TSTP Solution File: SWW478+3 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW478+3 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 01:17:17 EDT 2022
% Result : Theorem 4.18s 4.39s
% Output : Refutation 4.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWW478+3 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Sat Jun 4 11:25:17 EDT 2022
% 0.11/0.30 % CPUTime :
% 2.24/2.44 ============================== Prover9 ===============================
% 2.24/2.44 Prover9 (32) version 2009-11A, November 2009.
% 2.24/2.44 Process 30983 was started by sandbox on n032.cluster.edu,
% 2.24/2.44 Sat Jun 4 11:25:19 2022
% 2.24/2.44 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30830_n032.cluster.edu".
% 2.24/2.44 ============================== end of head ===========================
% 2.24/2.44
% 2.24/2.44 ============================== INPUT =================================
% 2.24/2.44
% 2.24/2.44 % Reading from file /tmp/Prover9_30830_n032.cluster.edu
% 2.24/2.44
% 2.24/2.44 set(prolog_style_variables).
% 2.24/2.44 set(auto2).
% 2.24/2.44 % set(auto2) -> set(auto).
% 2.24/2.44 % set(auto) -> set(auto_inference).
% 2.24/2.44 % set(auto) -> set(auto_setup).
% 2.24/2.44 % set(auto_setup) -> set(predicate_elim).
% 2.24/2.44 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.24/2.44 % set(auto) -> set(auto_limits).
% 2.24/2.44 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.24/2.44 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.24/2.44 % set(auto) -> set(auto_denials).
% 2.24/2.44 % set(auto) -> set(auto_process).
% 2.24/2.44 % set(auto2) -> assign(new_constants, 1).
% 2.24/2.44 % set(auto2) -> assign(fold_denial_max, 3).
% 2.24/2.44 % set(auto2) -> assign(max_weight, "200.000").
% 2.24/2.44 % set(auto2) -> assign(max_hours, 1).
% 2.24/2.44 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.24/2.44 % set(auto2) -> assign(max_seconds, 0).
% 2.24/2.44 % set(auto2) -> assign(max_minutes, 5).
% 2.24/2.44 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.24/2.44 % set(auto2) -> set(sort_initial_sos).
% 2.24/2.44 % set(auto2) -> assign(sos_limit, -1).
% 2.24/2.44 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.24/2.44 % set(auto2) -> assign(max_megs, 400).
% 2.24/2.44 % set(auto2) -> assign(stats, some).
% 2.24/2.44 % set(auto2) -> clear(echo_input).
% 2.24/2.44 % set(auto2) -> set(quiet).
% 2.24/2.44 % set(auto2) -> clear(print_initial_clauses).
% 2.24/2.44 % set(auto2) -> clear(print_given).
% 2.24/2.44 assign(lrs_ticks,-1).
% 2.24/2.44 assign(sos_limit,10000).
% 2.24/2.44 assign(order,kbo).
% 2.24/2.44 set(lex_order_vars).
% 2.24/2.44 clear(print_given).
% 2.24/2.44
% 2.24/2.44 % formulas(sos). % not echoed (1491 formulas)
% 2.24/2.44
% 2.24/2.44 ============================== end of input ==========================
% 2.24/2.44
% 2.24/2.44 % From the command line: assign(max_seconds, 300).
% 2.24/2.44
% 2.24/2.44 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.24/2.44
% 2.24/2.44 % Formulas that are not ordinary clauses:
% 2.24/2.44 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].
% 2.24/2.44 2 (all B_1_1 is_bool(finals_list_char(B_1_1))) # label(gsy_c_BigStep_Ofinals_000tc__List__Olist_Itc__String__Ochar_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 3 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 is_bool(conf_P373316194t_char(B_1_1,B_2_1,B_3_1,B_4_1))) # label(gsy_c_Conform_Oconf_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 4 (all B_1_1 all B_2_1 is_bool(d_list_char(B_1_1,B_2_1))) # label(gsy_c_DefAss_O_092_060D_062_000tc__List__Olist_Itc__String__Ochar_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 5 (all B_1_1 is_bool(preallocated(B_1_1))) # label(gsy_c_Exceptions_Opreallocated) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 6 (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].
% 2.24/2.44 7 (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(axiom) # label(non_clause). [assumption].
% 2.24/2.44 8 (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].
% 2.24/2.44 9 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 all B_5_1 is_bool(wTrt(B_1_1,B_2_1,B_3_1,B_4_1,B_5_1))) # label(gsy_c_Progress_OWTrt_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 10 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 all B_5_1 is_bool(wTrts(B_1_1,B_2_1,B_3_1,B_4_1,B_5_1))) # label(gsy_c_Progress_OWTrts_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 11 (all B_1_1 all B_2_1 is_bool(assigned(B_1_1,B_2_1))) # label(gsy_c_SmallStep_Oassigned) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 12 (all B_1_1 all B_2_1 all B_3_1 is_bool(fields1147507508t_char(B_1_1,B_2_1,B_3_1))) # label(gsy_c_TypeRel_OFields_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 13 (all B_1_1 is_bool(is_refT(B_1_1))) # label(gsy_c_Type_Ois__refT) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 14 (all B_1_1 all B_2_1 is_bool(wf_pro755087577t_char(B_1_1,B_2_1))) # label(gsy_c_WellForm_Owf__prog_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Stri) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 15 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 all B_5_1 is_bool(wTrt_1(B_1_1,B_2_1,B_3_1,B_4_1,B_5_1))) # label(gsy_c_WellTypeRT_OWTrt) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 16 (all B_1_1 all B_2_1 all B_3_1 all B_4_1 all B_5_1 is_bool(wTrts_1(B_1_1,B_2_1,B_3_1,B_4_1,B_5_1))) # label(gsy_c_WellTypeRT_OWTrts) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 17 (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].
% 2.24/2.44 18 (all B_1_1 all B_2_1 (is_bool(B_2_1) -> is_bool(hAPP_bool_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 19 (all B_1_1 all B_2_1 is_bool(hAPP_list_char_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__String__Ochar_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 20 (all B_1_1 all B_2_1 is_bool(hAPP_l902158906r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mt) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 21 (all B_1_1 all B_2_1 is_bool(hAPP_nat_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 22 (all B_1_1 all B_2_1 is_bool(hAPP_option_ty_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 23 (all B_1_1 all B_2_1 is_bool(hAPP_option_val_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 24 (all B_1_1 all B_2_1 is_bool(hAPP_o2007402111l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__String__Ochar_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 25 (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].
% 2.24/2.44 26 (all B_1_1 all B_2_1 is_bool(hAPP_val_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__Value__Oval_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 27 (all B_1_1 all B_2_1 is_bool(hAPP_f1776070952l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Expr__Obop_Mtc__fun_Itc__prod_Itc__Value__Oval_Mtc__V) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 28 (all B_1_1 all B_2_1 is_bool(hAPP_f570766339l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_Mt) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 29 (all B_1_1 all B_2_1 is_bool(hAPP_f2041029616l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__Str) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 30 (all B_1_1 all B_2_1 is_bool(hAPP_f539072365l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 31 (all B_1_1 all B_2_1 is_bool(hAPP_f998390560l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_M_001) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 32 (all B_1_1 all B_2_1 is_bool(hAPP_f986089162l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__HOL__Obool_J_00) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 33 (all B_1_1 all B_2_1 is_bool(hAPP_f1001225811y_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].
