT, v_ua______)) = class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 98.45/12.93 Proof:
% 98.45/12.93 hBOOL(hAPP(c_InductTermi_OIT, v_ua______))
% 98.45/12.93 = { by axiom 5 (cls_Beta_I6_J_0) }
% 98.45/12.93 true2
% 98.45/12.93 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.93 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
% 98.45/12.93 = { by lemma 15 R->L }
% 98.45/12.93 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 98.45/12.93 = { by lemma 16 R->L }
% 98.45/12.93 class_OrderedGroup_Omonoid__add(tc_nat)
% 98.45/12.93 = { by lemma 17 R->L }
% 98.45/12.93 class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
% 98.45/12.93
% 98.45/12.93 Lemma 19: hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))) = hBOOL(hAPP(c_InductTermi_OIT, v_ua______)).
% 98.45/12.93 Proof:
% 98.45/12.93 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)))
% 98.45/12.93 = { by axiom 12 (cls_Beta_I1_J_0) }
% 98.45/12.93 true2
% 98.45/12.93 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.93 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
% 98.45/12.93 = { by lemma 15 R->L }
% 98.45/12.93 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 98.45/12.93 = { by lemma 16 R->L }
% 98.45/12.93 class_OrderedGroup_Omonoid__add(tc_nat)
% 98.45/12.93 = { by lemma 17 R->L }
% 98.45/12.93 class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
% 98.45/12.93 = { by lemma 18 R->L }
% 98.45/12.93 hBOOL(hAPP(c_InductTermi_OIT, v_ua______))
% 98.45/12.93
% 98.45/12.93 Lemma 20: hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))) = hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))).
% 98.45/12.93 Proof:
% 98.45/12.93 hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)))
% 98.45/12.93 = { by axiom 14 (cls_CHAINED_0) }
% 98.45/12.93 true2
% 98.45/12.93 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.93 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat)
% 98.45/12.93 = { by lemma 15 R->L }
% 98.45/12.93 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 98.45/12.93 = { by lemma 16 R->L }
% 98.45/12.93 class_OrderedGroup_Omonoid__add(tc_nat)
% 98.45/12.93 = { by lemma 17 R->L }
% 98.45/12.93 class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
% 98.45/12.93 = { by lemma 18 R->L }
% 98.45/12.93 hBOOL(hAPP(c_InductTermi_OIT, v_ua______))
% 98.45/12.93 = { by lemma 19 R->L }
% 98.45/12.93 hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)))
% 98.45/12.93
% 98.45/12.93 Goal 1 (cls_conjecture_0): c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____) = true2.
% 98.45/12.93 Proof:
% 98.45/12.93 c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.93 = { by axiom 8 (cls_subject__reduction_H_0) R->L }
% 98.45/12.93 fresh115(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.93 = { by lemma 20 }
% 98.45/12.93 fresh115(hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.93 = { by lemma 19 }
% 98.45/12.93 fresh115(hBOOL(hAPP(c_InductTermi_OIT, v_ua______)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 18 }
% 98.45/12.94 fresh115(class_Ring__and__Field_Ocomm__semiring__1(tc_nat), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 17 }
% 98.45/12.94 fresh115(class_OrderedGroup_Omonoid__add(tc_nat), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 16 }
% 98.45/12.94 fresh115(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 15 }
% 98.45/12.94 fresh115(class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) }
% 98.45/12.94 fresh115(true2, hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by axiom 13 (cls_T_0) R->L }
% 98.45/12.94 fresh115(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 20 }
% 98.45/12.94 fresh115(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 19 }
% 98.45/12.94 fresh115(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), hBOOL(hAPP(c_InductTermi_OIT, v_ua______)), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 18 }
% 98.45/12.94 fresh115(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), class_Ring__and__Field_Ocomm__semiring__1(tc_nat), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 17 }
% 98.45/12.94 fresh115(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), class_OrderedGroup_Omonoid__add(tc_nat), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 16 }
% 98.45/12.94 fresh115(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by lemma 15 }
% 98.45/12.94 fresh115(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) }
% 98.45/12.94 fresh115(c_Type_Otyping(c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____), true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))
% 98.45/12.94 = { by axiom 11 (cls_subject__reduction_H_0) }
