TSTP Solution File: SWW476+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW476+1 : 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 : Thu Jul 21 01:17:13 EDT 2022
% Result : Unknown 237.40s 237.71s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW476+1 : TPTP v8.1.0. Released v5.3.0.
% 0.06/0.13 % 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 : Sun Jun 5 21:55:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.97/1.33 ============================== Prover9 ===============================
% 0.97/1.33 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.33 Process 28586 was started by sandbox2 on n021.cluster.edu,
% 0.97/1.33 Sun Jun 5 21:55:50 2022
% 0.97/1.33 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28416_n021.cluster.edu".
% 0.97/1.33 ============================== end of head ===========================
% 0.97/1.33
% 0.97/1.33 ============================== INPUT =================================
% 0.97/1.33
% 0.97/1.33 % Reading from file /tmp/Prover9_28416_n021.cluster.edu
% 0.97/1.33
% 0.97/1.33 set(prolog_style_variables).
% 0.97/1.33 set(auto2).
% 0.97/1.33 % set(auto2) -> set(auto).
% 0.97/1.33 % set(auto) -> set(auto_inference).
% 0.97/1.33 % set(auto) -> set(auto_setup).
% 0.97/1.33 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.33 % set(auto) -> set(auto_limits).
% 0.97/1.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.33 % set(auto) -> set(auto_denials).
% 0.97/1.33 % set(auto) -> set(auto_process).
% 0.97/1.33 % set(auto2) -> assign(new_constants, 1).
% 1.04/1.33 % set(auto2) -> assign(fold_denial_max, 3).
% 1.04/1.33 % set(auto2) -> assign(max_weight, "200.000").
% 1.04/1.33 % set(auto2) -> assign(max_hours, 1).
% 1.04/1.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.04/1.33 % set(auto2) -> assign(max_seconds, 0).
% 1.04/1.33 % set(auto2) -> assign(max_minutes, 5).
% 1.04/1.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.04/1.33 % set(auto2) -> set(sort_initial_sos).
% 1.04/1.33 % set(auto2) -> assign(sos_limit, -1).
% 1.04/1.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.04/1.33 % set(auto2) -> assign(max_megs, 400).
% 1.04/1.33 % set(auto2) -> assign(stats, some).
% 1.04/1.33 % set(auto2) -> clear(echo_input).
% 1.04/1.33 % set(auto2) -> set(quiet).
% 1.04/1.33 % set(auto2) -> clear(print_initial_clauses).
% 1.04/1.33 % set(auto2) -> clear(print_given).
% 1.04/1.33 assign(lrs_ticks,-1).
% 1.04/1.33 assign(sos_limit,10000).
% 1.04/1.33 assign(order,kbo).
% 1.04/1.33 set(lex_order_vars).
% 1.04/1.33 clear(print_given).
% 1.04/1.33
% 1.04/1.33 % formulas(sos). % not echoed (345 formulas)
% 1.04/1.33
% 1.04/1.33 ============================== end of input ==========================
% 1.04/1.33
% 1.04/1.33 % From the command line: assign(max_seconds, 300).
% 1.04/1.33
% 1.04/1.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.04/1.33
% 1.04/1.33 % Formulas that are not ordinary clauses:
% 1.04/1.33 1 (all B_1_1 is_bool(final_list_char(B_1_1))) # label(gsy_c_BigStep_Ofinal_000tc__List__Olist_Itc__String__Ochar_J) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 2 (all B_1_1 all B_2_1 is_bool(hconf_97414254t_char(B_1_1,B_2_1))) # label(gsy_c_Conform_Ohconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 3 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 is_bool(lconf_496643946t_char(B_1_1,B_2_1,B_3_1,B_4_1))) # label(gsy_c_Conform_Olconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 4 (all B_1_1 is_bool(distinct_list_char(B_1_1))) # label(gsy_c_List_Odistinct_000tc__List__Olist_Itc__String__Ochar_J) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 5 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_a52822260ion_ty(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 6 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_a1834344429ion_ty(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oo) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 7 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_a283687028t_char(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Expr__Oexp) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 8 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_a839443437t_char(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olis) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 9 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_a2039389316_ty_ty(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Type__Oty) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 10 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_a1073113293ty_val(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__Value__Ova) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 11 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_a1880637950ion_ty(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 12 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_all2_ty_ty(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Type__Oty_000tc__Type__Oty) # label(hypothesis) # label(non_clause). [assumption].
% 1.04/1.33 13 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_a1462908359ion_ty(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Value__Oval_000tc__Option__Ooption_Itc__Type__Oty_) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 14 (all B_1_1 all B_2_1 all B_3_1 is_bool(list_all2_val_ty(B_1_1,B_2_1,B_3_1))) # label(gsy_c_List_Olist__all2_000tc__Value__Oval_000tc__Type__Oty) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 15 (all B_1_1 all B_2_1 is_bool(hext(B_1_1,B_2_1))) # label(gsy_c_Objects_Ohext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 16 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 all B_5 is_bool(wTrt(B_1_1,B_2_1,B_3_1,B_4_1,B_5))) # label(gsy_c_WellTypeRT_OWTrt) # label(hypothesis) # label(non_clause). [assumption].
% 1.04/1.33 17 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 all B_5 is_bool(wTrts(B_1_1,B_2_1,B_3_1,B_4_1,B_5))) # label(gsy_c_WellTypeRT_OWTrts) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 18 (all B_1_1 all B_2_1 is_bool(hAPP_e544220455r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_000tc__HOL_) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 19 (all B_1_1 all B_2_1 is_bool(hAPP_ty_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Type__Oty_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 20 (all B_1_1 all B_2_1 is_bool(hAPP_f1033709212l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Option__Ooption) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 21 (all B_1_1 all B_2_1 is_bool(hAPP_f1715346603l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 22 (all B_1_1 all B_2_1 is_bool(hAPP_P1708370145l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_M) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 23 (all B_1_1 all B_2_1 is_bool(hAPP_P92196306r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 24 (all B_1_1 all B_2_1 is_bool(hAPP_P1235399154l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 25 (all B_1_1 all B_2_1 is_bool(hAPP_P1907982426r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__List__Ol) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 26 (all B_1_1 all B_2_1 is_bool(hAPP_P2118621157r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__Oexp_Itc__) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 27 (all B_1_1 all B_2_1 is_bool(hAPP_P159683425l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 28 (all B_1_1 all B_2_1 is_bool(hAPP_P282169671l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 29 (all B_1_1 all B_2_1 is_bool(member_exp_list_char(B_1_1,B_2_1))) # label(gsy_c_member_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 30 (all B_1_1 all B_2_1 is_bool(member_list_char(B_1_1,B_2_1))) # label(gsy_c_member_000tc__List__Olist_Itc__String__Ochar_J) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 31 (all B_1_1 all B_2_1 is_bool(member_option_ty(B_1_1,B_2_1))) # label(gsy_c_member_000tc__Option__Ooption_Itc__Type__Oty_J) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 32 (all B_1_1 all B_2_1 is_bool(member_ty(B_1_1,B_2_1))) # label(gsy_c_member_000tc__Type__Oty) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 33 (all B_1_1 all B_2_1 is_bool(member_val(B_1_1,B_2_1))) # label(gsy_c_member_000tc__Value__Oval) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 34 (all B_1_1 all B_2_1 is_bool(member773094996on_val(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String_) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 35 (all B_1_1 all B_2_1 is_bool(member1420286996t_char(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 36 (all B_1_1 all B_2_1 is_bool(member1322055188on_val(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fu) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 37 (all B_1_1 all B_2_1 is_bool(member125098544t_char(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_I) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 38 (all B_1_1 all B_2_1 is_bool(member1161907014t_char(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 39 (all B_1_1 all B_2_1 is_bool(member563141460on_val(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 40 (all B_1_1 all B_2_1 is_bool(member808015754on_val(B_1_1,B_2_1))) # label(gsy_c_member_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_It) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 41 (all Pa all Xs hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Xs,Xs))) # label(fact_0_widens__refl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 42 (all P_3 all T_4 hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_3),T_4),T_4))) # label(fact_1_widen__refl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 43 (all Us all Pa all Ss all Tsa (hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss,Tsa)) -> (hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa,Us)) -> hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ss,Us))))) # label(fact_2_widens__trans) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 44 (all Pa all Xs all Ys (hBOOL(list_all2_val_ty(Pa,Xs,Ys)) -> size_size_list_val(Xs) = size_size_list_ty(Ys))) # label(fact_3_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 45 (all Pa all Xs all Ys (hBOOL(list_all2_ty_ty(Pa,Xs,Ys)) -> size_size_list_ty(Xs) = size_size_list_ty(Ys))) # label(fact_4_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 46 (all Pa all Xs all Ys (hBOOL(list_a283687028t_char(Pa,Xs,Ys)) -> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys))) # label(fact_5_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 47 (all Pa all Xs all Ys (hBOOL(list_a1073113293ty_val(Pa,Xs,Ys)) -> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys))) # label(fact_6_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 48 (all Pa all Xs all Ys (hBOOL(list_a2039389316_ty_ty(Pa,Xs,Ys)) -> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys))) # label(fact_7_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 49 (all Pa all Xs all Ys (hBOOL(list_a839443437t_char(Pa,Xs,Ys)) -> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_8_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 50 (all Pa all Xs all Ys (hBOOL(list_a52822260ion_ty(Pa,Xs,Ys)) -> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_9_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 51 (all Pa all Xs all Ys (hBOOL(list_a1462908359ion_ty(Pa,Xs,Ys)) -> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_10_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 52 (all Pa all Xs all Ys (hBOOL(list_a1880637950ion_ty(Pa,Xs,Ys)) -> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_11_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 53 (all Pa all Xs all Ys (hBOOL(list_a1834344429ion_ty(Pa,Xs,Ys)) -> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_12_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 54 (all F all Xs size_size_list_val(hAPP_l1892737211st_val(map_list_char_val(F),Xs)) = size_s2113983095t_char(Xs)) # label(fact_13_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 55 (all F all Xs size_s1143674878t_char(hAPP_l732421366t_char(map_va1934808527t_char(F),Xs)) = size_size_list_val(Xs)) # label(fact_14_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 56 (all F all Xs size_s1050794909ion_ty(hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs)) = size_size_list_ty(Xs)) # label(fact_15_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 57 (all F all Xs size_s1050794909ion_ty(hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs)) = size_size_list_val(Xs)) # label(fact_16_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 58 (all F all Xs size_s1050794909ion_ty(hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs)) = size_s1143674878t_char(Xs)) # label(fact_17_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 59 (all F all Xs size_s1050794909ion_ty(hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs)) = size_s2113983095t_char(Xs)) # label(fact_18_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 60 (all F all Xs size_s1143674878t_char(hAPP_l330149622t_char(map_op1779340173t_char(F),Xs)) = size_s1050794909ion_ty(Xs)) # label(fact_19_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 61 (all F all Xs size_size_list_val(hAPP_l336371937st_val(map_option_ty_val(F),Xs)) = size_s1050794909ion_ty(Xs)) # label(fact_20_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 62 (all F all Xs size_size_list_ty(hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs)) = size_s1050794909ion_ty(Xs)) # label(fact_21_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 