% 2.24/2.44 34 (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_002) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 35 (all B_1_1 all B_2_1 is_bool(hAPP_f1776419603l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__List__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 36 (all B_1_1 all B_2_1 is_bool(hAPP_f678833350l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__fun_It) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 37 (all B_1_1 all B_2_1 is_bool(hAPP_f1795246582l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 38 (all B_1_1 all B_2_1 is_bool(hAPP_f1931964053l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_003) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 39 (all B_1_1 all B_2_1 is_bool(hAPP_f1520735791l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_Itc__prod_I_004) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 40 (all B_1_1 all B_2_1 is_bool(hAPP_f1889282162l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Type__Oty_J_Mtc__fun_Itc__prod_Itc__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 41 (all B_1_1 all B_2_1 is_bool(hAPP_f1118567467l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Value__Oval_J_Mtc__fun_Itc__Expr__Oe) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 42 (all B_1_1 all B_2_1 is_bool(hAPP_f1409772418l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__O) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 43 (all B_1_1 all B_2_1 is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 44 (all B_1_1 all B_2_1 is_bool(hAPP_f61040418l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc__List__O) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 45 (all B_1_1 all B_2_1 is_bool(hAPP_f2071159779l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__Value__Oval_Mtc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 46 (all B_1_1 all B_2_1 is_bool(hAPP_f1450446905l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 47 (all B_1_1 all B_2_1 (is_fun1083000568p_bool(B_2_1) -> is_bool(hAPP_f1854361213l_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 48 (all B_1_1 all B_2_1 is_bool(hAPP_f742333458l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 49 (all B_1_1 all B_2_1 is_bool(hAPP_f588675559l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 50 (all B_1_1 all B_2_1 is_bool(hAPP_f91506671l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_005) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 51 (all B_1_1 all B_2_1 is_bool(hAPP_f434955681l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_006) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.44 52 (all B_1_1 all B_2_1 is_bool(hAPP_f1734260017l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 53 (all B_1_1 all B_2_1 is_bool(hAPP_f837795298l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_007) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 54 (all B_1_1 all B_2_1 is_bool(hAPP_f861853459l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olis_008) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 55 (all B_1_1 all B_2_1 is_bool(hAPP_f82569901l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 56 (all B_1_1 all B_2_1 is_bool(hAPP_f479632753l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_009) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 57 (all B_1_1 all B_2_1 is_bool(hAPP_f1780084320l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__O_010) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 58 (all B_1_1 all B_2_1 is_bool(hAPP_f2106398425l_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].
% 2.24/2.45 59 (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__011) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 60 (all B_1_1 all B_2_1 is_bool(hAPP_f1134950784l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 61 (all B_1_1 all B_2_1 is_bool(hAPP_f515912112l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 62 (all B_1_1 all B_2_1 is_bool(hAPP_f483496539l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__012) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 63 (all B_1_1 all B_2_1 is_bool(hAPP_f2050077417l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod__013) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 64 (all B_1_1 all B_2_1 is_bool(hAPP_f433445541l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Oli) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 65 (all B_1_1 all B_2_1 is_bool(hAPP_f1746574980l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 66 (all B_1_1 all B_2_1 is_bool(hAPP_f1314764175l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__O) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 67 (all B_1_1 all B_2_1 is_bool(hAPP_f348753975l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__O) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 68 (all B_1_1 all B_2_1 is_bool(hAPP_f288221747l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 69 (all B_1_1 all B_2_1 is_bool(hAPP_f1161798306l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__014) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 70 (all B_1_1 all B_2_1 is_bool(hAPP_f1748390065l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__015) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 71 (all B_1_1 all B_2_1 is_bool(hAPP_f2028441009l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__HOL__Ob) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 72 (all B_1_1 all B_2_1 is_bool(hAPP_f1661305905l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 73 (all B_1_1 all B_2_1 is_bool(hAPP_f966411375l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 74 (all B_1_1 all B_2_1 is_bool(hAPP_f1754555101l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc_016) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 75 (all B_1_1 all B_2_1 is_bool(hAPP_f983152497l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 76 (all B_1_1 all B_2_1 is_bool(hAPP_f126136681l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 77 (all B_1_1 all B_2_1 is_bool(hAPP_f1453283057l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) # label(hypothesis) # label(non_clause). [assumption].
% 2.24/2.45 78 (all B_1_1 all B_2_1 is_bool(hAPP_f458849545l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 79 (all B_1_1 all B_2_1 is_bool(hAPP_f595031537l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 80 (all B_1_1 all B_2_1 is_bool(hAPP_f528956081l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__017) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 81 (all B_1_1 all B_2_1 is_bool(hAPP_f851858423l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 82 (all B_1_1 all B_2_1 is_bool(hAPP_f665343921l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__018) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 83 (all B_1_1 all B_2_1 is_bool(hAPP_f538118321l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__019) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 84 (all B_1_1 all B_2_1 is_bool(hAPP_f272179441l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__020) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 85 (all B_1_1 all B_2_1 is_bool(hAPP_f258424141l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 86 (all B_1_1 all B_2_1 is_bool(hAPP_f1145574243l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 87 (all B_1_1 all B_2_1 is_bool(hAPP_f126445617l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 88 (all B_1_1 all B_2_1 is_bool(hAPP_f2129782055l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 89 (all B_1_1 all B_2_1 is_bool(hAPP_f1297673713l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 90 (all B_1_1 all B_2_1 is_bool(hAPP_f1261741735l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__O) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 91 (all B_1_1 all B_2_1 is_bool(hAPP_f1980787287l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 92 (all B_1_1 all B_2_1 (is_fun1083000568p_bool(B_1_1) -> is_bool(hAPP_P1085566419p_bool(B_1_1,B_2_1)))) # label(gsy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__Expr__Obop_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 93 (all B_1_1 all B_2_1 is_bool(hAPP_P943837928l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc__Value__Ov) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 94 (all B_1_1 all B_2_1 is_bool(hAPP_P1632759357r_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].
% 2.24/2.45 95 (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_021) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 96 (all B_1_1 all B_2_1 is_bool(hAPP_P499022727r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 97 (all B_1_1 all B_2_1 is_bool(hAPP_P71593144l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St_022) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 98 (all B_1_1 all B_2_1 is_bool(hAPP_P2014166431r_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].
% 2.24/2.45 99 (all B_1_1 all B_2_1 is_bool(hAPP_P476431815r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__023) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 100 (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__024) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 101 (all B_1_1 all B_2_1 is_bool(hAPP_P449474095r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List__Olist_It) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 102 (all B_1_1 all B_2_1 is_bool(hAPP_P748443392y_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Type__Oty_J_00) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 103 (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].
% 2.24/2.45 104 (all B_1_1 all B_2_1 is_bool(hAPP_P1680401186r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 105 (all B_1_1 all B_2_1 is_bool(hAPP_P1384137393r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_025) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 106 (all B_1_1 all B_2_1 is_bool(hAPP_P659547099r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_Itc__List_026) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 107 (all B_1_1 all B_2_1 is_bool(hAPP_P1574824955y_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__List__Olist_Itc__T) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 108 (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].
% 2.24/2.45 109 (all B_1_1 all B_2_1 is_bool(hAPP_P1187139874r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc__Type__Ot) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 110 (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].
% 2.24/2.45 111 (all B_1_1 all B_2_1 is_bool(hAPP_P2115985549l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 112 (all B_1_1 all B_2_1 is_bool(hAPP_P2053453961y_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 113 (all B_1_1 all B_2_1 is_bool(hAPP_P828904212r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___027) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 114 (all B_1_1 all B_2_1 is_bool(hAPP_P1926698759r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___028) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 115 (all B_1_1 all B_2_1 is_bool(hAPP_P929938951l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__HOL__Obool) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 116 (all B_1_1 all B_2_1 is_bool(hAPP_P468446343l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 117 (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].
% 2.24/2.45 118 (all B_1_1 all B_2_1 is_bool(hAPP_P2077557811l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_029) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 119 (all B_1_1 all B_2_1 is_bool(hAPP_P504978887l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 120 (all B_1_1 all B_2_1 is_bool(hAPP_P738987199l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 121 (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].
