% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/StrongNorm/prob_281__5212424_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:38:54.568

% Could-be-implicit typings (3)
thf(ty_n_t__LambdaType__Otype, type,
    type : $tType).
thf(ty_n_t__Lambda__OdB, type,
    dB : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (20)
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_InductTermi_OIT, type,
    it : dB > $o).
thf(sy_c_LambdaType_Oshift_001t__LambdaType__Otype, type,
    shift_type : (nat > type) > nat > type > nat > type).
thf(sy_c_LambdaType_Otyping, type,
    typing : (nat > type) > dB > type > $o).
thf(sy_c_Lambda_Obeta, type,
    beta : dB > dB > $o).
thf(sy_c_Lambda_OdB_OAbs, type,
    abs : dB > dB).
thf(sy_c_Lambda_OdB_OVar, type,
    var : nat > dB).
thf(sy_c_Lambda_Olift, type,
    lift : dB > nat > dB).
thf(sy_c_Lambda_Osubst, type,
    subst : dB > dB > nat > dB).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Lambda__OdB_M_062_It__Lambda__OdB_M_Eo_J_J, type,
    ord_less_eq_dB_dB_o : (dB > dB > $o) > (dB > dB > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Lambda__OdB_M_Eo_J, type,
    ord_less_eq_dB_o : (dB > $o) > (dB > $o) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Relation_Oconversep_001t__Lambda__OdB_001t__Lambda__OdB, type,
    conversep_dB_dB : (dB > dB > $o) > dB > dB > $o).
thf(sy_c_Transitive__Closure_Ortranclp_001t__Lambda__OdB, type,
    transi72828568clp_dB : (dB > dB > $o) > dB > dB > $o).
thf(sy_c_Wellfounded_Oaccp_001t__Lambda__OdB, type,
    accp_dB : (dB > dB > $o) > dB > $o).
thf(sy_c_Wellfounded_OwfP_001t__Lambda__OdB, type,
    wfP_dB : (dB > dB > $o) > $o).
thf(sy_v_T, type,
    t : type).
thf(sy_v_e, type,
    e : nat > type).
thf(sy_v_t, type,
    t2 : dB).

% Relevant facts (95)
thf(fact_0__092_060open_062IT_At_092_060close_062, axiom,
    ((it @ t2))). % \<open>IT t\<close>
thf(fact_1__092_060open_062e_A_092_060turnstile_062_At_A_058_AT_092_060close_062, axiom,
    ((typing @ e @ t2 @ t))). % \<open>e \<turnstile> t : T\<close>
thf(fact_2_conversep__eq, axiom,
    (((conversep_dB_dB @ (^[Y : dB]: (^[Z : dB]: (Y = Z)))) = (^[Y : dB]: (^[Z : dB]: (Y = Z)))))). % conversep_eq
thf(fact_3_conversep__iff, axiom,
    ((conversep_dB_dB = (^[R : dB > dB > $o]: (^[A : dB]: (^[B : dB]: (R @ B @ A))))))). % conversep_iff
thf(fact_4_conversep__inject, axiom,
    ((![R2 : dB > dB > $o, S : dB > dB > $o]: (((conversep_dB_dB @ R2) = (conversep_dB_dB @ S)) = (R2 = S))))). % conversep_inject