63 (all F all Xs size_s2113983095t_char(hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs)) = size_s1050794909ion_ty(Xs)) # label(fact_22_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 64 (all F all Xs size_s2113983095t_char(hAPP_l407174677t_char(map_li1333403488t_char(F),Xs)) = size_s2113983095t_char(Xs)) # label(fact_23_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 65 (all F all Xs size_s1699857438on_val(hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs)) = size_s1699857438on_val(Xs)) # label(fact_24_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 66 (all F all Xs size_size_list_val(hAPP_l228474410st_val(map_option_val_val(F),Xs)) = size_s1595297126on_val(Xs)) # label(fact_25_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 67 (all F all Xs size_s1595297126on_val(hAPP_l297961988on_val(map_li50976719on_val(F),Xs)) = size_s2113983095t_char(Xs)) # label(fact_26_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 68 (all F all Xs size_s1050794909ion_ty(hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs)) = size_s1050794909ion_ty(Xs)) # label(fact_27_length__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 69 (all F all Xs all G all Ys (hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) -> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_28_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 70 (all F all Xs all G all Ys (hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) -> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_29_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 71 (all F all Xs all G all Ys (hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) -> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_30_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 72 (all F all Xs all G all Ys (hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) -> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_31_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 73 (all F all Xs all G all Ys (hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys))) # label(fact_32_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 74 (all F all Xs all G all Ys (hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys))) # label(fact_33_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 75 (all F all Xs all G all Ys (hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys))) # label(fact_34_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 76 (all F all Xs all G all Ys (hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_35_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 77 (all F all Xs all G all Ys (hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l1607890493on_val(map_ex1598883030on_val(G),Ys) -> size_s2113983095t_char(Xs) = size_s1143674878t_char(Ys))) # label(fact_36_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 78 (all F all Xs all G all Ys (hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys))) # label(fact_37_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 79 (all F all Xs all G all Ys (hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l2011456725t_char(map_ex101166958t_char(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys))) # label(fact_38_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 80 (all F all Xs all G all Ys (hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1539861698st_val(map_ex740158547ar_val(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys))) # label(fact_39_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 81 (all F all Xs all G all Ys (hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l2065413838t_char(map_ex2109939687t_char(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys))) # label(fact_40_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 82 (all F all Xs all G all Ys (hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l110066169ist_ty(map_exp_list_char_ty(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s1143674878t_char(Ys))) # label(fact_41_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 83 (all F all Xs all G all Ys (hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l922645359t_char(map_val_list_char(G),Ys) -> size_s2113983095t_char(Xs) = size_size_list_val(Ys))) # label(fact_42_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 84 (all F all Xs all G all Ys (hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l382831894on_val(map_va527586287on_val(G),Ys) -> size_s1699857438on_val(Xs) = size_size_list_val(Ys))) # label(fact_43_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 85 (all F all Xs all G all Ys (hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l273806049st_val(map_val_val(G),Ys) -> size_s1595297126on_val(Xs) = size_size_list_val(Ys))) # label(fact_44_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 86 (all F all Xs all G all Ys (hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l761459294on_val(map_val_option_val(G),Ys) -> size_s2113983095t_char(Xs) = size_size_list_val(Ys))) # label(fact_45_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 87 (all F all Xs all G all Ys (hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l273806049st_val(map_val_val(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys))) # label(fact_46_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 88 (all F all Xs all G all Ys (hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l922645359t_char(map_val_list_char(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys))) # label(fact_47_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 89 (all F all Xs all G all Ys (hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l1085267864ist_ty(map_val_ty(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_val(Ys))) # label(fact_48_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 90 (all F all Xs all G all Ys (hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) -> size_s2113983095t_char(Xs) = size_size_list_val(Ys))) # label(fact_49_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 91 (all F all Xs all G all Ys (hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys) -> size_s1143674878t_char(Xs) = size_size_list_val(Ys))) # label(fact_50_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 92 (all F all Xs all G all Ys (hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l402740472t_char(map_ty_list_char(G),Ys) -> size_s2113983095t_char(Xs) = size_size_list_ty(Ys))) # label(fact_51_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 93 (all F all Xs all G all Ys (hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l1634001311on_val(map_ty891785382on_val(G),Ys) -> size_s1699857438on_val(Xs) = size_size_list_ty(Ys))) # label(fact_52_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 94 (all F all Xs all G all Ys (hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l1530663448st_val(map_ty_val(G),Ys) -> size_s1595297126on_val(Xs) = size_size_list_ty(Ys))) # label(fact_53_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 95 (all F all Xs all G all Ys (hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l1014734695on_val(map_ty_option_val(G),Ys) -> size_s2113983095t_char(Xs) = size_size_list_ty(Ys))) # label(fact_54_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 96 (all F all Xs all G all Ys (hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l578807295t_char(map_ty_exp_list_char(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys))) # label(fact_55_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 97 (all F all Xs all G all Ys (hAPP_l336371937st_val(map_option_ty_val(F),Xs) = hAPP_l1530663448st_val(map_ty_val(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys))) # label(fact_56_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 98 (all F all Xs all G all Ys (hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l402740472t_char(map_ty_list_char(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys))) # label(fact_57_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 99 (all F all Xs all G all Ys (hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_list_ty_list_ty(map_ty_ty(G),Ys) -> size_s1050794909ion_ty(Xs) = size_size_list_ty(Ys))) # label(fact_58_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 100 (all F all Xs all G all Ys (hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) -> size_s2113983095t_char(Xs) = size_size_list_ty(Ys))) # label(fact_59_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 101 (all F all Xs all G all Ys (hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys) -> size_s1143674878t_char(Xs) = size_size_list_ty(Ys))) # label(fact_60_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 102 (all F all Xs all G all Ys (hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = hAPP_l418486716on_val(map_li1100402823on_val(G),Ys) -> size_s1699857438on_val(Xs) = size_s2113983095t_char(Ys))) # label(fact_61_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 103 (all F all Xs all G all Ys (hAPP_l228474410st_val(map_option_val_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys) -> size_s1595297126on_val(Xs) = size_s2113983095t_char(Ys))) # label(fact_62_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 104 (all F all Xs all G all Ys (hAPP_l305548949ion_ty(map_op1363057580ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_63_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 105 (all F all Xs all G all Ys (hAPP_l330149622t_char(map_op1779340173t_char(F),Xs) = hAPP_l740678812t_char(map_li1249123943t_char(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_64_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 106 (all F all Xs all G all Ys (hAPP_l1368737135t_char(map_op1924521862t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_65_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 107 (all F all Xs all G all Ys (hAPP_l1583451544ist_ty(map_option_ty_ty(F),Xs) = hAPP_l1871878770ist_ty(map_list_char_ty(G),Ys) -> size_s1050794909ion_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_66_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 108 (all F all Xs all G all Ys (hAPP_l2065413838t_char(map_ex2109939687t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) -> size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys))) # label(fact_67_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 109 (all F all Xs all G all Ys (hAPP_l1557845365on_val(map_ex840371726on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) -> size_s1143674878t_char(Xs) = size_s1699857438on_val(Ys))) # label(fact_68_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 110 (all F all Xs all G all Ys (hAPP_l1539861698st_val(map_ex740158547ar_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) -> size_s1143674878t_char(Xs) = size_s1595297126on_val(Ys))) # label(fact_69_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 111 (all F all Xs all G all Ys (hAPP_l1607890493on_val(map_ex1598883030on_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) -> size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys))) # label(fact_70_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 112 (all F all Xs all G all Ys (hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) -> size_s1143674878t_char(Xs) = size_s2113983095t_char(Ys))) # label(fact_71_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 113 (all F all Xs all G all Ys (hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) -> size_s1143674878t_char(Xs) = size_s1143674878t_char(Ys))) # label(fact_72_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 114 (all F all Xs all G all Ys (hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) -> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_73_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 115 (all F all Xs all G all Ys (hAPP_l2011456725t_char(map_ex101166958t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) -> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_74_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 116 (all F all Xs all G all Ys (hAPP_l1539861698st_val(map_ex740158547ar_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) -> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_75_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 117 (all F all Xs all G all Ys (hAPP_l2065413838t_char(map_ex2109939687t_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys) -> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_76_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 118 (all F all Xs all G all Ys (hAPP_l110066169ist_ty(map_exp_list_char_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys) -> size_s1143674878t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_77_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 119 (all F all Xs all G all Ys (hAPP_l922645359t_char(map_val_list_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) -> size_size_list_val(Xs) = size_s2113983095t_char(Ys))) # label(fact_78_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 120 (all F all Xs all G all Ys (hAPP_l382831894on_val(map_va527586287on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) -> size_size_list_val(Xs) = size_s1699857438on_val(Ys))) # label(fact_79_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 121 (all F all Xs all G all Ys (hAPP_l273806049st_val(map_val_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) -> size_size_list_val(Xs) = size_s1595297126on_val(Ys))) # label(fact_80_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 122 (all F all Xs all G all Ys (hAPP_l761459294on_val(map_val_option_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) -> size_size_list_val(Xs) = size_s2113983095t_char(Ys))) # label(fact_81_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 123 (all F all Xs all G all Ys (hAPP_l273806049st_val(map_val_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) -> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_82_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 124 (all F all Xs all G all Ys (hAPP_l922645359t_char(map_val_list_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys) -> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_83_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 125 (all F all Xs all G all Ys (hAPP_l1085267864ist_ty(map_val_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys) -> size_size_list_val(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_84_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 126 (all F all Xs all G all Ys (hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) -> size_size_list_val(Xs) = size_s2113983095t_char(Ys))) # label(fact_85_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 127 (all F all Xs all G all Ys (hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) -> size_size_list_val(Xs) = size_s1143674878t_char(Ys))) # label(fact_86_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.33 128 (all F all Xs all G all Ys (hAPP_l402740472t_char(map_ty_list_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) -> size_size_list_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_87_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 129 (all F all Xs all G all Ys (hAPP_l1634001311on_val(map_ty891785382on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) -> size_size_list_ty(Xs) = size_s1699857438on_val(Ys))) # label(fact_88_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 130 (all F all Xs all G all Ys (hAPP_l1530663448st_val(map_ty_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) -> size_size_list_ty(Xs) = size_s1595297126on_val(Ys))) # label(fact_89_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 131 (all F all Xs all G all Ys (hAPP_l1014734695on_val(map_ty_option_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) -> size_size_list_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_90_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 132 (all F all Xs all G all Ys (hAPP_l578807295t_char(map_ty_exp_list_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) -> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_91_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 133 (all F all Xs all G all Ys (hAPP_l1530663448st_val(map_ty_val(F),Xs) = hAPP_l336371937st_val(map_option_ty_val(G),Ys) -> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_92_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 134 (all F all Xs all G all Ys (hAPP_l402740472t_char(map_ty_list_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys) -> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_93_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 135 (all F all Xs all G all Ys (hAPP_list_ty_list_ty(map_ty_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys) -> size_size_list_ty(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_94_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 136 (all F all Xs all G all Ys (hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) -> size_size_list_ty(Xs) = size_s2113983095t_char(Ys))) # label(fact_95_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 137 (all F all Xs all G all Ys (hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) -> size_size_list_ty(Xs) = size_s1143674878t_char(Ys))) # label(fact_96_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 138 (all F all Xs all G all Ys (hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l407174677t_char(map_li1333403488t_char(G),Ys) -> size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys))) # label(fact_97_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 139 (all F all Xs all G all Ys (hAPP_l418486716on_val(map_li1100402823on_val(F),Xs) = hAPP_l1695428693on_val(map_Pr1655409582on_val(G),Ys) -> size_s2113983095t_char(Xs) = size_s1699857438on_val(Ys))) # label(fact_98_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 140 (all F all Xs all G all Ys (hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l228474410st_val(map_option_val_val(G),Ys) -> size_s2113983095t_char(Xs) = size_s1595297126on_val(Ys))) # label(fact_99_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 141 (all F all Xs all G all Ys (hAPP_l297961988on_val(map_li50976719on_val(F),Xs) = hAPP_l297961988on_val(map_li50976719on_val(G),Ys) -> size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys))) # label(fact_100_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 142 (all F all Xs all G all Ys (hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l305548949ion_ty(map_op1363057580ion_ty(G),Ys) -> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_101_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 143 (all F all Xs all G all Ys (hAPP_l740678812t_char(map_li1249123943t_char(F),Xs) = hAPP_l330149622t_char(map_op1779340173t_char(G),Ys) -> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_102_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 144 (all F all Xs all G all Ys (hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = hAPP_l1368737135t_char(map_op1924521862t_char(G),Ys) -> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_103_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 145 (all F all Xs all G all Ys (hAPP_l1871878770ist_ty(map_list_char_ty(F),Xs) = hAPP_l1583451544ist_ty(map_option_ty_ty(G),Ys) -> size_s2113983095t_char(Xs) = size_s1050794909ion_ty(Ys))) # label(fact_104_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 146 (all F all Xs all G all Ys (hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1491470139ion_ty(map_li771939206ion_ty(G),Ys) -> size_s2113983095t_char(Xs) = size_s2113983095t_char(Ys))) # label(fact_105_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 147 (all F all Xs all G all Ys (hAPP_l1491470139ion_ty(map_li771939206ion_ty(F),Xs) = hAPP_l1002225652ion_ty(map_ex1548475405ion_ty(G),Ys) -> size_s2113983095t_char(Xs) = size_s1143674878t_char(Ys))) # label(fact_106_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 148 (all X_1 all Pa ((all A all B_1 all C_3 all D hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D)))))) -> hBOOL(hAPP_P92196306r_bool(Pa,X_1)))) # label(fact_107_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 149 (all X_1 all Pa ((all A all B_1 all C_3 all D hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,produc1259058957on_val(B_1,produc899768717on_val(C_3,D)))))) -> hBOOL(hAPP_P282169671l_bool(Pa,X_1)))) # label(fact_108_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 150 (all Y_5 -(all A all B_1 all C_3 all D Y_5 != produc921874948t_char(A,produc1909267824t_char(B_1,produc1916172923t_char(C_3,D))))) # label(fact_109_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 151 (all Y_3 -(all A all B_1 all C_3 all D Y_3 != produc1441475159on_val(A,produc1259058957on_val(B_1,produc899768717on_val(C_3,D))))) # label(fact_110_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 152 (all A_5 all B_4 all A_4 all B_3 (produc921874948t_char(A_5,B_4) = produc921874948t_char(A_4,B_3) -> -(A_5 = A_4 -> B_4 != B_3))) # label(fact_111_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 153 (all A_5 all B_4 all A_4 all B_3 (produc1909267824t_char(A_5,B_4) = produc1909267824t_char(A_4,B_3) -> -(A_5 = A_4 -> B_4 != B_3))) # label(fact_112_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 154 (all A_5 all B_4 all A_4 all B_3 (produc1916172923t_char(A_5,B_4) = produc1916172923t_char(A_4,B_3) -> -(A_5 = A_4 -> B_4 != B_3))) # label(fact_113_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 155 (all A_1 all B all A_3 all B_2 (produc899768717on_val(A_1,B) = produc899768717on_val(A_3,B_2) -> -(A_1 = A_3 -> B != B_2))) # label(fact_114_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 156 (all A_1 all B all A_3 all B_2 (produc1441475159on_val(A_1,B) = produc1441475159on_val(A_3,B_2) -> -(A_1 = A_3 -> B != B_2))) # label(fact_115_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 157 (all A_1 all B all A_3 all B_2 (produc1259058957on_val(A_1,B) = produc1259058957on_val(A_3,B_2) -> -(A_1 = A_3 -> B != B_2))) # label(fact_116_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 158 (all A_1 all B all A_3 all B_2 (produc823076510on_val(A_1,B) = produc823076510on_val(A_3,B_2) -> -(A_1 = A_3 -> B != B_2))) # label(fact_117_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 159 (all A_1 all B all A_3 all B_2 (produc921874948t_char(A_1,B) = produc921874948t_char(A_3,B_2) <-> A_1 = A_3 & B = B_2)) # label(fact_118_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 160 (all A_1 all B all A_3 all B_2 (produc1909267824t_char(A_1,B) = produc1909267824t_char(A_3,B_2) <-> A_1 = A_3 & B = B_2)) # label(fact_119_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 161 (all A_1 all B all A_3 all B_2 (produc1916172923t_char(A_1,B) = produc1916172923t_char(A_3,B_2) <-> A_1 = A_3 & B = B_2)) # label(fact_120_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 162 (all A_1 all B all A_3 all B_2 (produc899768717on_val(A_1,B) = produc899768717on_val(A_3,B_2) <-> A_1 = A_3 & B = B_2)) # label(fact_121_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 163 (all A_1 all B all A_3 all B_2 (produc1441475159on_val(A_1,B) = produc1441475159on_val(A_3,B_2) <-> A_1 = A_3 & B = B_2)) # label(fact_122_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 164 (all A_1 all B all A_3 all B_2 (produc1259058957on_val(A_1,B) = produc1259058957on_val(A_3,B_2) <-> A_1 = A_3 & B = B_2)) # label(fact_123_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 165 (all A_1 all B all A_3 all B_2 (produc823076510on_val(A_1,B) = produc823076510on_val(A_3,B_2) <-> A_1 = A_3 & B = B_2)) # label(fact_124_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 166 (all Pa ((all X1 hBOOL(hAPP_P92196306r_bool(Pa,X1))) <-> (all A all B_1 hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,B_1)))))) # label(fact_125_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 167 (all Pa ((all X1 hBOOL(hAPP_P1907982426r_bool(Pa,X1))) <-> (all A all B_1 hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,B_1)))))) # label(fact_126_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 168 (all Pa ((all X1 hBOOL(hAPP_P2118621157r_bool(Pa,X1))) <-> (all A all B_1 hBOOL(hAPP_P2118621157r_bool(Pa,produc1916172923t_char(A,B_1)))))) # label(fact_127_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 169 (all Pa ((all X1 hBOOL(hAPP_P159683425l_bool(Pa,X1))) <-> (all A all B_1 hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A,B_1)))))) # label(fact_128_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 170 (all Pa ((all X1 hBOOL(hAPP_P282169671l_bool(Pa,X1))) <-> (all A all B_1 hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,B_1)))))) # label(fact_129_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 171 (all Pa ((all X1 hBOOL(hAPP_P1708370145l_bool(Pa,X1))) <-> (all A all B_1 hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,B_1)))))) # label(fact_130_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 172 (all Pa ((all X1 hBOOL(hAPP_P1235399154l_bool(Pa,X1))) <-> (all A all B_1 hBOOL(hAPP_P1235399154l_bool(Pa,produc823076510on_val(A,B_1)))))) # label(fact_131_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 173 (all Xs_2 all Ys_2 (size_s1050794909ion_ty(Xs_2) != size_s1050794909ion_ty(Ys_2) -> Xs_2 != Ys_2)) # label(fact_132_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 174 (all Xs_2 all Ys_2 (size_s2113983095t_char(Xs_2) != size_s2113983095t_char(Ys_2) -> Xs_2 != Ys_2)) # label(fact_133_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 175 (all Xs_2 all Ys_2 (size_size_list_ty(Xs_2) != size_size_list_ty(Ys_2) -> Xs_2 != Ys_2)) # label(fact_134_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 176 (all Xs_2 all Ys_2 (size_size_list_val(Xs_2) != size_size_list_val(Ys_2) -> Xs_2 != Ys_2)) # label(fact_135_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 177 (all Xs_2 all Ys_2 (size_s1143674878t_char(Xs_2) != size_s1143674878t_char(Ys_2) -> Xs_2 != Ys_2)) # label(fact_136_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 178 (all Xs all Ys (Xs = Ys <-> hBOOL(list_all2_ty_ty(fequal_ty,Xs,Ys)))) # label(fact_137_list__all2__eq) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 179 (all T_3 all P_2 all S_2 all U (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_2),U)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),U),T_3)) -> hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_2),T_3))))) # label(fact_138_widen__trans) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 180 (all Y_4 -(all A all B_1 all C_3 Y_4 != produc921874948t_char(A,produc1909267824t_char(B_1,C_3)))) # label(fact_139_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 181 (all Y_4 -(all A all B_1 all C_3 Y_4 != produc1909267824t_char(A,produc1916172923t_char(B_1,C_3)))) # label(fact_140_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 182 (all Y_3 -(all A all B_1 all C_3 Y_3 != produc1441475159on_val(A,produc1259058957on_val(B_1,C_3)))) # label(fact_141_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 183 (all Y_3 -(all A all B_1 all C_3 Y_3 != produc1259058957on_val(A,produc899768717on_val(B_1,C_3)))) # label(fact_142_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 