% 2.24/2.45 122 (all B_1_1 all B_2_1 is_bool(hAPP_P1333315679l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 123 (all B_1_1 all B_2_1 is_bool(hAPP_P1002912327r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 124 (all B_1_1 all B_2_1 is_bool(hAPP_P824029447r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___030) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 125 (all B_1_1 all B_2_1 is_bool(hAPP_P27757617y_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 126 (all B_1_1 all B_2_1 is_bool(hAPP_P2010574925r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List_031) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 127 (all B_1_1 all B_2_1 is_bool(hAPP_P124632071l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 128 (all B_1_1 all B_2_1 is_bool(hAPP_P975284999r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 129 (all B_1_1 all B_2_1 is_bool(hAPP_P929449287r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_032) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 130 (all B_1_1 all B_2_1 is_bool(hAPP_P1240100515r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 131 (all B_1_1 all B_2_1 is_bool(hAPP_P1183499705r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 132 (all B_1_1 all B_2_1 is_bool(hAPP_P801803911r_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 133 (all B_1_1 all B_2_1 is_bool(hAPP_P2123002749l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mtc__prod_I) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 134 (all B_1_1 all B_2_1 is_bool(hAPP_P1221872711l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 135 (all B_1_1 all B_2_1 is_bool(hAPP_P378063101l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 136 (all B_1_1 all B_2_1 is_bool(hAPP_P2028072621l_bool(B_1_1,B_2_1))) # label(gsy_c_hAPP_000tc__prod_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 137 (all F_1 all X_2 fun_up1149430426on_val(F_1,X_2,hAPP_l207779698on_val(F_1,X_2)) = F_1) # label(fact_2_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 138 (all F_1 all X_2 fun_up424764369ion_ty(F_1,X_2,hAPP_l512744617ion_ty(F_1,X_2)) = F_1) # label(fact_3_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 139 (all F_1 all X_2 fun_up2041264236on_val(F_1,X_2,hAPP_n546249108on_val(F_1,X_2)) = F_1) # label(fact_4_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 140 (all F_1 all X_2 fun_up204312361on_val(F_1,X_2,hAPP_P2094403585on_val(F_1,X_2)) = F_1) # label(fact_5_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 141 (all M_1 all A all B all X_2 all Y_2 (hAPP_l207779698on_val(fun_up1149430426on_val(M_1,A,hAPP_val_option_val(some_val,B)),X_2) = hAPP_val_option_val(some_val,Y_2) <-> X_2 = A & B = Y_2 | X_2 != A & hAPP_l207779698on_val(M_1,X_2) = hAPP_val_option_val(some_val,Y_2))) # label(fact_7_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 142 (all M_1 all A all B all X_2 all Y_2 (hAPP_l512744617ion_ty(fun_up424764369ion_ty(M_1,A,hAPP_ty_option_ty(some_ty,B)),X_2) = hAPP_ty_option_ty(some_ty,Y_2) <-> X_2 = A & B = Y_2 | X_2 != A & hAPP_l512744617ion_ty(M_1,X_2) = hAPP_ty_option_ty(some_ty,Y_2))) # label(fact_8_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 143 (all M_1 all A all B all X_2 all Y_2 (hAPP_n546249108on_val(fun_up2041264236on_val(M_1,A,hAPP_P1510515380on_val(some_P948696889on_val,B)),X_2) = hAPP_P1510515380on_val(some_P948696889on_val,Y_2) <-> X_2 = A & B = Y_2 | X_2 != A & hAPP_n546249108on_val(M_1,X_2) = hAPP_P1510515380on_val(some_P948696889on_val,Y_2))) # label(fact_9_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 144 (all M_1 all A all B all X_2 all Y_2 (hAPP_P2094403585on_val(fun_up204312361on_val(M_1,A,hAPP_val_option_val(some_val,B)),X_2) = hAPP_val_option_val(some_val,Y_2) <-> X_2 = A & B = Y_2 | X_2 != A & hAPP_P2094403585on_val(M_1,X_2) = hAPP_val_option_val(some_val,Y_2))) # label(fact_10_map__upd__Some__unfold) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 145 (all T_2 all K all X_2 (hAPP_l207779698on_val(T_2,K) = hAPP_val_option_val(some_val,X_2) -> fun_up1149430426on_val(T_2,K,hAPP_val_option_val(some_val,X_2)) = T_2)) # label(fact_11_map__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 146 (all T_2 all K all X_2 (hAPP_l512744617ion_ty(T_2,K) = hAPP_ty_option_ty(some_ty,X_2) -> fun_up424764369ion_ty(T_2,K,hAPP_ty_option_ty(some_ty,X_2)) = T_2)) # label(fact_12_map__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 147 (all T_2 all K all X_2 (hAPP_n546249108on_val(T_2,K) = hAPP_P1510515380on_val(some_P948696889on_val,X_2) -> fun_up2041264236on_val(T_2,K,hAPP_P1510515380on_val(some_P948696889on_val,X_2)) = T_2)) # label(fact_13_map__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 148 (all T_2 all K all X_2 (hAPP_P2094403585on_val(T_2,K) = hAPP_val_option_val(some_val,X_2) -> fun_up204312361on_val(T_2,K,hAPP_val_option_val(some_val,X_2)) = T_2)) # label(fact_14_map__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 149 (all M_1 all A all X_2 all N all Y_2 (fun_up1149430426on_val(M_1,A,hAPP_val_option_val(some_val,X_2)) = fun_up1149430426on_val(N,A,hAPP_val_option_val(some_val,Y_2)) -> X_2 = Y_2)) # label(fact_15_map__upd__eqD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 150 (all M_1 all A all X_2 all N all Y_2 (fun_up424764369ion_ty(M_1,A,hAPP_ty_option_ty(some_ty,X_2)) = fun_up424764369ion_ty(N,A,hAPP_ty_option_ty(some_ty,Y_2)) -> X_2 = Y_2)) # label(fact_16_map__upd__eqD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 151 (all M_1 all A all X_2 all N all Y_2 (fun_up2041264236on_val(M_1,A,hAPP_P1510515380on_val(some_P948696889on_val,X_2)) = fun_up2041264236on_val(N,A,hAPP_P1510515380on_val(some_P948696889on_val,Y_2)) -> X_2 = Y_2)) # label(fact_17_map__upd__eqD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 152 (all M_1 all A all X_2 all N all Y_2 (fun_up204312361on_val(M_1,A,hAPP_val_option_val(some_val,X_2)) = fun_up204312361on_val(N,A,hAPP_val_option_val(some_val,Y_2)) -> X_2 = Y_2)) # label(fact_18_map__upd__eqD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 153 (all Ta all Ea (hBOOL(hAPP_P159683425l_bool(typeSa1700205512_sconf(p,Ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,hAPP_val_option_val(some_val,v))))) -> (hBOOL(wTrt_1(p,ha,Ea,ea,Ta)) -> (exists T_5 (hBOOL(wTrt_1(p,h_a,Ea,e_a,T_5)) & hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(p),T_5),Ta))))))) # label(fact_19_InitBlockRed_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 154 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 all E_4 hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_4))))))) -> hBOOL(hAPP_P2028072621l_bool(Pa,X_2)))) # label(fact_20_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 155 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 all E_4 hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_4))))))) -> hBOOL(hAPP_P378063101l_bool(Pa,X_2)))) # label(fact_21_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 156 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 all E_4 hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,D_2),E_4))))))) -> hBOOL(hAPP_P824029447r_bool(Pa,X_2)))) # label(fact_22_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 157 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 all E_4 hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,D_2),E_4))))))) -> hBOOL(hAPP_P975284999r_bool(Pa,X_2)))) # label(fact_23_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 158 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 all E_4 hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,D_2),E_4))))))) -> hBOOL(hAPP_P1384137393r_bool(Pa,X_2)))) # label(fact_24_prod__induct5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 159 (all Y_2 -(all A_1 all B_2 all C_4 all D_2 all E_4 Y_2 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_4)))))) # label(fact_25_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 160 (all Y_2 -(all A_1 all B_2 all C_4 all D_2 all E_4 Y_2 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,D_2),E_4)))))) # label(fact_26_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 161 (all Y_7 -(all A_1 all B_2 all C_4 all D_2 all E_4 Y_7 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,D_2),E_4)))))) # label(fact_27_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 162 (all Y_7 -(all A_1 all B_2 all C_4 all D_2 all E_4 Y_7 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,D_2),E_4)))))) # label(fact_28_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 163 (all Y_7 -(all A_1 all B_2 all C_4 all D_2 all E_4 Y_7 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,D_2),E_4)))))) # label(fact_29_prod__cases5) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 164 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),D_2)))))) -> hBOOL(hAPP_P1384137393r_bool(Pa,X_2)))) # label(fact_30_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 165 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2)))))) -> hBOOL(hAPP_P282169671l_bool(Pa,X_2)))) # label(fact_31_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 166 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2)))))) -> hBOOL(hAPP_P1333315679l_bool(Pa,X_2)))) # label(fact_32_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 167 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2)))))) -> hBOOL(hAPP_P92196306r_bool(Pa,X_2)))) # label(fact_33_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 168 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D_2)))))) -> hBOOL(hAPP_P1680401186r_bool(Pa,X_2)))) # label(fact_34_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 169 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),D_2)))))) -> hBOOL(hAPP_P378063101l_bool(Pa,X_2)))) # label(fact_35_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 170 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 (is_bop(B_2) -> hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_2),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,C_4),D_2))))))) -> hBOOL(hAPP_P738987199l_bool(Pa,X_2)))) # label(fact_36_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 171 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),D_2)))))) -> hBOOL(hAPP_P2028072621l_bool(Pa,X_2)))) # label(fact_37_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 172 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),D_2)))))) -> hBOOL(hAPP_P824029447r_bool(Pa,X_2)))) # label(fact_38_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 173 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2)))))) -> hBOOL(hAPP_P1240100515r_bool(Pa,X_2)))) # label(fact_39_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 174 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),D_2)))))) -> hBOOL(hAPP_P975284999r_bool(Pa,X_2)))) # label(fact_40_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 175 (all X_2 all Pa ((all A_1 all B_2 all C_4 all D_2 hBOOL(hAPP_P929449287r_bool(Pa,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D_2)))))) -> hBOOL(hAPP_P929449287r_bool(Pa,X_2)))) # label(fact_41_prod__induct4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 176 (all Y_6 -(all A_1 all B_2 all C_4 all D_2 Y_6 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),hAPP_P1661798543t_char(hAPP_t1369077401t_char(produc1545444669t_char,C_4),D_2))))) # label(fact_42_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 177 (all Y_2 -(all A_1 all B_2 all C_4 all D_2 Y_2 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2))))) # label(fact_43_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 178 (all Y_2 -(all A_1 all B_2 all C_4 all D_2 Y_2 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,C_4),D_2))))) # label(fact_44_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 179 (all Y_6 -(all A_1 all B_2 all C_4 all D_2 Y_6 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2))))) # label(fact_45_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 180 (all Y_6 -(all A_1 all B_2 all C_4 all D_2 Y_6 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D_2))))) # label(fact_46_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 181 (all Y_2 -(all A_1 all B_2 all C_4 all D_2 Y_2 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_4),D_2))))) # label(fact_47_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 182 (all Y_6 -(all A_1 all B_2 all C_4 all D_2 (is_bop(B_2) -> Y_6 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_2),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,C_4),D_2)))))) # label(fact_48_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 183 (all Y_2 -(all A_1 all B_2 all C_4 all D_2 Y_2 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,C_4),D_2))))) # label(fact_49_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 184 (all Y_6 -(all A_1 all B_2 all C_4 all D_2 Y_6 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,C_4),D_2))))) # label(fact_50_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 185 (all Y_6 -(all A_1 all B_2 all C_4 all D_2 Y_6 