TSTP Solution File: SCT169+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT169+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 : 600s
% DateTime : Mon Jul 18 22:04:20 EDT 2022
% Result : Unknown 190.13s 190.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT169+3 : TPTP v8.1.0. Released v5.3.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 00:46:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.51/1.92 ============================== Prover9 ===============================
% 1.51/1.92 Prover9 (32) version 2009-11A, November 2009.
% 1.51/1.92 Process 22437 was started by sandbox on n021.cluster.edu,
% 1.51/1.92 Sat Jul 2 00:46:15 2022
% 1.51/1.92 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22284_n021.cluster.edu".
% 1.51/1.92 ============================== end of head ===========================
% 1.51/1.92
% 1.51/1.92 ============================== INPUT =================================
% 1.51/1.92
% 1.51/1.92 % Reading from file /tmp/Prover9_22284_n021.cluster.edu
% 1.51/1.92
% 1.51/1.92 set(prolog_style_variables).
% 1.51/1.92 set(auto2).
% 1.51/1.92 % set(auto2) -> set(auto).
% 1.51/1.92 % set(auto) -> set(auto_inference).
% 1.51/1.92 % set(auto) -> set(auto_setup).
% 1.51/1.92 % set(auto_setup) -> set(predicate_elim).
% 1.51/1.92 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.51/1.92 % set(auto) -> set(auto_limits).
% 1.51/1.92 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.51/1.92 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.51/1.92 % set(auto) -> set(auto_denials).
% 1.51/1.92 % set(auto) -> set(auto_process).
% 1.51/1.92 % set(auto2) -> assign(new_constants, 1).
% 1.51/1.92 % set(auto2) -> assign(fold_denial_max, 3).
% 1.51/1.92 % set(auto2) -> assign(max_weight, "200.000").
% 1.51/1.92 % set(auto2) -> assign(max_hours, 1).
% 1.51/1.92 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.51/1.92 % set(auto2) -> assign(max_seconds, 0).
% 1.51/1.92 % set(auto2) -> assign(max_minutes, 5).
% 1.51/1.92 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.51/1.92 % set(auto2) -> set(sort_initial_sos).
% 1.51/1.92 % set(auto2) -> assign(sos_limit, -1).
% 1.51/1.92 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.51/1.92 % set(auto2) -> assign(max_megs, 400).
% 1.51/1.92 % set(auto2) -> assign(stats, some).
% 1.51/1.92 % set(auto2) -> clear(echo_input).
% 1.51/1.92 % set(auto2) -> set(quiet).
% 1.51/1.92 % set(auto2) -> clear(print_initial_clauses).
% 1.51/1.92 % set(auto2) -> clear(print_given).
% 1.51/1.92 assign(lrs_ticks,-1).
% 1.51/1.92 assign(sos_limit,10000).
% 1.51/1.92 assign(order,kbo).
% 1.51/1.92 set(lex_order_vars).
% 1.51/1.92 clear(print_given).
% 1.51/1.92
% 1.51/1.92 % formulas(sos). % not echoed (1284 formulas)
% 1.51/1.92
% 1.51/1.92 ============================== end of input ==========================
% 1.51/1.92
% 1.51/1.92 % From the command line: assign(max_seconds, 300).
% 1.51/1.92
% 1.51/1.92 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.51/1.92
% 1.51/1.92 % Formulas that are not ordinary clauses:
% 1.51/1.92 1 (all B_1_1 all B_2_1 (is_Arr1861959080le_alt(B_2_1) -> is_bool(hAPP_A862370221t_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 2 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 3 (all B_1_1 all B_2_1 is_Arr1861959080le_alt(hAPP_l1105242632le_alt(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 4 (all B_1_1 all B_2_1 is_bool(hAPP_l1386638586t_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa_001) # label(hypothesis) # label(non_clause). [assumption].
% 1.51/1.92 5 (all B_1_1 all B_2_1 is_bool(hAPP_list_bool_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 6 (all B_1_1 all B_2_1 is_bool(hAPP_list_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__Nat__Onat_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 7 (all B_1_1 all B_2_1 is_Arr1861959080le_alt(hAPP_n401316912le_alt(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 8 (all B_1_1 all B_2_1 is_bool(hAPP_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 9 (all B_1_1 all B_2_1 is_bool(hAPP_f2013399995l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 10 (all B_1_1 all B_2_1 is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 11 (all B_1_1 all B_2_1 is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 12 (exists A_74 exists B_1 exists C (is_Arr1861959080le_alt(A_74) & is_Arr1861959080le_alt(B_1) & is_Arr1861959080le_alt(C) & hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_74),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,B_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,C),nil_Ar126264853le_alt))))))) # label(fact_0_alt3) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 13 (all A_84 all List_2 nil_bool != hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,A_84),List_2)) # label(fact_3_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 14 (all A_85 all List_4 nil_Ar126264853le_alt != hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_85),List_4)) # label(fact_4_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 15 (all A_85 all List_4 nil_nat != hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,A_85),List_4)) # label(fact_5_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 16 (all A_84 all List_2 hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,A_84),List_2) != nil_bool) # label(fact_6_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 17 (all A_84 all List_2 hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_84),List_2) != nil_Ar126264853le_alt) # label(fact_7_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 18 (all A_84 all List_2 hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,A_84),List_2) != nil_nat) # label(fact_8_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 19 (all Xs (Xs != nil_bool <-> (exists Y_25 exists Ys_6 (is_bool(Y_25) & Xs = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Ys_6))))) # label(fact_9_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 20 (all Xs (Xs != nil_Ar126264853le_alt <-> (exists Y_25 exists Ys_6 (is_Arr1861959080le_alt(Y_25) & Xs = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),Ys_6))))) # label(fact_10_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 21 (all Xs (Xs != nil_nat <-> (exists Y_25 exists Ys_6 Xs = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),Ys_6)))) # label(fact_11_neq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 22 (all Y_2 (Y_2 != nil_bool -> -(all A_74 all List_3 (is_bool(A_74) -> Y_2 != hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,A_74),List_3))))) # label(fact_12_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 23 (all Y_68 (Y_68 != nil_Ar126264853le_alt -> -(all A_74 all List_3 (is_Arr1861959080le_alt(A_74) -> Y_68 != hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_74),List_3))))) # label(fact_13_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 24 (all Y_68 (Y_68 != nil_nat -> -(all A_74 all List_3 Y_68 != hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,A_74),List_3)))) # label(fact_14_list_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 25 (all Xs all X_1 Xs != hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) # label(fact_15_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 26 (all Xs_97 all X_126 Xs_97 != hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_126),Xs_97)) # label(fact_16_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 27 (all Xs_97 all X_126 Xs_97 != hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_126),Xs_97)) # label(fact_17_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 28 (all X_1 all Xs hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) != Xs) # label(fact_18_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 29 (all X_125 all Xs_96 hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_125),Xs_96) != Xs_96) # label(fact_19_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 30 (all X_125 all Xs_96 hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_125),Xs_96) != Xs_96) # label(fact_20_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 31 (all Aa all List_1 all A_84 all List_2 (hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Aa),List_1) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,A_84),List_2) <-> (hBOOL(Aa) <-> hBOOL(A_84)) & List_1 = List_2)) # label(fact_21_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 32 (all Aa all List_1 all A_84 all List_2 (is_Arr1861959080le_alt(Aa) & is_Arr1861959080le_alt(A_84) -> (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Aa),List_1) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_84),List_2) <-> Aa = A_84 & List_1 = List_2))) # label(fact_22_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 33 (all Aa all List_1 all A_84 all List_2 (hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Aa),List_1) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,A_84),List_2) <-> Aa = A_84 & List_1 = List_2)) # label(fact_23_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 34 (all V_1 all Va_1 splice_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,V_1),Va_1),nil_bool) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,V_1),Va_1)) # label(fact_24_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 35 (all V all Va splice360969192le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,V),Va),nil_Ar126264853le_alt) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,V),Va)) # label(fact_25_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 36 (all V all Va splice_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,V),Va),nil_nat) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,V),Va)) # label(fact_26_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 37 (all X_1 hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_1),nil_bool) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool)) # label(fact_27_insert__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 38 (all X_124 hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_124),nil_Ar126264853le_alt) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_124),nil_Ar126264853le_alt)) # label(fact_28_insert__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 39 (all X_124 hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_124),nil_nat) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_124),nil_nat)) # label(fact_29_insert__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 40 (all P_1 all Xs (Xs != nil_bool -> ((all X_4 (is_bool(X_4) -> hBOOL(hAPP_list_bool_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),nil_bool))))) -> ((all X_4 all Xs_19 (is_bool(X_4) -> (Xs_19 != nil_bool -> (hBOOL(hAPP_list_bool_bool(P_1,Xs_19)) -> hBOOL(hAPP_list_bool_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Xs_19))))))) -> hBOOL(hAPP_list_bool_bool(P_1,Xs)))))) # label(fact_30_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 41 (all P_1 all Xs (Xs != nil_Ar126264853le_alt -> ((all X_4 (is_Arr1861959080le_alt(X_4) -> hBOOL(hAPP_l1386638586t_bool(P_1,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),nil_Ar126264853le_alt))))) -> ((all X_4 all Xs_19 (is_Arr1861959080le_alt(X_4) -> (Xs_19 != nil_Ar126264853le_alt -> (hBOOL(hAPP_l1386638586t_bool(P_1,Xs_19)) -> hBOOL(hAPP_l1386638586t_bool(P_1,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Xs_19))))))) -> hBOOL(hAPP_l1386638586t_bool(P_1,Xs)))))) # label(fact_31_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 42 (all P_1 all Xs (Xs != nil_nat -> ((all X_4 hBOOL(hAPP_list_nat_bool(P_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),nil_nat)))) -> ((all X_4 all Xs_19 (Xs_19 != nil_nat -> (hBOOL(hAPP_list_nat_bool(P_1,Xs_19)) -> hBOOL(hAPP_list_nat_bool(P_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Xs_19)))))) -> hBOOL(hAPP_list_nat_bool(P_1,Xs)))))) # label(fact_32_list__nonempty__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 43 (all Xs_95 (Xs_95 != nil_Ar126264853le_alt -> (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_95)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,butlas1262502241le_alt(Xs_95)))))) # label(fact_33_distinct__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 44 (all Xs_95 (Xs_95 != nil_nat -> (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_95)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,butlast_nat(Xs_95)))))) # label(fact_34_distinct__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 45 (all X_123 all Xs_94 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_94)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_123),Xs_94))))) # label(fact_37_distinct__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 46 (all X_123 all Xs_94 (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_94)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_123),Xs_94))))) # label(fact_38_distinct__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 47 (all X_1 all Xs all Y_2 all Ys splice_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Ys)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),splice_bool(Xs,Ys)))) # label(fact_39_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 48 (all X_122 all Xs_93 all Y_67 all Ys_31 splice360969192le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_122),Xs_93),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_67),Ys_31)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_122),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_67),splice360969192le_alt(Xs_93,Ys_31)))) # label(fact_40_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 49 (all X_122 all Xs_93 all Y_67 all Ys_31 splice_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_122),Xs_93),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_67),Ys_31)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_122),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_67),splice_nat(Xs_93,Ys_31)))) # label(fact_41_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 50 (all Xs_92 splice360969192le_alt(Xs_92,nil_Ar126264853le_alt) = Xs_92) # label(fact_42_splice__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 51 (all Xs_92 splice_nat(Xs_92,nil_nat) = Xs_92) # label(fact_43_splice__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 52 (all Ys_30 splice360969192le_alt(nil_Ar126264853le_alt,Ys_30) = Ys_30) # label(fact_44_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 53 (all Ys_30 splice_nat(nil_nat,Ys_30) = Ys_30) # label(fact_45_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 54 (all X_1 all Xs ((Xs = nil_bool -> butlast_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = nil_bool) & (Xs != nil_bool -> butlast_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),butlast_bool(Xs))))) # label(fact_46_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 55 (all X_121 all Xs_91 ((Xs_91 = nil_Ar126264853le_alt -> butlas1262502241le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_121),Xs_91)) = nil_Ar126264853le_alt) & (Xs_91 != nil_Ar126264853le_alt -> butlas1262502241le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_121),Xs_91)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_121),butlas1262502241le_alt(Xs_91))))) # label(fact_47_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 56 (all X_121 all Xs_91 ((Xs_91 = nil_nat -> butlast_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_121),Xs_91)) = nil_nat) & (Xs_91 != nil_nat -> butlast_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_121),Xs_91)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_121),butlast_nat(Xs_91))))) # label(fact_48_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 57 (all F1 all F2 list_c380068407le_alt(F1,F2,nil_Ar126264853le_alt) = F1) # label(fact_49_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 58 (all F1 all F2 list_c554461815at_nat(F1,F2,nil_nat) = F1) # label(fact_50_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 59 (all F1 all F2 all Aa all List_1 list_c380068407le_alt(F1,F2,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Aa),List_1)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(F2,Aa),List_1)) # label(fact_51_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 60 (all F1 all F2 all Aa all List_1 list_c554461815at_nat(F1,F2,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Aa),List_1)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(F2,Aa),List_1)) # label(fact_52_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 61 (all Xs (Xs = nil_Ar126264853le_alt <-> hBOOL(hAPP_l1386638586t_bool(null_A361035805le_alt,Xs)))) # label(fact_53_eq__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 62 (all Xs (Xs = nil_nat <-> hBOOL(hAPP_list_nat_bool(null_nat,Xs)))) # label(fact_54_eq__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 63 (all Xs (hBOOL(hAPP_l1386638586t_bool(null_A361035805le_alt,Xs)) <-> Xs = nil_Ar126264853le_alt)) # label(fact_55_List_Onull__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 64 (all Xs (hBOOL(hAPP_list_nat_bool(null_nat,Xs)) <-> Xs = nil_nat)) # label(fact_56_List_Onull__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 65 (all X_1 all Xs -hBOOL(hAPP_list_bool_bool(null_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)))) # label(fact_59_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 66 (all X_120 all Xs_90 -hBOOL(hAPP_l1386638586t_bool(null_A361035805le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_120),Xs_90)))) # label(fact_60_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 67 (all X_120 all Xs_90 -hBOOL(hAPP_list_nat_bool(null_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_120),Xs_90)))) # label(fact_61_null__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 68 (all Xs all X_1 butlast_bool(hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool))) = Xs) # label(fact_62_butlast__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 69 (all Xs_89 all X_119 butlas1262502241le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_89),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_119),nil_Ar126264853le_alt))) = Xs_89) # label(fact_63_butlast__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 70 (all Xs_89 all X_119 butlast_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_89),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_119),nil_nat))) = Xs_89) # label(fact_64_butlast__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 71 (all X_118 hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_118),nil_nat)))) # label(fact_65_sorted__single) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 72 (all X_1 all Xs (Xs = nil_bool -> (hBOOL(hAPP_list_bool_bool(last_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) <-> hBOOL(X_1)))) # label(fact_66_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 73 (all X_117 all Xs_88 (is_Arr1861959080le_alt(X_117) -> (Xs_88 = nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_117),Xs_88)) = X_117))) # label(fact_67_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 74 (all X_117 all Xs_88 (Xs_88 = nil_nat -> hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_117),Xs_88)) = X_117)) # label(fact_68_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 75 (all Xs_87 all Ys_29 all Zs_6 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_87),Ys_29)),Zs_6) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_87),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_29),Zs_6))) # label(fact_70_append__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 76 (all Xs_87 all Ys_29 all Zs_6 hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_87),Ys_29)),Zs_6) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_87),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_29),Zs_6))) # label(fact_71_append__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 77 (all Xs all Ys all Zs all Ts (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Zs),Ts) <-> (exists Us_1 (Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Zs),Us_1) & hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Us_1),Ys) = Ts | hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Us_1) = Zs & Ys = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Us_1),Ts))))) # label(fact_72_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 78 (all Xs all Ys all Zs all Ts (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Zs),Ts) <-> (exists Us_1 (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Zs),Us_1) & hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Us_1),Ys) = Ts | hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Us_1) = Zs & Ys = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Us_1),Ts))))) # label(fact_73_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 79 (all Xs all Ys all Zs (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Zs) <-> Ys = Zs)) # label(fact_74_same__append__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 80 (all Xs all Ys all Zs (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Zs) <-> Ys = Zs)) # label(fact_75_same__append__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 81 (all Ys all Xs all Zs (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),Xs) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Zs),Xs) <-> Ys = Zs)) # label(fact_76_append__same__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 82 (all Ys all Xs all Zs (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),Xs) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Zs),Xs) <-> Ys = Zs)) # label(fact_77_append__same__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 83 (all Ys_28 all Us all Xs_86 all Xs1_2 all Zs_5 (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_86),Xs1_2) = Zs_5 -> (Ys_28 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs1_2),Us) -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_86),Ys_28) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Zs_5),Us)))) # label(fact_78_append__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 84 (all Ys_28 all Us all Xs_86 all Xs1_2 all Zs_5 (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_86),Xs1_2) = Zs_5 -> (Ys_28 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs1_2),Us) -> hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_86),Ys_28) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Zs_5),Us)))) # label(fact_79_append__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 85 (all Xs_85 all Ys_27 (Ys_27 = nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_85),Ys_27)) = hAPP_l1105242632le_alt(last_A57386030le_alt,Xs_85))) # label(fact_80_last__appendL) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 86 (all Xs_85 all Ys_27 (Ys_27 = nil_nat -> hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_85),Ys_27)) = hAPP_list_nat_nat(last_nat,Xs_85))) # label(fact_81_last__appendL) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 87 (all Xs_84 all Ys_26 (Ys_26 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_84),Ys_26)) = hAPP_l1105242632le_alt(last_A57386030le_alt,Ys_26))) # label(fact_82_last__appendR) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 88 (all Xs_84 all Ys_26 (Ys_26 != nil_nat -> hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_84),Ys_26)) = hAPP_list_nat_nat(last_nat,Ys_26))) # label(fact_83_last__appendR) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 89 (all Xs_83 all Ys_25 ((Ys_25 = nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_83),Ys_25)) = hAPP_l1105242632le_alt(last_A57386030le_alt,Xs_83)) & (Ys_25 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_83),Ys_25)) = hAPP_l1105242632le_alt(last_A57386030le_alt,Ys_25)))) # label(fact_84_last__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 90 (all Xs_83 all Ys_25 ((Ys_25 = nil_nat -> hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_83),Ys_25)) = hAPP_list_nat_nat(last_nat,Xs_83)) & (Ys_25 != nil_nat -> hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_83),Ys_25)) = hAPP_list_nat_nat(last_nat,Ys_25)))) # label(fact_85_last__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 91 (all F all X_1 all Xs maps_A461338881le_alt(F,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(F,X_1)),maps_A461338881le_alt(F,Xs))) # label(fact_86_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 92 (all F all X_1 all Xs maps_n2115510812le_alt(F,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_n1875670159le_alt(F,X_1)),maps_n2115510812le_alt(F,Xs))) # label(fact_87_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 93 (all F all X_1 all Xs maps_bool_nat(F,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_bool_list_nat(F,X_1)),maps_bool_nat(F,Xs))) # label(fact_88_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 94 (all Xs all X_1 (hBOOL(hAPP_list_bool_bool(last_bool,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool)))) <-> hBOOL(X_1))) # label(fact_89_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 95 (all Xs_82 all X_116 (is_Arr1861959080le_alt(X_116) -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_82),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_116),nil_Ar126264853le_alt))) = X_116)) # label(fact_90_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 96 (all Xs_82 all X_116 hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_82),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_116),nil_nat))) = X_116) # label(fact_91_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 97 (all X_1 all Xs all Ys hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)),Ys) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys))) # label(fact_92_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 98 (all X_115 all Xs_81 all Ys_24 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_115),Xs_81)),Ys_24) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_115),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_81),Ys_24))) # label(fact_93_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 99 (all X_115 all Xs_81 all Ys_24 hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_115),Xs_81)),Ys_24) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_115),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_81),Ys_24))) # label(fact_94_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 100 (all Xs all Zs all X_1 all Xs1_1 all Ys (hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs1_1) = Ys -> (Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs1_1),Zs) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),Zs)))) # label(fact_95_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 101 (all Xs_80 all Zs_4 all X_114 all Xs1 all Ys_23 (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_114),Xs1) = Ys_23 -> (Xs_80 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs1),Zs_4) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_114),Xs_80) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_23),Zs_4)))) # label(fact_96_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 102 (all Xs_80 all Zs_4 all X_114 all Xs1 all Ys_23 (hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_114),Xs1) = Ys_23 -> (Xs_80 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs1),Zs_4) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_114),Xs_80) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_23),Zs_4)))) # label(fact_97_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 103 (all Ys_22 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,nil_Ar126264853le_alt),Ys_22) = Ys_22) # label(fact_98_append__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 104 (all Ys_22 hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,nil_nat),Ys_22) = Ys_22) # label(fact_99_append__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 105 (all Xs all Ys (nil_Ar126264853le_alt = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) <-> Xs = nil_Ar126264853le_alt & Ys = nil_Ar126264853le_alt)) # label(fact_100_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 106 (all Xs all Ys (nil_nat = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys) <-> Xs = nil_nat & Ys = nil_nat)) # label(fact_101_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 107 (all Xs_79 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_79),nil_Ar126264853le_alt) = Xs_79) # label(fact_102_append__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 108 (all Xs_79 hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_79),nil_nat) = Xs_79) # label(fact_103_append__Nil2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 109 (all Xs all Ys (Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) <-> Ys = nil_Ar126264853le_alt)) # label(fact_104_self__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 110 (all Xs all Ys (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys) <-> Ys = nil_nat)) # label(fact_105_self__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 111 (all Ys all Xs (Ys = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) <-> Xs = nil_Ar126264853le_alt)) # label(fact_106_self__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 112 (all Ys all Xs (Ys = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys) <-> Xs = nil_nat)) # label(fact_107_self__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 113 (all Xs all Ys (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) = nil_Ar126264853le_alt <-> Xs = nil_Ar126264853le_alt & Ys = nil_Ar126264853le_alt)) # label(fact_108_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 114 (all Xs all Ys (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys) = nil_nat <-> Xs = nil_nat & Ys = nil_nat)) # label(fact_109_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 115 (all Xs all Ys (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) = Xs <-> Ys = nil_Ar126264853le_alt)) # label(fact_110_append__self__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 116 (all Xs all Ys (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys) = Xs <-> Ys = nil_nat)) # label(fact_111_append__self__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.92 117 (all Xs all Ys (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) = Ys <-> Xs = nil_Ar126264853le_alt)) # label(fact_112_append__self__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 118 (all Xs all Ys (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys) = Ys <-> Xs = nil_nat)) # label(fact_113_append__self__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 119 (all Xs_78 all Ys_21 (Xs_78 = Ys_21 -> Xs_78 = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,nil_Ar126264853le_alt),Ys_21))) # label(fact_114_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 120 (all Xs_78 all Ys_21 (Xs_78 = Ys_21 -> Xs_78 = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,nil_nat),Ys_21))) # label(fact_115_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 121 (all Xs all X_1 all Ys (hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool)) = Ys <-> Ys != nil_bool & butlast_bool(Ys) = Xs & (hBOOL(hAPP_list_bool_bool(last_bool,Ys)) <-> hBOOL(X_1)))) # label(fact_116_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 122 (all Xs all X_1 all Ys (is_Arr1861959080le_alt(X_1) -> (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt)) = Ys <-> Ys != nil_Ar126264853le_alt & butlas1262502241le_alt(Ys) = Xs & hAPP_l1105242632le_alt(last_A57386030le_alt,Ys) = X_1))) # label(fact_117_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 123 (all Xs all X_1 all Ys (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat)) = Ys <-> Ys != nil_nat & butlast_nat(Ys) = Xs & hAPP_list_nat_nat(last_nat,Ys) = X_1)) # label(fact_118_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 124 (all Xs (Xs != nil_bool -> hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,butlast_bool(Xs)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,hAPP_list_bool_bool(last_bool,Xs)),nil_bool)) = Xs)) # label(fact_119_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 125 (all Xs_77 (Xs_77 != nil_Ar126264853le_alt -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,butlas1262502241le_alt(Xs_77)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,hAPP_l1105242632le_alt(last_A57386030le_alt,Xs_77)),nil_Ar126264853le_alt)) = Xs_77)) # label(fact_120_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 126 (all Xs_77 (Xs_77 != nil_nat -> hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,butlast_nat(Xs_77)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,hAPP_list_nat_nat(last_nat,Xs_77)),nil_nat)) = Xs_77)) # label(fact_121_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 127 (all Ys all Zs all X_1 all Xs (hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),Zs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) <-> Ys = nil_bool & Zs = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) | (exists Ys_20 (Ys = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Ys_20) & hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_20),Zs) = Xs)))) # label(fact_122_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 128 (all Ys all Zs all X_1 all Xs (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),Zs) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs) <-> Ys = nil_Ar126264853le_alt & Zs = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs) | (exists Ys_20 (Ys = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Ys_20) & hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_20),Zs) = Xs)))) # label(fact_123_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 129 (all Ys all Zs all X_1 all Xs (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),Zs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs) <-> Ys = nil_nat & Zs = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs) | (exists Ys_20 (Ys = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Ys_20) & hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_20),Zs) = Xs)))) # label(fact_124_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 130 (all X_1 all Xs all Ys all Zs (hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),Zs) <-> Ys = nil_bool & hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) = Zs | (exists Ys_20 (hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Ys_20) = Ys & Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_20),Zs))))) # label(fact_125_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 131 (all X_1 all Xs all Ys all Zs (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),Zs) <-> Ys = nil_Ar126264853le_alt & hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs) = Zs | (exists Ys_20 (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Ys_20) = Ys & Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_20),Zs))))) # label(fact_126_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 132 (all X_1 all Xs all Ys all Zs (hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),Zs) <-> Ys = nil_nat & hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs) = Zs | (exists Ys_20 (hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Ys_20) = Ys & Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_20),Zs))))) # label(fact_127_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 133 (all Xs all X_1 all Ys all Y_2 (hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),nil_bool)) <-> Xs = Ys & (hBOOL(X_1) <-> hBOOL(Y_2)))) # label(fact_128_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 134 (all Xs all X_1 all Ys all Y_2 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_2) -> (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),nil_Ar126264853le_alt)) <-> Xs = Ys & X_1 = Y_2))) # label(fact_129_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 135 (all Xs all X_1 all Ys all Y_2 (hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),nil_nat)) <-> Xs = Ys & X_1 = Y_2)) # label(fact_130_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 136 (all Xs_76 all Ys_19 ((Ys_19 = nil_Ar126264853le_alt -> butlas1262502241le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_76),Ys_19)) = butlas1262502241le_alt(Xs_76)) & (Ys_19 != nil_Ar126264853le_alt -> butlas1262502241le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_76),Ys_19)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_76),butlas1262502241le_alt(Ys_19))))) # label(fact_131_butlast__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 137 (all Xs_76 all Ys_19 ((Ys_19 = nil_nat -> butlast_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_76),Ys_19)) = butlast_nat(Xs_76)) & (Ys_19 != nil_nat -> butlast_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_76),Ys_19)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_76),butlast_nat(Ys_19))))) # label(fact_132_butlast__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 138 (all Xs_75 (Xs_75 != nil_nat -> (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_75)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,butlast_nat(Xs_75)))))) # label(fact_133_sorted__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 139 (all X_1 all Xs (hBOOL(hAPP_list_bool_bool(last_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) <-> (Xs = nil_bool -> hBOOL(X_1)) & (Xs != nil_bool -> hBOOL(hAPP_list_bool_bool(last_bool,Xs))))) # label(fact_134_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 140 (all X_113 all Xs_74 (is_Arr1861959080le_alt(X_113) -> (Xs_74 = nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_113),Xs_74)) = X_113) & (Xs_74 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_113),Xs_74)) = hAPP_l1105242632le_alt(last_A57386030le_alt,Xs_74)))) # label(fact_135_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 141 (all X_113 all Xs_74 ((Xs_74 = nil_nat -> hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_113),Xs_74)) = X_113) & (Xs_74 != nil_nat -> hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_113),Xs_74)) = hAPP_list_nat_nat(last_nat,Xs_74)))) # label(fact_136_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 142 (all X_1 all Xs (Xs != nil_bool -> (hBOOL(hAPP_list_bool_bool(last_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) <-> hBOOL(hAPP_list_bool_bool(last_bool,Xs))))) # label(fact_137_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 143 (all X_112 all Xs_73 (Xs_73 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_112),Xs_73)) = hAPP_l1105242632le_alt(last_A57386030le_alt,Xs_73))) # label(fact_138_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 144 (all X_112 all Xs_73 (Xs_73 != nil_nat -> hAPP_list_nat_nat(last_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_112),Xs_73)) = hAPP_list_nat_nat(last_nat,Xs_73))) # label(fact_139_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 145 (all Xs all P_1 (hBOOL(hAPP_list_bool_bool(P_1,nil_bool)) -> ((all X_4 all Xs_19 (is_bool(X_4) -> (hBOOL(hAPP_list_bool_bool(P_1,Xs_19)) -> hBOOL(hAPP_list_bool_bool(P_1,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_19),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),nil_bool))))))) -> hBOOL(hAPP_list_bool_bool(P_1,Xs))))) # label(fact_140_rev__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 146 (all Xs all P_1 (hBOOL(hAPP_l1386638586t_bool(P_1,nil_Ar126264853le_alt)) -> ((all X_4 all Xs_19 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_l1386638586t_bool(P_1,Xs_19)) -> hBOOL(hAPP_l1386638586t_bool(P_1,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_19),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),nil_Ar126264853le_alt))))))) -> hBOOL(hAPP_l1386638586t_bool(P_1,Xs))))) # label(fact_141_rev__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 147 (all Xs all P_1 (hBOOL(hAPP_list_nat_bool(P_1,nil_nat)) -> ((all X_4 all Xs_19 (hBOOL(hAPP_list_nat_bool(P_1,Xs_19)) -> hBOOL(hAPP_list_nat_bool(P_1,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_19),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),nil_nat)))))) -> hBOOL(hAPP_list_nat_bool(P_1,Xs))))) # label(fact_142_rev__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 148 (all Xs (Xs != nil_bool -> -(all Ys_6 all Y_25 (is_bool(Y_25) -> Xs != hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),nil_bool)))))) # label(fact_143_rev__cases) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 149 (all Xs_72 (Xs_72 != nil_Ar126264853le_alt -> -(all Ys_6 all Y_25 (is_Arr1861959080le_alt(Y_25) -> Xs_72 != hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),nil_Ar126264853le_alt)))))) # label(fact_144_rev__cases) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 150 (all Xs_72 (Xs_72 != nil_nat -> -(all Ys_6 all Y_25 Xs_72 != hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),nil_nat))))) # label(fact_145_rev__cases) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 151 (all Xs (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(equal_499625528le_alt,Xs),nil_Ar126264853le_alt)) <-> hBOOL(hAPP_l1386638586t_bool(null_A361035805le_alt,Xs)))) # label(fact_146_equal__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 152 (all Xs (hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(equal_equal_list_nat,Xs),nil_nat)) <-> hBOOL(hAPP_list_nat_bool(null_nat,Xs)))) # label(fact_147_equal__Nil__null) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 153 (all X_1 all Xs (rotate1322903650le_alt(nil_Ar126264853le_alt) = nil_Ar126264853le_alt & rotate1_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool)))) # label(fact_148_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 154 (all X_1 all Xs (rotate1_nat(nil_nat) = nil_nat & rotate1_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool)))) # label(fact_149_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 155 (all X_111 all Xs_71 (rotate1_nat(nil_nat) = nil_nat & rotate1322903650le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_111),Xs_71)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_71),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_111),nil_Ar126264853le_alt)))) # label(fact_150_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 156 (all X_111 all Xs_71 (rotate1322903650le_alt(nil_Ar126264853le_alt) = nil_Ar126264853le_alt & rotate1322903650le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_111),Xs_71)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_71),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_111),nil_Ar126264853le_alt)))) # label(fact_151_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 157 (all X_111 all Xs_71 (rotate1_nat(nil_nat) = nil_nat & rotate1_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_111),Xs_71)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_71),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_111),nil_nat)))) # label(fact_152_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 158 (all X_111 all Xs_71 (rotate1322903650le_alt(nil_Ar126264853le_alt) = nil_Ar126264853le_alt & rotate1_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_111),Xs_71)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_71),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_111),nil_nat)))) # label(fact_153_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 159 (all Ws_1 (-hBOOL(hAPP_list_bool_bool(distinct_bool,Ws_1)) -> (exists Xs_19 exists Ys_6 exists Zs_2 exists Y_25 (is_bool(Y_25) & Ws_1 = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs_19),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),nil_bool)),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),nil_bool)),Zs_2)))))))) # label(fact_154_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 160 (all Ws (-hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Ws)) -> (exists Xs_19 exists Ys_6 exists Zs_2 exists Y_25 (is_Arr1861959080le_alt(Y_25) & Ws = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_19),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),nil_Ar126264853le_alt)),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),nil_Ar126264853le_alt)),Zs_2)))))))) # label(fact_155_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 161 (all Ws (-hBOOL(hAPP_list_nat_bool(distinct_nat,Ws)) -> (exists Xs_19 exists Ys_6 exists Zs_2 exists Y_25 Ws = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_19),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),nil_nat)),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),nil_nat)),Zs_2))))))) # label(fact_156_not__distinct__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 162 (all I_1 all X_1 hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_bool_list_bool(replicate_bool(I_1),X_1)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),hAPP_bool_list_bool(replicate_bool(I_1),X_1))) # label(fact_157_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 163 (all I_13 all X_110 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(I_13),X_110)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_110),nil_Ar126264853le_alt)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_110),hAPP_A832564074le_alt(replic351609551le_alt(I_13),X_110))) # label(fact_158_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 164 (all I_13 all X_110 hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(replicate_nat(I_13),X_110)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_110),nil_nat)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_110),hAPP_nat_list_nat(replicate_nat(I_13),X_110))) # label(fact_159_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 165 (all X_1 all Xs rev_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,rev_bool(Xs)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool))) # label(fact_160_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 166 (all X_109 all Xs_70 rev_Ar2093961333le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_109),Xs_70)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,rev_Ar2093961333le_alt(Xs_70)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_109),nil_Ar126264853le_alt))) # label(fact_161_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 167 (all X_109 all Xs_70 rev_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_109),Xs_70)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,rev_nat(Xs_70)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_109),nil_nat))) # label(fact_162_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 168 (all Xs all Y_2 all Ys (rev_bool(Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Ys) <-> Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,rev_bool(Ys)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),nil_bool)))) # label(fact_163_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 