thf(fact_5_conversep__conversep, axiom,
    ((![R2 : dB > dB > $o]: ((conversep_dB_dB @ (conversep_dB_dB @ R2)) = R2)))). % conversep_conversep
thf(fact_6_IT__implies__termi, axiom,
    ((![T : dB]: ((it @ T) => (accp_dB @ (conversep_dB_dB @ beta) @ T))))). % IT_implies_termi
thf(fact_7_termi__implies__IT, axiom,
    ((![R2 : dB]: ((accp_dB @ (conversep_dB_dB @ beta) @ R2) => (it @ R2))))). % termi_implies_IT
thf(fact_8_conversepD, axiom,
    ((![R2 : dB > dB > $o, B2 : dB, A2 : dB]: ((conversep_dB_dB @ R2 @ B2 @ A2) => (R2 @ A2 @ B2))))). % conversepD
thf(fact_9_conversep_Ocases, axiom,
    ((![R2 : dB > dB > $o, A1 : dB, A22 : dB]: ((conversep_dB_dB @ R2 @ A1 @ A22) => (R2 @ A22 @ A1))))). % conversep.cases
thf(fact_10_conversep_Osimps, axiom,
    ((conversep_dB_dB = (^[R : dB > dB > $o]: (^[A12 : dB]: (^[A23 : dB]: (?[A : dB]: (?[B : dB]: (((A12 = B)) & ((((A23 = A)) & ((R @ A @ B))))))))))))). % conversep.simps
thf(fact_11_conversep_Ointros, axiom,
    ((![R2 : dB > dB > $o, A2 : dB, B2 : dB]: ((R2 @ A2 @ B2) => (conversep_dB_dB @ R2 @ B2 @ A2))))). % conversep.intros
thf(fact_12_conversep_Oinducts, axiom,
    ((![R2 : dB > dB > $o, X1 : dB, X2 : dB, P : dB > dB > $o]: ((conversep_dB_dB @ R2 @ X1 @ X2) => ((![A3 : dB, B3 : dB]: ((R2 @ A3 @ B3) => (P @ B3 @ A3))) => (P @ X1 @ X2)))))). % conversep.inducts
thf(fact_13_type__implies__IT, axiom,
    ((![E : nat > type, T : dB, T2 : type]: ((typing @ E @ T @ T2) => (it @ T))))). % type_implies_IT
thf(fact_14_subject__reduction, axiom,
    ((![E : nat > type, T : dB, T2 : type, T3 : dB]: ((typing @ E @ T @ T2) => ((beta @ T @ T3) => (typing @ E @ T3 @ T2)))))). % subject_reduction
thf(fact_15_accp__induct__rule, axiom,
    ((![R2 : dB > dB > $o, A2 : dB, P : dB > $o]: ((accp_dB @ R2 @ A2) => ((![X : dB]: ((accp_dB @ R2 @ X) => ((![Y2 : dB]: ((R2 @ Y2 @ X) => (P @ Y2))) => (P @ X)))) => (P @ A2)))))). % accp_induct_rule
thf(fact_16_not__accp__down, axiom,
    ((![R3 : dB > dB > $o, X3 : dB]: ((~ ((accp_dB @ R3 @ X3))) => (~ ((![Z2 : dB]: ((R3 @ Z2 @ X3) => (accp_dB @ R3 @ Z2))))))))). % not_accp_down
thf(fact_17_accp__downward, axiom,
    ((![R2 : dB > dB > $o, B2 : dB, A2 : dB]: ((accp_dB @ R2 @ B2) => ((R2 @ A2 @ B2) => (accp_dB @ R2 @ A2)))))). % accp_downward
thf(fact_18_accp_Oinducts, axiom,
    ((![R2 : dB > dB > $o, X3 : dB, P : dB > $o]: ((accp_dB @ R2 @ X3) => ((![X : dB]: ((![Y2 : dB]: ((R2 @ Y2 @ X) => (accp_dB @ R2 @ Y2))) => ((![Y2 : dB]: ((R2 @ Y2 @ X) => (P @ Y2))) => (P @ X)))) => (P @ X3)))))). % accp.inducts