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,C_4),D_2))))) # label(fact_51_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 186 (all Y_6 -(all A_1 all B_2 all C_4 all D_2 Y_6 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,C_4),D_2))))) # label(fact_52_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 187 (all Y_6 -(all A_1 all B_2 all C_4 all D_2 Y_6 != hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,C_4),D_2))))) # label(fact_53_prod__cases4) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 188 (all A_19 all B_5 all A_18 all B_4 (hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_19),B_5) = hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_55_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 189 (all A_19 all B_5 all A_18 all B_4 (hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_19),B_5) = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_56_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 190 (all A_19 all B_5 all A_18 all B_4 (hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_19),B_5) = hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_57_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 191 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_19),B_5) = hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_58_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 192 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_19),B_5) = hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_59_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 193 (all A_19 all B_5 all A_18 all B_4 (hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_19),B_5) = hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_60_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 194 (all A_19 all B_5 all A_18 all B_4 (hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_19),B_5) = hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_61_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 195 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_19),B_5) = hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_62_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 196 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_19),B_5) = hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_63_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 197 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_19),B_5) = hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_64_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 198 (all A all B all A_3 all B_3 (hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A),B) = hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_65_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 199 (all A_19 all B_5 all A_18 all B_4 (hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_19),B_5) = hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_66_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 200 (all A_19 all B_5 all A_18 all B_4 (hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_19),B_5) = hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_67_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 201 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_19),B_5) = hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_68_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 202 (all A all B all A_3 all B_3 (hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A),B) = hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_69_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 203 (all A all B all A_3 all B_3 (hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A),B) = hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_70_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 204 (all A all B all A_3 all B_3 (hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A),B) = hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_71_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 205 (all A_19 all B_5 all A_18 all B_4 (hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_19),B_5) = hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_72_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 206 (all A_19 all B_5 all A_18 all B_4 (hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_19),B_5) = hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_73_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 207 (all A_19 all B_5 all A_18 all B_4 (hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_19),B_5) = hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_74_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 208 (all A_19 all B_5 all A_18 all B_4 (hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A_19),B_5) = hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_75_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 209 (all A_19 all B_5 all A_18 all B_4 (hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A_19),B_5) = hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_76_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 210 (all A_19 all B_5 all A_18 all B_4 (hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_19),B_5) = hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_77_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 211 (all A_19 all B_5 all A_18 all B_4 (hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_19),B_5) = hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_78_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 212 (all A_19 all B_5 all A_18 all B_4 (is_bop(A_19) & is_bop(B_5) & is_bop(A_18) & is_bop(B_4) -> (hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A_19),B_5) = hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4)))) # label(fact_79_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 213 (all A all B all A_3 all B_3 (hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A),B) = hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_80_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 214 (all A all B all A_3 all B_3 (hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A),B) = hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_81_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 215 (all A all B all A_3 all B_3 (hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A),B) = hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_82_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 216 (all A all B all A_3 all B_3 (hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_83_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 217 (all A all B all A_3 all B_3 (hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_84_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 218 (all A all B all A_3 all B_3 (hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_85_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 219 (all A all B all A_3 all B_3 (hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B) = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_86_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 220 (all A_19 all B_5 all A_18 all B_4 (hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_19),B_5) = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_87_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 221 (all A_19 all B_5 all A_18 all B_4 (is_bop(A_19) & is_bop(A_18) -> (hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_19),B_5) = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4)))) # label(fact_88_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 222 (all A_19 all B_5 all A_18 all B_4 (hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_19),B_5) = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_89_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 223 (all A all B all A_3 all B_3 (hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B) = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_90_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 224 (all A all B all A_3 all B_3 (hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B) = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_3),B_3) -> -(A = A_3 -> B != B_3))) # label(fact_91_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 225 (all A_19 all B_5 all A_18 all B_4 (hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_19),B_5) = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_92_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 226 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_19),B_5) = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_93_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 227 (all A_19 all B_5 all A_18 all B_4 (hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_19),B_5) = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_94_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 228 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_19),B_5) = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_95_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 229 (all A_19 all B_5 all A_18 all B_4 (hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_19),B_5) = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_96_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 230 (all A_19 all B_5 all A_18 all B_4 (hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_19),B_5) = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_97_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 231 (all A_19 all B_5 all A_18 all B_4 (hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_19),B_5) = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_18),B_4) -> -(A_19 = A_18 -> B_5 != B_4))) # label(fact_98_Pair__inject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 232 (all A all B all A_3 all B_3 (hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A),B) = hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_99_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 233 (all A all B all A_3 all B_3 (hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A),B) = hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_100_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 234 (all A all B all A_3 all B_3 (hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A),B) = hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_101_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 235 (all A all B all A_3 all B_3 (hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A),B) = hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_102_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 236 (all A all B all A_3 all B_3 (hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A),B) = hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_103_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 237 (all A all B all A_3 all B_3 (hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A),B) = hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_104_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 238 (all A all B all A_3 all B_3 (hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A),B) = hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_105_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 239 (all A all B all A_3 all B_3 (hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A),B) = hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_106_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 240 (all A all B all A_3 all B_3 (hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A),B) = hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_107_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 241 (all A all B all A_3 all B_3 (hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A),B) = hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_108_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 242 (all A all B all A_3 all B_3 (hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A),B) = hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_109_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 243 (all A all B all A_3 all B_3 (hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A),B) = hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_110_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 244 (all A all B all A_3 all B_3 (hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A),B) = hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_111_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 245 (all A all B all A_3 all B_3 (hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A),B) = hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_112_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 246 (all A all B all A_3 all B_3 (hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A),B) = hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_113_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 247 (all A all B all A_3 all B_3 (hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A),B) = hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_114_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 248 (all A all B all A_3 all B_3 (hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A),B) = hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_115_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 249 (all A all B all A_3 all B_3 (hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A),B) = hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_116_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 250 (all A all B all A_3 all B_3 (hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A),B) = hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_117_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 251 (all A all B all A_3 all B_3 (hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A),B) = hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_118_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 252 (all A all B all A_3 all B_3 (hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A),B) = hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_119_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 253 (all A all B all A_3 all B_3 (hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A),B) = hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_120_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 254 (all A all B all A_3 all B_3 (hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A),B) = hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_121_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 255 (all A all B all A_3 all B_3 (hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A),B) = hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_122_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 256 (all A all B all A_3 all B_3 (is_bop(A) & is_bop(B) & is_bop(A_3) & is_bop(B_3) -> (hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A),B) = hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A_3),B_3) <-> A = A_3 & B = B_3))) # label(fact_123_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 257 (all A all B all A_3 all B_3 (hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A),B) = hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_124_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 258 (all A all B all A_3 all B_3 (hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A),B) = hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_125_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 259 (all A all B all A_3 all B_3 (hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A),B) = hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_126_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 260 (all A all B all A_3 all B_3 (hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B) = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_127_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 261 (all A all B all A_3 all B_3 (hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B) = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_128_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 262 (all A all B all A_3 all B_3 (hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B) = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_129_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 263 (all A all B all A_3 all B_3 (hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B) = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_130_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 264 (all A all B all A_3 all B_3 (hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B) = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_131_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 265 (all A all B all A_3 all B_3 (is_bop(A) & is_bop(A_3) -> (hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B) = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_3),B_3) <-> A = A_3 & B = B_3))) # label(fact_132_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 266 (all A all B all A_3 all B_3 (hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B) = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_133_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 267 (all A all B all A_3 all B_3 (hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B) = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_134_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 268 (all A all B all A_3 all B_3 (hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B) = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_135_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 269 (all A all B all A_3 all B_3 (hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B) = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_136_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 270 (all A all B all A_3 all B_3 (hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B) = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_137_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 271 (all A all B all A_3 all B_3 (hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B) = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_138_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 272 (all A all B all A_3 all B_3 (hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B) = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_139_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 273 (all A all B all A_3 all B_3 (hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B) = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_140_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 274 (all A all B all A_3 all B_3 (hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B) = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_141_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 275 (all A all B all A_3 all B_3 (hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B) = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_3),B_3) <-> A = A_3 & B = B_3)) # label(fact_142_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 276 (all Pa ((all X1 hBOOL(hAPP_P748443392y_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P748443392y_bool(Pa,hAPP_t1875766236har_ty(hAPP_l1948972481har_ty(produc251930284har_ty,A_1),B_2)))))) # label(fact_143_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 277 (all Pa ((all X1 hBOOL(hAPP_P27757617y_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P27757617y_bool(Pa,hAPP_t708040077har_ty(hAPP_P827589667har_ty(produc1265154397har_ty,A_1),B_2)))))) # label(fact_144_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 278 (all Pa ((all X1 hBOOL(hAPP_P1384137393r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),B_2)))))) # label(fact_145_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 279 (all Pa ((all X1 hBOOL(hAPP_P1002912327r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),B_2)))))) # label(fact_146_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 280 (all Pa ((all X1 hBOOL(hAPP_P801803911r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P801803911r_bool(Pa,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),B_2)))))) # label(fact_147_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 281 (all Pa ((all X1 hBOOL(hAPP_P929449287r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P929449287r_bool(Pa,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),B_2)))))) # label(fact_148_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.45 282 (all Pa ((all X1 hBOOL(hAPP_P975284999r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),B_2)))))) # label(fact_149_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 283 (all Pa ((all X1 hBOOL(hAPP_P1183499705r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),B_2)))))) # label(fact_150_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 284 (all Pa ((all X1 hBOOL(hAPP_P1240100515r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),B_2)))))) # label(fact_151_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 285 (all Pa ((all X1 hBOOL(hAPP_P824029447r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),B_2)))))) # label(fact_152_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 286 (all Pa ((all X1 hBOOL(hAPP_P2028072621l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),B_2)))))) # label(fact_153_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 287 (all Pa ((all X1 hBOOL(hAPP_P2123002749l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),B_2)))))) # label(fact_154_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 288 (all Pa ((all X1 hBOOL(hAPP_P738987199l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),B_2)))))) # label(fact_155_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 289 (all Pa ((all X1 hBOOL(hAPP_P2010574925r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),B_2)))))) # label(fact_156_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 290 (all Pa ((all X1 hBOOL(hAPP_P124632071l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),B_2)))))) # label(fact_157_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 291 (all Pa ((all X1 hBOOL(hAPP_P1221872711l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),B_2)))))) # label(fact_158_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 292 (all Pa ((all X1 hBOOL(hAPP_P378063101l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),B_2)))))) # label(fact_159_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 293 (all Pa ((all X1 hBOOL(hAPP_P499022727r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P499022727r_bool(Pa,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A_1),B_2)))))) # label(fact_160_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 294 (all Pa ((all X1 hBOOL(hAPP_P1632759357r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1632759357r_bool(Pa,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A_1),B_2)))))) # label(fact_161_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 295 (all Pa ((all X1 hBOOL(hAPP_P476431815r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P476431815r_bool(Pa,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A_1),B_2)))))) # label(fact_162_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 296 (all Pa ((all X1 hBOOL(hAPP_P2053453961y_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P2053453961y_bool(Pa,hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A_1),B_2)))))) # label(fact_163_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 297 (all Pa ((all X1 hBOOL(hAPP_P1926698759r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1926698759r_bool(Pa,hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,A_1),B_2)))))) # label(fact_164_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 298 (all Pa ((all X1 hBOOL(hAPP_P2115985549l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P2115985549l_bool(Pa,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A_1),B_2)))))) # label(fact_165_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 299 (all Pa ((all X1 hBOOL(hAPP_P1574824955y_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1574824955y_bool(Pa,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A_1),B_2)))))) # label(fact_166_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 300 (all Pa ((all X1 hBOOL(hAPP_P1085566419p_bool(Pa,X1))) <-> (all A_1 all B_2 (is_bop(A_1) & is_bop(B_2) -> hBOOL(hAPP_P1085566419p_bool(Pa,hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A_1),B_2))))))) # label(fact_167_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 301 (all Pa ((all X1 hBOOL(hAPP_P504978887l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P504978887l_bool(Pa,hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,A_1),B_2)))))) # label(fact_168_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 302 (all Pa ((all X1 hBOOL(hAPP_P2077557811l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P2077557811l_bool(Pa,hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A_1),B_2)))))) # label(fact_169_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 303 (all Pa ((all X1 hBOOL(hAPP_P468446343l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P468446343l_bool(Pa,hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,A_1),B_2)))))) # label(fact_170_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 304 (all Pa ((all X1 hBOOL(hAPP_P282169671l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2)))))) # label(fact_171_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 305 (all Pa ((all X1 hBOOL(hAPP_P1708370145l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2)))))) # label(fact_172_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 306 (all Pa ((all X1 hBOOL(hAPP_P159683425l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2)))))) # label(fact_173_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 307 (all Pa ((all X1 