184 (all X_1 all Pa ((all A all B_1 all C_3 hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,produc1909267824t_char(B_1,C_3))))) -> hBOOL(hAPP_P92196306r_bool(Pa,X_1)))) # label(fact_143_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 185 (all X_1 all Pa ((all A all B_1 all C_3 hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,produc1916172923t_char(B_1,C_3))))) -> hBOOL(hAPP_P1907982426r_bool(Pa,X_1)))) # label(fact_144_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 186 (all X_1 all Pa ((all A all B_1 all C_3 hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,produc1259058957on_val(B_1,C_3))))) -> hBOOL(hAPP_P282169671l_bool(Pa,X_1)))) # label(fact_145_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 187 (all X_1 all Pa ((all A all B_1 all C_3 hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,produc899768717on_val(B_1,C_3))))) -> hBOOL(hAPP_P1708370145l_bool(Pa,X_1)))) # label(fact_146_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 188 (all Pa all Ha all Vsa_1 all Ts_1 (hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Ts_1)) <-> (exists Ts_2 (hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa_1) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts_2) & hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_2,Ts_1)))))) # label(fact_147_confs__conv__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 189 (all Q all Pa all Xs all Ys (hBOOL(list_all2_ty_ty(Pa,Xs,Ys)) -> ((all Xs_1 all Ys_1 (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,Xs_1),Ys_1)) -> hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q,Xs_1),Ys_1)))) -> hBOOL(list_all2_ty_ty(Q,Xs,Ys))))) # label(fact_148_list__all2__mono) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 190 (all Q all Pa all Xs all Ys (hBOOL(list_all2_val_ty(Pa,Xs,Ys)) -> ((all Xs_1 all Ys_1 (hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Pa,Xs_1),Ys_1)) -> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(Q,Xs_1),Ys_1)))) -> hBOOL(list_all2_val_ty(Q,Xs,Ys))))) # label(fact_149_list__all2__mono) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 191 (all Xs all Pa ((all X_2 hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_2),X_2))) -> hBOOL(list_all2_ty_ty(Pa,Xs,Xs)))) # label(fact_150_list__all2__refl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 192 (all Xs all Ys all Q all Pa ((all X_2 all Y_1 (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Pa,X_2),Y_1)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(Q,Y_1),X_2)) -> X_2 = Y_1))) -> (hBOOL(list_all2_ty_ty(Pa,Xs,Ys)) -> (hBOOL(list_all2_ty_ty(Q,Ys,Xs)) -> Xs = Ys)))) # label(fact_151_list__all2__antisym) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 193 (all N_1 exists Xs_1 size_s1050794909ion_ty(Xs_1) = N_1) # label(fact_152_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 194 (all N_1 exists Xs_1 size_s1143674878t_char(Xs_1) = N_1) # label(fact_153_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 195 (all N_1 exists Xs_1 size_size_list_val(Xs_1) = N_1) # label(fact_154_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 196 (all N_1 exists Xs_1 size_size_list_ty(Xs_1) = N_1) # label(fact_155_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 197 (all N_1 exists Xs_1 size_s2113983095t_char(Xs_1) = N_1) # label(fact_156_Ex__list__of__length) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 198 (all T_2 all Pa all Ha all V_1 all Ta (hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),Ta),T_2)) -> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),T_2))))) # label(fact_157_conf__widen) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 199 (all Pa all Ha all V_1 all Ta (hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta) -> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta)))) # label(fact_158_typeof__conf) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 200 (all Ts_1 all Pa all Ha all Vsa_1 all Tsa (hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Tsa)) -> (hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Tsa,Ts_1)) -> hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Ts_1))))) # label(fact_159_confs__widens) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 201 (all Pa all Ha all V_1 all Ta (hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta)) <-> (exists T_1 (hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,T_1) & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1),Ta)))))) # label(fact_160_conf__def) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 202 (all Pa ((exists X1 hBOOL(hAPP_P1235399154l_bool(Pa,X1))) <-> (exists A exists B_1 hBOOL(hAPP_P1235399154l_bool(Pa,produc823076510on_val(A,B_1)))))) # label(fact_161_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 203 (all Pa ((exists X1 hBOOL(hAPP_P1708370145l_bool(Pa,X1))) <-> (exists A exists B_1 hBOOL(hAPP_P1708370145l_bool(Pa,produc1259058957on_val(A,B_1)))))) # label(fact_162_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 204 (all Pa ((exists X1 hBOOL(hAPP_P282169671l_bool(Pa,X1))) <-> (exists A exists B_1 hBOOL(hAPP_P282169671l_bool(Pa,produc1441475159on_val(A,B_1)))))) # label(fact_163_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 205 (all Pa ((exists X1 hBOOL(hAPP_P159683425l_bool(Pa,X1))) <-> (exists A exists B_1 hBOOL(hAPP_P159683425l_bool(Pa,produc899768717on_val(A,B_1)))))) # label(fact_164_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 206 (all Pa ((exists X1 hBOOL(hAPP_P2118621157r_bool(Pa,X1))) <-> (exists A exists B_1 hBOOL(hAPP_P2118621157r_bool(Pa,produc1916172923t_char(A,B_1)))))) # label(fact_165_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 207 (all Pa ((exists X1 hBOOL(hAPP_P1907982426r_bool(Pa,X1))) <-> (exists A exists B_1 hBOOL(hAPP_P1907982426r_bool(Pa,produc1909267824t_char(A,B_1)))))) # label(fact_166_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 208 (all Pa ((exists X1 hBOOL(hAPP_P92196306r_bool(Pa,X1))) <-> (exists A exists B_1 hBOOL(hAPP_P92196306r_bool(Pa,produc921874948t_char(A,B_1)))))) # label(fact_167_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 209 (all P -(all X_2 all Y_1 P != produc823076510on_val(X_2,Y_1))) # label(fact_168_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 210 (all P -(all X_2 all Y_1 P != produc1259058957on_val(X_2,Y_1))) # label(fact_169_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 211 (all P -(all X_2 all Y_1 P != produc1441475159on_val(X_2,Y_1))) # label(fact_170_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 212 (all P -(all X_2 all Y_1 P != produc899768717on_val(X_2,Y_1))) # label(fact_171_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 213 (all P_1 -(all X_2 all Y_1 P_1 != produc1916172923t_char(X_2,Y_1))) # label(fact_172_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 214 (all P_1 -(all X_2 all Y_1 P_1 != produc1909267824t_char(X_2,Y_1))) # label(fact_173_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 215 (all P_1 -(all X_2 all Y_1 P_1 != produc921874948t_char(X_2,Y_1))) # label(fact_174_PairE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 216 (all Y_3 -(all A all B_1 Y_3 != produc823076510on_val(A,B_1))) # label(fact_175_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 217 (all Y_3 -(all A all B_1 Y_3 != produc1259058957on_val(A,B_1))) # label(fact_176_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 218 (all Y_3 -(all A all B_1 Y_3 != produc1441475159on_val(A,B_1))) # label(fact_177_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 219 (all Y_3 -(all A all B_1 Y_3 != produc899768717on_val(A,B_1))) # label(fact_178_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 220 (all Y_2 -(all A all B_1 Y_2 != produc1916172923t_char(A,B_1))) # label(fact_179_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 221 (all Y_2 -(all A all B_1 Y_2 != produc1909267824t_char(A,B_1))) # label(fact_180_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 222 (all Y_2 -(all A all B_1 Y_2 != produc921874948t_char(A,B_1))) # label(fact_181_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 223 (all H all Pa all Ha all Vsa_1 all Tsa (hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,Ha),Vsa_1,Tsa)) -> (hBOOL(hext(Ha,H)) -> hBOOL(list_all2_val_ty(conf_P373316194t_char(Pa,H),Vsa_1,Tsa))))) # label(fact_182_confs__hext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 224 (all Pa all Ea all Ha all L_1 all E all H all L all Vsa_1 all Ps all Tsa (size_s2113983095t_char(Ps) = size_size_list_ty(Tsa) -> (size_s2113983095t_char(Ps) = size_size_list_val(Vsa_1) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,blocks(produc921874948t_char(Ps,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),E),produc899768717on_val(H,L))) -> (exists L_3 hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Ps,Vsa_1))),E),produc899768717on_val(H,L_3)))))))) # label(fact_183_blocksEval) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 225 (all Pa all V_1 all Ta all Ha all H (hBOOL(hext(Ha,H)) -> (hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_1),Ta)) -> hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,H),V_1),Ta))))) # label(fact_184_conf__hext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 226 (all V_1 all Ta all Ha all H (hBOOL(hext(Ha,H)) -> (hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta) -> hAPP_val_option_ty(typeof_h(H),V_1) = hAPP_ty_option_ty(some_ty,Ta)))) # label(fact_185_hext__typeof__mono) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 227 (all Pa all Ea all Ha all L_1 all E all H all L (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,produc899768717on_val(Ha,L_1)),E),produc899768717on_val(H,L))) -> hBOOL(hext(Ha,H)))) # label(fact_186_eval__hext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 228 (all Ha hBOOL(hext(Ha,Ha))) # label(fact_187_hext__refl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 229 (all H all Pa all Ha all E_1 all Ea all Ta (hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta)) -> (hBOOL(hext(Ha,H)) -> hBOOL(wTrt(Pa,H,E_1,Ea,Ta))))) # label(fact_188_WTrt__hext__mono) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 230 (all H_1 all Ha all H (hBOOL(hext(Ha,H)) -> (hBOOL(hext(H,H_1)) -> hBOOL(hext(Ha,H_1))))) # label(fact_189_hext__trans) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 231 (all Pa all E_1 all Ha all V_1 all Ta (hAPP_val_option_ty(typeof_h(Ha),V_1) = hAPP_ty_option_ty(some_ty,Ta) -> hBOOL(wTrt(Pa,Ha,E_1,hAPP_v834067052t_char(val_list_char,V_1),Ta)))) # label(fact_190_WTrtVal) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 232 (all Ha all L_1 all Pa all Ea all Vsa_1 all Vsa all Tsa (size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa) -> (size_size_list_val(Vsa_1) = size_size_list_ty(Tsa) -> (hBOOL(final_list_char(Ea)) -> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1))),transi2024712006on_val(red(Pa)))))))) # label(fact_191_blocksFinal) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 233 (all Pa all Ha all E_1 all Vsa_1 all Tsa (hBOOL(wTrts(Pa,Ha,E_1,hAPP_l732421366t_char(map_va1934808527t_char(val_list_char),Vsa_1),Tsa)) <-> hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(Ha)),Vsa_1) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Tsa))) # label(fact_192_WTrts__Val) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 234 (all A_1 all A_3 (hAPP_val_option_val(some_val,A_1) = hAPP_val_option_val(some_val,A_3) <-> A_1 = A_3)) # label(fact_193_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 235 (all A_1 all A_3 (hAPP_P1510515380on_val(some_P948696889on_val,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,A_3) <-> A_1 = A_3)) # label(fact_194_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 236 (all A_1 all A_3 (hAPP_ty_option_ty(some_ty,A_1) = hAPP_ty_option_ty(some_ty,A_3) <-> A_1 = A_3)) # label(fact_195_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 237 (all F all A_1 all B (hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B))) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B)))) # label(fact_196_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 238 (all F all A_1 all B (hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B)))) # label(fact_197_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 239 (all F all A_1 all B (hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B)))) # label(fact_198_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 240 (all F all A_1 all B (hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B))) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B)))) # label(fact_199_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 241 (all F all A_1 all B (hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B)))) # label(fact_200_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 242 (all F all A_1 all B (hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B))) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B)))) # label(fact_201_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 243 (all F all A_1 all B (hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B))) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B)))) # label(fact_202_curryI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 244 (all Pa all V_1 all S_1 hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S_1),hAPP_v834067052t_char(val_list_char,V_1)),S_1))) # label(fact_203_Val) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 245 (all Pa all V_1 all S_1 all E all S (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,V_1),S_1),E),S)) -> -(E = hAPP_v834067052t_char(val_list_char,V_1) -> S != S_1))) # label(fact_204_eval__cases_I2_J) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 246 (all H all Pa all Ha all E_1 all Es all Tsa (hBOOL(wTrts(Pa,Ha,E_1,Es,Tsa)) -> (hBOOL(hext(Ha,H)) -> hBOOL(wTrts(Pa,H,E_1,Es,Tsa))))) # label(fact_205_WTrts__hext__mono) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 247 (all Pa all Ha all E_1 all Es all Tsa (hBOOL(wTrts(Pa,Ha,E_1,Es,Tsa)) -> size_s1143674878t_char(Es) = size_size_list_ty(Tsa))) # label(fact_206_WTrts__same__length) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 248 (all Pa all Ea all S_1 all E all S (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),E),S)) -> hBOOL(final_list_char(E)))) # label(fact_207_eval__final) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 249 (all Pa all S_1 all Ea (hBOOL(final_list_char(Ea)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Ea,S_1),Ea),S_1)))) # label(fact_208_eval__finalId) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 250 (all F all A_1 all B (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B)) -> hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B))))) # label(fact_209_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 251 (all F all A_1 all B (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B)) -> hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B))))) # label(fact_210_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 252 (all F all A_1 all B (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B)) -> hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B))))) # label(fact_211_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 253 (all F all A_1 all B (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B)) -> hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B))))) # label(fact_212_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 254 (all F all A_1 all B (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B)) -> hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B))))) # label(fact_213_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 255 (all F all A_1 all B (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B)) -> hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B))))) # label(fact_214_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 256 (all F all A_1 all B (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B)) -> hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B))))) # label(fact_215_curryE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 257 (all F all A_1 all B (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F),A_1),B)) -> hBOOL(hAPP_P1235399154l_bool(F,produc823076510on_val(A_1,B))))) # label(fact_216_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 258 (all F all A_1 all B (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F),A_1),B)) -> hBOOL(hAPP_P1708370145l_bool(F,produc1259058957on_val(A_1,B))))) # label(fact_217_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 259 (all F all A_1 all B (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F),A_1),B)) -> hBOOL(hAPP_P282169671l_bool(F,produc1441475159on_val(A_1,B))))) # label(fact_218_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 260 (all F all A_1 all B (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F),A_1),B)) -> hBOOL(hAPP_P159683425l_bool(F,produc899768717on_val(A_1,B))))) # label(fact_219_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 261 (all F all A_1 all B (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F),A_1),B)) -> hBOOL(hAPP_P2118621157r_bool(F,produc1916172923t_char(A_1,B))))) # label(fact_220_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 262 (all F all A_1 all B (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F),A_1),B)) -> hBOOL(hAPP_P1907982426r_bool(F,produc1909267824t_char(A_1,B))))) # label(fact_221_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.34 263 (all F all A_1 all B (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F),A_1),B)) -> hBOOL(hAPP_P92196306r_bool(F,produc921874948t_char(A_1,B))))) # label(fact_222_curryD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 264 (all Ea all Ha all L_1 all E all H all L all Pa (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa))) -> hBOOL(hext(Ha,H)))) # label(fact_223_red__hext__incr) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 265 (all A_1 all R hBOOL(member773094996on_val(produc1441475159on_val(A_1,A_1),transi2024712006on_val(R)))) # label(fact_224_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 266 (all P all R (hBOOL(member773094996on_val(P,R)) -> hBOOL(member773094996on_val(P,transi2024712006on_val(R))))) # label(fact_225_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 267 (all E_1 all Ta all Ea all Ha all L_1 all E all H all L all Pa (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa))) -> (hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta)) -> (hBOOL(hconf_97414254t_char(Pa,Ha)) -> hBOOL(hconf_97414254t_char(Pa,H)))))) # label(fact_226_red__preserves__hconf) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 268 (all R transi2024712006on_val(transi2024712006on_val(R)) = transi2024712006on_val(R)) # label(fact_227_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 269 (all C_2 all A_1 all B all R (hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),R)) -> (hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),transi2024712006on_val(R))) -> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R)))))) # label(fact_228_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 270 (all C_2 all A_1 all B all R (hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R))) -> (hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),R)) -> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R)))))) # label(fact_229_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 271 (all C_2 all A_1 all B all R (hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R))) -> (hBOOL(member773094996on_val(produc1441475159on_val(B,C_2),transi2024712006on_val(R))) -> hBOOL(member773094996on_val(produc1441475159on_val(A_1,C_2),transi2024712006on_val(R)))))) # label(fact_230_rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 272 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) -> ((all A all B_1 all Aa all Ba (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(A,B_1)),transi2024712006on_val(R))) -> (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Aa,Ba)),R)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A),B_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)))))) # label(fact_231_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 273 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(Bx,By)),transi61620055on_val(R))) -> (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) -> ((all A all B_1 all Aa all Ba (hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(A,B_1)),transi61620055on_val(R))) -> (hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Aa,Ba)),R)) -> (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A),B_1)) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)))))) # label(fact_232_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 274 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R))) -> (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) -> ((all A all B_1 all Aa all Ba (hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(A,B_1)),transi910771962on_val(R))) -> (hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Aa,Ba)),R)) -> (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A),B_1)) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)))))) # label(fact_233_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 275 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R))) -> (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) -> ((all A all B_1 all Aa all Ba (hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(A,B_1)),transi921647814on_val(R))) -> (hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Aa,Ba)),R)) -> (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A),B_1)) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)))))) # label(fact_234_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 276 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(Bx,By)),transi1789604888t_char(R))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) -> ((all A all B_1 all Aa all Ba (hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(A,B_1)),transi1789604888t_char(R))) -> (hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Aa,Ba)),R)) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A),B_1)) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)))))) # label(fact_235_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 277 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(Bx,By)),transi1257872013t_char(R))) -> (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) -> ((all A all B_1 all Aa all Ba (hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(A,B_1)),transi1257872013t_char(R))) -> (hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Aa,Ba)),R)) -> (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A),B_1)) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)))))) # label(fact_236_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 278 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(Bx,By)),transi122195895t_char(R))) -> (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) -> ((all A all B_1 all Aa all Ba (hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(A,B_1)),transi122195895t_char(R))) -> (hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Aa,Ba)),R)) -> (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A),B_1)) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)))))) # label(fact_237_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 279 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ax,Ay),produc1259058957on_val(Bx,By)),transi2024712006on_val(R))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) -> ((all A all B_1 all Aa all Ba (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Aa,Ba)),R)) -> (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Aa,Ba),produc1259058957on_val(Bx,By)),transi2024712006on_val(R))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A),B_1)))))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)))))) # label(fact_238_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 280 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Ax,Ay),produc823076510on_val(Bx,By)),transi61620055on_val(R))) -> (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) -> ((all A all B_1 all Aa all Ba (hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Aa,Ba)),R)) -> (hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Aa,Ba),produc823076510on_val(Bx,By)),transi61620055on_val(R))) -> (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A),B_1)))))) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)))))) # label(fact_239_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 281 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Ax,Ay),produc1441475159on_val(Bx,By)),transi910771962on_val(R))) -> (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) -> ((all A all B_1 all Aa all Ba (hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Aa,Ba)),R)) -> (hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Aa,Ba),produc1441475159on_val(Bx,By)),transi910771962on_val(R))) -> (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A),B_1)))))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)))))) # label(fact_240_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 282 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Ax,Ay),produc899768717on_val(Bx,By)),transi921647814on_val(R))) -> (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) -> ((all A all B_1 all Aa all Ba (hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Aa,Ba)),R)) -> (hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Aa,Ba),produc899768717on_val(Bx,By)),transi921647814on_val(R))) -> (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A),B_1)))))) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)))))) # label(fact_241_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 283 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Ax,Ay),produc1916172923t_char(Bx,By)),transi1789604888t_char(R))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) -> ((all A all B_1 all Aa all Ba (hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Aa,Ba)),R)) -> (hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Aa,Ba),produc1916172923t_char(Bx,By)),transi1789604888t_char(R))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A),B_1)))))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)))))) # label(fact_242_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 284 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Ax,Ay),produc1909267824t_char(Bx,By)),transi1257872013t_char(R))) -> (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) -> ((all A all B_1 all Aa all Ba (hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Aa,Ba)),R)) -> (hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Aa,Ba),produc1909267824t_char(Bx,By)),transi1257872013t_char(R))) -> (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A),B_1)))))) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)))))) # label(fact_243_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 285 (all Pa all Ax all Ay all Bx all By all R (hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Ax,Ay),produc921874948t_char(Bx,By)),transi122195895t_char(R))) -> (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) -> ((all A all B_1 all Aa all Ba (hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Aa,Ba)),R)) -> (hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Aa,Ba),produc921874948t_char(Bx,By)),transi122195895t_char(R))) -> (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A),B_1)))))) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)))))) # label(fact_244_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 286 (all Xa_1 all Xb all Za all Zb all R (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa_1,Xb),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R))) -> (produc1259058957on_val(Xa_1,Xb) != produc1259058957on_val(Za,Zb) -> -(all A all B_1 (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Xa_1,Xb),produc1259058957on_val(A,B_1)),R)) -> -hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(A,B_1),produc1259058957on_val(Za,Zb)),transi2024712006on_val(R)))))))) # label(fact_245_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 287 (all Xa_1 all Xb all Za all Zb all R (hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Xa_1,Xb),produc823076510on_val(Za,Zb)),transi61620055on_val(R))) -> (produc823076510on_val(Xa_1,Xb) != produc823076510on_val(Za,Zb) -> -(all A all B_1 (hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(Xa_1,Xb),produc823076510on_val(A,B_1)),R)) -> -hBOOL(member1322055188on_val(produc499151895on_val(produc823076510on_val(A,B_1),produc823076510on_val(Za,Zb)),transi61620055on_val(R)))))))) # label(fact_246_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 288 (all Xa_1 all Xb all Za all Zb all R (hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa_1,Xb),produc1441475159on_val(Za,Zb)),transi910771962on_val(R))) -> (produc1441475159on_val(Xa_1,Xb) != produc1441475159on_val(Za,Zb) -> -(all A all B_1 (hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(Xa_1,Xb),produc1441475159on_val(A,B_1)),R)) -> -hBOOL(member808015754on_val(produc1564932627on_val(produc1441475159on_val(A,B_1),produc1441475159on_val(Za,Zb)),transi910771962on_val(R)))))))) # label(fact_247_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 289 (all Xa_1 all Xb all Za all Zb all R (hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa_1,Xb),produc899768717on_val(Za,Zb)),transi921647814on_val(R))) -> (produc899768717on_val(Xa_1,Xb) != produc899768717on_val(Za,Zb) -> -(all A all B_1 (hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(Xa_1,Xb),produc899768717on_val(A,B_1)),R)) -> -hBOOL(member563141460on_val(produc870913623on_val(produc899768717on_val(A,B_1),produc899768717on_val(Za,Zb)),transi921647814on_val(R)))))))) # label(fact_248_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 290 (all Xa_1 all Xb all Za all Zb all R (hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Xa_1,Xb),produc1916172923t_char(Za,Zb)),transi1789604888t_char(R))) -> (produc1916172923t_char(Xa_1,Xb) != produc1916172923t_char(Za,Zb) -> -(all A all B_1 (hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(Xa_1,Xb),produc1916172923t_char(A,B_1)),R)) -> -hBOOL(member1161907014t_char(produc1299387215t_char(produc1916172923t_char(A,B_1),produc1916172923t_char(Za,Zb)),transi1789604888t_char(R)))))))) # label(fact_249_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 291 (all Xa_1 all Xb all Za all Zb all R (hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Xa_1,Xb),produc1909267824t_char(Za,Zb)),transi1257872013t_char(R))) -> (produc1909267824t_char(Xa_1,Xb) != produc1909267824t_char(Za,Zb) -> -(all A all B_1 (hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(Xa_1,Xb),produc1909267824t_char(A,B_1)),R)) -> -hBOOL(member125098544t_char(produc57279289t_char(produc1909267824t_char(A,B_1),produc1909267824t_char(Za,Zb)),transi1257872013t_char(R)))))))) # label(fact_250_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 292 (all Xa_1 all Xb all Za all Zb all R (hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Xa_1,Xb),produc921874948t_char(Za,Zb)),transi122195895t_char(R))) -> (produc921874948t_char(Xa_1,Xb) != produc921874948t_char(Za,Zb) -> -(all A all B_1 (hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(Xa_1,Xb),produc921874948t_char(A,B_1)),R)) -> -hBOOL(member1420286996t_char(produc24551831t_char(produc921874948t_char(A,B_1),produc921874948t_char(Za,Zb)),transi122195895t_char(R)))))))) # label(fact_251_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 293 (all A_1 all B all R (hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R))) -> (A_1 != B -> -(all Y_1 (hBOOL(member773094996on_val(produc1441475159on_val(A_1,Y_1),transi2024712006on_val(R))) -> -hBOOL(member773094996on_val(produc1441475159on_val(Y_1,B),R))))))) # label(fact_252_rtranclE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 294 (all X_1 all Z_1 all R (hBOOL(member773094996on_val(produc1441475159on_val(X_1,Z_1),transi2024712006on_val(R))) -> (X_1 != Z_1 -> -(all Y_1 (hBOOL(member773094996on_val(produc1441475159on_val(X_1,Y_1),R)) -> -hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z_1),transi2024712006on_val(R)))))))) # label(fact_253_converse__rtranclE) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 295 (all Pa all A_1 all B all R (hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R))) -> (hBOOL(hAPP_P1708370145l_bool(Pa,B)) -> ((all Y_1 all Z (hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z),R)) -> (hBOOL(member773094996on_val(produc1441475159on_val(Z,B),transi2024712006on_val(R))) -> (hBOOL(hAPP_P1708370145l_bool(Pa,Z)) -> hBOOL(hAPP_P1708370145l_bool(Pa,Y_1)))))) -> hBOOL(hAPP_P1708370145l_bool(Pa,A_1)))))) # label(fact_254_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 296 (all Pa all A_1 all B all R (hBOOL(member773094996on_val(produc1441475159on_val(A_1,B),transi2024712006on_val(R))) -> (hBOOL(hAPP_P1708370145l_bool(Pa,A_1)) -> ((all Y_1 all Z (hBOOL(member773094996on_val(produc1441475159on_val(A_1,Y_1),transi2024712006on_val(R))) -> (hBOOL(member773094996on_val(produc1441475159on_val(Y_1,Z),R)) -> (hBOOL(hAPP_P1708370145l_bool(Pa,Y_1)) -> hBOOL(hAPP_P1708370145l_bool(Pa,Z)))))) -> hBOOL(hAPP_P1708370145l_bool(Pa,B)))))) # label(fact_255_rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 297 (all E_1 all Ta all Ea all Ha all L_1 all E all H all L all Pa (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa))) -> (hBOOL(wTrt(Pa,Ha,E_1,Ea,Ta)) -> (hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1)) -> hBOOL(lconf_496643946t_char(Pa,H,L,E_1)))))) # label(fact_256_red__preserves__lconf) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 298 (all L_2 all Ea all Ha all L_1 all E all H all L all Pa all Vsa_1 all Vsa all Tsa (size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa) -> (size_size_list_val(Vsa_1) = size_size_list_ty(Tsa) -> (hBOOL(distinct_list_char(Vsa)) -> (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Vsa,Vsa_1))),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa)))) -> (hBOOL(final_list_char(E)) -> (L_2 = overri2012515291on_val(L,L_1,set_list_char(Vsa)) -> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L_2))),transi2024712006on_val(red(Pa))))))))))) # label(fact_257_blocksRedsFinal) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 299 (all F all Xs all G (hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs) <-> (all X_2 (hBOOL(member_list_char(X_2,set_list_char(Xs))) -> hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2))))) # label(fact_258_map__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 300 (all F all Xs all G (hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs) <-> (all X_2 (hBOOL(member_val(X_2,set_val(Xs))) -> hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2))))) # label(fact_259_map__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 301 (all F all Xs all G (hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs) <-> (all X_2 (hBOOL(member_ty(X_2,set_ty(Xs))) -> hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2))))) # label(fact_260_map__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 302 (all F all Xs all G (hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs) <-> (all X_2 (hBOOL(member_val(X_2,set_val(Xs))) -> hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2))))) # label(fact_261_map__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 303 (all X_1 all A_2 (hBOOL(member773094996on_val(X_1,A_2)) <-> hBOOL(hAPP_P282169671l_bool(A_2,X_1)))) # label(fact_262_mem__def) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 304 (all H all Pa all Ha all L_1 all E_1 (hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1)) -> (hBOOL(hext(Ha,H)) -> hBOOL(lconf_496643946t_char(Pa,H,L_1,E_1))))) # label(fact_263_lconf__hext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 305 (all Pa all Ha all L_1 all E_1 (hBOOL(lconf_496643946t_char(Pa,Ha,L_1,E_1)) <-> (all V_3 all V_2 (hAPP_l207779698on_val(L_1,V_3) = hAPP_val_option_val(some_val,V_2) -> (exists T (hAPP_l512744617ion_ty(E_1,V_3) = hAPP_ty_option_ty(some_ty,T) & hBOOL(hAPP_ty_bool(hAPP_val_fun_ty_bool(conf_P373316194t_char(Pa,Ha),V_2),T)))))))) # label(fact_264_lconf__def) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 306 (all Ea all Ha all L_1 all E all H all L all Pa all Vsa_1 all Vsa all Tsa (size_s2113983095t_char(Vsa) = size_size_list_ty(Tsa) -> (size_size_list_val(Vsa_1) = size_size_list_ty(Tsa) -> (hBOOL(distinct_list_char(Vsa)) -> (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_up1085636310ar_val(L_1,Vsa,Vsa_1))),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa)))) -> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(Vsa_1,Ea)))),produc899768717on_val(Ha,L_1)),produc1259058957on_val(blocks(produc921874948t_char(Vsa,produc1909267824t_char(Tsa,produc1916172923t_char(hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(the_val,L)),Vsa),E)))),produc899768717on_val(H,overri2012515291on_val(L,L_1,set_list_char(Vsa))))),transi2024712006on_val(red(Pa))))))))) # label(fact_265_blocksReds) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 307 (all F all G comp_l1825390573t_char(map_option_val_val(F),map_li50976719on_val(G)) = map_list_char_val(comp_o1129292306t_char(F,G))) # label(fact_266_List_Omap_Ocomp) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 308 (all F all G comp_l1825390573t_char(map_option_val_val(F),map_li50976719on_val(G)) = map_list_char_val(comp_o1129292306t_char(F,G))) # label(fact_267_map__comp__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 309 (all F all G all Xs hAPP_l228474410st_val(map_option_val_val(F),hAPP_l297961988on_val(map_li50976719on_val(G),Xs)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F,G)),Xs)) # label(fact_268_map__map) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 310 (all F all G all List hAPP_l228474410st_val(map_option_val_val(F),hAPP_l297961988on_val(map_li50976719on_val(G),List)) = hAPP_l1892737211st_val(map_list_char_val(comp_o1129292306t_char(F,G)),List)) # label(fact_269_List_Omap_Ocompositionality) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 311 (all X_3 hAPP_option_val_val(the_val,hAPP_val_option_val(some_val,X_3)) = X_3) # label(fact_270_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 312 (all X_1 hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_P1510515380on_val(some_P948696889on_val,X_1)) = X_1) # label(fact_271_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 313 (all X_3 hAPP_option_ty_ty(the_ty,hAPP_ty_option_ty(some_ty,X_3)) = X_3) # label(fact_272_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 314 (all Ys all F ((exists Xs_1 Ys = hAPP_l1892737211st_val(map_list_char_val(F),Xs_1)) <-> (all X_2 (hBOOL(member_val(X_2,set_val(Ys))) -> (exists Xa X_2 = hAPP_list_char_val(F,Xa)))))) # label(fact_273_ex__map__conv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 315 (all Ys all F ((exists Xs_1 Ys = hAPP_l732421366t_char(map_va1934808527t_char(F),Xs_1)) <-> (all X_2 (hBOOL(member_exp_list_char(X_2,set_exp_list_char(Ys))) -> (exists Xa X_2 = hAPP_v834067052t_char(F,Xa)))))) # label(fact_274_ex__map__conv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 316 (all Ys all F ((exists Xs_1 Ys = hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs_1)) <-> (all X_2 (hBOOL(member_option_ty(X_2,set_option_ty(Ys))) -> (exists Xa X_2 = hAPP_ty_option_ty(F,Xa)))))) # label(fact_275_ex__map__conv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 317 (all Ys all F ((exists Xs_1 Ys = hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs_1)) <-> (all X_2 (hBOOL(member_option_ty(X_2,set_option_ty(Ys))) -> (exists Xa X_2 = hAPP_val_option_ty(F,Xa)))))) # label(fact_276_ex__map__conv) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 318 (all F all G all Xs ((all X_2 (hBOOL(member_list_char(X_2,set_list_char(Xs))) -> hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2))) -> hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Xs))) # label(fact_277_map__ext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 319 (all F all G all Xs ((all X_2 (hBOOL(member_val(X_2,set_val(Xs))) -> hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2))) -> hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Xs))) # label(fact_278_map__ext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 320 (all F all G all Xs ((all X_2 (hBOOL(member_ty(X_2,set_ty(Xs))) -> hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2))) -> hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Xs))) # label(fact_279_map__ext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 