thf(fact_19_accp__induct, axiom,
    ((![R2 : dB > dB > $o, A2 : dB, P : dB > $o]: ((accp_dB @ R2 @ A2) => ((![X : dB]: ((accp_dB @ R2 @ X) => ((![Y2 : dB]: ((R2 @ Y2 @ X) => (P @ Y2))) => (P @ X)))) => (P @ A2)))))). % accp_induct
thf(fact_20_accp_Ointros, axiom,
    ((![R2 : dB > dB > $o, X3 : dB]: ((![Y3 : dB]: ((R2 @ Y3 @ X3) => (accp_dB @ R2 @ Y3))) => (accp_dB @ R2 @ X3))))). % accp.intros
thf(fact_21_accp_Osimps, axiom,
    ((accp_dB = (^[R : dB > dB > $o]: (^[A : dB]: (?[X4 : dB]: (((A = X4)) & ((![Y4 : dB]: (((R @ Y4 @ X4)) => ((accp_dB @ R @ Y4)))))))))))). % accp.simps
thf(fact_22_accp_Ocases, axiom,
    ((![R2 : dB > dB > $o, A2 : dB]: ((accp_dB @ R2 @ A2) => (![Y2 : dB]: ((R2 @ Y2 @ A2) => (accp_dB @ R2 @ Y2))))))). % accp.cases
thf(fact_23_lift__IT, axiom,
    ((![T : dB, I : nat]: ((it @ T) => (it @ (lift @ T @ I)))))). % lift_IT
thf(fact_24_subject__reduction_H, axiom,
    ((![T : dB, T3 : dB, E : nat > type, T2 : type]: ((transi72828568clp_dB @ beta @ T @ T3) => ((typing @ E @ T @ T2) => (typing @ E @ T3 @ T2)))))). % subject_reduction'
thf(fact_25_accp__wfPD, axiom,
    ((![R2 : dB > dB > $o, X3 : dB]: ((wfP_dB @ R2) => (accp_dB @ R2 @ X3))))). % accp_wfPD
thf(fact_26_accp__wfPI, axiom,
    ((![R2 : dB > dB > $o]: ((![X_1 : dB]: (accp_dB @ R2 @ X_1)) => (wfP_dB @ R2))))). % accp_wfPI
thf(fact_27_wfP__accp__iff, axiom,
    ((wfP_dB = (^[R : dB > dB > $o]: (![X5 : dB]: (accp_dB @ R @ X5)))))). % wfP_accp_iff
thf(fact_28_conversep__mono, axiom,
    ((![R2 : dB > dB > $o, S : dB > dB > $o]: ((ord_less_eq_dB_dB_o @ (conversep_dB_dB @ R2) @ (conversep_dB_dB @ S)) = (ord_less_eq_dB_dB_o @ R2 @ S))))). % conversep_mono
thf(fact_29_Var__IT, axiom,
    ((![N : nat]: (it @ (var @ N))))). % Var_IT
thf(fact_30_subst__type__IT, axiom,
    ((![T : dB, E : nat > type, I : nat, U : type, T2 : type, U2 : dB]: ((it @ T) => ((typing @ (shift_type @ E @ I @ U) @ T @ T2) => ((it @ U2) => ((typing @ E @ U2 @ U) => (it @ (subst @ T @ U2 @ I))))))))). % subst_type_IT
thf(fact_31_shift__eq, axiom,
    ((![I : nat, J : nat, E : nat > type, T2 : type]: ((I = J) => ((shift_type @ E @ I @ T2 @ J) = T2))))). % shift_eq
thf(fact_32_lift__type, axiom,
    ((![E : nat > type, T : dB, T2 : type, I : nat, U : type]: ((typing @ E @ T @ T2) => (typing @ (shift_type @ E @ I @ U) @ (lift @ T @ I) @ T2))))). % lift_type