hBOOL(hAPP_P1235399154l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2)))))) # label(fact_174_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 308 (all Pa ((all X1 hBOOL(hAPP_P449474095r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2)))))) # label(fact_175_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 309 (all Pa ((all X1 hBOOL(hAPP_P943837928l_bool(Pa,X1))) <-> (all A_1 all B_2 (is_bop(A_1) -> hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2))))))) # label(fact_176_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 310 (all Pa ((all X1 hBOOL(hAPP_P929938951l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2)))))) # label(fact_177_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 311 (all Pa ((all X1 hBOOL(hAPP_P1333315679l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2)))))) # label(fact_178_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 312 (all Pa ((all X1 hBOOL(hAPP_P71593144l_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2)))))) # label(fact_179_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 313 (all Pa ((all X1 hBOOL(hAPP_P92196306r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2)))))) # label(fact_180_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 314 (all Pa ((all X1 hBOOL(hAPP_P1907982426r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2)))))) # label(fact_181_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 315 (all Pa ((all X1 hBOOL(hAPP_P2118621157r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2)))))) # label(fact_182_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 316 (all Pa ((all X1 hBOOL(hAPP_P1680401186r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2)))))) # label(fact_183_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 317 (all Pa ((all X1 hBOOL(hAPP_P659547099r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P659547099r_bool(Pa,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2)))))) # label(fact_184_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 318 (all Pa ((all X1 hBOOL(hAPP_P828904212r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P828904212r_bool(Pa,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2)))))) # label(fact_185_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 319 (all Pa ((all X1 hBOOL(hAPP_P2014166431r_bool(Pa,X1))) <-> (all A_1 all B_2 hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2)))))) # label(fact_186_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 320 (all F_1 all B all A all X_1 ((X_1 = A -> hAPP_l207779698on_val(fun_up1149430426on_val(F_1,A,B),X_1) = B) & (X_1 != A -> hAPP_l207779698on_val(fun_up1149430426on_val(F_1,A,B),X_1) = hAPP_l207779698on_val(F_1,X_1)))) # label(fact_187_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 321 (all F_1 all B all A all X_1 ((X_1 = A -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,A,B),X_1) = B) & (X_1 != A -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,A,B),X_1) = hAPP_l512744617ion_ty(F_1,X_1)))) # label(fact_188_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 322 (all F_1 all B all A all X_1 ((X_1 = A -> hAPP_n546249108on_val(fun_up2041264236on_val(F_1,A,B),X_1) = B) & (X_1 != A -> hAPP_n546249108on_val(fun_up2041264236on_val(F_1,A,B),X_1) = hAPP_n546249108on_val(F_1,X_1)))) # label(fact_189_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 323 (all F_1 all B all A all X_1 ((X_1 = A -> hAPP_P2094403585on_val(fun_up204312361on_val(F_1,A,B),X_1) = B) & (X_1 != A -> hAPP_P2094403585on_val(fun_up204312361on_val(F_1,A,B),X_1) = hAPP_P2094403585on_val(F_1,X_1)))) # label(fact_190_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 324 (all F_1 all X_2 all Y_2 (hAPP_l207779698on_val(F_1,X_2) = Y_2 -> fun_up1149430426on_val(F_1,X_2,Y_2) = F_1)) # label(fact_191_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 325 (all F_1 all X_2 all Y_2 (hAPP_l512744617ion_ty(F_1,X_2) = Y_2 -> fun_up424764369ion_ty(F_1,X_2,Y_2) = F_1)) # label(fact_192_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 326 (all F_1 all X_2 all Y_2 (hAPP_n546249108on_val(F_1,X_2) = Y_2 -> fun_up2041264236on_val(F_1,X_2,Y_2) = F_1)) # label(fact_193_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 327 (all F_1 all X_2 all Y_2 (hAPP_P2094403585on_val(F_1,X_2) = Y_2 -> fun_up204312361on_val(F_1,X_2,Y_2) = F_1)) # label(fact_194_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 328 (all F_1 all Y_2 all Z_1 all X_2 (Z_1 != X_2 -> hAPP_l207779698on_val(fun_up1149430426on_val(F_1,X_2,Y_2),Z_1) = hAPP_l207779698on_val(F_1,Z_1))) # label(fact_195_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 329 (all F_1 all Y_2 all Z_1 all X_2 (Z_1 != X_2 -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),Z_1) = hAPP_l512744617ion_ty(F_1,Z_1))) # label(fact_196_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 330 (all F_1 all Y_2 all Z_1 all X_2 (Z_1 != X_2 -> hAPP_n546249108on_val(fun_up2041264236on_val(F_1,X_2,Y_2),Z_1) = hAPP_n546249108on_val(F_1,Z_1))) # label(fact_197_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 331 (all F_1 all Y_2 all Z_1 all X_2 (Z_1 != X_2 -> hAPP_P2094403585on_val(fun_up204312361on_val(F_1,X_2,Y_2),Z_1) = hAPP_P2094403585on_val(F_1,Z_1))) # label(fact_198_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 332 (all M_1 all B all D_1 all A all C_2 (A != C_2 -> fun_up1149430426on_val(fun_up1149430426on_val(M_1,A,B),C_2,D_1) = fun_up1149430426on_val(fun_up1149430426on_val(M_1,C_2,D_1),A,B))) # label(fact_199_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 333 (all M_1 all B all D_1 all A all C_2 (A != C_2 -> fun_up424764369ion_ty(fun_up424764369ion_ty(M_1,A,B),C_2,D_1) = fun_up424764369ion_ty(fun_up424764369ion_ty(M_1,C_2,D_1),A,B))) # label(fact_200_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 334 (all M_1 all B all D_1 all A all C_2 (A != C_2 -> fun_up2041264236on_val(fun_up2041264236on_val(M_1,A,B),C_2,D_1) = fun_up2041264236on_val(fun_up2041264236on_val(M_1,C_2,D_1),A,B))) # label(fact_201_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 335 (all M_1 all B all D_1 all A all C_2 (A != C_2 -> fun_up204312361on_val(fun_up204312361on_val(M_1,A,B),C_2,D_1) = fun_up204312361on_val(fun_up204312361on_val(M_1,C_2,D_1),A,B))) # label(fact_202_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 336 (all F_1 all Y_2 all Z_1 all X_2 ((Z_1 = X_2 -> hAPP_l207779698on_val(fun_up1149430426on_val(F_1,X_2,Y_2),Z_1) = Y_2) & (Z_1 != X_2 -> hAPP_l207779698on_val(fun_up1149430426on_val(F_1,X_2,Y_2),Z_1) = hAPP_l207779698on_val(F_1,Z_1)))) # label(fact_203_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 337 (all F_1 all Y_2 all Z_1 all X_2 ((Z_1 = X_2 -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),Z_1) = Y_2) & (Z_1 != X_2 -> hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),Z_1) = hAPP_l512744617ion_ty(F_1,Z_1)))) # label(fact_204_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 338 (all F_1 all Y_2 all Z_1 all X_2 ((Z_1 = X_2 -> hAPP_n546249108on_val(fun_up2041264236on_val(F_1,X_2,Y_2),Z_1) = Y_2) & (Z_1 != X_2 -> hAPP_n546249108on_val(fun_up2041264236on_val(F_1,X_2,Y_2),Z_1) = hAPP_n546249108on_val(F_1,Z_1)))) # label(fact_205_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 339 (all F_1 all Y_2 all Z_1 all X_2 ((Z_1 = X_2 -> hAPP_P2094403585on_val(fun_up204312361on_val(F_1,X_2,Y_2),Z_1) = Y_2) & (Z_1 != X_2 -> hAPP_P2094403585on_val(fun_up204312361on_val(F_1,X_2,Y_2),Z_1) = hAPP_P2094403585on_val(F_1,Z_1)))) # label(fact_206_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 340 (all F_1 all X_2 all Y_2 hAPP_l207779698on_val(fun_up1149430426on_val(F_1,X_2,Y_2),X_2) = Y_2) # label(fact_207_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 341 (all F_1 all X_2 all Y_2 hAPP_l512744617ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),X_2) = Y_2) # label(fact_208_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 342 (all F_1 all X_2 all Y_2 hAPP_n546249108on_val(fun_up2041264236on_val(F_1,X_2,Y_2),X_2) = Y_2) # label(fact_209_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 343 (all F_1 all X_2 all Y_2 hAPP_P2094403585on_val(fun_up204312361on_val(F_1,X_2,Y_2),X_2) = Y_2) # label(fact_210_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 344 (all F_1 all X_2 all Y_2 all Z_1 fun_up1149430426on_val(fun_up1149430426on_val(F_1,X_2,Y_2),X_2,Z_1) = fun_up1149430426on_val(F_1,X_2,Z_1)) # label(fact_211_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 345 (all F_1 all X_2 all Y_2 all Z_1 fun_up424764369ion_ty(fun_up424764369ion_ty(F_1,X_2,Y_2),X_2,Z_1) = fun_up424764369ion_ty(F_1,X_2,Z_1)) # label(fact_212_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 346 (all F_1 all X_2 all Y_2 all Z_1 fun_up2041264236on_val(fun_up2041264236on_val(F_1,X_2,Y_2),X_2,Z_1) = fun_up2041264236on_val(F_1,X_2,Z_1)) # label(fact_213_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 347 (all F_1 all X_2 all Y_2 all Z_1 fun_up204312361on_val(fun_up204312361on_val(F_1,X_2,Y_2),X_2,Z_1) = fun_up204312361on_val(F_1,X_2,Z_1)) # label(fact_214_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 348 (all F_1 all X_2 all Y_2 (fun_up1149430426on_val(F_1,X_2,Y_2) = F_1 <-> hAPP_l207779698on_val(F_1,X_2) = Y_2)) # label(fact_215_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 349 (all F_1 all X_2 all Y_2 (fun_up424764369ion_ty(F_1,X_2,Y_2) = F_1 <-> hAPP_l512744617ion_ty(F_1,X_2) = Y_2)) # label(fact_216_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 350 (all F_1 all X_2 all Y_2 (fun_up2041264236on_val(F_1,X_2,Y_2) = F_1 <-> hAPP_n546249108on_val(F_1,X_2) = Y_2)) # label(fact_217_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 351 (all F_1 all X_2 all Y_2 (fun_up204312361on_val(F_1,X_2,Y_2) = F_1 <-> hAPP_P2094403585on_val(F_1,X_2) = Y_2)) # label(fact_218_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 352 (all P_4 all T_7 hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_4),T_7),T_7))) # label(fact_219_widen__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 353 (all Ea all Ta all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb)) -> hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H_b)))))) # label(fact_220_red__preserves__hconf) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 354 (all Ea all Ta all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea)) -> hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),L_b),Ea)))))) # label(fact_221_red__preserves__lconf) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 355 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),C_4)))) # label(fact_222_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 356 (all Y_2 -(all A_1 all B_2 all C_4 Y_2 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_2),C_4)))) # label(fact_223_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 357 (all Y_2 -(all A_1 all B_2 all C_4 Y_2 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4)))) # label(fact_224_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 358 (all Y_5 -(all A_1 all B_2 all C_4 (is_bop(A_1) -> Y_5 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_2),C_4))))) # label(fact_225_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 359 (all Y_2 -(all A_1 all B_2 all C_4 Y_2 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_2),C_4)))) # label(fact_226_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 360 (all Y_2 -(all A_1 all B_2 all C_4 Y_2 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4)))) # label(fact_227_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 361 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),C_4)))) # label(fact_228_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 362 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_2),C_4)))) # label(fact_229_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 363 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),C_4)))) # label(fact_230_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 364 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_2),C_4)))) # label(fact_231_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 365 (all Y_2 -(all A_1 all B_2 all C_4 Y_2 != hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),C_4)))) # label(fact_232_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 366 (all Y_2 -(all A_1 all B_2 all C_4 Y_2 != hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4)))) # label(fact_233_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 367 (all Y_2 -(all A_1 all B_2 all C_4 Y_2 != hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,B_2),C_4)))) # label(fact_234_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 368 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B_2),C_4)))) # label(fact_235_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 369 (all Y_5 -(all A_1 all B_2 all C_4 (is_bop(B_2) -> Y_5 != hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_2),C_4))))) # label(fact_236_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 370 