321 (all F all G all Xs ((all X_2 (hBOOL(member_val(X_2,set_val(Xs))) -> hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2))) -> hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Xs))) # label(fact_280_map__ext) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 322 (all F all G all Xs all Ys (Xs = Ys -> ((all X_2 (hBOOL(member_list_char(X_2,set_list_char(Ys))) -> hAPP_list_char_val(F,X_2) = hAPP_list_char_val(G,X_2))) -> hAPP_l1892737211st_val(map_list_char_val(F),Xs) = hAPP_l1892737211st_val(map_list_char_val(G),Ys)))) # label(fact_281_map__cong) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 323 (all F all G all Xs all Ys (Xs = Ys -> ((all X_2 (hBOOL(member_val(X_2,set_val(Ys))) -> hAPP_v834067052t_char(F,X_2) = hAPP_v834067052t_char(G,X_2))) -> hAPP_l732421366t_char(map_va1934808527t_char(F),Xs) = hAPP_l732421366t_char(map_va1934808527t_char(G),Ys)))) # label(fact_282_map__cong) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 324 (all F all G all Xs all Ys (Xs = Ys -> ((all X_2 (hBOOL(member_ty(X_2,set_ty(Ys))) -> hAPP_ty_option_ty(F,X_2) = hAPP_ty_option_ty(G,X_2))) -> hAPP_l1487035934ion_ty(map_ty_option_ty(F),Xs) = hAPP_l1487035934ion_ty(map_ty_option_ty(G),Ys)))) # label(fact_283_map__cong) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 325 (all F all G all Xs all Ys (Xs = Ys -> ((all X_2 (hBOOL(member_val(X_2,set_val(Ys))) -> hAPP_val_option_ty(F,X_2) = hAPP_val_option_ty(G,X_2))) -> hAPP_l2006940821ion_ty(map_val_option_ty(F),Xs) = hAPP_l2006940821ion_ty(map_val_option_ty(G),Ys)))) # label(fact_284_map__cong) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 326 (all F all Xs ((all X_2 (hBOOL(member_list_char(X_2,set_list_char(Xs))) -> hAPP_l1074208899t_char(F,X_2) = X_2)) -> hAPP_l407174677t_char(map_li1333403488t_char(F),Xs) = Xs)) # label(fact_285_map__idI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 327 (all F all Xs ((all X_2 (hBOOL(member773094996on_val(X_2,set_Pr1921835862on_val(Xs))) -> hAPP_P918220497on_val(F,X_2) = X_2)) -> hAPP_l1695428693on_val(map_Pr1655409582on_val(F),Xs) = Xs)) # label(fact_286_map__idI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 328 (all F all Ys all X_1 all Xs (-hBOOL(member_list_char(X_1,set_list_char(Xs))) -> hAPP_l207779698on_val(map_up1085636310ar_val(F,Xs,Ys),X_1) = hAPP_l207779698on_val(F,X_1))) # label(fact_287_map__upds__apply__nontin) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 329 (all F all Ys all X_1 all Xs (-hBOOL(member_list_char(X_1,set_list_char(Xs))) -> hAPP_l512744617ion_ty(map_up891053837har_ty(F,Xs,Ys),X_1) = hAPP_l512744617ion_ty(F,X_1))) # label(fact_288_map__upds__apply__nontin) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 330 (all L_0 all Ea all Ha all L_1 all E all H all L all Pa (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),transi2024712006on_val(red(Pa)))) -> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,L_1))),produc1259058957on_val(E,produc899768717on_val(H,map_ad325961431ar_val(L_0,L)))),transi2024712006on_val(red(Pa)))))) # label(fact_289_Red__lcl__add) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 331 (all M all N all K all Xx (hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,Xx) -> hAPP_l207779698on_val(map_ad325961431ar_val(M,N),K) = hAPP_val_option_val(some_val,Xx))) # label(fact_290_map__add__find__right) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 332 (all M1 all M2 all M3 map_ad325961431ar_val(M1,map_ad325961431ar_val(M2,M3)) = map_ad325961431ar_val(map_ad325961431ar_val(M1,M2),M3)) # label(fact_291_map__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.35 333 (all M1 all M2 all Xs all Ys map_ad325961431ar_val(M1,map_up1085636310ar_val(M2,Xs,Ys)) = map_up1085636310ar_val(map_ad325961431ar_val(M1,M2),Xs,Ys)) # label(fact_292_map__add__upds) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 334 (all M1 all M2 all Xs all Ys map_add_list_char_ty(M1,map_up891053837har_ty(M2,Xs,Ys)) = map_up891053837har_ty(map_add_list_char_ty(M1,M2),Xs,Ys)) # label(fact_293_map__add__upds) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 335 (all L_0 all Ea all Ha all L_1 all E all H all L all Pa (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,L_1)),produc1259058957on_val(E,produc899768717on_val(H,L))),red(Pa))) -> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,produc899768717on_val(Ha,map_ad325961431ar_val(L_0,L_1))),produc1259058957on_val(E,produc899768717on_val(H,map_ad325961431ar_val(L_0,L)))),red(Pa))))) # label(fact_294_red__lcl__add) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 336 (all Ha all H (hBOOL(hext(Ha,H)) <-> (all A all C_1 all Fs (hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs)) -> (exists Fs_1 hAPP_n546249108on_val(H,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs_1))))))) # label(fact_295_hext__def) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 337 (all A_1 all C all Fs_2 all Ha all H (hBOOL(hext(Ha,H)) -> (hAPP_n546249108on_val(Ha,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_2)) -> (exists Fs_1 hAPP_n546249108on_val(H,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C,Fs_1)))))) # label(fact_296_hext__objD) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 338 (all H all Ha ((all A all C_1 all Fs (hAPP_n546249108on_val(Ha,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs)) -> (exists Fs_1 hAPP_n546249108on_val(H,A) = hAPP_P1510515380on_val(some_P948696889on_val,produc823076510on_val(C_1,Fs_1))))) -> hBOOL(hext(Ha,H)))) # label(fact_297_hextI) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 339 (all C all V all E_2 all Ea all S_1 all V_1 all S all Pa (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa)))) -> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(Ea,C,V),E_2),S_1),produc1259058957on_val(hAPP_v834067052t_char(val_list_char,V_1),S)),transi2024712006on_val(red(Pa)))))) # label(fact_298_TryRedsVal) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 340 (all C all V all E_2 all Ea all S_1 all E all S all Pa (hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(Ea,S_1),produc1259058957on_val(E,S)),red(Pa))) -> hBOOL(member773094996on_val(produc1441475159on_val(produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(Ea,C,V),E_2),S_1),produc1259058957on_val(hAPP_e1353749905t_char(tryCatch_list_char(E,C,V),E_2),S)),red(Pa))))) # label(fact_299_red__reds_OTryRed) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 341 (all X all Y (-hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(fequal_ty,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Type__Oty_T) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 342 (all X all Y (X != Y | hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(fequal_ty,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Type__Oty_T) # label(axiom) # label(non_clause). [assumption].
% 1.04/1.41 343 -(hBOOL(wTrt(p,h,e_1,blocks(produc921874948t_char(vs_1,produc1909267824t_char(ts,produc1916172923t_char(vs,e)))),t)) <-> hBOOL(wTrt(p,h,map_up891053837har_ty(e_1,vs_1,ts),e,t)) & (exists Ts (hAPP_l2006940821ion_ty(map_val_option_ty(typeof_h(h)),vs) = hAPP_l1487035934ion_ty(map_ty_option_ty(some_ty),Ts) & hBOOL(list_all2_ty_ty(widen_2090681816t_char(p),Ts,ts))))) # label(conj_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.04/1.41
% 1.04/1.41 ============================== end of process non-clausal formulas ===
% 1.04/1.41
% 1.04/1.41 ============================== PROCESS INITIAL CLAUSES ===============
% 1.04/1.41
% 1.04/1.41 ============================== PREDICATE ELIMINATION =================
% 1.04/1.41
% 1.04/1.41 ============================== end predicate elimination =============
% 1.04/1.41
% 1.04/1.41 Auto_denials: (non-Horn, no changes).
% 1.04/1.56
% 1.04/1.56 Term ordering decisions:
% 1.04/1.56 Function symbol KB weights: some_ty=1. some_P948696889on_val=1. some_val=1. val_list_char=1. ts=1. h=1. p=1. vs=1. vs_1=1. e=1. e_1=1. fequal_ty=1. t=1. the_val=1. the_Pr431167171on_val=1. the_ty=1. c1=1. produc1441475159on_val=1. produc1259058957on_val=1. produc899768717on_val=1. produc1909267824t_char=1. member773094996on_val=1. produc1916172923t_char=1. produc921874948t_char=1. produc823076510on_val=1. hAPP_P1708370145l_bool=1. hAPP_P159683425l_bool=1. hAPP_P1907982426r_bool=1. hAPP_P2118621157r_bool=1. hAPP_e1833980889l_bool=1. hAPP_l1487035934ion_ty=1. hAPP_l2006940821ion_ty=1. hAPP_ty_bool=1. hAPP_l1892737211st_val=1. hAPP_P1116729363l_bool=1. hAPP_e544220455r_bool=1. hAPP_f1033709212l_bool=1. hAPP_f1175813647l_bool=1. hAPP_f1715346603l_bool=1. hAPP_l1062423959r_bool=1. hAPP_l1987619678r_bool=1. hAPP_l217977712r_bool=1. hAPP_l465799708l_bool=1. hAPP_ty_option_ty=1. hAPP_l732421366t_char=1. hAPP_v834067052t_char=1. hext=1. conf_P373316194t_char=1. hAPP_P282169671l_bool=1. hAPP_val_option_ty=1. member1161907014t_char=1. member125098544t_char=1. member1322055188on_val=1. member1420286996t_char=1. member563141460on_val=1. member808015754on_val=1. produc1299387215t_char=1. produc1564932627on_val=1. produc24551831t_char=1. produc499151895on_val=1. produc57279289t_char=1. produc870913623on_val=1. hAPP_P92196306r_bool=1. hAPP_ty_fun_ty_bool=1. hAPP_P1510515380on_val=1. hAPP_l407174677t_char=1. hAPP_val_fun_ty_bool=1. hAPP_P1235399154l_bool=1. hAPP_l1002225652ion_ty=1. hAPP_l1491470139ion_ty=1. hAPP_l297961988on_val=1. map_ad325961431ar_val=1. hAPP_l1695428693on_val=1. hAPP_l228474410st_val=1. hAPP_list_char_val=1. hAPP_val_option_val=1. member_val=1. hAPP_l1368737135t_char=1. hAPP_l1583451544ist_ty=1. hAPP_l305548949ion_ty=1. hAPP_l330149622t_char=1. hAPP_l336371937st_val=1. hAPP_n546249108on_val=1. hAPP_l207779698on_val=1. member_list_char=1. comp_o1129292306t_char=1. hAPP_l1530663448st_val=1. hAPP_l273806049st_val=1. hAPP_l402740472t_char=1. hAPP_l512744617ion_ty=1. hAPP_l922645359t_char=1. member_option_ty=1. member_ty=1. hAPP_e1353749905t_char=1. hAPP_l1539861698st_val=1. hAPP_l2065413838t_char=1. comp_l1825390573t_char=1. hAPP_l1014734695on_val=1. hAPP_l1085267864ist_ty=1. hAPP_l110066169ist_ty=1. hAPP_l1607890493on_val=1. hAPP_l1634001311on_val=1. hAPP_l1871878770ist_ty=1. hAPP_l2011456725t_char=1. hAPP_l382831894on_val=1. hAPP_l418486716on_val=1. hAPP_l578807295t_char=1. hAPP_l740678812t_char=1. hAPP_l761459294on_val=1. hAPP_list_ty_list_ty=1. hconf_97414254t_char=1. map_add_list_char_ty=1. member_exp_list_char=1. hAPP_P918220497on_val=1. hAPP_l1074208899t_char=1. hAPP_l1557845365on_val=1. hAPP_o1977518472on_val=1. hAPP_option_ty_ty=1. hAPP_option_val_val=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f67=1. f210=1. f211=1. f213=1. f214=1. f216=1. f217=1. f219=1. f220=1. f229=1. f230=1. f232=1. f233=1. f234=1. f236=1. f237=1. f238=1. size_s1050794909ion_ty=1. size_s2113983095t_char=1. transi2024712006on_val=1. size_size_list_ty=1. size_size_list_val=1. size_s1143674878t_char=1. map_ty_option_ty=1. map_val_option_ty=1. map_list_char_val=1. map_va1934808527t_char=1. red=1. widen_2090681816t_char=1. map_li50976719on_val=1. transi122195895t_char=1. transi1257872013t_char=1. transi1789604888t_char=1. transi61620055on_val=1. transi910771962on_val=1. transi921647814on_val=1. map_li1333403488t_char=1. map_option_val_val=1. map_ex1548475405ion_ty=1. map_li771939206ion_ty=1. typeof_h=1. map_Pr1655409582on_val=1. set_val=1. map_op1363057580ion_ty=1. map_op1779340173t_char=1. map_op1924521862t_char=1. map_option_ty_ty=1. map_option_ty_val=1. set_list_char=1. size_s1595297126on_val=1. size_s1699857438on_val=1. blocks=1. final_list_char=1. map_ty_list_char=1. map_ty_val=1. map_val_list_char=1. map_val_val=1. set_option_ty=1. set_ty=1. map_ex2109939687t_char=1. map_ex740158547ar_val=1. produc1159035454l_bool=1. produc156891095r_bool=1. produc1574020101r_bool=1. produc1911975310l_bool=1. produc2062775566l_bool=1. produc481748255l_bool=1. produc550034914r_bool=1. distinct_list_char=1. map_ex101166958t_char=1. map_ex1598883030on_val=1. map_exp_list_char_ty=1. map_li1100402823on_val=1. map_li1249123943t_char=1. map_list_char_ty=1. map_ty891785382on_val=1. map_ty_exp_list_char=1. map_ty_option_val=1. map_ty_ty=1. map_va527586287on_val=1. map_val_option_val=1. map_val_ty=1. set_exp_list_char=1. map_ex840371726on_val=1. set_Pr1921835862on_val=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f16=1. f17=1. f18=1. f19=1. f20=1. f21=1. f22=1. f23=1. f24=1. f25=1. f26=1. f27=1. f28=1. f29=1. f30=1. f31=1. f32=1. f33=1. f34=1. f35=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. f70=1. f71=1. f72=1. f73=1. f74=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. f113=1. f114=1. f115=1. f116=1. f117=1. f118=1. f119=1. f120=1. f121=1. f122=1. f123=1. f124=1. list_all2_ty_ty=1. list_all2_val_ty=1. eval=1. map_up1085636310ar_val=1. map_up891053837har_ty=1. tryCatch_list_char=1. overri2012515291on_val=1. list_a1073113293ty_val=1. list_a1462908359ion_ty=1. list_a1834344429ion_ty=1. list_a1880637950ion_ty=1. list_a2039389316_ty_ty=1. list_a283687028t_char=1. list_a52822260ion_ty=1. list_a839443437t_char=1. f196=1. f197=1. f202=1. f203=1. f204=1. f205=1. f209=1. f212=1. f215=1. f218=1. f221=1. f222=1. f223=1. f224=1. lconf_496643946t_char=1. f62=1. f63=1. f64=1. f65=1. f66=1. f68=1. f69=1. f75=1. f198=1. f199=1. f200=1. f201=1. f207=1. f208=1. f225=1. f226=1. f227=1. f228=1. wTrt=1. wTrts=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. f231=1. f235=1. f126=1. f127=1. f128=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. f156=1. f157=1. f158=1. f159=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. f206=1. f125=1.