thf(fact_33_subst__Var__IT, axiom,
    ((![R2 : dB, I : nat, J : nat]: ((it @ R2) => (it @ (subst @ R2 @ (var @ I) @ J)))))). % subst_Var_IT
thf(fact_34_subst__lemma, axiom,
    ((![E : nat > type, T : dB, T2 : type, E2 : nat > type, U2 : dB, U : type, I : nat]: ((typing @ E @ T @ T2) => ((typing @ E2 @ U2 @ U) => ((E = (shift_type @ E2 @ I @ U)) => (typing @ E2 @ (subst @ T @ U2 @ I) @ T2))))))). % subst_lemma
thf(fact_35_accp__downwards__aux, axiom,
    ((![R2 : dB > dB > $o, B2 : dB, A2 : dB]: ((transi72828568clp_dB @ R2 @ B2 @ A2) => ((accp_dB @ R2 @ A2) => (accp_dB @ R2 @ B2)))))). % accp_downwards_aux
thf(fact_36_accp__downwards, axiom,
    ((![R2 : dB > dB > $o, A2 : dB, B2 : dB]: ((accp_dB @ R2 @ A2) => ((transi72828568clp_dB @ R2 @ B2 @ A2) => (accp_dB @ R2 @ B2)))))). % accp_downwards
thf(fact_37_conversep__le__swap, axiom,
    ((![R2 : dB > dB > $o, S : dB > dB > $o]: ((ord_less_eq_dB_dB_o @ R2 @ (conversep_dB_dB @ S)) = (ord_less_eq_dB_dB_o @ (conversep_dB_dB @ R2) @ S))))). % conversep_le_swap
thf(fact_38_typing__elims_I1_J, axiom,
    ((![E : nat > type, I : nat, T2 : type]: ((typing @ E @ (var @ I) @ T2) => ((E @ I) = T2))))). % typing_elims(1)
thf(fact_39_typing_OVar, axiom,
    ((![Env : nat > type, X3 : nat, T2 : type]: (((Env @ X3) = T2) => (typing @ Env @ (var @ X3) @ T2))))). % typing.Var
thf(fact_40_subst__lift, axiom,
    ((![T : dB, K : nat, S : dB]: ((subst @ (lift @ T @ K) @ S @ K) = T)))). % subst_lift
thf(fact_41_subst__eq, axiom,
    ((![K : nat, U2 : dB]: ((subst @ (var @ K) @ U2 @ K) = U2)))). % subst_eq
thf(fact_42_lift__preserves__beta_H, axiom,
    ((![R2 : dB, S : dB, I : nat]: ((transi72828568clp_dB @ beta @ R2 @ S) => (transi72828568clp_dB @ beta @ (lift @ R2 @ I) @ (lift @ S @ I)))))). % lift_preserves_beta'
thf(fact_43_subst__preserves__beta_H, axiom,
    ((![R2 : dB, S : dB, T : dB, I : nat]: ((transi72828568clp_dB @ beta @ R2 @ S) => (transi72828568clp_dB @ beta @ (subst @ R2 @ T @ I) @ (subst @ S @ T @ I)))))). % subst_preserves_beta'
thf(fact_44_subst__preserves__beta2, axiom,
    ((![R2 : dB, S : dB, T : dB, I : nat]: ((beta @ R2 @ S) => (transi72828568clp_dB @ beta @ (subst @ T @ R2 @ I) @ (subst @ T @ S @ I)))))). % subst_preserves_beta2
thf(fact_45_subst__preserves__beta2_H, axiom,
    ((![R2 : dB, S : dB, T : dB, I : nat]: ((transi72828568clp_dB @ beta @ R2 @ S) => (transi72828568clp_dB @ beta @ (subst @ T @ R2 @ I) @ (subst @ T @ S @ I)))))). % subst_preserves_beta2'