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_2),C_4)))) # label(fact_237_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 371 (all Y_2 -(all A_1 all B_2 all C_4 Y_2 != hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),C_4)))) # label(fact_238_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 372 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),C_4)))) # label(fact_239_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 373 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),C_4)))) # label(fact_240_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 374 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_2),C_4)))) # label(fact_241_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 375 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),C_4)))) # label(fact_242_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 376 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),C_4)))) # label(fact_243_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 377 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_2),C_4)))) # label(fact_244_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 378 (all Y_5 -(all A_1 all B_2 all C_4 Y_5 != hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,B_2),C_4)))) # label(fact_245_prod__cases3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 379 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1384137393r_bool(Pa,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,A_1),hAPP_P976433298t_char(hAPP_l2048923787t_char(produc2016959032t_char,B_2),C_4))))) -> hBOOL(hAPP_P1384137393r_bool(Pa,X_2)))) # label(fact_246_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 380 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B_2),C_4))))) -> hBOOL(hAPP_P282169671l_bool(Pa,X_2)))) # label(fact_247_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 381 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4))))) -> hBOOL(hAPP_P1708370145l_bool(Pa,X_2)))) # label(fact_248_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 382 (all X_2 all Pa ((all A_1 all B_2 all C_4 (is_bop(A_1) -> hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_2),C_4)))))) -> hBOOL(hAPP_P943837928l_bool(Pa,X_2)))) # label(fact_249_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 383 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,B_2),C_4))))) -> hBOOL(hAPP_P1333315679l_bool(Pa,X_2)))) # label(fact_250_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 384 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4))))) -> hBOOL(hAPP_P71593144l_bool(Pa,X_2)))) # label(fact_251_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 385 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),C_4))))) -> hBOOL(hAPP_P92196306r_bool(Pa,X_2)))) # label(fact_252_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 386 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_2),C_4))))) -> hBOOL(hAPP_P1907982426r_bool(Pa,X_2)))) # label(fact_253_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 387 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),C_4))))) -> hBOOL(hAPP_P1680401186r_bool(Pa,X_2)))) # label(fact_254_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 388 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P659547099r_bool(Pa,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_2),C_4))))) -> hBOOL(hAPP_P659547099r_bool(Pa,X_2)))) # label(fact_255_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 389 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P378063101l_bool(Pa,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,A_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B_2),C_4))))) -> hBOOL(hAPP_P378063101l_bool(Pa,X_2)))) # label(fact_256_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 390 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1221872711l_bool(Pa,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,A_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,B_2),C_4))))) -> hBOOL(hAPP_P1221872711l_bool(Pa,X_2)))) # label(fact_257_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 391 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P124632071l_bool(Pa,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,A_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,B_2),C_4))))) -> hBOOL(hAPP_P124632071l_bool(Pa,X_2)))) # label(fact_258_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 392 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P2010574925r_bool(Pa,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,A_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B_2),C_4))))) -> hBOOL(hAPP_P2010574925r_bool(Pa,X_2)))) # label(fact_259_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 393 (all X_2 all Pa ((all A_1 all B_2 all C_4 (is_bop(B_2) -> hBOOL(hAPP_P738987199l_bool(Pa,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,A_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,B_2),C_4)))))) -> hBOOL(hAPP_P738987199l_bool(Pa,X_2)))) # label(fact_260_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 394 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P2123002749l_bool(Pa,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,A_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B_2),C_4))))) -> hBOOL(hAPP_P2123002749l_bool(Pa,X_2)))) # label(fact_261_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 395 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P2028072621l_bool(Pa,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,A_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B_2),C_4))))) -> hBOOL(hAPP_P2028072621l_bool(Pa,X_2)))) # label(fact_262_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 396 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P824029447r_bool(Pa,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,A_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,B_2),C_4))))) -> hBOOL(hAPP_P824029447r_bool(Pa,X_2)))) # label(fact_263_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 397 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1240100515r_bool(Pa,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,A_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,B_2),C_4))))) -> hBOOL(hAPP_P1240100515r_bool(Pa,X_2)))) # label(fact_264_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 398 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1183499705r_bool(Pa,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,A_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,B_2),C_4))))) -> hBOOL(hAPP_P1183499705r_bool(Pa,X_2)))) # label(fact_265_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 399 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P975284999r_bool(Pa,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,A_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,B_2),C_4))))) -> hBOOL(hAPP_P975284999r_bool(Pa,X_2)))) # label(fact_266_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 400 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P929449287r_bool(Pa,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,A_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,B_2),C_4))))) -> hBOOL(hAPP_P929449287r_bool(Pa,X_2)))) # label(fact_267_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 401 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P801803911r_bool(Pa,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,A_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,B_2),C_4))))) -> hBOOL(hAPP_P801803911r_bool(Pa,X_2)))) # label(fact_268_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 402 (all X_2 all Pa ((all A_1 all B_2 all C_4 hBOOL(hAPP_P1002912327r_bool(Pa,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,A_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,B_2),C_4))))) -> hBOOL(hAPP_P1002912327r_bool(Pa,X_2)))) # label(fact_269_prod__induct3) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 403 (all Ea all Ta all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> (hBOOL(wTrt_1(Pa,hp(S),Ea,Eb,Ta)) -> (hBOOL(hAPP_P159683425l_bool(typeSa1700205512_sconf(Pa,Ea),S)) -> hBOOL(hAPP_P159683425l_bool(typeSa1700205512_sconf(Pa,Ea),S_2)))))) # label(fact_270_red__preserves__sconf) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 404 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1734260017l_bool(hAPP_P53416969l_bool(member894971540t_char,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1734260017l_bool(hAPP_P53416969l_bool(member894971540t_char,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_271_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 405 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_272_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 406 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f479632753l_bool(hAPP_P153687689l_bool(member817832404t_char,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f479632753l_bool(hAPP_P153687689l_bool(member817832404t_char,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_273_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 407 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f288221747l_bool(hAPP_P569585933l_bool(member520253462har_ty,hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f288221747l_bool(hAPP_P569585933l_bool(member520253462har_ty,hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_274_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 408 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1748390065l_bool(hAPP_P1503283977l_bool(member1580476948t_char,hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1748390065l_bool(hAPP_P1503283977l_bool(member1580476948t_char,hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_275_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 409 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f348753975l_bool(hAPP_P1033205013l_bool(member273646106st_val,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f348753975l_bool(hAPP_P1033205013l_bool(member273646106st_val,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_276_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 410 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f433445541l_bool(hAPP_P1019319281l_bool(member104734088ist_ty,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f433445541l_bool(hAPP_P1019319281l_bool(member104734088ist_ty,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_277_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 411 (all S_4 all R_2 (is_fun1083000568p_bool(S_4) & is_fun1083000568p_bool(R_2) -> ((all X_1 all Xa (is_bop(X_1) & is_bop(Xa) -> (hBOOL(hAPP_f1854361213l_bool(hAPP_P1034346913l_bool(member978285664op_bop,hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1854361213l_bool(hAPP_P1034346913l_bool(member978285664op_bop,hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,X_1),Xa)),S_4))))) <-> R_2 = S_4))) # label(fact_278_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 412 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f983152497l_bool(hAPP_P1953134729l_bool(member781783252on_val,hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f983152497l_bool(hAPP_P1953134729l_bool(member781783252on_val,hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_279_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 413 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1754555101l_bool(hAPP_P1679186017l_bool(member1337019328on_val,hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1754555101l_bool(hAPP_P1679186017l_bool(member1337019328on_val,hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_280_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 414 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1661305905l_bool(hAPP_P1878549513l_bool(member490182804on_val,hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1661305905l_bool(hAPP_P1878549513l_bool(member490182804on_val,hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_281_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 415 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f91506671l_bool(hAPP_P2015860941l_bool(member840932460on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f91506671l_bool(hAPP_P2015860941l_bool(member840932460on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_282_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 416 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f966411375l_bool(hAPP_P998768845l_bool(member763590124on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f966411375l_bool(hAPP_P998768845l_bool(member763590124on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_283_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 417 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1134950784l_bool(hAPP_P1217996045l_bool(member1542417277on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1134950784l_bool(hAPP_P1217996045l_bool(member1542417277on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_284_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 