% 98.45/12.94 fresh114(hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by axiom 9 (cls_converse__rtranclp__into__rtranclp_0) R->L }
% 98.45/12.94 fresh114(fresh245(X, X, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), Y), true2, c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.94 fresh114(fresh245(X, X, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), Y), class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 15 R->L }
% 98.45/12.94 fresh114(fresh245(X, X, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), Y), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 16 R->L }
% 98.45/12.94 fresh114(fresh245(X, X, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), Y), class_OrderedGroup_Omonoid__add(tc_nat), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 17 R->L }
% 98.45/12.94 fresh114(fresh245(X, X, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), Y), class_Ring__and__Field_Ocomm__semiring__1(tc_nat), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 18 R->L }
% 98.45/12.94 fresh114(fresh245(X, X, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), Y), hBOOL(hAPP(c_InductTermi_OIT, v_ua______)), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 19 R->L }
% 98.45/12.94 fresh114(fresh245(X, X, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), Y), hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 20 R->L }
% 98.45/12.94 fresh114(fresh245(X, X, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), Y), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by axiom 9 (cls_converse__rtranclp__into__rtranclp_0) }
% 98.45/12.94 fresh114(hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by axiom 10 (cls_r__into__rtranclp_0) R->L }
% 98.45/12.94 fresh114(fresh131(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), true2, c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.94 fresh114(fresh131(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat), c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 15 R->L }
% 98.45/12.94 fresh114(fresh131(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 16 R->L }
% 98.45/12.94 fresh114(fresh131(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), class_OrderedGroup_Omonoid__add(tc_nat), c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 17 R->L }
% 98.45/12.94 fresh114(fresh131(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), class_Ring__and__Field_Ocomm__semiring__1(tc_nat), c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 18 R->L }
% 98.45/12.94 fresh114(fresh131(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), hBOOL(hAPP(c_InductTermi_OIT, v_ua______)), c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 19 R->L }
% 98.45/12.94 fresh114(fresh131(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.94 = { by lemma 20 R->L }
% 98.45/12.95 fresh114(fresh131(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Lambda_Obeta, tc_Lambda_OdB, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by axiom 7 (cls_r__into__rtranclp_0) }
% 98.45/12.95 fresh114(true2, hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by axiom 1 (clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) R->L }
% 98.45/12.95 fresh114(class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by lemma 15 R->L }
% 98.45/12.95 fresh114(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by lemma 16 R->L }
% 98.45/12.95 fresh114(class_OrderedGroup_Omonoid__add(tc_nat), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by lemma 17 R->L }
% 98.45/12.95 fresh114(class_Ring__and__Field_Ocomm__semiring__1(tc_nat), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by lemma 18 R->L }
% 98.45/12.95 fresh114(hBOOL(hAPP(c_InductTermi_OIT, v_ua______)), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by lemma 19 R->L }
% 98.45/12.95 fresh114(hBOOL(hAPP(c_InductTermi_OIT, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by lemma 20 R->L }
% 98.45/12.95 fresh114(hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), hBOOL(hAPP(hAPP(c_Lambda_Obeta, c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(c_Lambda_OdB_OApp, c_Lambda_OdB_OAbs(v_r____)), v_a____), v_as____, tc_Lambda_OdB, tc_Lambda_OdB)), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB))), c_Type_Oshift(v_e____, v_i____, v_T____, tc_Type_Otype), c_List_Ofoldl(c_Lambda_OdB_OApp, hAPP(hAPP(hAPP(c_Lambda_Osubst, v_r____), v_a____), c_HOL_Ozero__class_Ozero(tc_nat)), v_as____, tc_Lambda_OdB, tc_Lambda_OdB), v_T_H____)
% 98.45/12.95 = { by axiom 6 (cls_subject__reduction_H_0) }
% 98.45/12.95 true2
% 98.45/12.95 % SZS output end Proof
% 98.45/12.95
% 98.45/12.95 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------