thf(fact_46_dB_Oinject_I1_J, axiom,
    ((![X1 : nat, Y1 : nat]: (((var @ X1) = (var @ Y1)) = (X1 = Y1))))). % dB.inject(1)
thf(fact_47_beta__cases_I1_J, axiom,
    ((![I : nat, T : dB]: (~ ((beta @ (var @ I) @ T)))))). % beta_cases(1)
thf(fact_48_subst__preserves__beta, axiom,
    ((![R2 : dB, S : dB, T : dB, I : nat]: ((beta @ R2 @ S) => (beta @ (subst @ R2 @ T @ I) @ (subst @ S @ T @ I)))))). % subst_preserves_beta
thf(fact_49_lift__preserves__beta, axiom,
    ((![R2 : dB, S : dB, I : nat]: ((beta @ R2 @ S) => (beta @ (lift @ R2 @ I) @ (lift @ S @ I)))))). % lift_preserves_beta
thf(fact_50_r__into__rtranclp, axiom,
    ((![R2 : dB > dB > $o, X3 : dB, Y5 : dB]: ((R2 @ X3 @ Y5) => (transi72828568clp_dB @ R2 @ X3 @ Y5))))). % r_into_rtranclp
thf(fact_51_rtranclp__idemp, axiom,
    ((![R2 : dB > dB > $o]: ((transi72828568clp_dB @ (transi72828568clp_dB @ R2)) = (transi72828568clp_dB @ R2))))). % rtranclp_idemp
thf(fact_52_leq__conversepI, axiom,
    ((![R3 : dB > dB > $o]: ((R3 = (^[Y : dB]: (^[Z : dB]: (Y = Z)))) => (ord_less_eq_dB_dB_o @ R3 @ (conversep_dB_dB @ R3)))))). % leq_conversepI
thf(fact_53_accp__subset__induct, axiom,
    ((![D : dB > $o, R3 : dB > dB > $o, X3 : dB, P : dB > $o]: ((ord_less_eq_dB_o @ D @ (accp_dB @ R3)) => ((![X : dB, Z2 : dB]: ((D @ X) => ((R3 @ Z2 @ X) => (D @ Z2)))) => ((D @ X3) => ((![X : dB]: ((D @ X) => ((![Z3 : dB]: ((R3 @ Z3 @ X) => (P @ Z3))) => (P @ X)))) => (P @ X3)))))))). % accp_subset_induct
thf(fact_54_accp__subset, axiom,
    ((![R1 : dB > dB > $o, R22 : dB > dB > $o]: ((ord_less_eq_dB_dB_o @ R1 @ R22) => (ord_less_eq_dB_o @ (accp_dB @ R22) @ (accp_dB @ R1)))))). % accp_subset
thf(fact_55_mono__rtranclp, axiom,
    ((![X3 : dB > dB > $o, Y5 : dB > dB > $o, A2 : dB, B2 : dB]: ((![A3 : dB, B3 : dB]: ((X3 @ A3 @ B3) => (Y5 @ A3 @ B3))) => ((transi72828568clp_dB @ X3 @ A2 @ B2) => (transi72828568clp_dB @ Y5 @ A2 @ B2)))))). % mono_rtranclp
thf(fact_56_rtranclp_Ocases, axiom,
    ((![R2 : dB > dB > $o, A1 : dB, A22 : dB]: ((transi72828568clp_dB @ R2 @ A1 @ A22) => ((~ ((A22 = A1))) => (~ ((![B3 : dB]: ((transi72828568clp_dB @ R2 @ A1 @ B3) => (~ ((R2 @ B3 @ A22)))))))))))). % rtranclp.cases
thf(fact_57_rtranclp_Osimps, axiom,
    ((transi72828568clp_dB = (^[R : dB > dB > $o]: (^[A12 : dB]: (^[A23 : dB]: (((?[A : dB]: (((A12 = A)) & ((A23 = A))))) | ((?[A : dB]: (?[B : dB]: (?[C : dB]: (((A12 = A)) & ((((A23 = C)) & ((((transi72828568clp_dB @ R @ A @ B)) & ((R @ B @ C)))))))))))))))))). % rtranclp.simps