169 (all Xs all Y_2 all Ys (rev_Ar2093961333le_alt(Xs) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys) <-> Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,rev_Ar2093961333le_alt(Ys)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),nil_Ar126264853le_alt)))) # label(fact_164_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 170 (all Xs all Y_2 all Ys (rev_nat(Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Ys) <-> Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,rev_nat(Ys)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),nil_nat)))) # label(fact_165_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 171 (all Ys_18 all Xs_69 (Xs_69 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(hd_Arr805754088le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_69),Ys_18)) = hAPP_l1105242632le_alt(hd_Arr805754088le_alt,Xs_69))) # label(fact_166_hd__append2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 172 (all Ys_18 all Xs_69 (Xs_69 != nil_nat -> hAPP_list_nat_nat(hd_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_69),Ys_18)) = hAPP_list_nat_nat(hd_nat,Xs_69))) # label(fact_167_hd__append2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 173 (all Ys_17 all Xs_68 ((Xs_68 = nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(hd_Arr805754088le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_68),Ys_17)) = hAPP_l1105242632le_alt(hd_Arr805754088le_alt,Ys_17)) & (Xs_68 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(hd_Arr805754088le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_68),Ys_17)) = hAPP_l1105242632le_alt(hd_Arr805754088le_alt,Xs_68)))) # label(fact_168_hd__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 174 (all Ys_17 all Xs_68 ((Xs_68 = nil_nat -> hAPP_list_nat_nat(hd_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_68),Ys_17)) = hAPP_list_nat_nat(hd_nat,Ys_17)) & (Xs_68 != nil_nat -> hAPP_list_nat_nat(hd_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_68),Ys_17)) = hAPP_list_nat_nat(hd_nat,Xs_68)))) # label(fact_169_hd__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 175 (all Ys_16 all Xs_67 (Xs_67 != nil_Ar126264853le_alt -> tl_Arr1453005548le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_67),Ys_16)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,tl_Arr1453005548le_alt(Xs_67)),Ys_16))) # label(fact_170_tl__append2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 176 (all Ys_16 all Xs_67 (Xs_67 != nil_nat -> tl_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_67),Ys_16)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,tl_nat(Xs_67)),Ys_16))) # label(fact_171_tl__append2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 177 (all Xs all Ys (rev_nat(Xs) = rev_nat(Ys) <-> Xs = Ys)) # label(fact_172_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 178 (all Xs all Ys (rev_Ar2093961333le_alt(Xs) = rev_Ar2093961333le_alt(Ys) <-> Xs = Ys)) # label(fact_173_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 179 (all Xs all Ys (rev_nat(Xs) = Ys <-> Xs = rev_nat(Ys))) # label(fact_174_rev__swap) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 180 (all Xs all Ys (rev_Ar2093961333le_alt(Xs) = Ys <-> Xs = rev_Ar2093961333le_alt(Ys))) # label(fact_175_rev__swap) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 181 (all X_1 all A (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A)) <-> hBOOL(hAPP_A862370221t_bool(A,X_1)))) # label(fact_176_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 182 (all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) <-> hBOOL(hAPP_nat_bool(A,X_1)))) # label(fact_177_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 183 (all P_1 collect_nat(P_1) = P_1) # label(fact_178_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 184 (all N_44 all X_108 rev_nat(hAPP_nat_list_nat(replicate_nat(N_44),X_108)) = hAPP_nat_list_nat(replicate_nat(N_44),X_108)) # label(fact_179_rev__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 185 (all N_44 all X_108 rev_Ar2093961333le_alt(hAPP_A832564074le_alt(replic351609551le_alt(N_44),X_108)) = hAPP_A832564074le_alt(replic351609551le_alt(N_44),X_108)) # label(fact_180_rev__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 186 (all Xs_66 rev_nat(rev_nat(Xs_66)) = Xs_66) # label(fact_181_rev__rev__ident) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 187 (all Xs_66 rev_Ar2093961333le_alt(rev_Ar2093961333le_alt(Xs_66)) = Xs_66) # label(fact_182_rev__rev__ident) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 188 (all X_1 all Y_2 (hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(equal_equal_list_nat,X_1),Y_2)) <-> X_1 = Y_2)) # label(fact_183_equal__list__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 189 (all X_1 all Y_2 (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(equal_499625528le_alt,X_1),Y_2)) <-> X_1 = Y_2)) # label(fact_184_equal__list__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 190 (all Xs (rev_Ar2093961333le_alt(Xs) = nil_Ar126264853le_alt <-> Xs = nil_Ar126264853le_alt)) # label(fact_185_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 191 (all Xs (rev_nat(Xs) = nil_nat <-> Xs = nil_nat)) # label(fact_186_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 192 (all Xs (nil_Ar126264853le_alt = rev_Ar2093961333le_alt(Xs) <-> Xs = nil_Ar126264853le_alt)) # label(fact_187_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 193 (all Xs (nil_nat = rev_nat(Xs) <-> Xs = nil_nat)) # label(fact_188_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 194 (all Xs_65 all Ys_15 rev_Ar2093961333le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_65),Ys_15)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,rev_Ar2093961333le_alt(Ys_15)),rev_Ar2093961333le_alt(Xs_65))) # label(fact_191_rev__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 195 (all Xs_65 all Ys_15 rev_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_65),Ys_15)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,rev_nat(Ys_15)),rev_nat(Xs_65))) # label(fact_192_rev__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 196 (all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,rev_Ar2093961333le_alt(Xs))) <-> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)))) # label(fact_193_distinct__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 197 (all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,rev_nat(Xs))) <-> hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)))) # label(fact_194_distinct__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 198 (all Xs_64 (Xs_64 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(last_A57386030le_alt,rev_Ar2093961333le_alt(Xs_64)) = hAPP_l1105242632le_alt(hd_Arr805754088le_alt,Xs_64))) # label(fact_195_last__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 199 (all Xs_64 (Xs_64 != nil_nat -> hAPP_list_nat_nat(last_nat,rev_nat(Xs_64)) = hAPP_list_nat_nat(hd_nat,Xs_64))) # label(fact_196_last__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 200 (all Xs_63 (Xs_63 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(hd_Arr805754088le_alt,rev_Ar2093961333le_alt(Xs_63)) = hAPP_l1105242632le_alt(last_A57386030le_alt,Xs_63))) # label(fact_197_hd__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 201 (all Xs_63 (Xs_63 != nil_nat -> hAPP_list_nat_nat(hd_nat,rev_nat(Xs_63)) = hAPP_list_nat_nat(last_nat,Xs_63))) # label(fact_198_hd__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 202 (all N_43 all X_107 all K_6 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_43),X_107)),hAPP_A832564074le_alt(replic351609551le_alt(K_6),X_107)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(K_6),X_107)),hAPP_A832564074le_alt(replic351609551le_alt(N_43),X_107))) # label(fact_199_append__replicate__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 203 (all N_43 all X_107 all K_6 hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(replicate_nat(N_43),X_107)),hAPP_nat_list_nat(replicate_nat(K_6),X_107)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(replicate_nat(K_6),X_107)),hAPP_nat_list_nat(replicate_nat(N_43),X_107))) # label(fact_200_append__replicate__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 204 (all Xs (Xs != nil_bool -> rotate1_bool(Xs) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,tl_bool(Xs)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,hAPP_list_bool_bool(hd_bool,Xs)),nil_bool)))) # label(fact_201_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 205 (all Xs_62 (Xs_62 != nil_Ar126264853le_alt -> rotate1322903650le_alt(Xs_62) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,tl_Arr1453005548le_alt(Xs_62)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,hAPP_l1105242632le_alt(hd_Arr805754088le_alt,Xs_62)),nil_Ar126264853le_alt)))) # label(fact_202_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 206 (all Xs_62 (Xs_62 != nil_nat -> rotate1_nat(Xs_62) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,tl_nat(Xs_62)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,hAPP_list_nat_nat(hd_nat,Xs_62)),nil_nat)))) # label(fact_203_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 207 (all X_1 all Xs tl_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = Xs) # label(fact_204_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 208 (all X_106 all Xs_61 tl_Arr1453005548le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_106),Xs_61)) = Xs_61) # label(fact_205_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 209 (all X_106 all Xs_61 tl_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_106),Xs_61)) = Xs_61) # label(fact_206_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 210 (all X_1 all Xs (hBOOL(hAPP_list_bool_bool(hd_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) <-> hBOOL(X_1))) # label(fact_209_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 211 (all X_105 all Xs_60 (is_Arr1861959080le_alt(X_105) -> hAPP_l1105242632le_alt(hd_Arr805754088le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_105),Xs_60)) = X_105)) # label(fact_210_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 212 (all X_105 all Xs_60 hAPP_list_nat_nat(hd_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_105),Xs_60)) = X_105) # label(fact_211_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 213 (all Xs_59 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_59)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,tl_Arr1453005548le_alt(Xs_59))))) # label(fact_212_distinct__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 214 (all Xs_59 (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_59)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,tl_nat(Xs_59))))) # label(fact_213_distinct__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 215 (all Xs_58 (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_58)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,tl_nat(Xs_58))))) # label(fact_214_sorted__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 216 (all Xs (rotate1322903650le_alt(Xs) = nil_Ar126264853le_alt <-> Xs = nil_Ar126264853le_alt)) # label(fact_215_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 217 (all Xs (rotate1_nat(Xs) = nil_nat <-> Xs = nil_nat)) # label(fact_216_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 218 (all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,rotate1322903650le_alt(Xs))) <-> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)))) # label(fact_217_distinct1__rotate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 219 (all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,rotate1_nat(Xs))) <-> hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)))) # label(fact_218_distinct1__rotate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 220 (all X_1 all Xs (hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool) = rev_bool(Xs) <-> Xs = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool))) # label(fact_219_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 221 (all X_1 all Xs (hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt) = rev_Ar2093961333le_alt(Xs) <-> Xs = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt))) # label(fact_220_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 222 (all X_1 all Xs (hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat) = rev_nat(Xs) <-> Xs = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat))) # label(fact_221_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 223 (all Xs all X_1 (rev_bool(Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool) <-> Xs = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool))) # label(fact_222_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 224 (all Xs all X_1 (rev_Ar2093961333le_alt(Xs) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt) <-> Xs = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt))) # label(fact_223_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 225 (all Xs all X_1 (rev_nat(Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat) <-> Xs = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat))) # label(fact_224_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 226 (all N_1 all X_1 all Xs hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_bool_list_bool(replicate_bool(N_1),X_1)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_bool_list_bool(replicate_bool(N_1),X_1)),Xs))) # label(fact_225_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 227 (all N_42 all X_104 all Xs_57 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_42),X_104)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_104),Xs_57)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_104),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_42),X_104)),Xs_57))) # label(fact_226_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 228 (all N_42 all X_104 all Xs_57 hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(replicate_nat(N_42),X_104)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_104),Xs_57)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_104),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(replicate_nat(N_42),X_104)),Xs_57))) # label(fact_227_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 229 (all X_103 hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(equal_equal_list_nat,X_103),X_103))) # label(fact_230_equal__refl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 230 (all X_103 hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(equal_499625528le_alt,X_103),X_103))) # label(fact_231_equal__refl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 231 (all X_1 all Y_2 (hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(equal_equal_list_nat,X_1),Y_2)) <-> X_1 = Y_2)) # label(fact_232_equal__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 232 (all X_1 all Y_2 (hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(equal_499625528le_alt,X_1),Y_2)) <-> X_1 = Y_2)) # label(fact_233_equal__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 233 (all P_1 all Xs (dropWh156852662le_alt(P_1,Xs) != nil_Ar126264853le_alt -> -hBOOL(hAPP_A862370221t_bool(P_1,hAPP_l1105242632le_alt(hd_Arr805754088le_alt,dropWh156852662le_alt(P_1,Xs)))))) # label(fact_236_hd__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 234 (all P_1 all Xs (dropWhile_nat(P_1,Xs) != nil_nat -> -hBOOL(hAPP_nat_bool(P_1,hAPP_list_nat_nat(hd_nat,dropWhile_nat(P_1,Xs)))))) # label(fact_237_hd__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 235 (all P_1 -hBOOL(hAPP_l1386638586t_bool(list_e1226799320le_alt(P_1),nil_Ar126264853le_alt))) # label(fact_238_list__ex1__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 236 (all P_1 -hBOOL(hAPP_list_nat_bool(list_ex1_nat(P_1),nil_nat))) # label(fact_239_list__ex1__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 237 (all Y_66 -hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,nil_Ar126264853le_alt),Y_66))) # label(fact_240_member__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 238 (all Y_66 -hBOOL(hAPP_nat_bool(hAPP_l1821533378t_bool(member_nat_1,nil_nat),Y_66))) # label(fact_241_member__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 239 (all Y_2 all X_1 all Xs (hBOOL(hAPP_list_bool_bool(listMem_bool(X_1),Xs)) -> hBOOL(hAPP_list_bool_bool(listMem_bool(X_1),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Xs))))) # label(fact_242_insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 240 (all Y_65 all X_102 all Xs_56 (hBOOL(hAPP_l1386638586t_bool(listMe1065601537le_alt(X_102),Xs_56)) -> hBOOL(hAPP_l1386638586t_bool(listMe1065601537le_alt(X_102),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_65),Xs_56))))) # label(fact_243_insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 241 (all Y_65 all X_102 all Xs_56 (hBOOL(hAPP_list_nat_bool(listMem_nat(X_102),Xs_56)) -> hBOOL(hAPP_list_nat_bool(listMem_nat(X_102),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_65),Xs_56))))) # label(fact_244_insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 242 (all X_1 all Xs all Y_2 (hBOOL(hAPP_bool_bool(hAPP_l96088310l_bool(member_bool_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)),Y_2)) <-> (hBOOL(X_1) <-> hBOOL(Y_2)) | hBOOL(hAPP_bool_bool(hAPP_l96088310l_bool(member_bool_1,Xs),Y_2)))) # label(fact_245_member__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 243 (all X_1 all Xs all Y_2 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_2) -> (hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)),Y_2)) <-> X_1 = Y_2 | hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,Xs),Y_2))))) # label(fact_246_member__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 244 (all X_1 all Xs all Y_2 (hBOOL(hAPP_nat_bool(hAPP_l1821533378t_bool(member_nat_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)),Y_2)) <-> X_1 = Y_2 | hBOOL(hAPP_nat_bool(hAPP_l1821533378t_bool(member_nat_1,Xs),Y_2)))) # label(fact_247_member__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 245 (all X_1 all Xs hBOOL(hAPP_list_bool_bool(listMem_bool(X_1),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)))) # label(fact_248_elem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 246 (all X_101 all Xs_55 hBOOL(hAPP_l1386638586t_bool(listMe1065601537le_alt(X_101),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_101),Xs_55)))) # label(fact_249_elem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 247 (all X_101 all Xs_55 hBOOL(hAPP_list_nat_bool(listMem_nat(X_101),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_101),Xs_55)))) # label(fact_250_elem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 248 (all Xs all P_1 all X_1 ((hBOOL(hAPP_bool_bool(P_1,X_1)) -> dropWhile_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = dropWhile_bool(P_1,Xs)) & (-hBOOL(hAPP_bool_bool(P_1,X_1)) -> dropWhile_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)))) # label(fact_251_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 249 (all Xs all P_1 all X_1 ((hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> dropWh156852662le_alt(P_1,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = dropWh156852662le_alt(P_1,Xs)) & (-hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> dropWh156852662le_alt(P_1,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)))) # label(fact_252_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 250 (all Xs all P_1 all X_1 ((hBOOL(hAPP_nat_bool(P_1,X_1)) -> dropWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = dropWhile_nat(P_1,Xs)) & (-hBOOL(hAPP_nat_bool(P_1,X_1)) -> dropWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)))) # label(fact_253_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 251 (all P_1 dropWh156852662le_alt(P_1,nil_Ar126264853le_alt) = nil_Ar126264853le_alt) # label(fact_254_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 252 (all P_1 dropWhile_nat(P_1,nil_nat) = nil_nat) # label(fact_255_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 253 (all P_1 all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,dropWh156852662le_alt(P_1,Xs))))) # label(fact_256_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 254 (all P_1 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,dropWhile_nat(P_1,Xs))))) # label(fact_257_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 255 (all P_1 all Xs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,dropWhile_nat(P_1,Xs))))) # label(fact_258_sorted__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 256 (all P_1 all Xs all Y_2 all Ys (dropWhile_bool(P_1,Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Ys) <-> Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,takeWhile_bool(P_1,Xs)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Ys)) & -hBOOL(hAPP_bool_bool(P_1,Y_2)))) # label(fact_259_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 257 (all P_1 all Xs all Y_2 all Ys (dropWh156852662le_alt(P_1,Xs) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys) <-> Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,takeWh536362254le_alt(P_1,Xs)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys)) & -hBOOL(hAPP_A862370221t_bool(P_1,Y_2)))) # label(fact_260_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 258 (all P_1 all Xs all Y_2 all Ys (dropWhile_nat(P_1,Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Ys) <-> Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,takeWhile_nat(P_1,Xs)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Ys)) & -hBOOL(hAPP_nat_bool(P_1,Y_2)))) # label(fact_261_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 259 (all A1 all A2 (hBOOL(hAPP_list_bool_bool(listMem_bool(A1),A2)) <-> (exists X_4 exists Xs_19 (is_bool(X_4) & (hBOOL(A1) <-> hBOOL(X_4)) & A2 = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Xs_19))) | (exists X_4 exists Xs_19 exists Y_25 (is_bool(X_4) & is_bool(Y_25) & (hBOOL(A1) <-> hBOOL(X_4)) & A2 = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Xs_19) & hBOOL(hAPP_list_bool_bool(listMem_bool(X_4),Xs_19)))))) # label(fact_262_ListMem_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 260 (all A1 all A2 (is_Arr1861959080le_alt(A1) -> (hBOOL(hAPP_l1386638586t_bool(listMe1065601537le_alt(A1),A2)) <-> (exists X_4 exists Xs_19 (is_Arr1861959080le_alt(X_4) & A1 = X_4 & A2 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Xs_19))) | (exists X_4 exists Xs_19 exists Y_25 (is_Arr1861959080le_alt(X_4) & is_Arr1861959080le_alt(Y_25) & A1 = X_4 & A2 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),Xs_19) & hBOOL(hAPP_l1386638586t_bool(listMe1065601537le_alt(X_4),Xs_19))))))) # label(fact_263_ListMem_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 261 (all A1 all A2 (hBOOL(hAPP_list_nat_bool(listMem_nat(A1),A2)) <-> (exists X_4 exists Xs_19 (A1 = X_4 & A2 = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Xs_19))) | (exists X_4 exists Xs_19 exists Y_25 (A1 = X_4 & A2 = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),Xs_19) & hBOOL(hAPP_list_nat_bool(listMem_nat(X_4),Xs_19)))))) # label(fact_264_ListMem_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 262 (all P_1 all Xs hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,takeWh536362254le_alt(P_1,Xs)),dropWh156852662le_alt(P_1,Xs)) = Xs) # label(fact_265_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 263 (all P_1 all Xs hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,takeWhile_nat(P_1,Xs)),dropWhile_nat(P_1,Xs)) = Xs) # label(fact_266_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 264 (all X_100 all N_41 (is_Arr1861959080le_alt(X_100) -> (N_41 != zero_zero_nat -> hAPP_l1105242632le_alt(hd_Arr805754088le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_41),X_100)) = X_100))) # label(fact_267_hd__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 265 (all X_100 all N_41 (N_41 != zero_zero_nat -> hAPP_list_nat_nat(hd_nat,hAPP_nat_list_nat(replicate_nat(N_41),X_100)) = X_100)) # label(fact_268_hd__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 266 (all X_99 all N_40 (N_40 != zero_zero_nat -> hAPP_list_nat_nat(last_nat,hAPP_nat_list_nat(replicate_nat(N_40),X_99)) = X_99)) # label(fact_269_last__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 267 (all X_99 all N_40 (is_Arr1861959080le_alt(X_99) -> (N_40 != zero_zero_nat -> hAPP_l1105242632le_alt(last_A57386030le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_40),X_99)) = X_99))) # label(fact_270_last__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 268 (all Xs all Ys all P_1 (hBOOL(hAPP_list_bool_bool(hAPP_l273023249l_bool(P_1,nil_Ar126264853le_alt),nil_bool)) -> ((all X_4 all Xs_19 (is_Arr1861959080le_alt(X_4) -> hBOOL(hAPP_list_bool_bool(hAPP_l273023249l_bool(P_1,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Xs_19)),nil_bool)))) -> ((all Y_25 all Ys_6 (is_bool(Y_25) -> hBOOL(hAPP_list_bool_bool(hAPP_l273023249l_bool(P_1,nil_Ar126264853le_alt),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Ys_6))))) -> ((all X_4 all Xs_19 all Y_25 all Ys_6 (is_Arr1861959080le_alt(X_4) & is_bool(Y_25) -> (hBOOL(hAPP_list_bool_bool(hAPP_l273023249l_bool(P_1,Xs_19),Ys_6)) -> hBOOL(hAPP_list_bool_bool(hAPP_l273023249l_bool(P_1,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Xs_19)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Ys_6)))))) -> hBOOL(hAPP_list_bool_bool(hAPP_l273023249l_bool(P_1,Xs),Ys))))))) # label(fact_271_list__induct2_H) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 269 (all Xs all Ys all P_1 (hBOOL(hAPP_list_bool_bool(hAPP_l1101248310l_bool(P_1,nil_nat),nil_bool)) -> ((all X_4 all Xs_19 hBOOL(hAPP_list_bool_bool(hAPP_l1101248310l_bool(P_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Xs_19)),nil_bool))) -> ((all Y_25 all Ys_6 (is_bool(Y_25) -> hBOOL(hAPP_list_bool_bool(hAPP_l1101248310l_bool(P_1,nil_nat),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Ys_6))))) -> ((all X_4 all Xs_19 all Y_25 all Ys_6 (is_bool(Y_25) -> (hBOOL(hAPP_list_bool_bool(hAPP_l1101248310l_bool(P_1,Xs_19),Ys_6)) -> hBOOL(hAPP_list_bool_bool(hAPP_l1101248310l_bool(P_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Xs_19)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Ys_6)))))) -> hBOOL(hAPP_list_bool_bool(hAPP_l1101248310l_bool(P_1,Xs),Ys))))))) # label(fact_272_list__induct2_H) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 270 (all Xs all Ys all P_1 (hBOOL(hAPP_l1386638586t_bool(hAPP_l1686219315t_bool(P_1,nil_bool),nil_Ar126264853le_alt)) -> ((all X_4 all Xs_19 (is_bool(X_4) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1686219315t_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Xs_19)),nil_Ar126264853le_alt)))) -> ((all Y_25 all Ys_6 (is_Arr1861959080le_alt(Y_25) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1686219315t_bool(P_1,nil_bool),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),Ys_6))))) -> ((all X_4 all Xs_19 all Y_25 all Ys_6 (is_bool(X_4) & is_Arr1861959080le_alt(Y_25) -> (hBOOL(hAPP_l1386638586t_bool(hAPP_l1686219315t_bool(P_1,Xs_19),Ys_6)) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1686219315t_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Xs_19)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),Ys_6)))))) -> hBOOL(hAPP_l1386638586t_bool(hAPP_l1686219315t_bool(P_1,Xs),Ys))))))) # label(fact_273_list__induct2_H) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 271 (all Xs all Ys all P_1 (hBOOL(hAPP_list_nat_bool(hAPP_l909187928t_bool(P_1,nil_bool),nil_nat)) -> ((all X_4 all Xs_19 (is_bool(X_4) -> hBOOL(hAPP_list_nat_bool(hAPP_l909187928t_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Xs_19)),nil_nat)))) -> ((all Y_25 all Ys_6 hBOOL(hAPP_list_nat_bool(hAPP_l909187928t_bool(P_1,nil_bool),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),Ys_6)))) -> ((all X_4 all Xs_19 all Y_25 all Ys_6 (is_bool(X_4) -> (hBOOL(hAPP_list_nat_bool(hAPP_l909187928t_bool(P_1,Xs_19),Ys_6)) -> hBOOL(hAPP_list_nat_bool(hAPP_l909187928t_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Xs_19)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),Ys_6)))))) -> hBOOL(hAPP_list_nat_bool(hAPP_l909187928t_bool(P_1,Xs),Ys))))))) # label(fact_274_list__induct2_H) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 272 (all R_2 hBOOL(hAPP_l1386638586t_bool(listre53232751le_alt(R_2,nil_Ar126264853le_alt),nil_Ar126264853le_alt))) # label(fact_275_listrelp_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 273 (all R_2 hBOOL(hAPP_list_nat_bool(listrelp_nat(R_2,nil_nat),nil_nat))) # label(fact_276_listrelp_ONil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 274 (all Xs all Ys all R_2 all X_1 all Y_2 (hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(R_2,X_1),Y_2)) -> (hBOOL(hAPP_list_bool_bool(listrelp_bool(R_2,Xs),Ys)) -> hBOOL(hAPP_list_bool_bool(listrelp_bool(R_2,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Ys)))))) # label(fact_277_listrelp_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 275 (all Xs all Ys all R_2 all X_1 all Y_2 (hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(R_2,X_1),Y_2)) -> (hBOOL(hAPP_l1386638586t_bool(listre53232751le_alt(R_2,Xs),Ys)) -> hBOOL(hAPP_l1386638586t_bool(listre53232751le_alt(R_2,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_2),Ys)))))) # label(fact_278_listrelp_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 276 (all Xs all Ys all R_2 all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(R_2,X_1),Y_2)) -> (hBOOL(hAPP_list_nat_bool(listrelp_nat(R_2,Xs),Ys)) -> hBOOL(hAPP_list_nat_bool(listrelp_nat(R_2,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Ys)))))) # label(fact_279_listrelp_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 277 (all P_1 takeWh536362254le_alt(P_1,nil_Ar126264853le_alt) = nil_Ar126264853le_alt) # label(fact_280_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 278 (all P_1 takeWhile_nat(P_1,nil_nat) = nil_nat) # label(fact_281_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 279 (all M_1 all X_1 all N_1 all Y_2 (hAPP_nat_list_nat(replicate_nat(M_1),X_1) = hAPP_nat_list_nat(replicate_nat(N_1),Y_2) <-> M_1 = N_1 & (M_1 != zero_zero_nat -> X_1 = Y_2))) # label(fact_282_replicate__eq__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 280 (all M_1 all X_1 all N_1 all Y_2 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_2) -> (hAPP_A832564074le_alt(replic351609551le_alt(M_1),X_1) = hAPP_A832564074le_alt(replic351609551le_alt(N_1),Y_2) <-> M_1 = N_1 & (M_1 != zero_zero_nat -> X_1 = Y_2)))) # label(fact_283_replicate__eq__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 281 (all P_1 all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,takeWh536362254le_alt(P_1,Xs))))) # label(fact_284_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 282 (all P_1 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,takeWhile_nat(P_1,Xs))))) # label(fact_285_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 283 (all P_1 all Xs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,takeWhile_nat(P_1,Xs))))) # label(fact_286_sorted__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 284 (all X_98 hAPP_A832564074le_alt(replic351609551le_alt(zero_zero_nat),X_98) = nil_Ar126264853le_alt) # label(fact_287_replicate__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 285 (all X_98 hAPP_nat_list_nat(replicate_nat(zero_zero_nat),X_98) = nil_nat) # label(fact_288_replicate__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 286 (all N_1 all X_1 (nil_Ar126264853le_alt = hAPP_A832564074le_alt(replic351609551le_alt(N_1),X_1) <-> N_1 = zero_zero_nat)) # label(fact_289_empty__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 287 (all N_1 all X_1 (nil_nat = hAPP_nat_list_nat(replicate_nat(N_1),X_1) <-> N_1 = zero_zero_nat)) # label(fact_290_empty__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 288 (all N_1 all X_1 (hAPP_A832564074le_alt(replic351609551le_alt(N_1),X_1) = nil_Ar126264853le_alt <-> N_1 = zero_zero_nat)) # label(fact_291_replicate__empty) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 289 (all N_1 all X_1 (hAPP_nat_list_nat(replicate_nat(N_1),X_1) = nil_nat <-> N_1 = zero_zero_nat)) # label(fact_292_replicate__empty) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 290 (all Xs all P_1 all X_1 ((hBOOL(hAPP_bool_bool(P_1,X_1)) -> takeWhile_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),takeWhile_bool(P_1,Xs))) & (-hBOOL(hAPP_bool_bool(P_1,X_1)) -> takeWhile_bool(P_1,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = nil_bool))) # label(fact_293_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 291 (all Xs all P_1 all X_1 ((hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> takeWh536362254le_alt(P_1,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),takeWh536362254le_alt(P_1,Xs))) & (-hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> takeWh536362254le_alt(P_1,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = nil_Ar126264853le_alt))) # label(fact_294_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 292 (all Xs all P_1 all X_1 ((hBOOL(hAPP_nat_bool(P_1,X_1)) -> takeWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),takeWhile_nat(P_1,Xs))) & (-hBOOL(hAPP_nat_bool(P_1,X_1)) -> takeWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = nil_nat))) # label(fact_295_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 293 (all Xs all L_2 all P_1 all X_1 (-hBOOL(hAPP_bool_bool(P_1,X_1)) -> takeWhile_bool(P_1,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),L_2))) = takeWhile_bool(P_1,Xs))) # label(fact_296_takeWhile__tail) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 294 (all Xs all L_2 all P_1 all X_1 (-hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> takeWh536362254le_alt(P_1,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),L_2))) = takeWh536362254le_alt(P_1,Xs))) # label(fact_297_takeWhile__tail) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 295 (all Xs all L_2 all P_1 all X_1 (-hBOOL(hAPP_nat_bool(P_1,X_1)) -> takeWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),L_2))) = takeWhile_nat(P_1,Xs))) # label(fact_298_takeWhile__tail) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 296 (all X_1 all A ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A)) -> sublist_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool),A) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A)) -> sublist_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool),A) = nil_bool))) # label(fact_299_sublist__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 297 (all X_1 all A ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A)) -> sublis888024346le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt),A) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A)) -> sublis888024346le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt),A) = nil_Ar126264853le_alt))) # label(fact_300_sublist__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 298 (all X_1 all A ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A)) -> sublist_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat),A) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A)) -> sublist_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat),A) = nil_nat))) # label(fact_301_sublist__singleton) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 299 (all R_2 all A1 all A2 (hBOOL(hAPP_list_bool_bool(listrelp_bool(R_2,A1),A2)) <-> A1 = nil_bool & A2 = nil_bool | (exists X_4 exists Y_25 exists Xs_19 exists Ys_6 (is_bool(X_4) & is_bool(Y_25) & A1 = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Xs_19) & A2 = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Ys_6) & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(R_2,X_4),Y_25)) & hBOOL(hAPP_list_bool_bool(listrelp_bool(R_2,Xs_19),Ys_6)))))) # label(fact_302_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 300 (all R_2 all A1 all A2 (hBOOL(hAPP_l1386638586t_bool(listre53232751le_alt(R_2,A1),A2)) <-> A1 = nil_Ar126264853le_alt & A2 = nil_Ar126264853le_alt | (exists X_4 exists Y_25 exists Xs_19 exists Ys_6 (is_Arr1861959080le_alt(X_4) & is_Arr1861959080le_alt(Y_25) & A1 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Xs_19) & A2 = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),Ys_6) & hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(R_2,X_4),Y_25)) & hBOOL(hAPP_l1386638586t_bool(listre53232751le_alt(R_2,Xs_19),Ys_6)))))) # label(fact_303_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 301 (all R_2 all A1 all A2 (hBOOL(hAPP_list_nat_bool(listrelp_nat(R_2,A1),A2)) <-> A1 = nil_nat & A2 = nil_nat | (exists X_4 exists Y_25 exists Xs_19 exists Ys_6 (A1 = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Xs_19) & A2 = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),Ys_6) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(R_2,X_4),Y_25)) & hBOOL(hAPP_list_nat_bool(listrelp_nat(R_2,Xs_19),Ys_6)))))) # label(fact_304_listrelp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 302 (all Fa list_s1237850263le_alt(Fa,nil_Ar126264853le_alt) = zero_zero_nat) # label(fact_305_list_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 303 (all Fa list_size_nat(Fa,nil_nat) = zero_zero_nat) # label(fact_306_list_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 304 (all X_1 (zero_zero_nat = X_1 <-> X_1 = zero_zero_nat)) # label(fact_307_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 305 (all Xs (Xs != nil_bool -> (hBOOL(hAPP_list_bool_bool(hd_bool,Xs)) <-> hBOOL(hAPP_nat_bool(nth_bool(Xs),zero_zero_nat))))) # label(fact_308_hd__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 306 (all Xs_54 (Xs_54 != nil_Ar126264853le_alt -> hAPP_l1105242632le_alt(hd_Arr805754088le_alt,Xs_54) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_54),zero_zero_nat))) # label(fact_309_hd__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 307 (all Xs_54 (Xs_54 != nil_nat -> hAPP_list_nat_nat(hd_nat,Xs_54) = hAPP_nat_nat(nth_nat(Xs_54),zero_zero_nat))) # label(fact_310_hd__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 308 (all F all X_1 hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),nil_nat) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat)) # label(fact_311_insort__key_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.93 309 (all Xs (Xs != nil_Ar126264853le_alt -> (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) -> takeWh536362254le_alt(cOMBB_2104979073le_alt(fNot,hAPP_A1664620203t_bool(cOMBC_1628726426t_bool(fequal1160105444le_alt),hAPP_l1105242632le_alt(last_A57386030le_alt,Xs))),Xs) = butlas1262502241le_alt(Xs)))) # label(fact_312_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 310 (all Xs (Xs != nil_nat -> (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> takeWhile_nat(cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),hAPP_list_nat_nat(last_nat,Xs))),Xs) = butlast_nat(Xs)))) # label(fact_313_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 311 (all X_1 all Xs ((hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_1),Xs) = Xs) & (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_1),Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)))) # label(fact_314_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 312 (all X_1 all Xs ((hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_1),Xs) = Xs) & (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_1),Xs) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)))) # label(fact_315_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 313 (all X_1 all Xs ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_1),Xs) = Xs) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_1),Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)))) # label(fact_316_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 314 (all F all X_1 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),Xs))) <-> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)))) # label(fact_317_distinct__insort) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 315 (all X_1 all Y_2 all Xs hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(cOMBI_nat),X_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(cOMBI_nat),Y_2),Xs)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(cOMBI_nat),Y_2),hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(cOMBI_nat),X_1),Xs))) # label(fact_318_insort__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 316 (all I_11 all X_1 all Xs (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,sublis888024346le_alt(Xs,I_11)))))) # label(fact_319_notin__set__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 317 (all I_11 all X_1 all Xs (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,sublist_nat(Xs,I_11)))))) # label(fact_320_notin__set__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 318 (all Xs all F all X_1 all Y_2 (hAPP_nat_nat(F,X_1) != hAPP_nat_nat(F,Y_2) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),Y_2),hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),Xs)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),Y_2),Xs)))) # label(fact_321_insort__key__left__comm) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 319 (all X_1 all Xs all I_11 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,sublis888024346le_alt(Xs,I_11)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))) # label(fact_322_in__set__sublistD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 320 (all X_1 all Xs all I_11 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,sublist_nat(Xs,I_11)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_323_in__set__sublistD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 321 (all X_1 all Xs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(cOMBI_nat),X_1),Xs))) <-> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)))) # label(fact_324_sorted__insort) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 322 (all Xs all Ys tl_Arr1453005548le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys)) = list_c380068407le_alt(tl_Arr1453005548le_alt(Ys),cOMBK_1696648346le_alt(hAPP_l568342716le_alt(cOMBC_1058495865le_alt(append1166636842le_alt),Ys)),Xs)) # label(fact_325_tl__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 323 (all Xs all Ys tl_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys)) = list_c554461815at_nat(tl_nat(Ys),cOMBK_1717478773at_nat(hAPP_l710375585st_nat(cOMBC_950362600st_nat(append_nat),Ys)),Xs)) # label(fact_326_tl__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 324 (all Y_2 all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),hAPP_l96088310l_bool(set_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)))) -> (hBOOL(Y_2) <-> hBOOL(X_1)) | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),hAPP_l96088310l_bool(set_bool,Xs))))) # label(fact_327_set__ConsD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 325 (all Y_2 all X_1 all Xs (is_Arr1861959080le_alt(Y_2) & is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Y_2),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)))) -> Y_2 = X_1 | hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Y_2),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs)))))) # label(fact_328_set__ConsD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 326 (all Y_2 all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)))) -> Y_2 = X_1 | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_329_set__ConsD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 327 (all Xs hAPP_l82377208t_bool(set_Ar1565008694le_alt,rev_Ar2093961333le_alt(Xs)) = hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs)) # label(fact_330_set__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 328 (all Xs hAPP_l1821533378t_bool(set_nat,rev_nat(Xs)) = hAPP_l1821533378t_bool(set_nat,Xs)) # label(fact_331_set__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 329 (all P_1 all Xs (takeWh536362254le_alt(P_1,Xs) = Xs <-> (all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_4))))))) # label(fact_332_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 330 (all P_1 all Xs (takeWhile_nat(P_1,Xs) = Xs <-> (all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))))) # label(fact_333_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 331 (all X_1 all P_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,takeWh536362254le_alt(P_1,Xs)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_1)))) # label(fact_334_set__takeWhileD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 332 (all X_1 all P_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,takeWhile_nat(P_1,Xs)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_1)))) # label(fact_335_set__takeWhileD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 333 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,butlas1262502241le_alt(Xs)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))) # label(fact_336_in__set__butlastD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 334 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,butlast_nat(Xs)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_337_in__set__butlastD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 335 (all F all Aa all Xs hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),Aa),Xs) != nil_nat) # label(fact_338_insort__not__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 336 (all Xs hAPP_l82377208t_bool(set_Ar1565008694le_alt,rotate1322903650le_alt(Xs)) = hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs)) # label(fact_339_set__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 337 (all Xs hAPP_l1821533378t_bool(set_nat,rotate1_nat(Xs)) = hAPP_l1821533378t_bool(set_nat,Xs)) # label(fact_340_set__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 338 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_1),Xs) = Xs)) # label(fact_341_in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 339 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_1),Xs) = Xs)) # label(fact_342_in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 340 (all P_1 all Xs (hBOOL(hAPP_l1386638586t_bool(list_e1226799320le_alt(P_1),Xs)) <-> (exists X_4 (is_Arr1861959080le_alt(X_4) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)) & (all Y_25 (is_Arr1861959080le_alt(Y_25) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Y_25),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,Y_25)) -> Y_25 = X_4))))))) # label(fact_345_list__ex1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 341 (all P_1 all Xs (hBOOL(hAPP_list_nat_bool(list_ex1_nat(P_1),Xs)) <-> (exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)) & (all Y_25 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_25),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,Y_25)) -> Y_25 = X_4)))))) # label(fact_346_list__ex1__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 342 (all Xs all X_1 (hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,Xs),X_1)) <-> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))) # label(fact_347_List_Omember__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 343 (all Xs all X_1 (hBOOL(hAPP_nat_bool(hAPP_l1821533378t_bool(member_nat_1,Xs),X_1)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_348_List_Omember__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 344 (all X_1 all Xs (hBOOL(hAPP_l1386638586t_bool(listMe1065601537le_alt(X_1),Xs)) <-> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))) # label(fact_349_ListMem__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 345 (all X_1 all Xs (hBOOL(hAPP_list_nat_bool(listMem_nat(X_1),Xs)) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_350_ListMem__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 346 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) <-> hBOOL(hAPP_A862370221t_bool(hAPP_l82377208t_bool(member345038890le_alt,Xs),X_1)))) # label(fact_351_in__set__member) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 347 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) <-> hBOOL(hAPP_nat_bool(hAPP_l1821533378t_bool(member_nat_1,Xs),X_1)))) # label(fact_352_in__set__member) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 348 (all X_1 all Xs (hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) -> dropWhile_bool(cOMBB_bool_bool_bool(fNot,hAPP_b589554111l_bool(cOMBC_bool_bool_bool(fequal_bool),X_1)),rev_bool(Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),rev_bool(takeWhile_bool(cOMBB_bool_bool_bool(fNot,hAPP_b589554111l_bool(cOMBC_bool_bool_bool(fequal_bool),X_1)),Xs)))))) # label(fact_353_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 349 (all X_1 all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> dropWh156852662le_alt(cOMBB_2104979073le_alt(fNot,hAPP_A1664620203t_bool(cOMBC_1628726426t_bool(fequal1160105444le_alt),X_1)),rev_Ar2093961333le_alt(Xs)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),rev_Ar2093961333le_alt(takeWh536362254le_alt(cOMBB_2104979073le_alt(fNot,hAPP_A1664620203t_bool(cOMBC_1628726426t_bool(fequal1160105444le_alt),X_1)),Xs)))))) # label(fact_354_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 350 (all X_1 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> dropWhile_nat(cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),rev_nat(Xs)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),rev_nat(takeWhile_nat(cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),Xs)))))) # label(fact_355_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 351 (all X_1 all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> takeWh536362254le_alt(cOMBB_2104979073le_alt(fNot,hAPP_A1664620203t_bool(cOMBC_1628726426t_bool(fequal1160105444le_alt),X_1)),rev_Ar2093961333le_alt(Xs)) = rev_Ar2093961333le_alt(tl_Arr1453005548le_alt(dropWh156852662le_alt(cOMBB_2104979073le_alt(fNot,hAPP_A1664620203t_bool(cOMBC_1628726426t_bool(fequal1160105444le_alt),X_1)),Xs)))))) # label(fact_356_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 352 (all X_1 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> takeWhile_nat(cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),rev_nat(Xs)) = rev_nat(tl_nat(dropWhile_nat(cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),Xs)))))) # label(fact_357_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 353 (all A sublis888024346le_alt(nil_Ar126264853le_alt,A) = nil_Ar126264853le_alt) # label(fact_358_sublist__nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 354 (all A sublist_nat(nil_nat,A) = nil_nat) # label(fact_359_sublist__nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 355 (all I_11 all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,sublis888024346le_alt(Xs,I_11))))) # label(fact_360_distinct__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 356 (all I_11 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,sublist_nat(Xs,I_11))))) # label(fact_361_distinct__sublistI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 357 (all Xs rotate1_bool(Xs) = list_c1750880501l_bool(nil_bool,cOMBB_1663860504l_bool(cOMBC_1789016513t_bool(append_bool),hAPP_l1045755451t_bool(cOMBC_80330970t_bool(cons_bool),nil_bool)),Xs)) # label(fact_362_rotate1__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 358 (all Xs rotate1322903650le_alt(Xs) = list_c380068407le_alt(nil_Ar126264853le_alt,cOMBB_881934114le_alt(cOMBC_1058495865le_alt(append1166636842le_alt),hAPP_l618618165le_alt(cOMBC_1919297930le_alt(cons_A1216297413le_alt),nil_Ar126264853le_alt)),Xs)) # label(fact_363_rotate1__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 359 (all Xs rotate1_nat(Xs) = list_c554461815at_nat(nil_nat,cOMBB_472649634at_nat(cOMBC_950362600st_nat(append_nat),hAPP_l383341732st_nat(cOMBC_1204473209st_nat(cons_nat),nil_nat)),Xs)) # label(fact_364_rotate1__def) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 360 (all X_1 all Xs (hBOOL(hAPP_nat_bool(nth_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)),zero_zero_nat)) <-> hBOOL(X_1))) # label(fact_365_nth__Cons__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 361 (all X_97 all Xs_53 (is_Arr1861959080le_alt(X_97) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_97),Xs_53)),zero_zero_nat) = X_97)) # label(fact_366_nth__Cons__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 362 (all X_97 all Xs_53 hAPP_nat_nat(nth_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_97),Xs_53)),zero_zero_nat) = X_97) # label(fact_367_nth__Cons__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 363 (all X_1 all Xs (hBOOL(hAPP_list_bool_bool(distinct_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) <-> -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)))) # label(fact_368_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 364 (all X_1 all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs))) <-> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)))) # label(fact_369_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 365 (all X_1 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs))) <-> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)))) # label(fact_370_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 366 (all X_1 all N_1 all Y_2 (is_Arr1861959080le_alt(X_1) & is_Arr1861959080le_alt(Y_2) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_1),Y_2)))) <-> X_1 = Y_2 & N_1 != zero_zero_nat))) # label(fact_371_in__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 367 (all X_1 all N_1 all Y_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,hAPP_nat_list_nat(replicate_nat(N_1),Y_2)))) <-> X_1 = Y_2 & N_1 != zero_zero_nat)) # label(fact_372_in__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 368 (all P_1 all N_1 all Aa ((exists X_4 (is_Arr1861959080le_alt(X_4) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_1),Aa)))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) <-> hBOOL(hAPP_A862370221t_bool(P_1,Aa)) & N_1 != zero_zero_nat)) # label(fact_373_Bex__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 369 (all P_1 all N_1 all Aa ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,hAPP_nat_list_nat(replicate_nat(N_1),Aa)))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) <-> hBOOL(hAPP_nat_bool(P_1,Aa)) & N_1 != zero_zero_nat)) # label(fact_374_Bex__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 370 (all P_1 all N_1 all Aa ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_1),Aa)))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_4))))) <-> hBOOL(hAPP_A862370221t_bool(P_1,Aa)) | N_1 = zero_zero_nat)) # label(fact_375_Ball__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 371 (all P_1 all N_1 all Aa ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,hAPP_nat_list_nat(replicate_nat(N_1),Aa)))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))) <-> hBOOL(hAPP_nat_bool(P_1,Aa)) | N_1 = zero_zero_nat)) # label(fact_376_Ball__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 372 (all Ys all Xs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) -> (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Ys)) -> (hBOOL(hAPP_list_nat_bool(distinct_nat,Ys)) -> (hAPP_l1821533378t_bool(set_nat,Xs) = hAPP_l1821533378t_bool(set_nat,Ys) -> Xs = Ys)))))) # label(fact_377_sorted__distinct__set__unique) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 373 (all Ys all P_1 all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> (-hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> takeWh536362254le_alt(P_1,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys)) = takeWh536362254le_alt(P_1,Xs)))) # label(fact_378_takeWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 374 (all Ys all P_1 all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> (-hBOOL(hAPP_nat_bool(P_1,X_1)) -> takeWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys)) = takeWhile_nat(P_1,Xs)))) # label(fact_379_takeWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 375 (all As (As != nil_Ar126264853le_alt -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_l1105242632le_alt(last_A57386030le_alt,As)),hAPP_l82377208t_bool(set_Ar1565008694le_alt,As))))) # label(fact_380_last__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 376 (all As (As != nil_nat -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_list_nat_nat(last_nat,As)),hAPP_l1821533378t_bool(set_nat,As))))) # label(fact_381_last__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 377 (all P_1 all Xs (dropWh156852662le_alt(P_1,Xs) = nil_Ar126264853le_alt <-> (all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_4))))))) # label(fact_382_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 378 (all P_1 all Xs (dropWhile_nat(P_1,Xs) = nil_nat <-> (all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))))) # label(fact_383_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 379 (all Ys all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,butlas1262502241le_alt(Xs)))) | hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,butlas1262502241le_alt(Ys)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,butlas1262502241le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys))))))) # label(fact_384_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 380 (all Ys all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,butlast_nat(Xs)))) | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,butlast_nat(Ys)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,butlast_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys))))))) # label(fact_385_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 381 (all Xs (Xs != nil_Ar126264853le_alt -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_l1105242632le_alt(hd_Arr805754088le_alt,Xs)),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))) # label(fact_386_hd__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 382 (all Xs (Xs != nil_nat -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_list_nat_nat(hd_nat,Xs)),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_387_hd__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 383 (all Ys all P_1 all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> (-hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> dropWh156852662le_alt(P_1,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,dropWh156852662le_alt(P_1,Xs)),Ys)))) # label(fact_388_dropWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 384 (all Ys all P_1 all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> (-hBOOL(hAPP_nat_bool(P_1,X_1)) -> dropWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,dropWhile_nat(P_1,Xs)),Ys)))) # label(fact_389_dropWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 385 (all X_1 all Xs (-hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(insert_bool,X_1),Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) # label(fact_390_not__in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 386 (all X_1 all Xs (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(insert960637483le_alt,X_1),Xs) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs))) # label(fact_391_not__in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 387 (all X_1 all Xs (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(insert_nat,X_1),Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs))) # label(fact_392_not__in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 388 (all Ys all P_1 all Xs ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_4))))) -> dropWh156852662le_alt(P_1,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys)) = dropWh156852662le_alt(P_1,Ys))) # label(fact_393_dropWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 389 (all Ys all P_1 all Xs ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))) -> dropWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys)) = dropWhile_nat(P_1,Ys))) # label(fact_394_dropWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 390 (all Ys all P_1 all Xs ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_4))))) -> takeWh536362254le_alt(P_1,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),takeWh536362254le_alt(P_1,Ys)))) # label(fact_395_takeWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 391 (all Ys all P_1 all Xs ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))) -> takeWhile_nat(P_1,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),takeWhile_nat(P_1,Ys)))) # label(fact_396_takeWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 392 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) <-> (exists Ys_6 exists Zs_2 Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Zs_2))))) # label(fact_397_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 393 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) <-> (exists Ys_6 exists Zs_2 Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs_2))))) # label(fact_398_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 394 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) <-> (exists Ys_6 exists Zs_2 Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Zs_2))))) # label(fact_399_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 395 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) <-> (exists Ys_6 exists Zs_2 (Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Zs_2)) & -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Zs_2))))))) # label(fact_400_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 396 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) <-> (exists Ys_6 exists Zs_2 (Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs_2)) & -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Zs_2))))))) # label(fact_401_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 397 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) <-> (exists Ys_6 exists Zs_2 (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Zs_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Zs_2))))))) # label(fact_402_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 398 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) <-> (exists Ys_6 exists Zs_2 (Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Zs_2)) & -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Ys_6))))))) # label(fact_403_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 399 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) <-> (exists Ys_6 exists Zs_2 (Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs_2)) & -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Ys_6))))))) # label(fact_404_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 400 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) <-> (exists Ys_6 exists Zs_2 (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Zs_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Ys_6))))))) # label(fact_405_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 401 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_bool_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 (is_bool(X_4) -> ((exists Zs_2 Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Zs_2))) -> -hBOOL(hAPP_bool_bool(P_1,X_4))))))) # label(fact_406_split__list__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 402 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 (is_Arr1861959080le_alt(X_4) -> ((exists Zs_2 Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Zs_2))) -> -hBOOL(hAPP_A862370221t_bool(P_1,X_4))))))) # label(fact_407_split__list__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 403 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 ((exists Zs_2 Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Zs_2))) -> -hBOOL(hAPP_nat_bool(P_1,X_4)))))) # label(fact_408_split__list__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 404 (all Q_1 all P_1 all L_2 all K_3 (L_2 = K_3 -> ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,L_2))) -> (hBOOL(hAPP_A862370221t_bool(P_1,X_4)) <-> hBOOL(hAPP_A862370221t_bool(Q_1,X_4)))))) -> dropWh156852662le_alt(P_1,L_2) = dropWh156852662le_alt(Q_1,K_3)))) # label(fact_409_dropWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 405 (all Q_1 all P_1 all L_2 all K_3 (L_2 = K_3 -> ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,L_2))) -> (hBOOL(hAPP_nat_bool(P_1,X_4)) <-> hBOOL(hAPP_nat_bool(Q_1,X_4))))) -> dropWhile_nat(P_1,L_2) = dropWhile_nat(Q_1,K_3)))) # label(fact_410_dropWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 406 (all Q_1 all P_1 all L_2 all K_3 (L_2 = K_3 -> ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,L_2))) -> (hBOOL(hAPP_A862370221t_bool(P_1,X_4)) <-> hBOOL(hAPP_A862370221t_bool(Q_1,X_4)))))) -> takeWh536362254le_alt(P_1,L_2) = takeWh536362254le_alt(Q_1,K_3)))) # label(fact_411_takeWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 407 (all Q_1 all P_1 all L_2 all K_3 (L_2 = K_3 -> ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,L_2))) -> (hBOOL(hAPP_nat_bool(P_1,X_4)) <-> hBOOL(hAPP_nat_bool(Q_1,X_4))))) -> takeWhile_nat(P_1,L_2) = takeWhile_nat(Q_1,K_3)))) # label(fact_412_takeWhile__cong) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 408 (all F all X_1 all Xs map_fi80499576t_bool(F,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = option718651152l_bool(map_fi80499576t_bool(F,Xs),hAPP_l1045755451t_bool(cOMBC_80330970t_bool(cons_bool),map_fi80499576t_bool(F,Xs)),hAPP_A524667246n_bool(F,X_1))) # label(fact_413_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 409 (all F all X_1 all Xs map_fi2015041583lt_nat(F,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = option306705938at_nat(map_fi2015041583lt_nat(F,Xs),hAPP_l383341732st_nat(cOMBC_1204473209st_nat(cons_nat),map_fi2015041583lt_nat(F,Xs)),hAPP_A1356081999on_nat(F,X_1))) # label(fact_414_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 410 (all F all X_1 all Xs map_fi695734538le_alt(F,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = option468438226le_alt(map_fi695734538le_alt(F,Xs),hAPP_l618618165le_alt(cOMBC_1919297930le_alt(cons_A1216297413le_alt),map_fi695734538le_alt(F,Xs)),hAPP_A373227306le_alt(F,X_1))) # label(fact_415_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 411 (all F all X_1 all Xs map_filter_nat_bool(F,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = option718651152l_bool(map_filter_nat_bool(F,Xs),hAPP_l1045755451t_bool(cOMBC_80330970t_bool(cons_bool),map_filter_nat_bool(F,Xs)),hAPP_nat_option_bool(F,X_1))) # label(fact_416_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 412 (all F all X_1 all Xs map_filter_nat_nat(F,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = option306705938at_nat(map_filter_nat_nat(F,Xs),hAPP_l383341732st_nat(cOMBC_1204473209st_nat(cons_nat),map_filter_nat_nat(F,Xs)),hAPP_nat_option_nat(F,X_1))) # label(fact_417_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 413 (all F all X_1 all Xs map_fi302768037le_alt(F,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = option468438226le_alt(map_fi302768037le_alt(F,Xs),hAPP_l618618165le_alt(cOMBC_1919297930le_alt(cons_A1216297413le_alt),map_fi302768037le_alt(F,Xs)),hAPP_n2020361039le_alt(F,X_1))) # label(fact_418_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 414 (all F all X_1 all Xs map_fi1996871376le_alt(F,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = option468438226le_alt(map_fi1996871376le_alt(F,Xs),hAPP_l618618165le_alt(cOMBC_1919297930le_alt(cons_A1216297413le_alt),map_fi1996871376le_alt(F,Xs)),hAPP_b803953466le_alt(F,X_1))) # label(fact_419_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 415 (all F all X_1 all Xs map_filter_bool_nat(F,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = option306705938at_nat(map_filter_bool_nat(F,Xs),hAPP_l383341732st_nat(cOMBC_1204473209st_nat(cons_nat),map_filter_bool_nat(F,Xs)),hAPP_bool_option_nat(F,X_1))) # label(fact_420_map__filter__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 416 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_bool_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 (is_bool(X_4) -> ((exists Zs_2 Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Zs_2))) -> (hBOOL(hAPP_bool_bool(P_1,X_4)) -> -(all Xa (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Xa),hAPP_l96088310l_bool(set_bool,Ys_6))) -> -hBOOL(hAPP_bool_bool(P_1,Xa)))))))))) # label(fact_421_split__list__first__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 417 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 (is_Arr1861959080le_alt(X_4) -> ((exists Zs_2 Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Zs_2))) -> (hBOOL(hAPP_A862370221t_bool(P_1,X_4)) -> -(all Xa (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Ys_6))) -> -hBOOL(hAPP_A862370221t_bool(P_1,Xa)))))))))) # label(fact_422_split__list__first__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 418 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 ((exists Zs_2 Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Zs_2))) -> (hBOOL(hAPP_nat_bool(P_1,X_4)) -> -(all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),hAPP_l1821533378t_bool(set_nat,Ys_6))) -> -hBOOL(hAPP_nat_bool(P_1,Xa))))))))) # label(fact_423_split__list__first__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 419 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_bool_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 all Zs_2 (is_bool(X_4) -> (Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Zs_2)) -> (hBOOL(hAPP_bool_bool(P_1,X_4)) -> -(all Xa (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Xa),hAPP_l96088310l_bool(set_bool,Zs_2))) -> -hBOOL(hAPP_bool_bool(P_1,Xa)))))))))) # label(fact_424_split__list__last__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 420 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 all Zs_2 (is_Arr1861959080le_alt(X_4) -> (Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Zs_2)) -> (hBOOL(hAPP_A862370221t_bool(P_1,X_4)) -> -(all Xa (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Zs_2))) -> -hBOOL(hAPP_A862370221t_bool(P_1,Xa)))))))))) # label(fact_425_split__list__last__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 421 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) -> -(all Ys_6 all X_4 all Zs_2 (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Zs_2)) -> (hBOOL(hAPP_nat_bool(P_1,X_4)) -> -(all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),hAPP_l1821533378t_bool(set_nat,Zs_2))) -> -hBOOL(hAPP_nat_bool(P_1,Xa))))))))) # label(fact_426_split__list__last__propE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 422 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) -> (exists Ys_6 exists Zs_2 (Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Zs_2)) & -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Ys_6))))))) # label(fact_427_split__list__first) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 423 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> (exists Ys_6 exists Zs_2 (Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs_2)) & -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Ys_6))))))) # label(fact_428_split__list__first) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 424 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> (exists Ys_6 exists Zs_2 (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Zs_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Ys_6))))))) # label(fact_429_split__list__first) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 425 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) -> (exists Ys_6 exists Zs_2 (Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Zs_2)) & -hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Zs_2))))))) # label(fact_430_split__list__last) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 426 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> (exists Ys_6 exists Zs_2 (Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs_2)) & -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Zs_2))))))) # label(fact_431_split__list__last) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 427 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> (exists Ys_6 exists Zs_2 (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Zs_2)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Zs_2))))))) # label(fact_432_split__list__last) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 428 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) -> (exists Ys_6 exists Zs_2 Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Zs_2))))) # label(fact_433_split__list) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 429 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> (exists Ys_6 exists Zs_2 Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Zs_2))))) # label(fact_434_split__list) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 430 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> (exists Ys_6 exists Zs_2 Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Zs_2))))) # label(fact_435_split__list) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 431 (all P_1 all Xs ((exists X_4 (is_bool(X_4) & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_bool_bool(P_1,X_4)))) <-> (exists Ys_6 exists X_4 (is_bool(X_4) & (exists Zs_2 Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Zs_2))) & hBOOL(hAPP_bool_bool(P_1,X_4)) & (all Xa (is_bool(Xa) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Xa),hAPP_l96088310l_bool(set_bool,Ys_6))) -> -hBOOL(hAPP_bool_bool(P_1,Xa))))))))) # label(fact_436_split__list__first__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 432 (all P_1 all Xs ((exists X_4 (is_Arr1861959080le_alt(X_4) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) <-> (exists Ys_6 exists X_4 (is_Arr1861959080le_alt(X_4) & (exists Zs_2 Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Zs_2))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)) & (all Xa (is_Arr1861959080le_alt(Xa) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Ys_6))) -> -hBOOL(hAPP_A862370221t_bool(P_1,Xa))))))))) # label(fact_437_split__list__first__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 433 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) <-> (exists Ys_6 exists X_4 ((exists Zs_2 Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Zs_2))) & hBOOL(hAPP_nat_bool(P_1,X_4)) & (all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),hAPP_l1821533378t_bool(set_nat,Ys_6))) -> -hBOOL(hAPP_nat_bool(P_1,Xa)))))))) # label(fact_438_split__list__first__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 434 (all P_1 all Xs ((exists X_4 (is_bool(X_4) & hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_bool_bool(P_1,X_4)))) <-> (exists Ys_6 exists X_4 exists Zs_2 (is_bool(X_4) & Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Zs_2)) & hBOOL(hAPP_bool_bool(P_1,X_4)) & (all Xa (is_bool(Xa) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Xa),hAPP_l96088310l_bool(set_bool,Zs_2))) -> -hBOOL(hAPP_bool_bool(P_1,Xa))))))))) # label(fact_439_split__list__last__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 435 (all P_1 all Xs ((exists X_4 (is_Arr1861959080le_alt(X_4) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) <-> (exists Ys_6 exists X_4 exists Zs_2 (is_Arr1861959080le_alt(X_4) & Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Zs_2)) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)) & (all Xa (is_Arr1861959080le_alt(Xa) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Zs_2))) -> -hBOOL(hAPP_A862370221t_bool(P_1,Xa))))))))) # label(fact_440_split__list__last__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 436 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) <-> (exists Ys_6 exists X_4 exists Zs_2 (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Zs_2)) & hBOOL(hAPP_nat_bool(P_1,X_4)) & (all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),hAPP_l1821533378t_bool(set_nat,Zs_2))) -> -hBOOL(hAPP_nat_bool(P_1,Xa)))))))) # label(fact_441_split__list__last__prop__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 437 (all X_1 all L_2 all A sublist_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),L_2),A) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,if_list_bool(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),nil_bool),nil_bool)),sublist_bool(L_2,collect_nat(hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),A))))) # label(fact_442_sublist__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 438 (all X_1 all L_2 all A sublis888024346le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),L_2),A) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,if_lis1340954026le_alt(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),nil_Ar126264853le_alt),nil_Ar126264853le_alt)),sublis888024346le_alt(L_2,collect_nat(hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),A))))) # label(fact_443_sublist__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 439 (all X_1 all L_2 all A sublist_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),L_2),A) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,if_list_nat(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),A),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),nil_nat),nil_nat)),sublist_nat(L_2,collect_nat(hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),A))))) # label(fact_444_sublist__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 440 (all X_1 all Xs all N_1 (hBOOL(hAPP_nat_bool(nth_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(nth_bool(Xs),N_1)))) # label(fact_445_nth__Cons__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 441 (all X_96 all Xs_52 all N_39 hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_96),Xs_52)),hAPP_nat_nat(suc,N_39)) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_52),N_39)) # label(fact_446_nth__Cons__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 442 (all X_96 all Xs_52 all N_39 hAPP_nat_nat(nth_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_96),Xs_52)),hAPP_nat_nat(suc,N_39)) = hAPP_nat_nat(nth_nat(Xs_52),N_39)) # label(fact_447_nth__Cons__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 443 (all N_1 all X_1 hAPP_bool_list_bool(replicate_bool(hAPP_nat_nat(suc,N_1)),X_1) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),hAPP_bool_list_bool(replicate_bool(N_1),X_1))) # label(fact_448_replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 444 (all N_38 all X_95 hAPP_A832564074le_alt(replic351609551le_alt(hAPP_nat_nat(suc,N_38)),X_95) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_95),hAPP_A832564074le_alt(replic351609551le_alt(N_38),X_95))) # label(fact_449_replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 445 (all N_38 all X_95 hAPP_nat_list_nat(replicate_nat(hAPP_nat_nat(suc,N_38)),X_95) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_95),hAPP_nat_list_nat(replicate_nat(N_38),X_95))) # label(fact_450_replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 446 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_451_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 447 (all M zero_zero_nat != hAPP_nat_nat(suc,M)) # label(fact_452_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 448 (all Nat_5 hAPP_nat_nat(suc,Nat_5) != zero_zero_nat) # label(fact_453_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 449 (all M hAPP_nat_nat(suc,M) != zero_zero_nat) # label(fact_454_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 450 (all Nat_4 zero_zero_nat != hAPP_nat_nat(suc,Nat_4)) # label(fact_455_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 451 (all M zero_zero_nat != hAPP_nat_nat(suc,M)) # label(fact_456_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 452 (all X_1 all Xs all N_1 hAPP_nat_list_nat(nth_list_nat(hAPP_l1734754389st_nat(hAPP_l1872445307st_nat(cons_list_nat,X_1),Xs)),N_1) = hAPP_nat_list_nat(nat_case_list_nat(X_1,nth_list_nat(Xs)),N_1)) # label(fact_457_nth_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 453 (all X_1 all Xs all N_1 hAPP_n1875670159le_alt(nth_li2119471145le_alt(hAPP_l1891879573le_alt(hAPP_l656323104le_alt(cons_l650111674le_alt,X_1),Xs)),N_1) = hAPP_n1875670159le_alt(nat_ca14895078le_alt(X_1,nth_li2119471145le_alt(Xs)),N_1)) # label(fact_458_nth_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 454 (all X_1 all Xs all N_1 (hBOOL(hAPP_nat_bool(nth_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)),N_1)) <-> hBOOL(hAPP_nat_bool(nat_case_bool(X_1,nth_bool(Xs)),N_1)))) # label(fact_459_nth_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 455 (all X_1 all Xs all N_1 hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)),N_1) = hAPP_n401316912le_alt(nat_ca391302041le_alt(X_1,nth_Ar1113433366le_alt(Xs)),N_1)) # label(fact_460_nth_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 456 (all X_1 all Xs all N_1 hAPP_nat_nat(nth_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)),N_1) = hAPP_nat_nat(nat_case_nat(X_1,nth_nat(Xs)),N_1)) # label(fact_461_nth_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 457 (all F1 all F2 hAPP_nat_list_nat(nat_case_list_nat(F1,F2),zero_zero_nat) = F1) # label(fact_462_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 458 (all F1 all F2 hAPP_n1875670159le_alt(nat_ca14895078le_alt(F1,F2),zero_zero_nat) = F1) # label(fact_463_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 459 (all F1 all F2 (is_Arr1861959080le_alt(F1) -> hAPP_n401316912le_alt(nat_ca391302041le_alt(F1,F2),zero_zero_nat) = F1)) # label(fact_464_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 460 (all F1 all F2 hAPP_nat_nat(nat_case_nat(F1,F2),zero_zero_nat) = F1) # label(fact_465_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 461 (all F1 all F2 (hBOOL(hAPP_nat_bool(nat_case_bool(F1,F2),zero_zero_nat)) <-> hBOOL(F1))) # label(fact_466_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 462 (all F1 all F2 all Nat_3 hAPP_nat_list_nat(nat_case_list_nat(F1,F2),hAPP_nat_nat(suc,Nat_3)) = hAPP_nat_list_nat(F2,Nat_3)) # label(fact_467_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 463 (all F1 all F2 all Nat_3 hAPP_n1875670159le_alt(nat_ca14895078le_alt(F1,F2),hAPP_nat_nat(suc,Nat_3)) = hAPP_n1875670159le_alt(F2,Nat_3)) # label(fact_468_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 464 (all F1 all F2 all Nat_3 hAPP_n401316912le_alt(nat_ca391302041le_alt(F1,F2),hAPP_nat_nat(suc,Nat_3)) = hAPP_n401316912le_alt(F2,Nat_3)) # label(fact_469_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 465 (all F1 all F2 all Nat_3 hAPP_nat_nat(nat_case_nat(F1,F2),hAPP_nat_nat(suc,Nat_3)) = hAPP_nat_nat(F2,Nat_3)) # label(fact_470_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 466 (all F1 all F2 all Nat_3 (hBOOL(hAPP_nat_bool(nat_case_bool(F1,F2),hAPP_nat_nat(suc,Nat_3))) <-> hBOOL(hAPP_nat_bool(F2,Nat_3)))) # label(fact_471_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 467 (all N N != hAPP_nat_nat(suc,N)) # label(fact_472_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 468 (all N hAPP_nat_nat(suc,N) != N) # label(fact_473_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 469 (all Nat_3 all Nat_2 (hAPP_nat_nat(suc,Nat_3) = hAPP_nat_nat(suc,Nat_2) <-> Nat_3 = Nat_2)) # label(fact_474_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 470 (all X all Y (hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) -> X = Y)) # label(fact_475_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 471 (all N (N != zero_zero_nat -> (exists M_5 N = hAPP_nat_nat(suc,M_5)))) # label(fact_476_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 472 (all N_1 all P_1 (hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) -> ((all N_19 (hBOOL(hAPP_nat_bool(P_1,N_19)) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_19))))) -> hBOOL(hAPP_nat_bool(P_1,N_1))))) # label(fact_477_nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 473 (all P_1 all K_3 (hBOOL(hAPP_nat_bool(P_1,K_3)) -> ((all N_19 (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_19))) -> hBOOL(hAPP_nat_bool(P_1,N_19)))) -> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat))))) # label(fact_478_zero__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 474 (all Y (Y != zero_zero_nat -> -(all Nat_1 Y != hAPP_nat_nat(suc,Nat_1)))) # label(fact_479_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 475 (all N_1 all Xs (Xs != nil_bool -> hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,hAPP_nat_nat(suc,N_1)),Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,hAPP_list_bool_bool(hd_bool,Xs)),hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,N_1),tl_bool(Xs))))) # label(fact_480_take__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 476 (all N_37 all Xs_51 (Xs_51 != nil_Ar126264853le_alt -> hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(suc,N_37)),Xs_51) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,hAPP_l1105242632le_alt(hd_Arr805754088le_alt,Xs_51)),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_37),tl_Arr1453005548le_alt(Xs_51))))) # label(fact_481_take__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 477 (all N_37 all Xs_51 (Xs_51 != nil_nat -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(suc,N_37)),Xs_51) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,hAPP_list_nat_nat(hd_nat,Xs_51)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_37),tl_nat(Xs_51))))) # label(fact_482_take__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 478 (all X_1 all Xs (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord297828738at_nat(cOMBI_nat),X_1),Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(cOMBI_nat),X_1),Xs))) # label(fact_483_insort__insert__insort) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 479 (all P_1 all X_1 all Xs (hBOOL(hAPP_list_bool_bool(list_ex1_bool(P_1),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) <-> (hBOOL(hAPP_bool_bool(P_1,X_1)) -> hBOOL(hAPP_list_bool_bool(list_all_bool(cOMBS_bool_bool_bool(cOMBB_1914122979l_bool(fdisj,cOMBB_bool_bool_bool(fNot,P_1)),hAPP_b589554111l_bool(fequal_bool,X_1))),Xs))) & (-hBOOL(hAPP_bool_bool(P_1,X_1)) -> hBOOL(hAPP_list_bool_bool(list_ex1_bool(P_1),Xs))))) # label(fact_484_list__ex1__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.94 480 (all P_1 all X_1 all Xs (hBOOL(hAPP_l1386638586t_bool(list_e1226799320le_alt(P_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs))) <-> (hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(cOMBS_1393264256l_bool(cOMBB_803794783le_alt(fdisj,cOMBB_2104979073le_alt(fNot,P_1)),hAPP_A1664620203t_bool(fequal1160105444le_alt,X_1))),Xs))) & (-hBOOL(hAPP_A862370221t_bool(P_1,X_1)) -> hBOOL(hAPP_l1386638586t_bool(list_e1226799320le_alt(P_1),Xs))))) # label(fact_485_list__ex1__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 481 (all P_1 all X_1 all Xs (hBOOL(hAPP_list_nat_bool(list_ex1_nat(P_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs))) <-> (hBOOL(hAPP_nat_bool(P_1,X_1)) -> hBOOL(hAPP_list_nat_bool(list_all_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,cOMBB_bool_bool_nat(fNot,P_1)),hAPP_n1699378549t_bool(fequal_nat,X_1))),Xs))) & (-hBOOL(hAPP_nat_bool(P_1,X_1)) -> hBOOL(hAPP_list_nat_bool(list_ex1_nat(P_1),Xs))))) # label(fact_486_list__ex1__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 482 (all Aa all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Aa),hAPP_l1821533378t_bool(set_nat,Xs))) -> (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(cOMBI_nat),Aa),hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,Aa),Xs)) = Xs))) # label(fact_487_insort__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 483 (all X_94 all Y_64 all Zs_3 hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_94),hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,Y_64),Zs_3)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,Y_64),hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_94),Zs_3))) # label(fact_488_remove1__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 484 (all X_94 all Y_64 all Zs_3 hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_94),hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,Y_64),Zs_3)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,Y_64),hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_94),Zs_3))) # label(fact_489_remove1__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 485 (all N_36 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_36),nil_Ar126264853le_alt) = nil_Ar126264853le_alt) # label(fact_490_take__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 486 (all N_36 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_36),nil_nat) = nil_nat) # label(fact_491_take__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 487 (all X_1 all N_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_1),Xs)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))) # label(fact_492_in__set__takeD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 488 (all X_1 all N_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_1),Xs)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_493_in__set__takeD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 489 (all I_12 all Xs_50 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_50)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,I_12),Xs_50))))) # label(fact_494_distinct__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 490 (all I_12 all Xs_50 (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_50)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,I_12),Xs_50))))) # label(fact_495_distinct__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 491 (all N_35 all Xs_49 (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_49)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_35),Xs_49))))) # label(fact_496_sorted__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 492 (all Xs all Y_2 all X_1 (((hBOOL(X_1) <-> hBOOL(Y_2)) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(remove1_bool,X_1),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Xs)) = Xs) & ((hBOOL(X_1) <-> -hBOOL(Y_2)) -> hAPP_l1189022293t_bool(hAPP_b994696797t_bool(remove1_bool,X_1),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(remove1_bool,X_1),Xs))))) # label(fact_497_remove1_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 493 (all Xs_48 all X_93 all Y_63 (is_Arr1861959080le_alt(X_93) & is_Arr1861959080le_alt(Y_63) -> (X_93 = Y_63 -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_93),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_63),Xs_48)) = Xs_48) & (X_93 != Y_63 -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_93),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_63),Xs_48)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_63),hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_93),Xs_48))))) # label(fact_498_remove1_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 494 (all Xs_48 all X_93 all Y_63 ((X_93 = Y_63 -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_93),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_63),Xs_48)) = Xs_48) & (X_93 != Y_63 -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_93),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_63),Xs_48)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_63),hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_93),Xs_48))))) # label(fact_499_remove1_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 495 (all X_92 hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_92),nil_Ar126264853le_alt) = nil_Ar126264853le_alt) # label(fact_500_remove1_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 496 (all X_92 hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_92),nil_nat) = nil_nat) # label(fact_501_remove1_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 497 (all Xs all Aa all Ba (is_Arr1861959080le_alt(Aa) & is_Arr1861959080le_alt(Ba) -> (Aa != Ba -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Aa),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,Ba),Xs)))) <-> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Aa),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))))) # label(fact_502_in__set__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 498 (all Xs all Aa all Ba (Aa != Ba -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Aa),hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,Ba),Xs)))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Aa),hAPP_l1821533378t_bool(set_nat,Xs)))))) # label(fact_503_in__set__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 499 (all Y_2 all X_1 all Xs (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,Y_2),Xs)))))) # label(fact_504_notin__set__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 500 (all Y_2 all X_1 all Xs (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,Y_2),Xs)))))) # label(fact_505_notin__set__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 501 (all X_1 all Xs (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_1),Xs) = Xs)) # label(fact_506_remove1__idem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 502 (all X_1 all Xs (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_1),Xs) = Xs)) # label(fact_507_remove1__idem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 503 (all X_91 all Xs_47 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_47)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_91),Xs_47))))) # label(fact_508_distinct__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 504 (all X_91 all Xs_47 (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_47)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_91),Xs_47))))) # label(fact_509_distinct__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 505 (all A_83 all Xs_46 (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_46)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,A_83),Xs_46))))) # label(fact_510_sorted__remove1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 506 (all P_1 all X_1 all Xs (hBOOL(hAPP_list_bool_bool(list_all_bool(P_1),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))) <-> hBOOL(hAPP_bool_bool(P_1,X_1)) & hBOOL(hAPP_list_bool_bool(list_all_bool(P_1),Xs)))) # label(fact_511_list__all__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 507 (all P_1 all X_1 all Xs (hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs))) <-> hBOOL(hAPP_A862370221t_bool(P_1,X_1)) & hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),Xs)))) # label(fact_512_list__all__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 508 (all P_1 all X_1 all Xs (hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs))) <-> hBOOL(hAPP_nat_bool(P_1,X_1)) & hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),Xs)))) # label(fact_513_list__all__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 509 (all P_1 hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),nil_Ar126264853le_alt))) # label(fact_514_list__all__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 510 (all P_1 hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),nil_nat))) # label(fact_515_list__all__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 511 (all P_1 all Xs (hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),Xs)) <-> (all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_4))))))) # label(fact_516_list__all__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 512 (all P_1 all Xs (hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),Xs)) <-> (all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))))) # label(fact_517_list__all__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 513 (all P_1 all Xs all Ys (hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys))) <-> hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),Xs)) & hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),Ys)))) # label(fact_518_list__all__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 514 (all P_1 all Xs all Ys (hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys))) <-> hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),Xs)) & hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),Ys)))) # label(fact_519_list__all__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 515 (all P_1 all Xs (hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),rev_nat(Xs))) <-> hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),Xs)))) # label(fact_520_list__all__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 516 (all P_1 all Xs (hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),rev_Ar2093961333le_alt(Xs))) <-> hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),Xs)))) # label(fact_521_list__all__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 517 (all Xs_45 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,zero_zero_nat),Xs_45) = nil_Ar126264853le_alt) # label(fact_522_take__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 518 (all Xs_45 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,zero_zero_nat),Xs_45) = nil_nat) # label(fact_523_take__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 519 (all N_1 all Xs (hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_1),Xs) = nil_Ar126264853le_alt <-> N_1 = zero_zero_nat | Xs = nil_Ar126264853le_alt)) # label(fact_524_take__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 520 (all N_1 all Xs (hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_1),Xs) = nil_nat <-> N_1 = zero_zero_nat | Xs = nil_nat)) # label(fact_525_take__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 521 (all N_1 all X_1 all Xs hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,hAPP_nat_nat(suc,N_1)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,N_1),Xs))) # label(fact_526_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 522 (all N_34 all X_90 all Xs_44 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(suc,N_34)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_90),Xs_44)) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_90),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_34),Xs_44))) # label(fact_527_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 523 (all N_34 all X_90 all Xs_44 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(suc,N_34)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_90),Xs_44)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_90),hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_34),Xs_44))) # label(fact_528_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 524 (all X_1 all Xs hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(cOMBI_nat),X_1),Xs)) = Xs) # label(fact_529_remove1__insort) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 525 (all N_33 all Xs_43 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_33),tl_Arr1453005548le_alt(Xs_43)) = tl_Arr1453005548le_alt(hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(suc,N_33)),Xs_43))) # label(fact_530_take__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 526 (all N_33 all Xs_43 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_33),tl_nat(Xs_43)) = tl_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(suc,N_33)),Xs_43))) # label(fact_531_take__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 527 (all N_1 all X_1 all Xs hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,N_1),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_nat_list_bool(nat_case_list_bool(nil_bool,cOMBB_1891801486ol_nat(hAPP_b994696797t_bool(cons_bool,X_1),hAPP_l1656175496t_bool(cOMBC_1038295629t_bool(take_bool),Xs))),N_1)) # label(fact_532_take__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 528 (all N_1 all X_1 all Xs hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_1),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs)) = hAPP_n1875670159le_alt(nat_ca14895078le_alt(nil_Ar126264853le_alt,cOMBB_903467948lt_nat(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),hAPP_l382792410le_alt(cOMBC_1511969967le_alt(take_A1601602045le_alt),Xs))),N_1)) # label(fact_533_take__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 529 (all N_1 all X_1 all Xs hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = hAPP_nat_list_nat(nat_case_list_nat(nil_nat,cOMBB_850496866at_nat(hAPP_n280362926st_nat(cons_nat,X_1),hAPP_l383341732st_nat(cOMBC_1204473209st_nat(take_nat),Xs))),N_1)) # label(fact_534_take__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 530 (all F all X_1 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord297828738at_nat(F),X_1),Xs))))) # label(fact_535_distinct__insort__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 531 (all Ys all X_1 all Xs ((hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_1),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_1),Xs)),Ys)) & (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_1),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_1),Ys))))) # label(fact_536_remove1__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 532 (all Ys all X_1 all Xs ((hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_1),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_1),Xs)),Ys)) & (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_1),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_1),Ys))))) # label(fact_537_remove1__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 533 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord297828738at_nat(cOMBI_nat),X_1),Xs) = Xs)) # label(fact_538_insort__insert__triv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 534 (all X_1 all Xs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord297828738at_nat(cOMBI_nat),X_1),Xs))))) # label(fact_539_sorted__insort__insert) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 535 (all G all F all Xs all Ys (Xs = Ys -> ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Ys))) -> (hBOOL(hAPP_A862370221t_bool(F,X_4)) <-> hBOOL(hAPP_A862370221t_bool(G,X_4)))))) -> (hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(F),Xs)) <-> hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(G),Ys)))))) # label(fact_540_list__all__cong) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 536 (all G all F all Xs all Ys (Xs = Ys -> ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Ys))) -> (hBOOL(hAPP_nat_bool(F,X_4)) <-> hBOOL(hAPP_nat_bool(G,X_4))))) -> (hBOOL(hAPP_list_nat_bool(list_all_nat(F),Xs)) <-> hBOOL(hAPP_list_nat_bool(list_all_nat(G),Ys)))))) # label(fact_541_list__all__cong) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 537 (all Xs_42 all Ys_14 ((all I_4 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,I_4),Xs_42) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,I_4),Ys_14)) -> Xs_42 = Ys_14)) # label(fact_542_take__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 538 (all Xs_42 all Ys_14 ((all I_4 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,I_4),Xs_42) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,I_4),Ys_14)) -> Xs_42 = Ys_14)) # label(fact_543_take__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 539 (all Fa all Aa all List_1 list_size_bool(Fa,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Aa),List_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_bool_nat(Fa,Aa)),list_size_bool(Fa,List_1))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_544_list_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 540 (all Fa all Aa all List_1 list_s1237850263le_alt(Fa,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Aa),List_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_A2113590458lt_nat(Fa,Aa)),list_s1237850263le_alt(Fa,List_1))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_545_list_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 541 (all Fa all Aa all List_1 list_size_nat(Fa,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Aa),List_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(Fa,Aa)),list_size_nat(Fa,List_1))),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_546_list_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 542 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 (is_Arr1861959080le_alt(X_4) & (exists Zs_2 Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Zs_2))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))))) # label(fact_547_split__list__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 543 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 ((exists Zs_2 Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Zs_2))) & hBOOL(hAPP_nat_bool(P_1,X_4)))))) # label(fact_548_split__list__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 544 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_bool_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 (is_bool(X_4) & (exists Zs_2 Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Zs_2))) & hBOOL(hAPP_bool_bool(P_1,X_4)))))) # label(fact_549_split__list__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 545 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 exists Zs_2 (is_Arr1861959080le_alt(X_4) & Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Zs_2)) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)) & (all Xa (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Zs_2))) -> -hBOOL(hAPP_A862370221t_bool(P_1,Xa)))))))) # label(fact_550_split__list__last__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 546 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 exists Zs_2 (Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Zs_2)) & hBOOL(hAPP_nat_bool(P_1,X_4)) & (all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),hAPP_l1821533378t_bool(set_nat,Zs_2))) -> -hBOOL(hAPP_nat_bool(P_1,Xa)))))))) # label(fact_551_split__list__last__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 547 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_bool_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 exists Zs_2 (is_bool(X_4) & Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Zs_2)) & hBOOL(hAPP_bool_bool(P_1,X_4)) & (all Xa (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Xa),hAPP_l96088310l_bool(set_bool,Zs_2))) -> -hBOOL(hAPP_bool_bool(P_1,Xa)))))))) # label(fact_552_split__list__last__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 548 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 (is_Arr1861959080le_alt(X_4) & (exists Zs_2 Xs = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Ys_6),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_4),Zs_2))) & hBOOL(hAPP_A862370221t_bool(P_1,X_4)) & (all Xa (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,Xa),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Ys_6))) -> -hBOOL(hAPP_A862370221t_bool(P_1,Xa)))))))) # label(fact_553_split__list__first__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 549 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) & hBOOL(hAPP_nat_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 ((exists Zs_2 Xs = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Ys_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Zs_2))) & hBOOL(hAPP_nat_bool(P_1,X_4)) & (all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),hAPP_l1821533378t_bool(set_nat,Ys_6))) -> -hBOOL(hAPP_nat_bool(P_1,Xa)))))))) # label(fact_554_split__list__first__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 550 (all P_1 all Xs ((exists X_4 (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) & hBOOL(hAPP_bool_bool(P_1,X_4)))) -> (exists Ys_6 exists X_4 (is_bool(X_4) & (exists Zs_2 Xs = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Ys_6),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_4),Zs_2))) & hBOOL(hAPP_bool_bool(P_1,X_4)) & (all Xa (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Xa),hAPP_l96088310l_bool(set_bool,Ys_6))) -> -hBOOL(hAPP_bool_bool(P_1,Xa)))))))) # label(fact_555_split__list__first__prop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 551 (all Xs rev_nat(Xs) = foldl_list_nat_nat(cOMBC_1204473209st_nat(cons_nat),nil_nat,Xs)) # label(fact_556_rev__foldl__cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 552 (all Xs rev_Ar2093961333le_alt(Xs) = foldl_1200072380le_alt(cOMBC_1919297930le_alt(cons_A1216297413le_alt),nil_Ar126264853le_alt,Xs)) # label(fact_557_rev__foldl__cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 553 (all Xs rev_bool(Xs) = foldl_list_bool_bool(cOMBC_80330970t_bool(cons_bool),nil_bool,Xs)) # label(fact_558_rev__foldl__cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 554 (all X_1 all Zs hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),foldl_nat_nat(plus_plus_nat,zero_zero_nat,Zs)) = foldl_nat_nat(plus_plus_nat,X_1,Zs)) # label(fact_559_foldl__absorb0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 555 (all B_70 all A_82 all C_43 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_70),A_82) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_43),A_82) -> B_70 = C_43)) # label(fact_560_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 556 (all A_81 all B_69 all C_42 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_81),B_69) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_81),C_42) -> B_69 = C_42)) # label(fact_561_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 557 (all A_80 all B_68 all C_41 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_80),B_68) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_80),C_41) -> B_68 = C_41)) # label(fact_562_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 558 (all Ba all Aa all C_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),Aa) <-> Ba = C_2)) # label(fact_563_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 559 (all Aa all Ba all C_2 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),C_2) <-> Ba = C_2)) # label(fact_564_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 560 (all A_79 all B_67 all C_40 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_79),B_67)),C_40) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_79),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_67),C_40))) # label(fact_565_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 561 (all X_1 all Y_2 all Zs foldl_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),Y_2),Zs) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),foldl_nat_nat(plus_plus_nat,Y_2,Zs))) # label(fact_566_foldl__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 562 (all M_1 all K_3 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_3) <-> M_1 = N_1)) # label(fact_567_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 563 (all K_3 all M_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),N_1) <-> M_1 = N_1)) # label(fact_568_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 564 (all M all N all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K))) # label(fact_569_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 565 (all X all Y all Z_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z_3))) # label(fact_570_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 566 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)) # label(fact_571_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 567 (all A_78 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_78),zero_zero_nat) = A_78) # label(fact_572_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 568 (all A_77 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_77),zero_zero_nat) = A_77) # label(fact_573_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 569 (all A_76 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_76) = A_76) # label(fact_574_add__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 570 (all A_75 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_75) = A_75) # label(fact_575_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 571 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N) = M -> N = zero_zero_nat)) # label(fact_576_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 572 (all M_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = zero_zero_nat <-> M_1 = zero_zero_nat & N_1 = zero_zero_nat)) # label(fact_577_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 573 (all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),zero_zero_nat) = M) # label(fact_578_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 574 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N) = N) # label(fact_579_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 575 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),hAPP_nat_nat(suc,N))) # label(fact_580_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 576 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N))) # label(fact_581_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 577 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N))) # label(fact_582_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 578 (all F all Aa all X_1 all Xs foldl_nat_nat(F,Aa,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = foldl_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,Aa),X_1),Xs)) # label(fact_583_foldl__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 579 (all F all Aa foldl_nat_nat(F,Aa,nil_nat) = Aa) # label(fact_584_foldl__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 580 (all F all Aa all Xs all Ys foldl_nat_nat(F,Aa,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys)) = foldl_nat_nat(F,foldl_nat_nat(F,Aa,Xs),Ys)) # label(fact_585_foldl__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 581 (all M_1 all N_1 (hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) <-> M_1 = hAPP_nat_nat(suc,zero_zero_nat) & N_1 = zero_zero_nat | M_1 = zero_zero_nat & N_1 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_586_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 582 (all M_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1) = hAPP_nat_nat(suc,zero_zero_nat) <-> M_1 = hAPP_nat_nat(suc,zero_zero_nat) & N_1 = zero_zero_nat | M_1 = zero_zero_nat & N_1 = hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_587_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 583 (all N_32 all M_8 all X_89 hAPP_A832564074le_alt(replic351609551le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_32),M_8)),X_89) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_32),X_89)),hAPP_A832564074le_alt(replic351609551le_alt(M_8),X_89))) # label(fact_588_replicate__add) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 584 (all N_32 all M_8 all X_89 hAPP_nat_list_nat(replicate_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_32),M_8)),X_89) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(replicate_nat(N_32),X_89)),hAPP_nat_list_nat(replicate_nat(M_8),X_89))) # label(fact_589_replicate__add) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 585 (all S_2 all Xs all F ((all X_4 all Y_25 all S_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,S_3),X_4)),Y_25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,S_3),Y_25)),X_4)) -> foldl_nat_nat(F,S_2,rev_nat(Xs)) = foldl_nat_nat(F,S_2,Xs))) # label(fact_590_foldl__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 586 (all F all G all L_2 all K_3 all Aa all Ba (Aa = Ba -> (L_2 = K_3 -> ((all A_74 all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,L_2))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,A_74),X_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(G,A_74),X_4))) -> foldl_nat_nat(F,Aa,L_2) = foldl_nat_nat(G,Ba,K_3))))) # label(fact_591_foldl__cong) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 587 (all F all Xs all P_1 all S_2 (hBOOL(hAPP_nat_bool(P_1,S_2)) -> ((all S_3 all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> (hBOOL(hAPP_nat_bool(P_1,S_3)) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,S_3),X_4)))))) -> hBOOL(hAPP_nat_bool(P_1,foldl_nat_nat(F,S_2,Xs)))))) # label(fact_592_foldl__weak__invariant) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 588 (all Xs linord852754176at_nat(cOMBI_nat,Xs) = foldl_list_nat_nat(cOMBC_1204473209st_nat(linord1850739451at_nat(cOMBI_nat)),nil_nat,Xs)) # label(fact_593_sort__foldl__insort) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 589 (all A_73 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A_73) = A_73) # label(fact_594_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 590 (all A_72 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_72),zero_zero_nat) = A_72) # label(fact_595_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 591 (all Ba all Aa (Ba = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) <-> Aa = zero_zero_nat)) # label(fact_596_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 592 (all M_1 all Ns (foldl_nat_nat(plus_plus_nat,M_1,Ns) = zero_zero_nat <-> M_1 = zero_zero_nat & (all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Ns))) -> X_4 = zero_zero_nat)))) # label(fact_597_sum__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 593 (all Xs hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,linord852754176at_nat(cOMBI_nat,Xs)))) # label(fact_598_sorted__sort) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 594 (all A_71 all B_66 all C_39 all D_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_71),B_66)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_39),D_9)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_71),C_39)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_66),D_9))) # label(fact_599_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 595 (all A_70 all B_65 all C_38 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_70),B_65)),C_38) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_70),C_38)),B_65)) # label(fact_600_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 596 (all A_69 all B_64 all C_37 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_69),B_64)),C_37) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_69),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_64),C_37))) # label(fact_601_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 597 (all A_68 all C_36 all D_8 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_68),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_36),D_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_68),C_36)),D_8)) # label(fact_602_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 598 (all A_67 all C_35 all D_7 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_67),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_35),D_7)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_35),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_67),D_7))) # label(fact_603_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 599 (all A_66 all C_34 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_66),C_34) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_34),A_66)) # label(fact_604_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 600 (all F all X_1 all Xs linord852754176at_nat(F,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),linord852754176at_nat(F,Xs))) # label(fact_605_sort__key__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 601 (all S_2 all Xs all X_1 all F ((all X_4 all Y_25 all S_3 hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,S_3),X_4)),Y_25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,S_3),Y_25)),X_4)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,foldl_nat_nat(F,S_2,Xs)),X_1) = foldl_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,S_2),X_1),Xs))) # label(fact_606_foldl__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 602 (all Nat hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,Nat)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_607_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 603 (all Xs foldl_nat_nat(plus_plus_nat,zero_zero_nat,Xs) = hAPP_nat_nat(foldr_nat_nat(plus_plus_nat,Xs),zero_zero_nat)) # label(fact_608_foldl__foldr1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 604 (all Aa all Xs foldl_nat_nat(plus_plus_nat,Aa,Xs) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),hAPP_nat_nat(foldr_nat_nat(plus_plus_nat,Xs),zero_zero_nat))) # label(fact_609_foldl__foldr1__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 605 (all F all P_1 all Xs all Q_1 all X_1 (hBOOL(hAPP_nat_bool(Q_1,X_1)) -> ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))) -> ((all X_4 all Y_25 (hBOOL(hAPP_nat_bool(P_1,X_4)) & hBOOL(hAPP_nat_bool(Q_1,Y_25)) -> hBOOL(hAPP_nat_bool(Q_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,Y_25),X_4))))) -> hBOOL(hAPP_nat_bool(Q_1,foldl_nat_nat(F,X_1,Xs))))))) # label(fact_610_foldl__invariant) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 606 (all Xs all Aa hAPP_nat_nat(foldr_nat_nat(plus_plus_nat,Xs),Aa) = foldl_nat_nat(plus_plus_nat,Aa,Xs)) # label(fact_612_foldr__conv__foldl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 607 (all F all Xs all Aa hAPP_nat_nat(foldr_nat_nat(F,Xs),Aa) = foldl_nat_nat(cOMBC_nat_nat_nat(F),Aa,rev_nat(Xs))) # label(fact_613_foldr__foldl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 608 (all F all Aa all Xs foldl_nat_nat(F,Aa,Xs) = hAPP_nat_nat(foldr_nat_nat(cOMBC_nat_nat_nat(F),rev_nat(Xs)),Aa)) # label(fact_614_foldl__foldr) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 609 (all Nat hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,Nat)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_615_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 610 (all Y_2 all Xs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,rev_nat(Xs))) -> (Xs = nil_nat -> hAPP_nat_nat(foldr_nat_nat(ord_max_nat,Xs),Y_2) = Y_2) & (Xs != nil_nat -> hAPP_nat_nat(foldr_nat_nat(ord_max_nat,Xs),Y_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(nth_nat(Xs),zero_zero_nat)),Y_2)))) # label(fact_616_foldr__max__sorted) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 611 (all N_1 all Ns (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,N_1),hAPP_l1821533378t_bool(set_nat,Ns))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),foldl_nat_nat(plus_plus_nat,zero_zero_nat,Ns))))) # label(fact_617_elem__le__sum) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 612 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_620_le0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 613 (all N hAPP_nat_nat(size_size_nat,N) = N) # label(fact_621_nat__size) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 614 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N))) # label(fact_622_le__refl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 615 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)))) # label(fact_623_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 616 (all M all N (M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_624_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 617 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K))))) # label(fact_625_le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 618 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> M = N))) # label(fact_626_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 619 (all X_88 all Y_62 all Z_26 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_88),Y_62)),Z_26) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_88),Z_26)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_62),Z_26))) # label(fact_627_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 620 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,N),zero_zero_nat) = N) # label(fact_628_max__0R) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 621 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,zero_zero_nat),N) = N) # label(fact_629_max__0L) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 622 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,M),N))) # label(fact_630_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 623 (all Aa all C_2 all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),C_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),C_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_631_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 624 (all C_2 all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)))) # label(fact_632_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 625 (all C_33 all A_65 all B_63 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_65),B_63)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_65),C_33)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_63),C_33))))) # label(fact_633_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 626 (all C_32 all A_64 all B_62 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_64),B_62)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_32),A_64)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_32),B_62))))) # label(fact_634_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 627 (all C_31 all D_6 all A_63 all B_61 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_63),B_61)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_31),D_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_63),C_31)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_61),D_6)))))) # label(fact_635_add__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 628 (all A_62 all C_30 all B_60 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_62),C_30)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_60),C_30))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_62),B_60)))) # label(fact_636_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 629 (all C_29 all A_61 all B_59 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_29),A_61)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_29),B_59))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_61),B_59)))) # label(fact_637_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 630 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N))) # label(fact_638_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 631 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),zero_zero_nat)) <-> N_1 = zero_zero_nat)) # label(fact_639_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 632 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N))) # label(fact_640_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 633 (all M_1 all N_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1)))) # label(fact_641_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 634 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) | M_1 = hAPP_nat_nat(suc,N_1))) # label(fact_642_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 635 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),hAPP_nat_nat(suc,M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)))) # label(fact_643_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 636 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_644_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 637 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,N))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> M = hAPP_nat_nat(suc,N)))) # label(fact_645_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 638 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_646_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 639 (all N all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)))) # label(fact_647_le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 640 (all N all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)))) # label(fact_648_le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 641 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) <-> (exists K_2 N_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2)))) # label(fact_649_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 642 (all K_3 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_650_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 643 (all M all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M))))) # label(fact_651_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 644 (all M all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),J))))) # label(fact_652_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 645 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))))) # label(fact_653_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 646 (all K all L all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L)))))) # label(fact_654_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 647 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)))) # label(fact_655_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 648 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_656_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 649 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)),N)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N))))) # label(fact_657_add__leE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 650 (all N_1 all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(suc,N_1)),M_1) = hAPP_nat_nat(nat_case_nat(hAPP_nat_nat(suc,N_1),cOMBB_nat_nat_nat(suc,hAPP_nat_fun_nat_nat(ord_max_nat,N_1))),M_1)) # label(fact_658_max__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 651 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(nat_case_nat(hAPP_nat_nat(suc,N_1),cOMBB_nat_nat_nat(suc,hAPP_nat_fun_nat_nat(cOMBC_nat_nat_nat(ord_max_nat),N_1))),M_1)) # label(fact_659_max__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 652 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)) <-> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),N_1)))) # label(fact_660_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 653 (all B_58 all A_60 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_60),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_58),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_60),B_58)),zero_zero_nat))))) # label(fact_661_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 654 (all B_57 all A_59 all C_28 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),C_28)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_57),A_59)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_57),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_59),C_28)))))) # label(fact_662_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 655 (all B_56 all C_27 all A_58 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_58)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_56),C_27)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_56),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_58),C_27)))))) # label(fact_663_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 656 (all Y_2 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),Y_2)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_1),Y_2) = zero_zero_nat <-> X_1 = zero_zero_nat & Y_2 = zero_zero_nat)))) # label(fact_664_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 657 (all B_55 all A_57 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_57)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_55)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_57),B_55)))))) # label(fact_665_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 658 (all Zs_1 all X_87 all Y_61 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_87),Y_61)) -> (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_61),Zs_1))) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_87),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_61),Zs_1))))))) # label(fact_666_sorted__many) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 659 (all X_1 all Y_2 all Zs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Zs)))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) & hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Zs))))) # label(fact_667_sorted__many__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 660 (all Ys all F all X_1 all Y_2 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,X_1)),hAPP_nat_nat(F,Y_2))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Ys)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Ys))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,X_1)),hAPP_nat_nat(F,Y_2))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),Ys)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_2),hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),Ys))))) # label(fact_668_insort__key_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 661 (all Y_2 all F all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),hAPP_A2113590458lt_nat(F,X_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),list_s1237850263le_alt(F,Xs)))))) # label(fact_669_list__size__estimation_H) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.95 662 (all Y_2 all F all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),hAPP_nat_nat(F,X_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),list_size_nat(F,Xs)))))) # label(fact_670_list__size__estimation_H) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 663 (all Ns all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),foldl_nat_nat(plus_plus_nat,N_1,Ns))))) # label(fact_672_start__le__sum) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 664 (all X_1 all Xs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs))) <-> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) & (all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),X_4)))))) # label(fact_673_sorted__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 665 (all Xs all Ys (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs),Ys))) <-> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) & hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Ys)) & (all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> (all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),hAPP_l1821533378t_bool(set_nat,Ys))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Xa)))))))) # label(fact_674_sorted__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 666 (all Aa (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Aa)) <-> Aa = nil_nat | (exists Xs_19 exists X_4 (Aa = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_4),Xs_19) & (all Xa (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),hAPP_l1821533378t_bool(set_nat,Xs_19))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Xa)))) & hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_19)))))) # label(fact_675_sorted_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 667 (all F all Aa all Xs ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Aa)),hAPP_nat_nat(F,X_4))))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),Aa),Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Aa),Xs))) # label(fact_676_insort__is__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 668 (all X_1 all Xs ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),X_4)))) -> (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs)))))) # label(fact_677_sorted_OCons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 669 (all N_1 all N_20 all F ((all N_19 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_19)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_19))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_20)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_1)),hAPP_nat_nat(F,N_20)))))) # label(fact_678_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 670 (all N all M_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_7)) -> (exists M_5 M_7 = hAPP_nat_nat(suc,M_5)))) # label(fact_679_Suc__le__D) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 671 (all X_86 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_86),X_86))) # label(fact_680_order__refl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 672 (all Xs all X_1 hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs)),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_1),Xs))))) # label(fact_681_set__subset__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 673 (all Xs all X_1 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_l1821533378t_bool(set_nat,Xs)),hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs))))) # label(fact_682_set__subset__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 674 (all Xs all X_1 hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_l96088310l_bool(set_bool,Xs)),hAPP_l96088310l_bool(set_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))))) # label(fact_683_set__subset__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 675 (all N_1 all Xs hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_1),Xs))),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs)))) # label(fact_684_set__take__subset) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 676 (all N_1 all Xs hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_1),Xs))),hAPP_l1821533378t_bool(set_nat,Xs)))) # label(fact_685_set__take__subset) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 677 (all X_1 all Xs hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(remove430413995le_alt,X_1),Xs))),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs)))) # label(fact_686_set__remove1__subset) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 678 (all X_1 all Xs hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(remove1_nat,X_1),Xs))),hAPP_l1821533378t_bool(set_nat,Xs)))) # label(fact_687_set__remove1__subset) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 679 (all Xs all I_11 hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_l82377208t_bool(set_Ar1565008694le_alt,sublis888024346le_alt(Xs,I_11))),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs)))) # label(fact_688_set__sublist__subset) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 680 (all Xs all I_11 hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_l1821533378t_bool(set_nat,sublist_nat(Xs,I_11))),hAPP_l1821533378t_bool(set_nat,Xs)))) # label(fact_689_set__sublist__subset) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 681 (all X_85 all Y_60 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_85),Y_60)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_60),X_85)))) # label(fact_690_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 682 (all X_1 all Y_2 (X_1 = Y_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)))) # label(fact_691_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 683 (all X_84 all Y_59 (X_84 = Y_59 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_84),Y_59)))) # label(fact_692_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 684 (all Y_2 all X_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_693_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 685 (all C_26 all A_56 all B_54 (A_56 = B_54 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_54),C_26)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_56),C_26))))) # label(fact_694_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 686 (all C_25 all A_55 all B_53 (A_55 = B_53 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_25),B_53)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_25),A_55))))) # label(fact_695_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 687 (all C_24 all A_54 all B_52 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_54),B_52)) -> (B_52 = C_24 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_54),C_24))))) # label(fact_696_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 688 (all C_23 all B_51 all A_53 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_51),A_53)) -> (B_51 = C_23 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_23),A_53))))) # label(fact_697_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 689 (all X_83 all Y_58 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_83),Y_58)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_58),X_83)) -> X_83 = Y_58))) # label(fact_698_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 690 (all Z_25 all X_82 all Y_57 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_82),Y_57)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_57),Z_25)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_82),Z_25))))) # label(fact_699_order__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 691 (all Y_56 all X_81 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_56),X_81)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_81),Y_56)) -> X_81 = Y_56))) # label(fact_700_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 692 (all Z_24 all Y_55 all X_80 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_55),X_80)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_24),Y_55)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_24),X_80))))) # label(fact_701_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 693 (all X_79 all Y_54 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_79),Y_54)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_54),X_79)))) # label(fact_702_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 694 (all Xs all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,M_1),Xs))),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_1),Xs)))))) # label(fact_703_set__take__subset__set__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 695 (all Xs all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,M_1),Xs))),hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_1),Xs)))))) # label(fact_704_set__take__subset__set__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 696 (all Z all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_1),Y_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z),X_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z),Y_2)))) # label(fact_705_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 697 (all X_78 all Least_3 ((all X_4 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Least_3),X_4))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_78),Least_3) = X_78)) # label(fact_706_max__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 698 (all X_77 all Least_2 ((all X_4 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Least_2),X_4))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Least_2),X_77) = X_77)) # label(fact_707_max__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 699 (all Z_3 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_3))))) # label(fact_709_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 700 (all Y all X all Z_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_3))))) # label(fact_710_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 701 (all C_2 all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A),B)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),A)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),B))))) # label(fact_711_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 702 (all C_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B))))) # label(fact_712_subsetD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 703 (all A_52 all B_50 all X_76 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_52),B_50)),X_76)) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_52),X_76)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_50),X_76))))) # label(fact_713_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 704 (all B_49 all D_5 all A_51 all C_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_51),C_22)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_49),D_5)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_51),B_49)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,C_22),D_5)))))) # label(fact_714_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 705 (all X_1 all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A),B)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),B))))) # label(fact_715_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 706 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_716_in__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 707 (all B all X_1 all A (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A),B)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),B))))) # label(fact_717_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 708 (all B all X_1 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_718_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 709 (all X_1 all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A),B)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),A)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),B))))) # label(fact_719_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 710 (all X_1 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))))) # label(fact_720_set__mp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 711 (all A_50 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_50),A_50) = A_50) # label(fact_721_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 712 (all A_49 all B_48 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_49),B_48) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,B_48),A_49)) # label(fact_722_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 713 (all X_75 all Y_53 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_75),Y_53) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_53),X_75)) # label(fact_723_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 714 (all A_48 all B_47 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_48),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_48),B_47)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_48),B_47)) # label(fact_724_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 715 (all X_74 all Y_52 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_74),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_74),Y_52)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_74),Y_52)) # label(fact_725_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 716 (all B_46 all A_47 all C_21 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,B_46),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_47),C_21)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_47),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,B_46),C_21))) # label(fact_726_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 717 (all X_73 all Y_51 all Z_23 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_73),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_51),Z_23)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_51),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_73),Z_23))) # label(fact_727_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 718 (all A_46 all B_45 all C_20 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_46),B_45)),C_20) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_46),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,B_45),C_20))) # label(fact_728_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 719 (all X_72 all Y_50 all Z_22 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_72),Y_50)),Z_22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_72),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_50),Z_22))) # label(fact_729_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 720 (all X_71 all Y_49 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_71),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_71),Y_49)))) # label(fact_730_le__maxI1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 721 (all Y_48 all X_70 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_48),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_70),Y_48)))) # label(fact_731_le__maxI2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 722 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_1),Y_2) = Y_2)) # label(fact_732_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 723 (all X_1 all Y_2 all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_1),Y_2)),Z)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Z)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),Z)))) # label(fact_733_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 724 (all B_44 all X_69 all A_45 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_69),A_45)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_69),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_45),B_44))))) # label(fact_734_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 725 (all A_44 all X_68 all B_43 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_68),B_43)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_68),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_44),B_43))))) # label(fact_735_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 726 (all X_67 all Y_47 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_67),Y_47)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_67),Y_47) = Y_47)) # label(fact_736_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 727 (all Y_46 all X_66 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_46),X_66)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_66),Y_46) = X_66)) # label(fact_737_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 728 (all B_42 all A_43 all X_65 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_43),X_65)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_42),X_65)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_43),B_42)),X_65))))) # label(fact_738_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 729 (all Z_21 all Y_45 all X_64 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_45),X_64)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_21),X_64)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_45),Z_21)),X_64))))) # label(fact_739_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 730 (all B all A ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),A)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),B))))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,A),B)))) # label(fact_740_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 731 (all B all A ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),B)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)))) # label(fact_741_subsetI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 732 (all F ((all I_4 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,I_4))),hAPP_nat_nat(F,I_4)))) -> (exists I_4 all K_2 hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_4),K_2)) = hAPP_nat_nat(F,I_4)))) # label(fact_742_weak__decr__stable) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 733 (all X_1 all Xs big_linorder_Max_nat(hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs))) = foldl_nat_nat(ord_max_nat,X_1,Xs)) # label(fact_743_Max__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 734 (all Q_1 all P_1 ((all X_4 (hBOOL(hAPP_nat_bool(P_1,X_4)) -> hBOOL(hAPP_nat_bool(Q_1,X_4)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,collect_nat(P_1)),collect_nat(Q_1))))) # label(fact_744_Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 735 (all R_1 all S_1 (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_f2014742713t_bool(cOMBC_1745481870l_bool(member1071917752le_alt),R_1)),hAPP_f2014742713t_bool(cOMBC_1745481870l_bool(member1071917752le_alt),S_1))) <-> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,R_1),S_1)))) # label(fact_745_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 736 (all R_1 all S_1 (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),R_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),S_1))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)))) # label(fact_746_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 737 (all X_1 all Xs big_Sup_fin_nat(ord_max_nat,hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_1),Xs))) = foldl_nat_nat(ord_max_nat,X_1,Xs)) # label(fact_747_min__max_OSup__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 738 (all C_2 all Aa all F all Ba (Aa = hAPP_nat_nat(F,Ba) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_2),Ba)) -> ((all X_4 all Y_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_25),X_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Y_25)),hAPP_nat_nat(F,X_4))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,C_2)),Aa)))))) # label(fact_748_xt1_I15_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 739 (all F all C_2 all Ba all Aa (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa)) -> (hAPP_nat_nat(F,Ba) = C_2 -> ((all X_4 all Y_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_25),X_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Y_25)),hAPP_nat_nat(F,X_4))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_2),hAPP_nat_nat(F,Aa))))))) # label(fact_749_xt1_I16_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 740 (all N_1 all P_1 ((all N_19 ((all M_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_5)),N_19)) -> hBOOL(hAPP_nat_bool(P_1,M_5)))) -> hBOOL(hAPP_nat_bool(P_1,N_19)))) -> hBOOL(hAPP_nat_bool(P_1,N_1)))) # label(fact_750_full__nat__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 741 (all Aa all List_1 hAPP_list_bool_nat(size_size_list_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Aa),List_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_list_bool_nat(size_size_list_bool,List_1)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_752_list_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 742 (all A_42 all List hAPP_list_nat_nat(size_size_list_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,A_42),List)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_list_nat_nat(size_size_list_nat,List)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_753_list_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 743 (all A_42 all List hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,A_42),List)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,List)),hAPP_nat_nat(suc,zero_zero_nat))) # label(fact_754_list_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 744 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1))) # label(fact_755_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 745 (all M_1 all N_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M_1),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBB_nat_nat_nat(suc,hAPP_nat_fun_nat_nat(cOMBC_nat_nat_nat(ord_min_nat),N_1))),M_1)) # label(fact_756_min__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 746 (all X_63 all A_41 all B_41 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_63),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_41),B_41))) -> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_63),A_41)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_63),B_41))))) # label(fact_757_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 747 (all B_40 all D_4 all A_40 all C_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_40),C_19)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_40),D_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_40),B_40)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,C_19),D_4)))))) # label(fact_758_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 748 (all Z_20 all X_62 all Y_44 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_62),Y_44)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_62),Z_20)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_62),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_44),Z_20)))))) # label(fact_759_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 749 (all B_39 all X_61 all A_39 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_61),A_39)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_61),B_39)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_61),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_39),B_39)))))) # label(fact_760_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 750 (all Y_43 all X_60 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_43),X_60)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_60),Y_43) = Y_43)) # label(fact_761_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 751 (all X_59 all Y_42 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_59),Y_42)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_59),Y_42) = X_59)) # label(fact_762_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 752 (all A_38 all B_38 all X_58 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_38),X_58)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_38),B_38)),X_58)))) # label(fact_763_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 753 (all B_37 all A_37 all X_57 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_37),X_57)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_37),B_37)),X_57)))) # label(fact_764_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 754 (all X_1 all Y_2 all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_2),Z))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Z)))) # label(fact_765_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 755 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_1),Y_2) = X_1)) # label(fact_766_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 756 (all X_56 all Y_41 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_56),Y_41)),Y_41))) # label(fact_767_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 757 (all X_55 all Y_40 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_55),Y_40)),X_55))) # label(fact_768_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 758 (all A_36 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_36),A_36) = A_36) # label(fact_769_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 759 (all A_35 all B_36 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_35),B_36) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,B_36),A_35)) # label(fact_770_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 760 (all X_54 all Y_39 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_54),Y_39) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_39),X_54)) # label(fact_771_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 761 (all A_34 all B_35 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_34),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_34),B_35)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_34),B_35)) # label(fact_772_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 762 (all X_53 all Y_38 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_53),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_53),Y_38)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_53),Y_38)) # label(fact_773_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 763 (all B_34 all A_33 all C_18 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,B_34),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_33),C_18)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_33),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,B_34),C_18))) # label(fact_774_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 764 (all X_52 all Y_37 all Z_19 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_52),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_37),Z_19)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_37),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_52),Z_19))) # label(fact_775_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 765 (all A_32 all B_33 all C_17 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_32),B_33)),C_17) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_32),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,B_33),C_17))) # label(fact_776_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 766 (all X_51 all Y_36 all Z_18 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_51),Y_36)),Z_18) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_51),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_36),Z_18))) # label(fact_777_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 767 (all X_50 all Y_35 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_50),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_50),Y_35)) = X_50) # label(fact_778_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 768 (all X_49 all Y_34 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_49),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_49),Y_34)) = X_49) # label(fact_779_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 769 (all X_48 all Y_33 all Z_17 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_48),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_33),Z_17)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_48),Y_33)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_48),Z_17))) # label(fact_780_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 770 (all X_47 all Y_32 all Z_16 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_47),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_32),Z_16)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_47),Y_32)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_47),Z_16))) # label(fact_781_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 771 (all Y_31 all Z_15 all X_46 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_31),Z_15)),X_46) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_31),X_46)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Z_15),X_46))) # label(fact_782_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 772 (all Y_30 all Z_14 all X_45 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_30),Z_14)),X_45) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_30),X_45)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Z_14),X_45))) # label(fact_783_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 773 (all Xs_41 hAPP_list_nat_nat(size_size_list_nat,rev_nat(Xs_41)) = hAPP_list_nat_nat(size_size_list_nat,Xs_41)) # label(fact_784_length__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 774 (all Xs_41 hAPP_l1872264749lt_nat(size_s1873794948le_alt,rev_Ar2093961333le_alt(Xs_41)) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_41)) # label(fact_785_length__rev) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 775 (all N_31 all Xs_40 all Ys_13 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_31),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_40),Ys_13)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_31),Xs_40)),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_31),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_40))),Ys_13))) # label(fact_786_take__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 776 (all N_31 all Xs_40 all Ys_13 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_31),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_40),Ys_13)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_31),Xs_40)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_31),hAPP_list_nat_nat(size_size_list_nat,Xs_40))),Ys_13))) # label(fact_787_take__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 777 (all X_44 all Y_29 all Z_13 hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_44),Y_29)),Z_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X_44),Z_13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y_29),Z_13))) # label(fact_788_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 778 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,zero_zero_nat),N) = zero_zero_nat) # label(fact_789_min__0L) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 779 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N),zero_zero_nat) = zero_zero_nat) # label(fact_790_min__0R) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 780 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M),N))) # label(fact_791_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 781 (all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N) = zero_zero_nat) # label(fact_792_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 782 (all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),zero_zero_nat) = M) # label(fact_793_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 783 (all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),M) = zero_zero_nat) # label(fact_794_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 784 (all M all N (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N) = zero_zero_nat -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M) = zero_zero_nat -> M = N))) # label(fact_795_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 785 (all M all N all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M)),N)),hAPP_nat_nat(suc,K)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)),K)) # label(fact_796_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 786 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) # label(fact_797_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 787 (all M all K all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) # label(fact_798_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 788 (all K all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) # label(fact_799_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 789 (all I all J all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))) # label(fact_800_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 790 (all N all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)),N) = M) # label(fact_801_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 791 (all M all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),N)),N) = M) # label(fact_802_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 792 (all I all J all K hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),J)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),K)),J)) # label(fact_803_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 793 (all M all I all N hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),I)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),I)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,M),N)),I)) # label(fact_804_min__diff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 794 (all X_43 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_43),X_43) = X_43) # label(fact_805_Min_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 795 (all N_30 all Xs_39 hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_30),Xs_39)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_39)),N_30)) # label(fact_806_length__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 796 (all N_30 all Xs_39 hAPP_list_nat_nat(size_size_list_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_30),Xs_39)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_39)),N_30)) # label(fact_807_length__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 797 (all Xs_38 all Ys_12 (hAPP_list_nat_nat(size_size_list_nat,Xs_38) != hAPP_list_nat_nat(size_size_list_nat,Ys_12) -> Xs_38 != Ys_12)) # label(fact_808_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 798 (all N_29 all M_6 all Xs_37 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_29),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,M_6),Xs_37)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N_29),M_6)),Xs_37)) # label(fact_809_take__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 799 (all N_29 all M_6 all Xs_37 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_29),hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,M_6),Xs_37)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,N_29),M_6)),Xs_37)) # label(fact_810_take__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 800 (all M all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)),M))) # label(fact_811_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 801 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),M))))) # label(fact_812_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.96 802 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),L)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),L))))) # label(fact_813_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 803 (all I all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),I)) = I)) # label(fact_814_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 804 (all N_1 all K_3 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),N_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_3) <-> M_1 = N_1)))) # label(fact_815_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 805 (all N all K all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)))) # label(fact_816_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 806 (all N_1 all K_3 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_3))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))))) # label(fact_817_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 807 (all X_1 all Y_2 all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_1),Y_2)),Z)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Z)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),Z)))) # label(fact_819_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 808 (all N_28 all X_42 hAPP_list_nat_nat(size_size_list_nat,hAPP_nat_list_nat(replicate_nat(N_28),X_42)) = N_28) # label(fact_820_length__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 809 (all N_28 all X_42 hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_A832564074le_alt(replic351609551le_alt(N_28),X_42)) = N_28) # label(fact_821_length__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 810 (all Xs_36 hAPP_list_nat_nat(size_size_list_nat,rotate1_nat(Xs_36)) = hAPP_list_nat_nat(size_size_list_nat,Xs_36)) # label(fact_822_length__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 811 (all Xs_36 hAPP_l1872264749lt_nat(size_s1873794948le_alt,rotate1322903650le_alt(Xs_36)) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_36)) # label(fact_823_length__rotate1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 812 (all X_41 all Y_28 all Z_12 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_41),Y_28)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_41),Z_12))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_41),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_28),Z_12))))) # label(fact_824_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 813 (all X_40 all Y_27 all Z_11 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_40),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_27),Z_11))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_40),Y_27)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_40),Z_11))))) # label(fact_825_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 814 (all N all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)) = zero_zero_nat) # label(fact_826_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 815 (all Xs (hAPP_list_nat_nat(size_size_list_nat,Xs) = zero_zero_nat <-> Xs = nil_nat)) # label(fact_829_length__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 816 (all Xs (hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs) = zero_zero_nat <-> Xs = nil_Ar126264853le_alt)) # label(fact_830_length__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 817 (all M_1 all N_1 (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N_1) = zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_831_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 818 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N) = zero_zero_nat)) # label(fact_832_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 819 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)))) # label(fact_833_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 820 (all X_1 all Xs all Ys (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_list_bool_nat(size_size_list_bool,Xs)),hAPP_list_bool_nat(size_size_list_bool,Ys))) -> Xs != hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Ys))) # label(fact_834_impossible__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 821 (all X_39 all Xs_35 all Ys_11 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_35)),hAPP_list_nat_nat(size_size_list_nat,Ys_11))) -> Xs_35 != hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_39),Ys_11))) # label(fact_835_impossible__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 822 (all X_39 all Xs_35 all Ys_11 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_35)),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_11))) -> Xs_35 != hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_39),Ys_11))) # label(fact_836_impossible__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 823 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),J))) # label(fact_837_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 824 (all J_1 all K_3 all I_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_3)),I_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_3))))) # label(fact_838_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 825 (all M all K all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M)),K))))) # label(fact_839_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 826 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) = M)) # label(fact_840_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 827 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J)),K))) # label(fact_841_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 828 (all I_1 all K_3 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),J_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_3))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_3)),J_1))))) # label(fact_842_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 829 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)),N) = M)) # label(fact_843_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 830 (all K_3 all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_1) = K_3 <-> J_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),I_1)))) # label(fact_844_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 831 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)))) # label(fact_845_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 832 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)),I) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I)),K))) # label(fact_846_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 833 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K)),I))) # label(fact_847_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 834 (all Xs_34 all Ys_10 hAPP_l1872264749lt_nat(size_s1873794948le_alt,hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_34),Ys_10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_34)),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_10))) # label(fact_848_length__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 835 (all Xs_34 all Ys_10 hAPP_list_nat_nat(size_size_list_nat,hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_34),Ys_10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_34)),hAPP_list_nat_nat(size_size_list_nat,Ys_10))) # label(fact_849_length__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 836 (all Xs_33 all N_27 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_33)),N_27)) -> hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_27),Xs_33) = Xs_33)) # label(fact_850_take__all) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 837 (all Xs_33 all N_27 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_33)),N_27)) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_27),Xs_33) = Xs_33)) # label(fact_851_take__all) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 838 (all I_10 all K_5 all X_38 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,I_10),hAPP_A832564074le_alt(replic351609551le_alt(K_5),X_38)) = hAPP_A832564074le_alt(replic351609551le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,I_10),K_5)),X_38)) # label(fact_852_take__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 839 (all I_10 all K_5 all X_38 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,I_10),hAPP_nat_list_nat(replicate_nat(K_5),X_38)) = hAPP_nat_list_nat(replicate_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,I_10),K_5)),X_38)) # label(fact_853_take__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 840 (all P_1 all Xs hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_list_nat_nat(size_size_list_nat,takeWhile_nat(P_1,Xs))),hAPP_list_nat_nat(size_size_list_nat,Xs)))) # label(fact_854_length__takeWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 841 (all P_1 all Xs hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,takeWh536362254le_alt(P_1,Xs))),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs)))) # label(fact_855_length__takeWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 842 (all F all X_1 all Xs hAPP_list_nat_nat(size_size_list_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(linord1850739451at_nat(F),X_1),Xs)) = hAPP_nat_nat(suc,hAPP_list_nat_nat(size_size_list_nat,Xs))) # label(fact_856_length__insort) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 843 (all P_1 all Xs hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_list_nat_nat(size_size_list_nat,dropWhile_nat(P_1,Xs))),hAPP_list_nat_nat(size_size_list_nat,Xs)))) # label(fact_857_length__dropWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 844 (all P_1 all Xs hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,dropWh156852662le_alt(P_1,Xs))),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs)))) # label(fact_858_length__dropWhile__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 845 (all N all M hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,N),M)) # label(fact_859_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 846 (all P_1 all Xs takeWh536362254le_alt(P_1,Xs) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_l1872264749lt_nat(size_s1873794948le_alt,takeWh536362254le_alt(P_1,Xs))),Xs)) # label(fact_860_takeWhile__eq__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 847 (all P_1 all Xs takeWhile_nat(P_1,Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_list_nat_nat(size_size_list_nat,takeWhile_nat(P_1,Xs))),Xs)) # label(fact_861_takeWhile__eq__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 848 (all Xs_32 all Ys_9 hAPP_list_nat_nat(size_size_list_nat,splice_nat(Xs_32,Ys_9)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_32)),hAPP_list_nat_nat(size_size_list_nat,Ys_9))) # label(fact_863_length__splice) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 849 (all Xs_32 all Ys_9 hAPP_l1872264749lt_nat(size_s1873794948le_alt,splice360969192le_alt(Xs_32,Ys_9)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_32)),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_9))) # label(fact_864_length__splice) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 850 (all M all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K))),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)))) # label(fact_865_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 851 (all M all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)),hAPP_nat_nat(suc,J)))) # label(fact_866_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 852 (all Xs all X_1 all Ys (hBOOL(hAPP_nat_bool(nth_bool(hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Ys))),hAPP_list_bool_nat(size_size_list_bool,Xs))) <-> hBOOL(X_1))) # label(fact_867_nth__append__length) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 853 (all Xs_31 all X_37 all Ys_8 (is_Arr1861959080le_alt(X_37) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_31),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_37),Ys_8))),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_31)) = X_37)) # label(fact_868_nth__append__length) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 854 (all Xs_31 all X_37 all Ys_8 hAPP_nat_nat(nth_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_31),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_37),Ys_8))),hAPP_list_nat_nat(size_size_list_nat,Xs_31)) = X_37) # label(fact_869_nth__append__length) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 855 (all Xs all Ys all N_1 (hBOOL(hAPP_nat_bool(nth_bool(hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_list_bool_nat(size_size_list_bool,Xs)),N_1))) <-> hBOOL(hAPP_nat_bool(nth_bool(Ys),N_1)))) # label(fact_870_nth__append__length__plus) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 856 (all Xs_30 all Ys_7 all N_26 hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_30),Ys_7)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_30)),N_26)) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Ys_7),N_26)) # label(fact_871_nth__append__length__plus) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 857 (all Xs_30 all Ys_7 all N_26 hAPP_nat_nat(nth_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_30),Ys_7)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_30)),N_26)) = hAPP_nat_nat(nth_nat(Ys_7),N_26)) # label(fact_872_nth__append__length__plus) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 858 (all X_36 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_36),X_36) = X_36) # label(fact_873_Max_Oidem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 859 (all L_2 all L_1 all A sublis888024346le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,L_2),L_1),A) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,sublis888024346le_alt(L_2,A)),sublis888024346le_alt(L_1,collect_nat(hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,hAPP_nat_fun_nat_nat(cOMBC_nat_nat_nat(plus_plus_nat),hAPP_l1872264749lt_nat(size_s1873794948le_alt,L_2)))),A))))) # label(fact_874_sublist__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 860 (all L_2 all L_1 all A sublist_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,L_2),L_1),A) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,sublist_nat(L_2,A)),sublist_nat(L_1,collect_nat(hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,hAPP_nat_fun_nat_nat(cOMBC_nat_nat_nat(plus_plus_nat),hAPP_list_nat_nat(size_size_list_nat,L_2)))),A))))) # label(fact_875_sublist__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 861 (all N_1 all M_1 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(suc,N_1)),M_1) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBB_nat_nat_nat(suc,hAPP_nat_fun_nat_nat(ord_min_nat,N_1))),M_1)) # label(fact_876_min__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 862 (all N_1 all Xs (hAPP_nat_nat(suc,N_1) = hAPP_list_bool_nat(size_size_list_bool,Xs) <-> (exists Y_25 exists Ys_6 (is_bool(Y_25) & Xs = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Ys_6) & hAPP_list_bool_nat(size_size_list_bool,Ys_6) = N_1)))) # label(fact_877_Suc__length__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 863 (all N_1 all Xs (hAPP_nat_nat(suc,N_1) = hAPP_list_nat_nat(size_size_list_nat,Xs) <-> (exists Y_25 exists Ys_6 (Xs = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),Ys_6) & hAPP_list_nat_nat(size_size_list_nat,Ys_6) = N_1)))) # label(fact_878_Suc__length__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 864 (all N_1 all Xs (hAPP_nat_nat(suc,N_1) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs) <-> (exists Y_25 exists Ys_6 (is_Arr1861959080le_alt(Y_25) & Xs = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),Ys_6) & hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_6) = N_1)))) # label(fact_879_Suc__length__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 865 (all Xs all N_1 (hAPP_list_bool_nat(size_size_list_bool,Xs) = hAPP_nat_nat(suc,N_1) <-> (exists Y_25 exists Ys_6 (is_bool(Y_25) & Xs = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_25),Ys_6) & hAPP_list_bool_nat(size_size_list_bool,Ys_6) = N_1)))) # label(fact_880_length__Suc__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 866 (all Xs all N_1 (hAPP_list_nat_nat(size_size_list_nat,Xs) = hAPP_nat_nat(suc,N_1) <-> (exists Y_25 exists Ys_6 (Xs = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_25),Ys_6) & hAPP_list_nat_nat(size_size_list_nat,Ys_6) = N_1)))) # label(fact_881_length__Suc__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 867 (all Xs all N_1 (hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs) = hAPP_nat_nat(suc,N_1) <-> (exists Y_25 exists Ys_6 (is_Arr1861959080le_alt(Y_25) & Xs = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_25),Ys_6) & hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_6) = N_1)))) # label(fact_882_length__Suc__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 868 (all X_35 all Y_26 all Z_10 ((all X_4 all Y_25 all Z_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_25),Z_9)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_4),Y_25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_4),Z_9))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_35),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_26),Z_10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_35),Y_26)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_35),Z_10)))) # label(fact_883_min__max_Odistrib__imp2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 869 (all X_34 all Y_24 all Z_8 ((all X_4 all Y_25 all Z_9 hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,Y_25),Z_9)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_4),Y_25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_4),Z_9))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_34),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Y_24),Z_8)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_34),Y_24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_34),Z_8)))) # label(fact_884_min__max_Odistrib__imp1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 870 (all I_1 all P_1 all K_3 (hBOOL(hAPP_nat_bool(P_1,K_3)) -> ((all N_19 (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,N_19))) -> hBOOL(hAPP_nat_bool(P_1,N_19)))) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K_3),I_1)))))) # label(fact_885_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 