% 10.40/10.66
% 10.40/10.66 ============================== end of process initial clauses ========
% 10.40/10.66
% 10.40/10.66 ============================== CLAUSES FOR SEARCH ====================
% 10.40/10.66
% 10.40/10.66 ============================== end of clauses for search =============
% 10.40/10.66
% 10.40/10.66 ============================== SEARCH ================================
% 10.40/10.66
% 10.40/10.66 % Starting search at 0.28 seconds.
% 10.40/10.66
% 10.40/10.66 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 167 (0.00 of 1.30 sec).
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=132.000, iters=3355
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=127.000, iters=3345
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=94.000, iters=3345
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=89.000, iters=3343
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=86.000, iters=3377
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=85.000, iters=3350
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=84.000, iters=3348
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=83.000, iters=3385
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=81.000, iters=3348
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=80.000, iters=3410
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=76.000, iters=3348
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=73.000, iters=3336
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=71.000, iters=3396
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=70.000, iters=3338
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=68.000, iters=3349
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=67.000, iters=3387
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=66.000, iters=3351
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=65.000, iters=3338
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=64.000, iters=3347
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=63.000, iters=3353
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=62.000, iters=3333
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=61.000, iters=3411
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=60.000, iters=3337
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=59.000, iters=3333
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=58.000, iters=3347
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=57.000, iters=3363
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=56.000, iters=3341
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=55.000, iters=3346
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=54.000, iters=3338
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=53.000, iters=3343
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=52.000, iters=3333
% 10.40/10.66
% 10.40/10.66 Low Water (keep): wt=51.000, iters=3368
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=5651, wt=192.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=5320, wt=186.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=5650, wt=179.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=5655, wt=175.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=5358, wt=173.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=6805, wt=169.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=13755, wt=38.000
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=50.000, iters=3334
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=14086, wt=37.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=14135, wt=36.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=14197, wt=35.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=14550, wt=34.000
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=14768, wt=33.000
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=49.000, iters=3333
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=48.000, iters=3334
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=47.000, iters=3346
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=46.000, iters=3343
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=45.000, iters=3431
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=44.000, iters=3349
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=43.000, iters=3421
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=42.000, iters=3593
% 237.40/237.71
% 237.40/237.71 Low Water (displace): id=25219, wt=31.000
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=41.000, iters=3380
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=40.000, iters=3336
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=39.000, iters=3358
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=38.000, iters=3396
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=37.000, iters=3350
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=36.000, iters=3374
% 237.40/237.71
% 237.40/237.71 Low Water (keep): wt=35.000, iters=3333
% 237.40/237.71
% 237.40/237.71 ============================== STATISTICS ============================
% 237.40/237.71
% 237.40/237.71 Given=16274. Generated=4105809. Kept=87185. proofs=0.
% 237.40/237.71 Usable=16203. Sos=8327. Demods=119. Limbo=2, Disabled=63139. Hints=0.
% 237.40/237.71 Kept_by_rule=0, Deleted_by_rule=19101.
% 237.40/237.71 Forward_subsumed=327837. Back_subsumed=10.
% 237.40/237.71 Sos_limit_deleted=3671686. Sos_displaced=61610. Sos_removed=0.
% 237.40/237.71 New_demodulators=280 (0 lex), Back_demodulated=1032. Back_unit_deleted=0.
% 237.40/237.71 Demod_attempts=213275047. Demod_rewrites=3300545.
% 237.40/237.71 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 237.40/237.71 Nonunit_fsub_feature_tests=2044764. Nonunit_bsub_feature_tests=2044.
% 237.40/237.71 Megabytes=419.43.
% 237.40/237.71 User_CPU=233.98, System_CPU=2.44, Wall_clock=237.
% 237.40/237.71
% 237.40/237.71 Megs malloced by palloc(): 400.
% 237.40/237.71 type (bytes each) gets frees in use bytes
% 237.40/237.71 chunk ( 104) 13006 13006 0 0.0 K
% 237.40/237.71 string_buf ( 8) 11321 11321 0 0.0 K
% 237.40/237.71 token ( 20) 31687 31687 0 0.0 K
% 237.40/237.71 pterm ( 16) 16992 16992 0 0.0 K
% 237.40/237.71 hashtab ( 8) 343 343 0 0.0 K
% 237.40/237.71 hashnode ( 8) 1209 1209 0 0.0 K
% 237.40/237.71 term ( 20) 276611338 274269730 2341608 45734.5 K
% 237.40/237.71 term arg arrays: 11973.6 K
% 237.40/237.71 attribute ( 12) 2853 114 2739 32.1 K
% 237.40/237.71 ilist ( 8) 2254411262 2254054787 356475 2785.0 K
% 237.40/237.71 plist ( 8) 1419117 1302283 116834 912.8 K
% 237.40/237.71 i2list ( 12) 49118104 49118104 0 0.0 K
% 237.40/237.71 just ( 12) 6106377 5979371 127006 1488.4 K
% 237.40/237.71 parajust ( 16) 1883617 1878019 5598 87.5 K
% 237.40/237.71 instancejust ( 8) 0 0 0 0.0 K
% 237.40/237.71 ivyjust ( 24) 0 0 0 0.0 K
% 237.40/237.71 formula ( 28) 13806 8462 5344 146.1 K
% 237.40/237.71 formula arg arrays: 18.2 K
% 237.40/237.71 topform ( 52) 4106639 4018624 88015 4469.5 K
% 237.40/237.71 clist_pos ( 20) 254993 167203 87790 1714.6 K
% 237.40/237.71 clist ( 16) 8 1 7 0.1 K
% 237.40/237.71 context ( 808) 28818443 28818441 2 1.6 K
% 237.40/237.71 trail ( 12) 20106879 20106877 2 0.0 K
% 237.40/237.71 ac_match_pos (70044) 0 0 0 0.0 K
% 237.40/237.71 ac_match_free_vars_pos (20020)
% 237.40/237.71 0 0 0 0.0 K
% 237.40/237.71 btm_state ( 60) 0 0 0 0.0 K
% 237.40/237.71 btu_state ( 60) 0 0 0 0.0 K
% 237.40/237.71 ac_position (285432) 0 0 0 0.0 K
% 237.40/237.71 fpa_trie ( 20) 4200663 868256 3332407 65086.1 K
% 237.40/237.71 fpa_state ( 28) 722517 722511 6 0.2 K
% 237.40/237.71 fpa_index ( 12) 10 0 10 0.1 K
% 237.40/237.71 fpa_chunk ( 20) 1522776 1141123 381653 7454.2 K
% 237.40/237.71 fpa_list ( 16) 1191451 0 1191451 18616.4 K
% 237.40/237.71 fpa_list chunks: 11903.9 K
% 237.40/237.71 discrim ( 12) 41703 16833 24870 291.4 K
% 237.40/237.71 discrim_pos ( 16) 3320305 3320305 0 0.0 K
% 237.40/237.71 flat2 ( 32) 11141333 11141333 0 0.0 K
% 237.40/237.71 flat ( 48) 0 0 0 0.0 K
% 237.40/237.71 flatterm ( 32) 294279703 294279703 0 0.0 K
% 237.40/237.71 mindex ( 28) 13 0 13 0.4 K
% 237.40/237.71 mindex_pos ( 56) 21353288 21353287 1 0.1 K
% 237.40/237.71 lindex ( 12) 5 0 5 0.1 K
% 237.40/237.71 clash ( 40) 0 0 0 0.0 K
% 237.40/237.71 di_tree ( 12) 73575599 53633079 19942520 233701.4 K
% 237.40/237.71 avl_node ( 20) 173969 157315 16654 325.3 K
% 237.40/237.71
% 237.40/237.71 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 237.40/237.71 List 1, length 11, 0.0 K
% 237.40/237.71 List 6, length 145, 3.4 K
% 237.40/237.71 List 7, length 103, 2.8 K
% 237.40/237.71 List 8, length 441, 13.8 K
% 237.40/237.71 List 9, length 13, 0.5 K
% 237.40/237.71 List 10, length 32, 1.2 K
% 237.40/237.71 List 11, length 8, 0.3 K
% 237.40/237.71 List 14, length 1, 0.1 K
% 237.40/237.71 List 15, length 2, 0.1 K
% 237.40/237.71 List 16, length 32, 2.0 K
% 237.40/237.71 List 26, length 113, 11.5 K
% 237.40/237.71 List 64, length 99, 24.8 K
% 237.40/237.71 List 202, length 2, 1.6 K
% 237.40/237.71
% 237.40/237.71 ============================== SELECTOR REPORT =======================
% 237.40/237.71 Sos_deleted=3671686, Sos_displaced=61610, Sos_size=8327
% 237.40/237.71 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 237.40/237.71 I 2147483647 high age 0 395
% 237.40/237.71 H 1 high weight 0 0
% 237.40/237.71 A 1 low age 8327 3176
% 237.40/237.71 F 4 low weight 0 1
% 237.40/237.71 T 4 low weight 8327 12702
% 237.40/237.71 ============================== end of selector report ================
% 237.40/237.71
% 237.40/237.71 ============================== end of statistics =====================
% 237.40/237.71
% 237.40/237.71 Exiting with failure.
% 237.40/237.71
% 237.40/237.71 Process 28586 exit (max_megs) Sun Jun 5 21:59:47 2022
% 237.40/237.71 Prover9 interrupted
%------------------------------------------------------------------------------