thf(fact_58_rtranclp__trans, axiom,
    ((![R2 : dB > dB > $o, X3 : dB, Y5 : dB, Z4 : dB]: ((transi72828568clp_dB @ R2 @ X3 @ Y5) => ((transi72828568clp_dB @ R2 @ Y5 @ Z4) => (transi72828568clp_dB @ R2 @ X3 @ Z4)))))). % rtranclp_trans
thf(fact_59_rtranclp__induct, axiom,
    ((![R2 : dB > dB > $o, A2 : dB, B2 : dB, P : dB > $o]: ((transi72828568clp_dB @ R2 @ A2 @ B2) => ((P @ A2) => ((![Y3 : dB, Z2 : dB]: ((transi72828568clp_dB @ R2 @ A2 @ Y3) => ((R2 @ Y3 @ Z2) => ((P @ Y3) => (P @ Z2))))) => (P @ B2))))))). % rtranclp_induct
thf(fact_60_rtranclp_Oinducts, axiom,
    ((![R2 : dB > dB > $o, X1 : dB, X2 : dB, P : dB > dB > $o]: ((transi72828568clp_dB @ R2 @ X1 @ X2) => ((![A3 : dB]: (P @ A3 @ A3)) => ((![A3 : dB, B3 : dB, C2 : dB]: ((transi72828568clp_dB @ R2 @ A3 @ B3) => ((P @ A3 @ B3) => ((R2 @ B3 @ C2) => (P @ A3 @ C2))))) => (P @ X1 @ X2))))))). % rtranclp.inducts
thf(fact_61_converse__rtranclpE, axiom,
    ((![R2 : dB > dB > $o, X3 : dB, Z4 : dB]: ((transi72828568clp_dB @ R2 @ X3 @ Z4) => ((~ ((X3 = Z4))) => (~ ((![Y3 : dB]: ((R2 @ X3 @ Y3) => (~ ((transi72828568clp_dB @ R2 @ Y3 @ Z4)))))))))))). % converse_rtranclpE
thf(fact_62_rtranclp_Ortrancl__refl, axiom,
    ((![R2 : dB > dB > $o, A2 : dB]: (transi72828568clp_dB @ R2 @ A2 @ A2)))). % rtranclp.rtrancl_refl
thf(fact_63_converse__rtranclp__induct, axiom,
    ((![R2 : dB > dB > $o, A2 : dB, B2 : dB, P : dB > $o]: ((transi72828568clp_dB @ R2 @ A2 @ B2) => ((P @ B2) => ((![Y3 : dB, Z2 : dB]: ((R2 @ Y3 @ Z2) => ((transi72828568clp_dB @ R2 @ Z2 @ B2) => ((P @ Z2) => (P @ Y3))))) => (P @ A2))))))). % converse_rtranclp_induct
thf(fact_64_rtranclp_Ortrancl__into__rtrancl, axiom,
    ((![R2 : dB > dB > $o, A2 : dB, B2 : dB, C3 : dB]: ((transi72828568clp_dB @ R2 @ A2 @ B2) => ((R2 @ B2 @ C3) => (transi72828568clp_dB @ R2 @ A2 @ C3)))))). % rtranclp.rtrancl_into_rtrancl
thf(fact_65_converse__rtranclp__into__rtranclp, axiom,
    ((![R2 : dB > dB > $o, A2 : dB, B2 : dB, C3 : dB]: ((R2 @ A2 @ B2) => ((transi72828568clp_dB @ R2 @ B2 @ C3) => (transi72828568clp_dB @ R2 @ A2 @ C3)))))). % converse_rtranclp_into_rtranclp
thf(fact_66_rtranclp__converseD, axiom,
    ((![R2 : dB > dB > $o, X3 : dB, Y5 : dB]: ((transi72828568clp_dB @ (conversep_dB_dB @ R2) @ X3 @ Y5) => (transi72828568clp_dB @ R2 @ Y5 @ X3))))). % rtranclp_converseD
thf(fact_67_rtranclp__converseI, axiom,