871 (all X_33 all Least_1 ((all X_4 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Least_1),X_4))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,Least_1),X_33) = Least_1)) # label(fact_886_min__leastL) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 872 (all B all C_2 all A (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),A)) -> (-hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),B)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),hAPP_f2014742713t_bool(hAPP_f2012267069t_bool(minus_988785290t_bool,A),B)))))) # label(fact_887_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 873 (all B all C_2 all A (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A)) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))))) # label(fact_888_DiffI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 874 (all C_2 all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),hAPP_f2014742713t_bool(hAPP_f2012267069t_bool(minus_988785290t_bool,A),B))) -> -(hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),A)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),B))))) # label(fact_889_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 875 (all C_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> -(hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B))))) # label(fact_890_DiffE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 876 (all A all B hAPP_f2014742713t_bool(hAPP_f2012267069t_bool(minus_988785290t_bool,A),B) = collec1729629178le_alt(cOMBS_1393264256l_bool(cOMBB_803794783le_alt(fconj,hAPP_f2014742713t_bool(cOMBC_1745481870l_bool(member1071917752le_alt),A)),cOMBB_2104979073le_alt(fNot,hAPP_f2014742713t_bool(cOMBC_1745481870l_bool(member1071917752le_alt),B))))) # label(fact_891_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 877 (all A all B hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B))))) # label(fact_892_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 878 (all C_2 all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),hAPP_f2014742713t_bool(hAPP_f2012267069t_bool(minus_988785290t_bool,A),B))) <-> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),A)) & -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),B)))) # label(fact_893_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 879 (all C_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) <-> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A)) & -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B)))) # label(fact_894_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 880 (all C_2 all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),hAPP_f2014742713t_bool(hAPP_f2012267069t_bool(minus_988785290t_bool,A),B))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),A)))) # label(fact_895_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 881 (all C_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A)))) # label(fact_896_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 882 (all C_2 all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),hAPP_f2014742713t_bool(hAPP_f2012267069t_bool(minus_988785290t_bool,A),B))) -> -hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),B)))) # label(fact_897_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 883 (all C_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) -> -hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B)))) # label(fact_898_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 884 (all X_32 all Least ((all X_4 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Least),X_4))) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_32),Least) = Least)) # label(fact_899_min__leastR) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 885 (all I_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,hAPP_nat_nat(suc,I_1)),Xs) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,I_1),Xs)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,hAPP_nat_bool(nth_bool(Xs),I_1)),nil_bool)))) # label(fact_900_take__Suc__conv__app__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 886 (all I_9 all Xs_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_9),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_29))) -> hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(suc,I_9)),Xs_29) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,I_9),Xs_29)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_29),I_9)),nil_Ar126264853le_alt)))) # label(fact_901_take__Suc__conv__app__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 887 (all I_9 all Xs_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_9),hAPP_list_nat_nat(size_size_list_nat,Xs_29))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(suc,I_9)),Xs_29) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,I_9),Xs_29)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,hAPP_nat_nat(nth_nat(Xs_29),I_9)),nil_nat)))) # label(fact_902_take__Suc__conv__app__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 888 (all I_8 all J_4 all Xs_28 (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,rev_nat(Xs_28))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_8),J_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_4),hAPP_list_nat_nat(size_size_list_nat,Xs_28))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(nth_nat(Xs_28),J_4)),hAPP_nat_nat(nth_nat(Xs_28),I_8))))))) # label(fact_903_sorted__rev__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 889 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_904_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 890 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N)))) # label(fact_905_lessI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 891 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))))) # label(fact_906_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 892 (all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N)))) # label(fact_907_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 893 (all N all J all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),N)),K)))) # label(fact_908_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 894 (all L all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L),M)))))) # label(fact_909_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 895 (all Z_7 all Y_23 all X_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_23),X_31)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_7),Y_23)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_7),X_31))))) # label(fact_910_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 896 (all Z_6 all X_30 all Y_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_30),Y_22)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_22),Z_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_30),Z_6))))) # label(fact_911_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 897 (all Z_5 all Y_21 all X_29 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_21),X_29)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),Y_21)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_5),X_29))))) # label(fact_912_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 898 (all Z_4 all X_28 all Y_20 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_28),Y_20)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_20),Z_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_28),Z_4))))) # label(fact_913_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 899 (all B_32 all A_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_32),A_31)) -> (A_31 != B_32 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_32),A_31))))) # label(fact_914_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 900 (all A_30 all B_31 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_30),B_31)) -> (A_30 != B_31 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_30),B_31))))) # label(fact_915_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 901 (all X_27 all Y_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_27),Y_19)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),Y_19)) | X_27 = Y_19)) # label(fact_916_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 902 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_917_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 903 (all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)))) # label(fact_918_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 904 (all X_26 all Y_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_18)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_26),Y_18)))) # label(fact_919_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 905 (all Y_17 all X_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_25)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_17)))) # label(fact_920_leD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 906 (all A_29 all B_30 (A_29 != B_30 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_30),A_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_30),A_29))))) # label(fact_921_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 907 (all A_28 all B_29 (A_28 != B_29 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_28),B_29)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_28),B_29))))) # label(fact_922_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 908 (all X_1 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_923_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 909 (all Y_16 all X_24 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),X_24)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_16)))) # label(fact_924_not__leE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 910 (all X_23 all Y_15 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_15)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),X_23)))) # label(fact_925_leI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 911 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) | X_1 = Y_2)) # label(fact_926_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 912 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) & -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)))) # label(fact_927_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 913 (all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) & X_1 != Y_2)) # label(fact_928_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 914 (all X_22 all Y_14 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_22),Y_14)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_14),X_22)))) # label(fact_929_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 915 (all X_1 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)))) # label(fact_930_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 916 (all X_1 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_1)))) # label(fact_931_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 917 (all Y all X all Z_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_3))))) # label(fact_932_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 918 (all Z_3 all X all Y (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z_3))))) # label(fact_933_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 919 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_934_not__less0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 920 (all N_1 (N_1 != zero_zero_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_935_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 921 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat))) # label(fact_936_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 922 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> N != zero_zero_nat)) # label(fact_937_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 923 (all N (N != zero_zero_nat -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)))) # label(fact_938_gr0I) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 924 (all M_1 all N_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_1))))) # label(fact_939_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 925 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) | M_1 = N_1)) # label(fact_940_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 926 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_941_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 927 (all N_1 all M_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_1))) <-> N_1 = M_1))) # label(fact_942_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 928 (all N all M (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M))) -> M = N))) # label(fact_943_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 929 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_944_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 930 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (hAPP_nat_nat(suc,M) != N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N))))) # label(fact_945_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 931 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K))))) # label(fact_946_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 932 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> M = N))) # label(fact_947_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 933 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_948_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 934 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,N))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_949_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 935 (all I all J -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J)),I))) # label(fact_950_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 936 (all J all I -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I)),I))) # label(fact_951_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 937 (all K_3 all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_3),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_952_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 938 (all M all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M))))) # label(fact_953_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 939 (all M all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),J))))) # label(fact_954_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 940 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))))) # label(fact_955_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 941 (all K all L all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L)))))) # label(fact_956_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 942 (all M all N all K all L (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K),L)) -> (hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),L) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),N) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_957_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 943 (all I all J all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J)),K)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)))) # label(fact_958_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 944 (all Z all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_1),Y_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z),X_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z),Y_2)))) # label(fact_959_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 945 (all X_1 all Y_2 all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,X_1),Y_2)),Z)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Z)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),Z)))) # label(fact_960_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 946 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) & M_1 != N_1)) # label(fact_961_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 947 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) | M_1 = N_1)) # label(fact_962_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 948 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_963_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 949 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> (M != N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))))) # label(fact_964_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 950 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) | M = N -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)))) # label(fact_965_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 951 (all P_1 all M_1 all N_1 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_1),M_1))) -> ((M_1 = N_1 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_1),M_1))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_1),M_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,N_1),M_1)))))) # label(fact_966_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 952 (all S all T (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) -> S != T)) # label(fact_967_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 953 (all N all M (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) -> M != N)) # label(fact_968_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 954 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_969_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 955 (all X all Y (X != Y -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X))))) # label(fact_970_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 956 (all M_1 all N_1 (M_1 != N_1 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)))) # label(fact_971_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 957 (all N -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N))) # label(fact_972_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 958 (all Aa all C_2 all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),C_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),C_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_973_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 959 (all C_2 all Aa all Ba (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),Ba))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)))) # label(fact_974_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 960 (all C_16 all A_27 all B_28 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_27),B_28)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_27),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_28),C_16))))) # label(fact_975_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 961 (all C_15 all A_26 all B_27 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_26),B_27)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_15),A_26)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_15),B_27))))) # label(fact_976_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 962 (all C_14 all D_3 all A_25 all B_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_25),B_26)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_14),D_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_25),C_14)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_26),D_3)))))) # label(fact_977_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 963 (all A_24 all C_13 all B_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_24),C_13)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_25),C_13))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_24),B_25)))) # label(fact_978_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 964 (all C_12 all A_23 all B_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_12),A_23)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_12),B_24))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_23),B_24)))) # label(fact_979_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 965 (all X_21 all Y_13 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),Y_13)) -> (X_21 != Y_13 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_13),X_21))))) # label(fact_980_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.97 966 (all X_20 all Y_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_20),Y_12)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_20)))) # label(fact_981_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 967 (all Z_2 all Y_11 all X_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_11),X_19)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),Y_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_19))))) # label(fact_982_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 968 (all Z_1 all X_18 all Y_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_18),Y_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_10),Z_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_18),Z_1))))) # label(fact_983_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 969 (all C_11 all B_23 all A_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_23),A_22)) -> (B_23 = C_11 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_11),A_22))))) # label(fact_984_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 970 (all C_10 all A_21 all B_22 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_21),B_22)) -> (B_22 = C_10 -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_21),C_10))))) # label(fact_985_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 971 (all C_9 all A_20 all B_21 (A_20 = B_21 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_9),B_21)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_9),A_20))))) # label(fact_986_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 972 (all C_8 all A_19 all B_20 (A_19 = B_20 -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_20),C_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_19),C_8))))) # label(fact_987_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 973 (all B_19 all A_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_18)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),B_19)))) # label(fact_988_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 974 (all A_17 all B_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_17),B_18)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_18),A_17)))) # label(fact_989_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 975 (all P_1 all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)) -> hBOOL(P_1)))) # label(fact_990_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 976 (all X_17 all Y_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_17),Y_9)) -> Y_9 != X_17)) # label(fact_991_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 977 (all X_16 all Y_8 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_16),Y_8)) -> X_16 != Y_8)) # label(fact_992_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 978 (all X_15 all Y_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_15),Y_7)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_7),X_15)))) # label(fact_993_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 979 (all X_14 all Y_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_14),Y_6)) -> -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_6),X_14)))) # label(fact_994_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 980 (all X_13 all Y_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_5)) -> X_13 != Y_5)) # label(fact_995_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 981 (all X_12 all Y_4 (X_12 != Y_4 -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_12),Y_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),X_12))))) # label(fact_996_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 982 (all Y_2 all X_1 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)) -> (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> X_1 = Y_2))) # label(fact_997_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 983 (all X_11 all Y_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_3)) | X_11 = Y_3 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_11)))) # label(fact_998_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 984 (all X_1 all Y_2 (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)) | X_1 = Y_2)) # label(fact_999_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 985 (all X_1 all Y_2 (X_1 != Y_2 <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_2)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_1)))) # label(fact_1000_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 986 (all X_10 -hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),X_10))) # label(fact_1001_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 987 (all A_16 all X_9 all B_17 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),B_17)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_16),B_17))))) # label(fact_1002_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 988 (all B_16 all X_8 all A_15 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),A_15)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_max_nat,A_15),B_16))))) # label(fact_1003_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 989 (all X_1 all Y_2 all Z (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_1),Y_2)),Z)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Z)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),Z)))) # label(fact_1004_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 990 (all Z all X_1 all Y_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z),hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,X_1),Y_2))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z),X_1)) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z),Y_2)))) # label(fact_1005_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 991 (all A_14 all B_15 all X_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_15),X_7)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_14),B_15)),X_7)))) # label(fact_1006_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 992 (all B_14 all A_13 all X_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_13),X_6)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(ord_min_nat,A_13),B_14)),X_6)))) # label(fact_1007_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 993 (all C_7 all D_2 all A_12 all B_13 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_12),B_13)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_7),D_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_7)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_13),D_2)))))) # label(fact_1008_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 994 (all C_6 all D_1 all A_11 all B_12 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_11),B_12)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_6),D_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_12),D_1)))))) # label(fact_1009_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 995 (all B_11 all A_10 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_10)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_11)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_10),B_11)))))) # label(fact_1010_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 996 (all B_10 all A_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_9),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_10),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),B_10)),zero_zero_nat))))) # label(fact_1011_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 997 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) <-> (exists M_5 N_1 = hAPP_nat_nat(suc,M_5)))) # label(fact_1012_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 998 (all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,zero_zero_nat))) <-> N_1 = zero_zero_nat)) # label(fact_1013_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 999 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))) <-> M_1 = zero_zero_nat | (exists J_2 (M_1 = hAPP_nat_nat(suc,J_2) & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),N_1)))))) # label(fact_1014_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1000 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1)) | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)))) # label(fact_1015_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1001 (all I all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M))))) # label(fact_1016_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1002 (all I all M hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),I))))) # label(fact_1017_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1003 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) <-> (exists K_2 N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2))))) # label(fact_1018_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1004 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1)))) # label(fact_1019_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1005 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)))) # label(fact_1020_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1006 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N_1)) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_1021_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1007 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,N))))) # label(fact_1022_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1008 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)))) # label(fact_1023_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1009 (all M_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_1))) <-> N_1 = M_1))) # label(fact_1024_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1010 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)))) # label(fact_1025_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1011 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)),M))))) # label(fact_1026_diff__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1012 (all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))) # label(fact_1027_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1013 (all M all N hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)),hAPP_nat_nat(suc,M)))) # label(fact_1028_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1014 (all M all N (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),N)) = M)) # label(fact_1029_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1015 (all I_1 all J_1 all K_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K_3))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_3)),J_1)))) # label(fact_1030_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1016 (all C_5 all A_8 all B_9 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_8),B_9)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_5),A_8)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_8),C_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B_9),C_5)))))) # label(fact_1031_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1017 (all N_1 all K_3 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),M_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),K_3))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)))))) # label(fact_1032_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1018 (all Xs all Ys (Xs = Ys <-> hAPP_list_bool_nat(size_size_list_bool,Xs) = hAPP_list_bool_nat(size_size_list_bool,Ys) & (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> (hBOOL(hAPP_nat_bool(nth_bool(Xs),I_4)) <-> hBOOL(hAPP_nat_bool(nth_bool(Ys),I_4))))))) # label(fact_1033_list__eq__iff__nth__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1019 (all Xs all Ys (Xs = Ys <-> hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys) & (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),I_4) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Ys),I_4))))) # label(fact_1034_list__eq__iff__nth__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1020 (all Xs all Ys (Xs = Ys <-> hAPP_list_nat_nat(size_size_list_nat,Xs) = hAPP_list_nat_nat(size_size_list_nat,Ys) & (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> hAPP_nat_nat(nth_nat(Xs),I_4) = hAPP_nat_nat(nth_nat(Ys),I_4))))) # label(fact_1035_list__eq__iff__nth__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1021 (all Xs all I_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),N_1)) -> (hBOOL(hAPP_nat_bool(nth_bool(hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,N_1),Xs)),I_1)) <-> hBOOL(hAPP_nat_bool(nth_bool(Xs),I_1))))) # label(fact_1036_nth__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1022 (all Xs_27 all I_7 all N_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_7),N_25)) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_25),Xs_27)),I_7) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_27),I_7))) # label(fact_1037_nth__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1023 (all Xs_27 all I_7 all N_25 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_7),N_25)) -> hAPP_nat_nat(nth_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_25),Xs_27)),I_7) = hAPP_nat_nat(nth_nat(Xs_27),I_7))) # label(fact_1038_nth__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1024 (all X_1 all I_1 all N_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),N_1)) -> (hBOOL(hAPP_nat_bool(nth_bool(hAPP_bool_list_bool(replicate_bool(N_1),X_1)),I_1)) <-> hBOOL(X_1)))) # label(fact_1039_nth__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1025 (all X_5 all I_6 all N_24 (is_Arr1861959080le_alt(X_5) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_6),N_24)) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_A832564074le_alt(replic351609551le_alt(N_24),X_5)),I_6) = X_5))) # label(fact_1040_nth__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1026 (all X_5 all I_6 all N_24 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_6),N_24)) -> hAPP_nat_nat(nth_nat(hAPP_nat_list_nat(replicate_nat(N_24),X_5)),I_6) = X_5)) # label(fact_1041_nth__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1027 (all Y_2 all F all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),hAPP_A2113590458lt_nat(F,X_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),list_s1237850263le_alt(F,Xs)))))) # label(fact_1042_list__size__estimation) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1028 (all Y_2 all F all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),hAPP_nat_nat(F,X_1))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),list_size_nat(F,Xs)))))) # label(fact_1043_list__size__estimation) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1029 (all X_4 hAPP_n1699378549t_bool(ord_less_nat,X_4) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_4))) # label(fact_1044_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1030 (all B_8 all A_7 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_8),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),B_8)),zero_zero_nat))))) # label(fact_1045_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1031 (all B_7 all A_6 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_7),zero_zero_nat)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),B_7)),zero_zero_nat))))) # label(fact_1046_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1032 (all B_6 all C_4 all A_5 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_5)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_6),C_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_6),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_5),C_4)))))) # label(fact_1047_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1033 (all B_5 all C_3 all A_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_4)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_5),C_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_4),C_3)))))) # label(fact_1048_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1034 (all B_4 all A_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),A_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),B_4)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_3),B_4)))))) # label(fact_1049_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1035 (all B_3 all A_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),B_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),B_3)))))) # label(fact_1050_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1036 (all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_list_nat_nat(size_size_list_nat,Xs))) <-> Xs != nil_nat)) # label(fact_1051_length__greater__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1037 (all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) <-> Xs != nil_Ar126264853le_alt)) # label(fact_1052_length__greater__0__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1038 (all X_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))))) # label(fact_1053_length__pos__if__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1039 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_list_nat_nat(size_size_list_nat,Xs))))) # label(fact_1054_length__pos__if__in__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1040 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat))) = N)) # label(fact_1055_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1041 (all I all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,I))),N)))) # label(fact_1056_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1042 (all P_1 all Aa all Ba (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Aa),Ba))) <-> -(hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) & -hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) | (exists D (Aa = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),D) & -hBOOL(hAPP_nat_bool(P_1,D))))))) # label(fact_1057_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1043 (all P_1 all Aa all Ba (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Aa),Ba))) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) -> hBOOL(hAPP_nat_bool(P_1,zero_zero_nat))) & (all D (Aa = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),D) -> hBOOL(hAPP_nat_bool(P_1,D)))))) # label(fact_1058_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1044 (all X_1 all Xs (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) <-> (exists I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_bool_nat(size_size_list_bool,Xs))) & (hBOOL(hAPP_nat_bool(nth_bool(Xs),I_4)) <-> hBOOL(X_1)))))) # label(fact_1059_in__set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1045 (all X_1 all Xs (is_Arr1861959080le_alt(X_1) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) <-> (exists I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) & hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),I_4) = X_1))))) # label(fact_1060_in__set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1046 (all X_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) <-> (exists I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_nat_nat(size_size_list_nat,Xs))) & hAPP_nat_nat(nth_nat(Xs),I_4) = X_1)))) # label(fact_1061_in__set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1047 (all P_1 all Xs ((all X_4 (is_bool(X_4) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) -> hBOOL(hAPP_bool_bool(P_1,X_4))))) <-> (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hBOOL(hAPP_bool_bool(P_1,hAPP_nat_bool(nth_bool(Xs),I_4))))))) # label(fact_1062_all__set__conv__all__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1048 (all P_1 all Xs ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_4))))) <-> (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),I_4))))))) # label(fact_1063_all__set__conv__all__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1049 (all P_1 all Xs ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))) <-> (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs),I_4))))))) # label(fact_1064_all__set__conv__all__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1050 (all N_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(nth_bool(Xs),N_1)),hAPP_l96088310l_bool(set_bool,Xs))))) # label(fact_1065_nth__mem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1051 (all N_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),N_1)),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))) # label(fact_1066_nth__mem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1052 (all N_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(nth_nat(Xs),N_1)),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_1067_nth__mem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1053 (all Xs (hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)) <-> (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> (all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> (I_4 != J_2 -> -(hBOOL(hAPP_nat_bool(nth_bool(Xs),I_4)) <-> hBOOL(hAPP_nat_bool(nth_bool(Xs),J_2)))))))))) # label(fact_1068_distinct__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1054 (all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) <-> (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> (all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> (I_4 != J_2 -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),I_4) != hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),J_2)))))))) # label(fact_1069_distinct__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1055 (all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) <-> (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> (all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> (I_4 != J_2 -> hAPP_nat_nat(nth_nat(Xs),I_4) != hAPP_nat_nat(nth_nat(Xs),J_2)))))))) # label(fact_1070_distinct__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1056 (all J_1 all I_1 all Xs (hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> ((hBOOL(hAPP_nat_bool(nth_bool(Xs),I_1)) <-> hBOOL(hAPP_nat_bool(nth_bool(Xs),J_1))) <-> I_1 = J_1))))) # label(fact_1071_nth__eq__iff__index__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1057 (all J_1 all I_1 all Xs (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> (hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),I_1) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),J_1) <-> I_1 = J_1))))) # label(fact_1072_nth__eq__iff__index__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1058 (all J_1 all I_1 all Xs (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> (hAPP_nat_nat(nth_nat(Xs),I_1) = hAPP_nat_nat(nth_nat(Xs),J_1) <-> I_1 = J_1))))) # label(fact_1073_nth__eq__iff__index__eq) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1059 (all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_list_bool_nat(size_size_list_bool,takeWhile_bool(P_1,Xs))),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> -hBOOL(hAPP_bool_bool(P_1,hAPP_nat_bool(nth_bool(Xs),hAPP_list_bool_nat(size_size_list_bool,takeWhile_bool(P_1,Xs))))))) # label(fact_1074_nth__length__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1060 (all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,takeWh536362254le_alt(P_1,Xs))),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> -hBOOL(hAPP_A862370221t_bool(P_1,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),hAPP_l1872264749lt_nat(size_s1873794948le_alt,takeWh536362254le_alt(P_1,Xs))))))) # label(fact_1075_nth__length__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1061 (all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_list_nat_nat(size_size_list_nat,takeWhile_nat(P_1,Xs))),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> -hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs),hAPP_list_nat_nat(size_size_list_nat,takeWhile_nat(P_1,Xs))))))) # label(fact_1076_nth__length__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1062 (all J_1 all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_list_bool_nat(size_size_list_bool,takeWhile_bool(P_1,Xs)))) -> (hBOOL(hAPP_nat_bool(nth_bool(takeWhile_bool(P_1,Xs)),J_1)) <-> hBOOL(hAPP_nat_bool(nth_bool(Xs),J_1))))) # label(fact_1077_takeWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1063 (all J_1 all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,takeWh536362254le_alt(P_1,Xs)))) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(takeWh536362254le_alt(P_1,Xs)),J_1) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),J_1))) # label(fact_1078_takeWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1064 (all J_1 all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_list_nat_nat(size_size_list_nat,takeWhile_nat(P_1,Xs)))) -> hAPP_nat_nat(nth_nat(takeWhile_nat(P_1,Xs)),J_1) = hAPP_nat_nat(nth_nat(Xs),J_1))) # label(fact_1079_takeWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1065 (all N_23 all Xs_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_23),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_26))) -> hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_23),butlas1262502241le_alt(Xs_26)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_23),Xs_26))) # label(fact_1080_take__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1066 (all N_23 all Xs_26 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_23),hAPP_list_nat_nat(size_size_list_nat,Xs_26))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_23),butlast_nat(Xs_26)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_23),Xs_26))) # label(fact_1081_take__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1067 (all P_1 all Xs (hBOOL(hAPP_list_bool_bool(list_all_bool(P_1),Xs)) <-> (all N_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_19),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hBOOL(hAPP_bool_bool(P_1,hAPP_nat_bool(nth_bool(Xs),N_19))))))) # label(fact_1082_list__all__length) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1068 (all P_1 all Xs (hBOOL(hAPP_l1386638586t_bool(list_a1557668565le_alt(P_1),Xs)) <-> (all N_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_19),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),N_19))))))) # label(fact_1083_list__all__length) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1069 (all P_1 all Xs (hBOOL(hAPP_list_nat_bool(list_all_nat(P_1),Xs)) <-> (all N_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_19),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs),N_19))))))) # label(fact_1084_list__all__length) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1070 (all Xs all Ys all N_1 (hBOOL(hAPP_nat_bool(nth_bool(hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys)),N_1)) <-> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hBOOL(hAPP_nat_bool(nth_bool(Xs),N_1))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hBOOL(hAPP_nat_bool(nth_bool(Ys),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_1),hAPP_list_bool_nat(size_size_list_bool,Xs))))))) # label(fact_1085_nth__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1071 (all Ys_5 all N_22 all Xs_25 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_22),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_25))) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_25),Ys_5)),N_22) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_25),N_22)) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_22),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_25))) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_25),Ys_5)),N_22) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Ys_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_22),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_25)))))) # label(fact_1086_nth__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1072 (all Ys_5 all N_22 all Xs_25 ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_22),hAPP_list_nat_nat(size_size_list_nat,Xs_25))) -> hAPP_nat_nat(nth_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_25),Ys_5)),N_22) = hAPP_nat_nat(nth_nat(Xs_25),N_22)) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_22),hAPP_list_nat_nat(size_size_list_nat,Xs_25))) -> hAPP_nat_nat(nth_nat(hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_25),Ys_5)),N_22) = hAPP_nat_nat(nth_nat(Ys_5),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_22),hAPP_list_nat_nat(size_size_list_nat,Xs_25)))))) # label(fact_1087_nth__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1073 (all I_5 all J_3 all Xs_24 (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_24)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_5),J_3)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_3),hAPP_list_nat_nat(size_size_list_nat,Xs_24))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(nth_nat(Xs_24),I_5)),hAPP_nat_nat(nth_nat(Xs_24),J_3))))))) # label(fact_1088_sorted__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1074 (all Xs (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs)) <-> (all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_4),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(nth_nat(Xs),I_4)),hAPP_nat_nat(nth_nat(Xs),J_2))))))))) # label(fact_1089_sorted__equals__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1075 (all N_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> (hBOOL(hAPP_nat_bool(nth_bool(rev_bool(Xs)),N_1)) <-> hBOOL(hAPP_nat_bool(nth_bool(Xs),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_list_bool_nat(size_size_list_bool,Xs)),hAPP_nat_nat(suc,N_1))))))) # label(fact_1090_rev__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1076 (all N_21 all Xs_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_21),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_23))) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(rev_Ar2093961333le_alt(Xs_23)),N_21) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_23)),hAPP_nat_nat(suc,N_21))))) # label(fact_1091_rev__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1077 (all N_21 all Xs_23 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_21),hAPP_list_nat_nat(size_size_list_nat,Xs_23))) -> hAPP_nat_nat(nth_nat(rev_nat(Xs_23)),N_21) = hAPP_nat_nat(nth_nat(Xs_23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_23)),hAPP_nat_nat(suc,N_21))))) # label(fact_1092_rev__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1078 (all J_1 all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_list_bool_nat(size_size_list_bool,dropWhile_bool(P_1,Xs)))) -> (hBOOL(hAPP_nat_bool(nth_bool(dropWhile_bool(P_1,Xs)),J_1)) <-> hBOOL(hAPP_nat_bool(nth_bool(Xs),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),hAPP_list_bool_nat(size_size_list_bool,takeWhile_bool(P_1,Xs)))))))) # label(fact_1093_dropWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1079 (all J_1 all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,dropWh156852662le_alt(P_1,Xs)))) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(dropWh156852662le_alt(P_1,Xs)),J_1) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,takeWh536362254le_alt(P_1,Xs)))))) # label(fact_1094_dropWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1080 (all J_1 all P_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),hAPP_list_nat_nat(size_size_list_nat,dropWhile_nat(P_1,Xs)))) -> hAPP_nat_nat(nth_nat(dropWhile_nat(P_1,Xs)),J_1) = hAPP_nat_nat(nth_nat(Xs),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),hAPP_list_nat_nat(size_size_list_nat,takeWhile_nat(P_1,Xs)))))) # label(fact_1095_dropWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1081 (all Xs_22 ((all I_4 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_4),J_2)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),hAPP_list_nat_nat(size_size_list_nat,Xs_22))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(nth_nat(Xs_22),I_4)),hAPP_nat_nat(nth_nat(Xs_22),J_2)))))) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_22)))) # label(fact_1096_sorted__nth__monoI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1082 (all P_1 all Xs all N_1 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hBOOL(hAPP_bool_bool(P_1,hAPP_nat_bool(nth_bool(Xs),I_4)))))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> -hBOOL(hAPP_bool_bool(P_1,hAPP_nat_bool(nth_bool(Xs),N_1)))) -> takeWhile_bool(P_1,Xs) = hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,N_1),Xs)))) # label(fact_1097_takeWhile__eq__take__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1083 (all P_1 all Xs all N_1 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),I_4)))))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> -hBOOL(hAPP_A862370221t_bool(P_1,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),N_1)))) -> takeWh536362254le_alt(P_1,Xs) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_1),Xs)))) # label(fact_1098_takeWhile__eq__take__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1084 (all P_1 all Xs all N_1 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),N_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs),I_4)))))) -> ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> -hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs),N_1)))) -> takeWhile_nat(P_1,Xs) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_1),Xs)))) # label(fact_1099_takeWhile__eq__take__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1085 (all P_1 all Xs all J_1 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),J_1)) -> hBOOL(hAPP_bool_bool(P_1,hAPP_nat_bool(nth_bool(Xs),I_4))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_list_bool_nat(size_size_list_bool,takeWhile_bool(P_1,Xs))))))) # label(fact_1100_length__takeWhile__less__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1086 (all P_1 all Xs all J_1 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),J_1)) -> hBOOL(hAPP_A862370221t_bool(P_1,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),I_4))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,takeWh536362254le_alt(P_1,Xs))))))) # label(fact_1101_length__takeWhile__less__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1087 (all P_1 all Xs all J_1 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),J_1)) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs),I_4))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_list_nat_nat(size_size_list_nat,takeWhile_nat(P_1,Xs))))))) # label(fact_1102_length__takeWhile__less__P__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1088 (all Ys all K_3 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_3),hAPP_list_bool_nat(size_size_list_bool,Ys))) -> ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_3)) -> (hBOOL(hAPP_nat_bool(nth_bool(Xs),I_4)) <-> hBOOL(hAPP_nat_bool(nth_bool(Ys),I_4))))) -> hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,K_3),Xs) = hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,K_3),Ys))))) # label(fact_1103_nth__take__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1089 (all Ys_4 all K_4 all Xs_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_21))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_4))) -> ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_4)) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_21),I_4) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Ys_4),I_4))) -> hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,K_4),Xs_21) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,K_4),Ys_4))))) # label(fact_1104_nth__take__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1090 (all Ys_4 all K_4 all Xs_21 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_4),hAPP_list_nat_nat(size_size_list_nat,Xs_21))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_4),hAPP_list_nat_nat(size_size_list_nat,Ys_4))) -> ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_4)) -> hAPP_nat_nat(nth_nat(Xs_21),I_4) = hAPP_nat_nat(nth_nat(Ys_4),I_4))) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,K_4),Xs_21) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,K_4),Ys_4))))) # label(fact_1105_nth__take__lemma) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1091 (all F all G all Xs ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A2113590458lt_nat(F,X_4)),hAPP_A2113590458lt_nat(G,X_4)))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,list_s1237850263le_alt(F,Xs)),list_s1237850263le_alt(G,Xs))))) # label(fact_1106_list__size__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1092 (all F all G all Xs ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,X_4)),hAPP_nat_nat(G,X_4))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,list_size_nat(F,Xs)),list_size_nat(G,Xs))))) # label(fact_1107_list__size__pointwise) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1093 (all C_2 all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le1384968325t_bool,A),B)) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),A)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,C_2),B))))) # label(fact_1108_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1094 (all C_2 all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B))))) # label(fact_1109_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1095 (all X_1 all P_1 all Xs ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hBOOL(hAPP_bool_bool(P_1,hAPP_nat_bool(nth_bool(Xs),I_4))))) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),hAPP_l96088310l_bool(set_bool,Xs))) -> hBOOL(hAPP_bool_bool(P_1,X_1))))) # label(fact_1110_all__nth__imp__all__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1096 (all X_1 all P_1 all Xs ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),I_4))))) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_1))))) # label(fact_1111_all__nth__imp__all__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1097 (all X_1 all P_1 all Xs ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs),I_4))))) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_1))))) # label(fact_1112_all__nth__imp__all__set) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1098 (all P_1 all N_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> ((all X_4 (is_bool(X_4) -> (hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_4),hAPP_l96088310l_bool(set_bool,Xs))) -> hBOOL(hAPP_bool_bool(P_1,X_4))))) -> hBOOL(hAPP_bool_bool(P_1,hAPP_nat_bool(nth_bool(Xs),N_1)))))) # label(fact_1113_list__ball__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1099 (all P_1 all N_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs))) -> ((all X_4 (is_Arr1861959080le_alt(X_4) -> (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_4),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))) -> hBOOL(hAPP_A862370221t_bool(P_1,X_4))))) -> hBOOL(hAPP_A862370221t_bool(P_1,hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs),N_1)))))) # label(fact_1114_list__ball__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1100 (all P_1 all N_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_nat_nat(size_size_list_nat,Xs))) -> ((all X_4 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_4),hAPP_l1821533378t_bool(set_nat,Xs))) -> hBOOL(hAPP_nat_bool(P_1,X_4)))) -> hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(nth_nat(Xs),N_1)))))) # label(fact_1115_list__ball__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1101 (all Xs all Ys (hAPP_list_bool_nat(size_size_list_bool,Xs) = hAPP_list_bool_nat(size_size_list_bool,Ys) -> ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> (hBOOL(hAPP_nat_bool(nth_bool(Xs),I_4)) <-> hBOOL(hAPP_nat_bool(nth_bool(Ys),I_4))))) -> Xs = Ys))) # label(fact_1116_nth__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1102 (all Xs_20 all Ys_3 (hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_20) = hAPP_l1872264749lt_nat(size_s1873794948le_alt,Ys_3) -> ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_20))) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_20),I_4) = hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Ys_3),I_4))) -> Xs_20 = Ys_3))) # label(fact_1117_nth__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1103 (all Xs_20 all Ys_3 (hAPP_list_nat_nat(size_size_list_nat,Xs_20) = hAPP_list_nat_nat(size_size_list_nat,Ys_3) -> ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),hAPP_list_nat_nat(size_size_list_nat,Xs_20))) -> hAPP_nat_nat(nth_nat(Xs_20),I_4) = hAPP_nat_nat(nth_nat(Ys_3),I_4))) -> Xs_20 = Ys_3))) # label(fact_1118_nth__equalityI) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1104 (all P_1 all K_3 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_3)) -> (exists X1 (is_bool(X1) & hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(P_1,I_4),X1)))))) <-> (exists Xs_19 (hAPP_list_bool_nat(size_size_list_bool,Xs_19) = K_3 & (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_3)) -> hBOOL(hAPP_bool_bool(hAPP_n1006566506l_bool(P_1,I_4),hAPP_nat_bool(nth_bool(Xs_19),I_4))))))))) # label(fact_1119_Skolem__list__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1105 (all P_1 all K_3 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_3)) -> (exists X1 (is_Arr1861959080le_alt(X1) & hBOOL(hAPP_A862370221t_bool(hAPP_n315299280t_bool(P_1,I_4),X1)))))) <-> (exists Xs_19 (hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_19) = K_3 & (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_3)) -> hBOOL(hAPP_A862370221t_bool(hAPP_n315299280t_bool(P_1,I_4),hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_19),I_4))))))))) # label(fact_1120_Skolem__list__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1106 (all P_1 all K_3 ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_3)) -> (exists X1 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,I_4),X1))))) <-> (exists Xs_19 (hAPP_list_nat_nat(size_size_list_nat,Xs_19) = K_3 & (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_3)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(P_1,I_4),hAPP_nat_nat(nth_nat(Xs_19),I_4))))))))) # label(fact_1121_Skolem__list__nth) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1107 (all M_1 all K_3 all F ((all M_5 all N_19 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_5),N_19)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_5)),hAPP_nat_nat(F,N_19))))) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M_1)),K_3)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_3)))))) # label(fact_1122_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1108 (all P_1 all I_1 all J_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> (hBOOL(hAPP_nat_bool(P_1,J_1)) -> ((all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),J_1)) -> (hBOOL(hAPP_nat_bool(P_1,hAPP_nat_nat(suc,I_4))) -> hBOOL(hAPP_nat_bool(P_1,I_4))))) -> hBOOL(hAPP_nat_bool(P_1,I_1)))))) # label(fact_1123_inc__induct) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1109 (all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) -> (exists K_2 N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2))))) # label(fact_1124_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1110 (all N_1 all P_1 (-hBOOL(hAPP_nat_bool(P_1,zero_zero_nat)) -> (hBOOL(hAPP_nat_bool(P_1,N_1)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N_1)) & (all I_4 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),K_2)) -> -hBOOL(hAPP_nat_bool(P_1,I_4)))) & hBOOL(hAPP_nat_bool(P_1,K_2))))))) # label(fact_1125_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1111 (all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> (exists K_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) & hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2) = J)))) # label(fact_1126_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1112 (all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) -> (exists M_5 N = hAPP_nat_nat(suc,M_5)))) # label(fact_1127_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1113 (all N_1 all N_20 all F ((all N_19 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,N_19)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_19))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_20)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,N_1)),hAPP_nat_nat(F,N_20)))))) # label(fact_1128_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1114 (all N_1 all M_1 all F ((all N_19 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,N_19)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_19))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,N_1)),hAPP_nat_nat(F,M_1))) <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1))))) # label(fact_1129_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1115 (all B_2 all C_1 all A_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),A_1)) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_2),C_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),C_1)))))) # label(fact_1130_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1116 (all A all B (hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le1384968325t_bool,A),B)) -> (exists B_1 (is_Arr1861959080le_alt(B_1) & hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,B_1),hAPP_f2014742713t_bool(hAPP_f2012267069t_bool(minus_988785290t_bool,B),A))))))) # label(fact_1131_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1117 (all A all B (hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) -> (exists B_1 hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B),A)))))) # label(fact_1132_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1118 (all I_1 all J_1 all F ((all I_4 all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_4),J_2)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_4)),hAPP_nat_nat(F,J_2))))) -> (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1)) -> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1)))))) # label(fact_1133_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1119 (all N_18 all Xs_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_18),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_18))) -> hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_18),Xs_18)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,hAPP_l1105242632le_alt(hd_Arr805754088le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_18),Xs_18))),nil_Ar126264853le_alt)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(suc,N_18)),Xs_18))) # label(fact_1134_take__hd__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1120 (all N_18 all Xs_18 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_18),hAPP_list_nat_nat(size_size_list_nat,Xs_18))) -> hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_18),Xs_18)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,hAPP_list_nat_nat(hd_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_18),Xs_18))),nil_nat)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(suc,N_18)),Xs_18))) # label(fact_1135_take__hd__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1121 (all N_1 all Xs (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_list_bool_nat(size_size_list_bool,Xs))) -> hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,N_1),Xs)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,hAPP_list_bool_bool(hd_bool,hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,N_1),Xs))),nil_bool)) = hAPP_l1189022293t_bool(hAPP_n479129736t_bool(take_bool,hAPP_nat_nat(suc,N_1)),Xs))) # label(fact_1136_take__hd__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1122 (all N_17 all X_3 all Xs_17 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,hAPP_nat_nat(suc,N_17)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,X_3),Xs_17)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_17),Xs_17)) # label(fact_1137_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1123 (all N_1 all X_1 all Xs hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,hAPP_nat_nat(suc,N_1)),hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)) = hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,N_1),Xs)) # label(fact_1138_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1124 (all N_17 all X_3 all Xs_17 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,hAPP_nat_nat(suc,N_17)),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,X_3),Xs_17)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_17),Xs_17)) # label(fact_1139_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1125 (all N_1 all Xs hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_1),Xs))),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs)))) # label(fact_1140_set__drop__subset) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1126 (all N_1 all Xs hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_1),Xs))),hAPP_l1821533378t_bool(set_nat,Xs)))) # label(fact_1141_set__drop__subset) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1127 (all N_16 all Xs_16 hAPP_list_nat_nat(size_size_list_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_16),Xs_16)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_16)),N_16)) # label(fact_1142_length__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1128 (all N_1 all Xs all Y_2 all Ys (hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,N_1),Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,Y_2),Ys) -> (hBOOL(hAPP_nat_bool(nth_bool(Xs),N_1)) <-> hBOOL(Y_2)))) # label(fact_1143_nth__via__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1129 (all N_15 all Xs_15 all Y_1 all Ys_2 (is_Arr1861959080le_alt(Y_1) -> (hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_15),Xs_15) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,Y_1),Ys_2) -> hAPP_n401316912le_alt(nth_Ar1113433366le_alt(Xs_15),N_15) = Y_1))) # label(fact_1144_nth__via__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1130 (all N_15 all Xs_15 all Y_1 all Ys_2 (hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_15),Xs_15) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,Y_1),Ys_2) -> hAPP_nat_nat(nth_nat(Xs_15),N_15) = Y_1)) # label(fact_1145_nth__via__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1131 (all N_14 all M_4 all Xs_14 hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_14),hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,M_4),Xs_14)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,M_4),hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_14),M_4)),Xs_14))) # label(fact_1146_take__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.98 1132 (all N_14 all M_4 all Xs_14 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_14),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,M_4),Xs_14)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,M_4),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_14),M_4)),Xs_14))) # label(fact_1147_take__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1133 (all N_13 all M_3 all Xs_13 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_13),hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,M_3),Xs_13)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_3),N_13)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_13),Xs_13))) # label(fact_1148_drop__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1134 (all N_13 all M_3 all Xs_13 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_13),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,M_3),Xs_13)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_3),N_13)),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_13),Xs_13))) # label(fact_1149_drop__take) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1135 (all N_12 all Xs_12 hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,N_12),Xs_12)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_12),Xs_12)) = Xs_12) # label(fact_1150_append__take__drop__id) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1136 (all N_12 all Xs_12 hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,N_12),Xs_12)),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_12),Xs_12)) = Xs_12) # label(fact_1151_append__take__drop__id) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1137 (all I_3 all K_1 all X_2 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,I_3),hAPP_nat_list_nat(replicate_nat(K_1),X_2)) = hAPP_nat_list_nat(replicate_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K_1),I_3)),X_2)) # label(fact_1152_drop__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1138 (all I_3 all K_1 all X_2 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,I_3),hAPP_A832564074le_alt(replic351609551le_alt(K_1),X_2)) = hAPP_A832564074le_alt(replic351609551le_alt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K_1),I_3)),X_2)) # label(fact_1153_drop__replicate) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1139 (all N_11 all Xs_11 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,hAPP_nat_nat(suc,N_11)),Xs_11) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_11),tl_nat(Xs_11))) # label(fact_1154_drop__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1140 (all N_11 all Xs_11 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,hAPP_nat_nat(suc,N_11)),Xs_11) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_11),tl_Arr1453005548le_alt(Xs_11))) # label(fact_1155_drop__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1141 (all N_10 all Xs_10 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_10),butlast_nat(Xs_10)) = butlast_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_10),Xs_10))) # label(fact_1156_drop__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1142 (all N_10 all Xs_10 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_10),butlas1262502241le_alt(Xs_10)) = butlas1262502241le_alt(hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_10),Xs_10))) # label(fact_1157_drop__butlast) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1143 (all N_9 all Xs_9 butlast_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_9),Xs_9)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_9),butlast_nat(Xs_9))) # label(fact_1158_butlast__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1144 (all N_9 all Xs_9 butlas1262502241le_alt(hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_9),Xs_9)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_9),butlas1262502241le_alt(Xs_9))) # label(fact_1159_butlast__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1145 (all I_2 all Xs_8 (hBOOL(hAPP_list_nat_bool(distinct_nat,Xs_8)) -> hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,I_2),Xs_8))))) # label(fact_1160_distinct__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1146 (all I_2 all Xs_8 (hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,Xs_8)) -> hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,I_2),Xs_8))))) # label(fact_1161_distinct__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1147 (all N_8 all Xs_7 (hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,Xs_7)) -> hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_8),Xs_7))))) # label(fact_1162_sorted__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1148 (all N_7 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_7),nil_nat) = nil_nat) # label(fact_1163_drop__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1149 (all N_7 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_7),nil_Ar126264853le_alt) = nil_Ar126264853le_alt) # label(fact_1164_drop__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1150 (all X_1 all N_1 all Xs (hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_1),Xs)))) -> hBOOL(hAPP_f2013399995l_bool(hAPP_A297543629l_bool(member1071917752le_alt,X_1),hAPP_l82377208t_bool(set_Ar1565008694le_alt,Xs))))) # label(fact_1165_in__set__dropD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1151 (all X_1 all N_1 all Xs (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_1),Xs)))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_l1821533378t_bool(set_nat,Xs))))) # label(fact_1166_in__set__dropD) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1152 (all N_6 all M_2 all Xs_6 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_6),hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,M_2),Xs_6)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_6),M_2)),Xs_6)) # label(fact_1167_drop__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1153 (all Xs_5 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,zero_zero_nat),Xs_5) = Xs_5) # label(fact_1168_drop__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1154 (all N_5 all Xs_4 tl_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_5),Xs_4)) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_5),tl_nat(Xs_4))) # label(fact_1169_tl__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1155 (all N_5 all Xs_4 tl_Arr1453005548le_alt(hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_5),Xs_4)) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_5),tl_Arr1453005548le_alt(Xs_4))) # label(fact_1170_tl__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1156 (all N_4 all Xs_3 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_4),tl_nat(Xs_3)) = tl_nat(hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_4),Xs_3))) # label(fact_1171_drop__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1157 (all N_4 all Xs_3 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_4),tl_Arr1453005548le_alt(Xs_3)) = tl_Arr1453005548le_alt(hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_4),Xs_3))) # label(fact_1172_drop__tl) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1158 (all Xs all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hBOOL(hAPP_f2013399995l_bool(hAPP_f1721660479l_bool(ord_le893483153t_bool,hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,M_1),Xs))),hAPP_l82377208t_bool(set_Ar1565008694le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_1),Xs)))))) # label(fact_1173_set__drop__subset__set__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1159 (all Xs all N_1 all M_1 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,M_1),Xs))),hAPP_l1821533378t_bool(set_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_1),Xs)))))) # label(fact_1174_set__drop__subset__set__drop) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1160 (all N_1 all Xs (hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_1),Xs) = nil_nat <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_list_nat_nat(size_size_list_nat,Xs)),N_1)))) # label(fact_1175_drop__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1161 (all N_1 all Xs (hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_1),Xs) = nil_Ar126264853le_alt <-> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs)),N_1)))) # label(fact_1176_drop__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1162 (all Xs_2 all N_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_list_nat_nat(size_size_list_nat,Xs_2)),N_3)) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_3),Xs_2) = nil_nat)) # label(fact_1177_drop__all) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1163 (all Xs_2 all N_3 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_2)),N_3)) -> hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_3),Xs_2) = nil_Ar126264853le_alt)) # label(fact_1178_drop__all) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1164 (all N_2 all Xs_1 all Ys_1 hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_2),hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,Xs_1),Ys_1)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,N_2),Xs_1)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),hAPP_list_nat_nat(size_size_list_nat,Xs_1))),Ys_1))) # label(fact_1179_drop__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1165 (all N_2 all Xs_1 all Ys_1 hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_2),hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs_1),Ys_1)) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,N_2),Xs_1)),hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N_2),hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs_1))),Ys_1))) # label(fact_1180_drop__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1166 (all Xs all Ys all Zs (hAPP_l726444215le_alt(hAPP_l568342716le_alt(append1166636842le_alt,Xs),Ys) = Zs <-> Xs = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(take_A1601602045le_alt,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs)),Zs) & Ys = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(drop_A186780501le_alt,hAPP_l1872264749lt_nat(size_s1873794948le_alt,Xs)),Zs))) # label(fact_1181_append__eq__conv__conj) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1167 (all I all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K)) -> (K != hAPP_nat_nat(suc,I) -> -(all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> K != hAPP_nat_nat(suc,J_2)))))) # label(fact_1182_lessE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1168 (all I all K (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K)) -> -(all J_2 (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) -> K != hAPP_nat_nat(suc,J_2))))) # label(fact_1183_Suc__lessE) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1169 (all M_1 all N_1 map_nat_nat(suc,hAPP_nat_list_nat(upt(M_1),N_1)) = hAPP_nat_list_nat(upt(hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N_1))) # label(fact_1184_map__Suc__upt) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1170 (all I all J hBOOL(hAPP_list_nat_bool(linorder_sorted_nat,hAPP_nat_list_nat(upt(I),J)))) # label(fact_1185_sorted__upt) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1171 (all I all K all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),J)) -> hAPP_nat_nat(nth_nat(hAPP_nat_list_nat(upt(I),J)),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K))) # label(fact_1186_nth__upt) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1172 (all I hAPP_nat_list_nat(upt(I),zero_zero_nat) = nil_nat) # label(fact_1187_upt__0) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1173 (all I all J ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hAPP_nat_list_nat(upt(I),J) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,I),hAPP_nat_list_nat(upt(hAPP_nat_nat(suc,I)),J))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hAPP_nat_list_nat(upt(I),J) = nil_nat))) # label(fact_1188_upt__rec) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1174 (all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hAPP_nat_list_nat(upt(I),J) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,I),hAPP_nat_list_nat(upt(hAPP_nat_nat(suc,I)),J)))) # label(fact_1189_upt__conv__Cons) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1175 (all M all I all J hAPP_l248265089st_nat(hAPP_n280362926st_nat(drop_nat,M),hAPP_nat_list_nat(upt(I),J)) = hAPP_nat_list_nat(upt(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M)),J)) # label(fact_1190_drop__upt) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1176 (all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J)) -> hAPP_list_nat_nat(hd_nat,hAPP_nat_list_nat(upt(I),J)) = I)) # label(fact_1191_hd__upt) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1177 (all I all J hBOOL(hAPP_list_nat_bool(distinct_nat,hAPP_nat_list_nat(upt(I),J)))) # label(fact_1192_distinct__upt) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1178 (all I all J hAPP_list_nat_nat(size_size_list_nat,hAPP_nat_list_nat(upt(I),J)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I)) # label(fact_1193_length__upt) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1179 (all I all M all N (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M)),N)) -> hAPP_l248265089st_nat(hAPP_n280362926st_nat(take_nat,M),hAPP_nat_list_nat(upt(I),N)) = hAPP_nat_list_nat(upt(I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M)))) # label(fact_1194_take__upt) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1180 (all J all I (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I)) -> hAPP_nat_list_nat(upt(I),J) = nil_nat)) # label(fact_1195_upt__conv__Nil) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1181 (all I_1 all J_1 (hAPP_nat_list_nat(upt(I_1),J_1) = nil_nat <-> J_1 = zero_zero_nat | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_1)))) # label(fact_1196_upt__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1182 (all I all J ((hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hAPP_nat_list_nat(upt(I),hAPP_nat_nat(suc,J)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(upt(I),J)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,J),nil_nat))) & (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hAPP_nat_list_nat(upt(I),hAPP_nat_nat(suc,J)) = nil_nat))) # label(fact_1197_upt__Suc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1183 (all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hAPP_nat_list_nat(upt(I),hAPP_nat_nat(suc,J)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(upt(I),J)),hAPP_l248265089st_nat(hAPP_n280362926st_nat(cons_nat,J),nil_nat)))) # label(fact_1198_upt__Suc__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1184 (all K all I all J (hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J)) -> hAPP_nat_list_nat(upt(I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(append_nat,hAPP_nat_list_nat(upt(I),J)),hAPP_nat_list_nat(upt(J),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))))) # label(fact_1199_upt__add__eq__append) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1185 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1186 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1187 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1188 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1189 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1190 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1191 (all Q all P (-hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1192 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1193 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1194 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1195 (all P hAPP_nat_nat(cOMBI_nat,P) = P) # label(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1196 (all X all Y (-hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1197 (all X all Y (X != Y | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Nat__Onat_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1198 (all X all Y (is_bool(X) & is_bool(Y) -> -hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__HOL__Obool_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1199 (all X all Y (X != Y | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)))) # label(help_fequal_2_1_fequal_000tc__HOL__Obool_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1200 (all X all Y if_list_nat(fTrue,X,Y) = X) # label(help_If_1_1_If_000tc__List__Olist_Itc__Nat__Onat_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1201 (all X all Y if_list_nat(fFalse,X,Y) = Y) # label(help_If_2_1_If_000tc__List__Olist_Itc__Nat__Onat_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1202 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__List__Olist_Itc__Nat__Onat_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1203 (all X all Y if_list_bool(fTrue,X,Y) = X) # label(help_If_1_1_If_000tc__List__Olist_Itc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1204 (all X all Y if_list_bool(fFalse,X,Y) = Y) # label(help_If_2_1_If_000tc__List__Olist_Itc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1205 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__List__Olist_Itc__HOL__Obool_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1206 (all X all Y (-hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(fequal_list_nat,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Nat__Onat_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1207 (all X all Y (X != Y | hBOOL(hAPP_list_nat_bool(hAPP_l120351551t_bool(fequal_list_nat,X),Y)))) # label(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Nat__Onat_J_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1208 (all P all Q all R hAPP_nat_nat(cOMBB_nat_nat_nat(P,Q),R) = hAPP_nat_nat(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1209 (all P all Q all R hAPP_nat_nat(hAPP_nat_fun_nat_nat(cOMBC_nat_nat_nat(P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1210 (all P all Q all R hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1211 (all P all Q all R hAPP_nat_bool(cOMBB_bool_bool_nat(P,Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1212 (all P all Q all R hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1213 (all P all Q all R hAPP_bool_bool(cOMBB_bool_bool_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_bool_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1214 (all P all Q all R hAPP_bool_bool(hAPP_b589554111l_bool(cOMBC_bool_bool_bool(P),Q),R) = hAPP_bool_bool(hAPP_b589554111l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1215 (all P all Q all R hAPP_bool_bool(cOMBS_bool_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_b589554111l_bool(P,R),hAPP_bool_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1216 (all X all Y (is_Arr1861959080le_alt(X) & is_Arr1861959080le_alt(Y) -> -hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(fequal1160105444le_alt,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1217 (all X all Y (X != Y | hBOOL(hAPP_A862370221t_bool(hAPP_A1664620203t_bool(fequal1160105444le_alt,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_T) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1218 (all X all Y if_lis1340954026le_alt(fTrue,X,Y) = X) # label(help_If_1_1_If_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1219 (all X all Y if_lis1340954026le_alt(fFalse,X,Y) = Y) # label(help_If_2_1_If_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1220 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_If_3_1_If_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1221 (all X all Y (-hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(fequal796301787le_alt,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1222 (all X all Y (X != Y | hBOOL(hAPP_l1386638586t_bool(hAPP_l1747810175t_bool(fequal796301787le_alt,X),Y)))) # label(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tp) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1223 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1224 (all P all Q all R hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1225 (all P all Q all R hAPP_b589554111l_bool(cOMBB_1914122979l_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_bool_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_002) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1226 (all P all Q all R hAPP_nat_list_nat(cOMBB_850496866at_nat(P,Q),R) = hAPP_l248265089st_nat(P,hAPP_nat_list_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Nat__Onat_J_000tc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1227 (all P all Q all R hAPP_nat_list_nat(hAPP_l383341732st_nat(cOMBC_1204473209st_nat(P),Q),R) = hAPP_l248265089st_nat(hAPP_n280362926st_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__Nat__Onat_J_000tc_) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1228 (all P all Q all R hAPP_A862370221t_bool(cOMBB_2104979073le_alt(P,Q),R) = hAPP_bool_bool(P,hAPP_A862370221t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order__) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1229 (all P all Q all R hAPP_nat_list_bool(cOMBB_1891801486ol_nat(P,Q),R) = hAPP_l1189022293t_bool(P,hAPP_nat_list_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__HOL__Obool_J_000tc__List__Olist_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1230 (all P all Q all R hAPP_nat_list_bool(hAPP_l1656175496t_bool(cOMBC_1038295629t_bool(P),Q),R) = hAPP_l1189022293t_bool(hAPP_n479129736t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__HOL__Obool_J_000tc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1231 (all P all Q all R hAPP_A862370221t_bool(cOMBS_1393264256l_bool(P,Q),R) = hAPP_bool_bool(hAPP_A822657487l_bool(P,R),hAPP_A862370221t_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1232 (all P all Q all R hAPP_bool_list_bool(hAPP_l1045755451t_bool(cOMBC_80330970t_bool(P),Q),R) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__List__Olist_Itc__HOL__Obool_J_000t) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1233 (all P all Q hAPP_n280362926st_nat(cOMBK_1717478773at_nat(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__List__Olist_Itc__Nat__Onat_J_Mtc__List__Oli) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1234 (all P all Q all R hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(P,Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1235 (all P all Q all R hAPP_l248265089st_nat(hAPP_l710375585st_nat(cOMBC_950362600st_nat(P),Q),R) = hAPP_l248265089st_nat(hAPP_l710375585st_nat(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Nat__Onat_J_000tc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1236 (all P all Q all R hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(cOMBC_1789016513t_bool(P),Q),R) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__HOL__Obool_J_000tc__List__Olist_Itc) # label(axiom) # label(non_clause). [assumption].