    ((![R2 : dB > dB > $o, Y5 : dB, X3 : dB]: ((transi72828568clp_dB @ R2 @ Y5 @ X3) => (transi72828568clp_dB @ (conversep_dB_dB @ R2) @ X3 @ Y5))))). % rtranclp_converseI
thf(fact_68_rtranclp__conversep, axiom,
    ((![R2 : dB > dB > $o]: ((transi72828568clp_dB @ (conversep_dB_dB @ R2)) = (conversep_dB_dB @ (transi72828568clp_dB @ R2)))))). % rtranclp_conversep
thf(fact_69_rtranclp__mono, axiom,
    ((![R2 : dB > dB > $o, S : dB > dB > $o]: ((ord_less_eq_dB_dB_o @ R2 @ S) => (ord_less_eq_dB_dB_o @ (transi72828568clp_dB @ R2) @ (transi72828568clp_dB @ S)))))). % rtranclp_mono
thf(fact_70_rtranclp__subset, axiom,
    ((![R3 : dB > dB > $o, S2 : dB > dB > $o]: ((ord_less_eq_dB_dB_o @ R3 @ S2) => ((ord_less_eq_dB_dB_o @ S2 @ (transi72828568clp_dB @ R3)) => ((transi72828568clp_dB @ S2) = (transi72828568clp_dB @ R3))))))). % rtranclp_subset
thf(fact_71_rtrancl__beta__Abs, axiom,
    ((![S : dB, S3 : dB]: ((transi72828568clp_dB @ beta @ S @ S3) => (transi72828568clp_dB @ beta @ (abs @ S) @ (abs @ S3)))))). % rtrancl_beta_Abs
thf(fact_72_dB_Oinject_I3_J, axiom,
    ((![X32 : dB, Y32 : dB]: (((abs @ X32) = (abs @ Y32)) = (X32 = Y32))))). % dB.inject(3)
thf(fact_73_abs, axiom,
    ((![S : dB, T : dB]: ((beta @ S @ T) => (beta @ (abs @ S) @ (abs @ T)))))). % abs
thf(fact_74_beta__cases_I2_J, axiom,
    ((![R2 : dB, S : dB]: ((beta @ (abs @ R2) @ S) => (~ ((![T4 : dB]: ((S = (abs @ T4)) => (~ ((beta @ R2 @ T4))))))))))). % beta_cases(2)
thf(fact_75_dB_Odistinct_I3_J, axiom,
    ((![X1 : nat, X32 : dB]: (~ (((var @ X1) = (abs @ X32))))))). % dB.distinct(3)
thf(fact_76_Lambda, axiom,
    ((![R2 : dB]: ((it @ R2) => (it @ (abs @ R2)))))). % Lambda
thf(fact_77_abs__typeE, axiom,
    ((![E : nat > type, T : dB, T2 : type]: ((typing @ E @ (abs @ T) @ T2) => (~ ((![U3 : type, V : type]: (~ ((typing @ (shift_type @ E @ zero_zero_nat @ U3) @ T @ V)))))))))). % abs_typeE
thf(fact_78_subst__lt, axiom,
    ((![J : nat, I : nat, U2 : dB]: ((ord_less_nat @ J @ I) => ((subst @ (var @ J) @ U2 @ I) = (var @ J)))))). % subst_lt
thf(fact_79_shift__gt, axiom,
    ((![J : nat, I : nat, E : nat > type, T2 : type]: ((ord_less_nat @ J @ I) => ((shift_type @ E @ I @ T2 @ J) = (E @ J)))))). % shift_gt
thf(fact_80_order_Onot__eq__order__implies__strict, axiom,
    ((![A2 : nat, B2 : nat]: ((~ ((A2 = B2))) => ((ord_less_eq_nat @ A2 @ B2) => (ord_less_nat @ A2 @ B2)))))). % order.not_eq_order_implies_strict
thf(fact_81_dual__order_Ostrict__implies__order, axiom,
    ((![B2 : nat, A2 : nat]: ((ord_less_nat @ B2 @ A2) => (ord_less_eq_nat @ B2 @ A2))))). % dual_order.strict_implies_order