% 1.51/1.99 1237 (all P all Q all R hAPP_A822657487l_bool(cOMBB_803794783le_alt(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_A862370221t_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1238 (all P all Q all R hAPP_A862370221t_bool(hAPP_A1664620203t_bool(cOMBC_1628726426t_bool(P),Q),R) = hAPP_A862370221t_bool(hAPP_A1664620203t_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1239 (all P all Q all R hAPP_n280362926st_nat(cOMBB_472649634at_nat(P,Q),R) = hAPP_l710375585st_nat(P,hAPP_nat_list_nat(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Nat__Onat_J_000tc__fun_Itc__List__O) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1240 (all P all Q all R hAPP_b994696797t_bool(cOMBB_1663860504l_bool(P,Q),R) = hAPP_l1947611924t_bool(P,hAPP_bool_list_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__HOL__Obool_J_000tc__fun_Itc__List__) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1241 (all P all Q all R hAPP_A862370221t_bool(hAPP_f2014742713t_bool(cOMBC_1745481870l_bool(P),Q),R) = hAPP_f2013399995l_bool(hAPP_A297543629l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_004) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1242 (all P all Q all R hAPP_n1875670159le_alt(cOMBB_903467948lt_nat(P,Q),R) = hAPP_l726444215le_alt(P,hAPP_n1875670159le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1243 (all P all Q all R hAPP_n1875670159le_alt(hAPP_l382792410le_alt(cOMBC_1511969967le_alt(P),Q),R) = hAPP_l726444215le_alt(hAPP_n2139729636le_alt(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1244 (all P all Q all R hAPP_A832564074le_alt(hAPP_l618618165le_alt(cOMBC_1919297930le_alt(P),Q),R) = hAPP_l726444215le_alt(hAPP_A408086601le_alt(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_005) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1245 (all P all Q hAPP_A408086601le_alt(cOMBK_1696648346le_alt(P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1246 (all P all Q all R hAPP_l726444215le_alt(hAPP_l568342716le_alt(cOMBC_1058495865le_alt(P),Q),R) = hAPP_l726444215le_alt(hAPP_l568342716le_alt(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1247 (all P all Q all R hAPP_A408086601le_alt(cOMBB_881934114le_alt(P,Q),R) = hAPP_l568342716le_alt(P,hAPP_A832564074le_alt(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____tpnf_006) # label(axiom) # label(non_clause). [assumption].
% 3.58/3.82 1248 -(exists C hBOOL(hAPP_l1386638586t_bool(distin1223878664le_alt,hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,a),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,b),hAPP_l726444215le_alt(hAPP_A408086601le_alt(cons_A1216297413le_alt,C),nil_Ar126264853le_alt)))))) # label(conj_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.58/3.82
% 3.58/3.82 ============================== end of process non-clausal formulas ===
% 3.58/3.82
% 3.58/3.82 ============================== PROCESS INITIAL CLAUSES ===============
% 3.58/3.82
% 3.58/3.82 ============================== PREDICATE ELIMINATION =================
% 3.58/3.82
% 3.58/3.82 ============================== end predicate elimination =============
% 3.58/3.82
% 3.58/3.82 Auto_denials: (non-Horn, no changes).
% 3.58/3.82
% 3.58/3.82 Term ordering decisions:
% 3.58/3.82 Function symbol KB weights: ord_less_nat=1. ord_less_eq_nat=1. plus_plus_nat=1. cons_bool=1. zero_zero_nat=1. nil_Ar126264853le_alt=1. cons_nat=1. cons_A1216297413le_alt=1. nil_nat=1. suc=1. append1166636842le_alt=1. append_nat=1. member_nat=1. nil_bool=1. member1071917752le_alt=1. set_nat=1. set_Ar1565008694le_alt=1. minus_minus_nat=1. size_size_list_nat=1. size_s1873794948le_alt=1. append_bool=1. ord_min_nat=1. ord_max_nat=1. size_size_list_bool=1. linorder_sorted_nat=1. set_bool=1. member_bool=1. take_A1601602045le_alt=1. take_nat=1. distinct_nat=1. distin1223878664le_alt=1. drop_nat=1. drop_A186780501le_alt=1. fNot=1. take_bool=1. last_A57386030le_alt=1. last_nat=1. last_bool=1. remove1_nat=1. ord_le1568362934t_bool=1. distinct_bool=1. ord_le893483153t_bool=1. remove430413995le_alt=1. cOMBI_nat=1. hd_nat=1. hd_Arr805754088le_alt=1. fFalse=1. fdisj=1. fTrue=1. fequal1160105444le_alt=1. fequal_nat=1. member345038890le_alt=1. member_nat_1=1. equal_499625528le_alt=1. equal_equal_list_nat=1. member_bool_1=1. fequal_bool=1. hd_bool=1. minus_2067140911t_bool=1. minus_988785290t_bool=1. null_A361035805le_alt=1. null_nat=1. insert960637483le_alt=1. insert_nat=1. remove1_bool=1. drop_bool=1. fconj=1. fequal796301787le_alt=1. fequal_list_nat=1. insert_bool=1. size_size_nat=1. nat_size=1. ord_le1384968325t_bool=1. bool_size=1. ord_le382113706t_bool=1. a=1. arrow_107136085le_alt=1. b=1. bool=1. cons_l650111674le_alt=1. cons_list_nat=1. ord_le742797417l_bool=1. null_bool=1. c1=1. c2=1. c3=1. hAPP_nat_bool=1. hAPP_nat_nat=1. hAPP_n1699378549t_bool=1. hAPP_nat_fun_nat_nat=1. hAPP_l248265089st_nat=1. hAPP_l726444215le_alt=1. hAPP_l1189022293t_bool=1. hAPP_n280362926st_nat=1. hAPP_b994696797t_bool=1. hAPP_list_nat_bool=1. hAPP_A408086601le_alt=1. hAPP_l1386638586t_bool=1. hAPP_list_bool_bool=1. hAPP_l568342716le_alt=1. hAPP_l710375585st_nat=1. hAPP_f54304608l_bool=1. hAPP_f2013399995l_bool=1. hAPP_n215258509l_bool=1. hAPP_A862370221t_bool=1. hAPP_l1821533378t_bool=1. hAPP_A297543629l_bool=1. hAPP_l82377208t_bool=1. hAPP_list_nat_nat=1. hAPP_bool_bool=1. hAPP_l1872264749lt_nat=1. hAPP_l1947611924t_bool=1. hAPP_list_bool_nat=1. hAPP_n2139729636le_alt=1. hAPP_nat_list_nat=1. hAPP_l96088310l_bool=1. hAPP_f387058535l_bool=1. hAPP_b1787118453l_bool=1. hAPP_n401316912le_alt=1. hAPP_l1686219315t_bool=1. hAPP_l273023249l_bool=1. takeWh536362254le_alt=1. hAPP_A832564074le_alt=1. takeWhile_nat=1. hAPP_l1105242632le_alt=1. dropWh156852662le_alt=1. dropWhile_nat=1. hAPP_n479129736t_bool=1. hAPP_l1101248310l_bool=1. hAPP_l909187928t_bool=1. hAPP_b589554111l_bool=1. takeWhile_bool=1. hAPP_f103356543l_bool=1. hAPP_f1721660479l_bool=1. listre53232751le_alt=1. hAPP_f800510211t_bool=1. listrelp_bool=1. hAPP_A1664620203t_bool=1. listrelp_nat=1. hAPP_f2014742713t_bool=1. sublis888024346le_alt=1. sublist_nat=1. list_s1237850263le_alt=1. cOMBB_2104979073le_alt=1. cOMBB_bool_bool_nat=1. dropWhile_bool=1. hAPP_bool_list_bool=1. hAPP_n1006566506l_bool=1. hAPP_n1875670159le_alt=1. hAPP_l120351551t_bool=1. hAPP_l1747810175t_bool=1. list_size_nat=1. hAPP_n315299280t_bool=1. nat_case_bool=1. nat_case_nat=1. foldr_nat_nat=1. hAPP_f1730770594t_bool=1. hAPP_f2012267069t_bool=1. cOMBB_1146692694ol_nat=1. cOMBB_bool_bool_bool=1. hAPP_l383341732st_nat=1. splice360969192le_alt=1. splice_nat=1. cOMBB_1015721476ol_nat=1. cOMBB_803794783le_alt=1. cOMBB_nat_nat_nat=1. cOMBS_1393264256l_bool=1. cOMBS_nat_bool_bool=1. hAPP_A2113590458lt_nat=1. hAPP_l618618165le_alt=1. cOMBB_1914122979l_bool=1. cOMBS_bool_bool_bool=1. hAPP_l1045755451t_bool=1. hAPP_nat_list_bool=1. linord852754176at_nat=1. nat_ca14895078le_alt=1. nat_case_list_nat=1. sublist_bool=1. hAPP_bool_nat=1. map_fi1996871376le_alt=1. map_fi2015041583lt_nat=1. map_fi302768037le_alt=1. map_fi695734538le_alt=1. map_fi80499576t_bool=1. map_filter_bool_nat=1. map_filter_nat_bool=1. map_filter_nat_nat=1. nat_ca391302041le_alt=1. splice_bool=1. cOMBB_1663860504l_bool=1. cOMBB_1891801486ol_nat=1. cOMBB_472649634at_nat=1. cOMBB_850496866at_nat=1. cOMBB_881934114le_alt=1. cOMBB_903467948lt_nat=1. hAPP_A822657487l_bool=1. hAPP_l1656175496t_bool=1. hAPP_l382792410le_alt=1. list_size_bool=1. maps_A461338881le_alt=1. maps_bool_nat=1. maps_n2115510812le_alt=1. big_Sup_fin_nat=1. hAPP_A1356081999on_nat=1. hAPP_A373227306le_alt=1. hAPP_A524667246n_bool=1. hAPP_b803953466le_alt=1. hAPP_bool_list_nat=1. hAPP_bool_option_nat=1. hAPP_f612708895l_bool=1. hAPP_l1734754389st_nat=1. hAPP_l1872445307st_nat=1. hAPP_l1891879573le_alt=1. hAPP_l656323104le_alt=1. hAPP_n2020361039le_alt=1. hAPP_nat_option_bool=1. hAPP_nat_option_nat=1. map_nat_nat=1. nat_case_list_bool=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f113=1. f114=1. f115=1. f117=1. f123=1. f124=1. f129=1. f130=1. f131=1. f132=1. f133=1. f134=1. f135=1. f136=1. f137=1. f138=1. f139=1. f140=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f154=1. f155=1. f160=1. f161=1. f162=1. f163=1. f164=1. f165=1. f166=1. f167=1. f168=1. f169=1. f170=1. f171=1. f172=1. f173=1. f174=1. f175=1. f176=1. f177=1. f178=1. f179=1. f180=1. f181=1. f182=1. f183=1. f184=1. f185=1. f186=1. f187=1. f188=1. f189=1. f190=1. f191=1. f192=1. f193=1. f194=1. f195=1. f196=1. f197=1. f198=1. f199=1. f201=1. f202=1. f203=1. f204=1. f206=1. f207=1. f208=1. f209=1. f211=1. f212=1. f213=1. f214=1. f216=1. f217=1. f218=1. f219=1. f221=1. f222=1. f223=1. f224=1. f227=1. f228=1. f230=1. f231=1. f234=1. f235=1. f236=1. f237=1. f238=1. f239=1. f240=1. f241=1. f242=1. f243=1. f244=1. f245=1. f246=1. f247=1. f248=1. f249=1. f250=1. f251=1. f252=1. f253=1. f254=1. f255=1. f256=1. f257=1. f258=1. f259=1. f260=1. f261=1. f262=1. f270=1. f277=1. f278=1. f279=1. f280=1. f285=1. f287=1. f288=1. f289=1. f290=1. f291=1. f294=1. f299=1. f300=1. f301=1. f302=1. f303=1. f304=1. f305=1. f306=1. f307=1. f308=1. f309=1. f310=1. f311=1. f319=1. f320=1. f322=1. f323=1. f324=1. f325=1. f326=1. f329=1. f330=1. f331=1. f332=1. f333=1. f334=1. f335=1. f336=1. f337=1. f344=1. f345=1. f346=1. f368=1. f369=1. f370=1. f371=1. f372=1. f375=1. f376=1. f379=1. f380=1. f386=1. f387=1. f388=1. f392=1. f393=1. f396=1. f397=1. nth_bool=1. nth_nat=1. nth_Ar1113433366le_alt=1. rev_nat=1. list_a1557668565le_alt=1. replic351609551le_alt=1. replicate_nat=1. rev_Ar2093961333le_alt=1. list_all_nat=1. listMem_bool=1. upt=1. listMe1065601537le_alt=1. butlast_nat=1. butlas1262502241le_alt=1. linord1850739451at_nat=1. tl_nat=1. tl_Arr1453005548le_alt=1. listMem_nat=1. list_e1226799320le_alt=1. rev_bool=1. list_ex1_nat=1. rotate1322903650le_alt=1. rotate1_nat=1. cOMBC_226598744l_bool=1. collect_nat=1. list_all_bool=1. butlast_bool=1. cOMBC_1204473209st_nat=1. cOMBC_nat_nat_bool=1. list_ex1_bool=1. replicate_bool=1. cOMBC_1745481870l_bool=1. cOMBC_nat_nat_nat=1. cOMBC_1628726426t_bool=1. cOMBC_1919297930le_alt=1. cOMBC_80330970t_bool=1. linord297828738at_nat=1. rotate1_bool=1. cOMBC_1058495865le_alt=1. cOMBC_950362600st_nat=1. cOMBC_bool_bool_bool=1. tl_bool=1. cOMBC_1038295629t_bool=1. cOMBC_1511969967le_alt=1. cOMBC_1789016513t_bool=1. cOMBK_1696648346le_alt=1. cOMBK_1717478773at_nat=1. max_nat=1. min_nat=1. nth_li2119471145le_alt=1. nth_list_nat=1. big_linorder_Max_nat=1. collec1729629178le_alt=1. undefi462180727le_alt=1. undefined_bool=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. f36=1. f37=1. f38=1. f39=1. f40=1. f41=1. f42=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f49=1. f50=1. f51=1. f52=1. f53=1. f226=1. f229=1. f281=1. f282=1. f292=1. f293=1. f321=1. f338=1. f339=1. f340=1. f341=1. f342=1. f343=1. f347=1. f348=1. f349=1. f350=1. f389=1. foldl_nat_nat=1. list_c380068407le_alt=1. list_c554461815at_nat=1. if_lis1340954026le_alt=1. if_list_bool=1. if_list_nat=1. option306705938at_nat=1. option468438226le_alt=1. foldl_list_nat_nat=1. option718651152l_bool=1. foldl_1200072380le_alt=1. foldl_list_bool_bool=1. list_c1750880501l_bool=1. f69=1. f70=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f94=1. f95=1. f96=1. f97=1. f98=1. f99=1. f100=1. f101=1. f102=1. f103=1. f104=1. f105=1. f106=1. f107=1. f108=1. f109=1. f110=1. f111=1. f112=1. f116=1. f118=1. f119=1. f120=1. f121=1. f122=1. f125=1. f126=1. f127=1. f128=1. f263=1. f264=1. f265=1. f283=1. f284=1. f286=1. f312=1. f313=1. f314=1. f315=1. f316=1. f317=1. f318=1. f327=1. f328=1. f351=1. f352=1. f353=1. f354=1. f355=1. f356=1. f357=1. f358=1. f359=1. f360=1. f361=1. f362=1. f363=1. f364=1. f365=1. f366=1. f367=1. f373=1. f374=1. f377=1. f378=1. f381=1. f382=1. f383=1. f384=1. f385=1. f390=1. f391=1. f394=1. f395=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f156=1. f157=1. f158=1. f159=1. f200=1. f205=1. f210=1. f232=1. f233=1. f268=1. f269=1. f271=1. f272=1. f273=1. f295=1. f296=1. f297=1. f298=1. f215=1. f220=1. f225=1. f274=1. f275=1. f276=1. f266=1. f267=1.
% 190.02/190.37
% 190.02/190.37 ============================== end of process initial clauses ========
% 190.02/190.37
% 190.02/190.37 ============================== CLAUSES FOR SEARCH ====================
% 190.02/190.37
% 190.02/190.37 ============================== end of clauses for search =============
% 190.02/190.37
% 190.02/190.37 ============================== SEARCH ================================
% 190.02/190.37
% 190.02/190.37 % Starting search at 2.07 seconds.
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=40.000, iters=3433
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=39.000, iters=3433
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=38.000, iters=3342
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=37.000, iters=3384
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=36.000, iters=3396
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=35.000, iters=3390
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=34.000, iters=3337
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=33.000, iters=3462
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=32.000, iters=3371
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=30.000, iters=3491
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=29.000, iters=3430
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=28.000, iters=3339
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=27.000, iters=3344
% 190.02/190.37
% 190.02/190.37 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 107 (0.00 of 3.60 sec).
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=26.000, iters=3380
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=25.000, iters=3369
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=24.000, iters=3348
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=23.000, iters=3334
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=22.000, iters=3356
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=21.000, iters=3353
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=20.000, iters=3334
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=19.000, iters=3334
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=18.000, iters=3335
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=17.000, iters=3348
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=16.000, iters=3403
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=15.000, iters=3552
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=5265, wt=97.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=5269, wt=91.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=5266, wt=81.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=5267, wt=80.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=5298, wt=79.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=5299, wt=73.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=5300, wt=72.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=5290, wt=71.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=4674, wt=53.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=10166, wt=50.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=14582, wt=40.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=10469, wt=39.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=13393, wt=38.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=13267, wt=37.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=12987, wt=36.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=14796, wt=12.000
% 190.02/190.37
% 190.02/190.37 Low Water (displace): id=16461, wt=11.000
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=14.000, iters=3334
% 190.02/190.37
% 190.02/190.37 Low Water (keep): wt=13.000, iters=3334
% 190.02/190.37
% 190.02/190.37 ============================== STATISTICS ============================
% 190.02/190.37
% 190.02/190.37 Given=16909. Generated=7890226. Kept=89586. proofs=0.
% 190.02/190.37 Usable=16479. Sos=9999. Demods=1537. Limbo=4, Disabled=65319. Hints=0.
% 190.02/190.37 Kept_by_rule=0, Deleted_by_rule=1280.
% 190.02/190.37 Forward_subsumed=974942. Back_subsumed=46.
% 190.02/190.37 Sos_limit_deleted=6824418. Sos_displaced=61901. Sos_removed=0.
% 190.02/190.37 New_demodulators=2297 (46 lex), Back_demodulated=1155. Back_unit_deleted=1.
% 190.02/190.37 Demod_attempts=167100151. Demod_rewrites=2371119.
% 190.02/190.37 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 190.02/190.37 Nonunit_fsub_feature_tests=310393. Nonunit_bsub_feature_tests=10108.
% 190.02/190.37 Megabytes=419.43.
% 190.02/190.37 User_CPU=184.01, System_CPU=4.61, Wall_clock=189.
% 190.02/190.37
% 190.02/190.37 Megs malloced by palloc(): 400.
% 190.02/190.37 type (bytes each) gets frees in use bytes
% 190.02/190.37 chunk ( 104) 48525 48525 0 0.0 K
% 190.02/190.37 string_buf ( 8) 41380 41380 0 0.0 K
% 190.02/190.37 token ( 20) 110042 110042 0 0.0 K
% 190.02/190.37 pterm ( 16) 63791 63791 0 0.0 K
% 190.02/190.37 hashtab ( 8) 1248 1248 0 0.0 K
% 190.02/190.37 hashnode ( 8) 4834 4834 0 0.0 K
% 190.02/190.37 term ( 20) 266200377 264923154 1277223 24945.8 K
% 190.02/190.37 term arg arrays: 5955.2 K
% 190.02/190.37 attribute ( 12) 11538 462 11076 129.8 K
% 190.13/190.38 ilist ( 8) 1285825641 1285392854 432787 3381.1 K
% 190.13/190.38 plist ( 8) 1251986 1118825 133161 1040.3 K
% 190.13/190.38 i2list ( 12) 82890088 82890088 0 0.0 K
% 190.13/190.38 just ( 12) 10725802 10603237 122565 1436.3 K
% 190.13/190.38 parajust ( 16) 5339046 5286885 52161 815.0 K
% 190.13/190.38 instancejust ( 8) 0 0 0 0.0 K
% 190.13/190.38 ivyjust ( 24) 0 0 0 0.0 K
% 190.13/190.38 formula ( 28) 50978 34590 16388 448.1 K
% 190.13/190.38 formula arg arrays: 54.3 K
% 190.13/190.38 topform ( 52) 7893690 7800640 93050 4725.2 K
% 190.13/190.38 clist_pos ( 20) 265907 172569 93338 1823.0 K
% 190.13/190.38 clist ( 16) 8 1 7 0.1 K
% 190.13/190.38 context ( 808) 49894088 49894086 2 1.6 K
% 190.13/190.38 trail ( 12) 27721201 27721199 2 0.0 K
% 190.13/190.38 ac_match_pos (70044) 0 0 0 0.0 K
% 190.13/190.38 ac_match_free_vars_pos (20020)
% 190.13/190.38 0 0 0 0.0 K
% 190.13/190.38 btm_state ( 60) 0 0 0 0.0 K
% 190.13/190.38 btu_state ( 60) 0 0 0 0.0 K
% 190.13/190.38 ac_position (285432) 0 0 0 0.0 K
% 190.13/190.38 fpa_trie ( 20) 636181 319021 317160 6194.5 K
% 190.13/190.38 fpa_state ( 28) 1674577 1674571 6 0.2 K
% 190.13/190.38 fpa_index ( 12) 10 0 10 0.1 K
% 190.13/190.38 fpa_chunk ( 20) 670920 547561 123359 2409.4 K
% 190.13/190.38 fpa_list ( 16) 399293 0 399293 6239.0 K
% 190.13/190.38 fpa_list chunks: 4600.3 K
% 190.13/190.38 discrim ( 12) 426906 352650 74256 870.2 K
% 190.13/190.38 discrim_pos ( 16) 12802658 12802658 0 0.0 K
% 190.13/190.38 flat2 ( 32) 142210621 142210621 0 0.0 K
% 190.13/190.38 flat ( 48) 0 0 0 0.0 K
% 190.13/190.38 flatterm ( 32) 268547191 268547191 0 0.0 K
% 190.13/190.38 mindex ( 28) 13 0 13 0.4 K
% 190.13/190.38 mindex_pos ( 56) 33975414 33975413 1 0.1 K
% 190.13/190.38 lindex ( 12) 5 0 5 0.1 K
% 190.13/190.38 clash ( 40) 0 0 0 0.0 K
% 190.13/190.38 di_tree ( 12) 79548375 50354332 29194043 342117.7 K
% 190.13/190.38 avl_node ( 20) 176821 156823 19998 390.6 K
% 190.13/190.38
% 190.13/190.38 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 190.13/190.38 List 1, length 4, 0.0 K
% 190.13/190.38 List 4, length 92, 1.4 K
% 190.13/190.38 List 5, length 35, 0.7 K
% 190.13/190.38 List 6, length 15, 0.4 K
% 190.13/190.38 List 7, length 30, 0.8 K
% 190.13/190.38 List 8, length 96, 3.0 K
% 190.13/190.38 List 9, length 3, 0.1 K
% 190.13/190.38 List 10, length 7, 0.3 K
% 190.13/190.38 List 11, length 12, 0.5 K
% 190.13/190.38 List 12, length 2, 0.1 K
% 190.13/190.38 List 14, length 1, 0.1 K
% 190.13/190.38 List 15, length 2, 0.1 K
% 190.13/190.38 List 16, length 36, 2.2 K
% 190.13/190.38 List 17, length 2, 0.1 K
% 190.13/190.38 List 22, length 1, 0.1 K
% 190.13/190.38 List 24, length 1, 0.1 K
% 190.13/190.38 List 26, length 111, 11.3 K
% 190.13/190.38 List 32, length 2, 0.2 K
% 190.13/190.38 List 64, length 1, 0.2 K
% 190.13/190.38 List 128, length 1, 0.5 K
% 190.13/190.38 List 202, length 2, 1.6 K
% 190.13/190.38
% 190.13/190.38 ============================== SELECTOR REPORT =======================
% 190.13/190.38 Sos_deleted=6824418, Sos_displaced=61901, Sos_size=9999
% 190.13/190.38 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 190.13/190.38 I 2147483647 high age 0 1944
% 190.13/190.38 H 1 high weight 0 0
% 190.13/190.38 A 1 low age 9999 1663
% 190.13/190.38 F 4 low weight 1333 6652
% 190.13/190.38 T 4 low weight 8666 6650
% 190.13/190.38 ============================== end of selector report ================
% 190.13/190.38
% 190.13/190.38 ============================== end of statistics =====================
% 190.13/190.38
% 190.13/190.38 Exiting with failure.
% 190.13/190.38
% 190.13/190.38 Process 22437 exit (max_megs) Sat Jul 2 00:49:24 2022
% 190.13/190.38 Prover9 interrupted
%------------------------------------------------------------------------------