thf(fact_82_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_nat = (^[B : nat]: (^[A : nat]: (((ord_less_eq_nat @ B @ A)) & ((~ ((A = B)))))))))). % dual_order.strict_iff_order
thf(fact_83_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_nat = (^[B : nat]: (^[A : nat]: (((ord_less_nat @ B @ A)) | ((A = B)))))))). % dual_order.order_iff_strict
thf(fact_84_order_Ostrict__implies__order, axiom,
    ((![A2 : nat, B2 : nat]: ((ord_less_nat @ A2 @ B2) => (ord_less_eq_nat @ A2 @ B2))))). % order.strict_implies_order
thf(fact_85_dual__order_Ostrict__trans2, axiom,
    ((![B2 : nat, A2 : nat, C3 : nat]: ((ord_less_nat @ B2 @ A2) => ((ord_less_eq_nat @ C3 @ B2) => (ord_less_nat @ C3 @ A2)))))). % dual_order.strict_trans2
thf(fact_86_dual__order_Ostrict__trans1, axiom,
    ((![B2 : nat, A2 : nat, C3 : nat]: ((ord_less_eq_nat @ B2 @ A2) => ((ord_less_nat @ C3 @ B2) => (ord_less_nat @ C3 @ A2)))))). % dual_order.strict_trans1
thf(fact_87_order_Ostrict__iff__order, axiom,
    ((ord_less_nat = (^[A : nat]: (^[B : nat]: (((ord_less_eq_nat @ A @ B)) & ((~ ((A = B)))))))))). % order.strict_iff_order
thf(fact_88_order_Oorder__iff__strict, axiom,
    ((ord_less_eq_nat = (^[A : nat]: (^[B : nat]: (((ord_less_nat @ A @ B)) | ((A = B)))))))). % order.order_iff_strict
thf(fact_89_order_Ostrict__trans2, axiom,
    ((![A2 : nat, B2 : nat, C3 : nat]: ((ord_less_nat @ A2 @ B2) => ((ord_less_eq_nat @ B2 @ C3) => (ord_less_nat @ A2 @ C3)))))). % order.strict_trans2
thf(fact_90_order_Ostrict__trans1, axiom,
    ((![A2 : nat, B2 : nat, C3 : nat]: ((ord_less_eq_nat @ A2 @ B2) => ((ord_less_nat @ B2 @ C3) => (ord_less_nat @ A2 @ C3)))))). % order.strict_trans1
thf(fact_91_not__le__imp__less, axiom,
    ((![Y5 : nat, X3 : nat]: ((~ ((ord_less_eq_nat @ Y5 @ X3))) => (ord_less_nat @ X3 @ Y5))))). % not_le_imp_less
thf(fact_92_less__le__not__le, axiom,
    ((ord_less_nat = (^[X4 : nat]: (^[Y4 : nat]: (((ord_less_eq_nat @ X4 @ Y4)) & ((~ ((ord_less_eq_nat @ Y4 @ X4)))))))))). % less_le_not_le
thf(fact_93_le__imp__less__or__eq, axiom,
    ((![X3 : nat, Y5 : nat]: ((ord_less_eq_nat @ X3 @ Y5) => ((ord_less_nat @ X3 @ Y5) | (X3 = Y5)))))). % le_imp_less_or_eq
thf(fact_94_le__less__linear, axiom,
    ((![X3 : nat, Y5 : nat]: ((ord_less_eq_nat @ X3 @ Y5) | (ord_less_nat @ Y5 @ X3))))). % le_less_linear

% Conjectures (1)
thf(conj_0, conjecture,
    ((accp_dB @ (conversep_dB_dB @ beta) @ t2))).