418 (all S_4 all R_2 ((all X_1 all Xa (is_bop(X_1) -> (hBOOL(hAPP_f742333458l_bool(hAPP_P1653675595l_bool(member1417904245al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f742333458l_bool(hAPP_P1653675595l_bool(member1417904245al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Xa)),S_4))))) <-> R_2 = S_4)) # label(fact_285_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 419 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_286_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 420 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f837795298l_bool(hAPP_P483670507l_bool(member1972431429on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f837795298l_bool(hAPP_P483670507l_bool(member1972431429on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_287_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 421 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1780084320l_bool(hAPP_P1472618637l_bool(member133545693t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1780084320l_bool(hAPP_P1472618637l_bool(member133545693t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_288_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 422 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1746574980l_bool(hAPP_P1198052655l_bool(member140606439t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1746574980l_bool(hAPP_P1198052655l_bool(member140606439t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_289_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 423 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1314764175l_bool(hAPP_P845017029l_bool(member699351154t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1314764175l_bool(hAPP_P845017029l_bool(member699351154t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_290_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 424 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f2050077417l_bool(hAPP_P1517699917l_bool(member1771544038t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f2050077417l_bool(hAPP_P1517699917l_bool(member1771544038t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_291_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 425 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1161798306l_bool(hAPP_P1327510541l_bool(member1379348767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1161798306l_bool(hAPP_P1327510541l_bool(member1379348767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_292_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 426 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f82569901l_bool(hAPP_P1293136973l_bool(member1840112042t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f82569901l_bool(hAPP_P1293136973l_bool(member1840112042t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_293_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 427 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_294_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 428 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_295_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 429 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_296_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 430 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_297_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 431 (all S_4 all R_2 ((all X_1 all Xa (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,X_1),Xa)),R_2)) <-> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,hAPP_P242904598t_char(hAPP_l1388836853t_char(produc1331140167t_char,X_1),Xa)),S_4)))) <-> R_2 = S_4)) # label(fact_298_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 432 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2))) # label(fact_299_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 433 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2))) # label(fact_300_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 434 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2))) # label(fact_301_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 435 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2))) # label(fact_302_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 436 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2))) # label(fact_303_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 437 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2))) # label(fact_304_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 438 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2))) # label(fact_305_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 439 (all Y_2 -(all A_1 all B_2 Y_2 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2))) # label(fact_306_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 440 (all Y_2 -(all A_1 all B_2 Y_2 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2))) # label(fact_307_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 441 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2))) # label(fact_308_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 442 (all Y_4 -(all A_1 all B_2 (is_bop(A_1) -> Y_4 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2)))) # label(fact_309_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 443 (all Y_4 -(all A_1 all B_2 Y_4 != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2))) # label(fact_310_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 444 (all Y_2 -(all A_1 all B_2 Y_2 != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2))) # label(fact_311_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 445 (all Y_2 -(all A_1 all B_2 Y_2 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2))) # label(fact_312_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 446 (all Y_2 -(all A_1 all B_2 Y_2 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2))) # label(fact_313_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 447 (all Y_2 -(all A_1 all B_2 Y_2 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2))) # label(fact_314_prod_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 448 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Y_1))) # label(fact_315_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 449 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Y_1))) # label(fact_316_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 450 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Y_1))) # label(fact_317_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 451 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Y_1))) # label(fact_318_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 452 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Y_1))) # label(fact_319_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 453 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Y_1))) # label(fact_320_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 454 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Y_1))) # label(fact_321_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 455 (all P_1 -(all X_1 all Y_1 P_1 != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Y_1))) # label(fact_322_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 456 (all P_1 -(all X_1 all Y_1 P_1 != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Y_1))) # label(fact_323_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 457 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Y_1))) # label(fact_324_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 458 (all P_3 -(all X_1 all Y_1 (is_bop(X_1) -> P_3 != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Y_1)))) # label(fact_325_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 459 (all P_3 -(all X_1 all Y_1 P_3 != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Y_1))) # label(fact_326_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 460 (all P_1 -(all X_1 all Y_1 P_1 != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_1))) # label(fact_327_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 461 (all P_1 -(all X_1 all Y_1 P_1 != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_1))) # label(fact_328_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 462 (all P_1 -(all X_1 all Y_1 P_1 != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Y_1))) # label(fact_329_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 463 (all P_1 -(all X_1 all Y_1 P_1 != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Y_1))) # label(fact_330_PairE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 464 (all Pa ((exists X1 hBOOL(hAPP_P2014166431r_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P2014166431r_bool(Pa,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2)))))) # label(fact_331_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 465 (all Pa ((exists X1 hBOOL(hAPP_P828904212r_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P828904212r_bool(Pa,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2)))))) # label(fact_332_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 466 (all Pa ((exists X1 hBOOL(hAPP_P659547099r_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P659547099r_bool(Pa,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2)))))) # label(fact_333_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 467 (all Pa ((exists X1 hBOOL(hAPP_P1680401186r_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P1680401186r_bool(Pa,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2)))))) # label(fact_334_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 468 (all Pa ((exists X1 hBOOL(hAPP_P2118621157r_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P2118621157r_bool(Pa,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2)))))) # label(fact_335_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 469 (all Pa ((exists X1 hBOOL(hAPP_P1907982426r_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P1907982426r_bool(Pa,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2)))))) # label(fact_336_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.46 470 (all Pa ((exists X1 hBOOL(hAPP_P92196306r_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P92196306r_bool(Pa,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2)))))) # label(fact_337_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 471 (all Pa ((exists X1 hBOOL(hAPP_P71593144l_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P71593144l_bool(Pa,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2)))))) # label(fact_338_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 472 (all Pa ((exists X1 hBOOL(hAPP_P1333315679l_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P1333315679l_bool(Pa,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2)))))) # label(fact_339_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 473 (all Pa ((exists X1 hBOOL(hAPP_P929938951l_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P929938951l_bool(Pa,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2)))))) # label(fact_340_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 474 (all Pa ((exists X1 hBOOL(hAPP_P943837928l_bool(Pa,X1))) <-> (exists A_1 exists B_2 (is_bop(A_1) & hBOOL(hAPP_P943837928l_bool(Pa,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2))))))) # label(fact_341_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 475 (all Pa ((exists X1 hBOOL(hAPP_P449474095r_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P449474095r_bool(Pa,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2)))))) # label(fact_342_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 476 (all Pa ((exists X1 hBOOL(hAPP_P1235399154l_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P1235399154l_bool(Pa,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2)))))) # label(fact_343_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 477 (all Pa ((exists X1 hBOOL(hAPP_P159683425l_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P159683425l_bool(Pa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2)))))) # label(fact_344_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 478 (all Pa ((exists X1 hBOOL(hAPP_P1708370145l_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P1708370145l_bool(Pa,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2)))))) # label(fact_345_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 479 (all Pa ((exists X1 hBOOL(hAPP_P282169671l_bool(Pa,X1))) <-> (exists A_1 exists B_2 hBOOL(hAPP_P282169671l_bool(Pa,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2)))))) # label(fact_346_split__paired__Ex) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 480 (all T_6 all P_2 all S_6 all U_1 (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_6),U_1)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),U_1),T_6)) -> hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(P_2),S_6),T_6))))) # label(fact_347_widen__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 481 (all Pa all Ea all S (hBOOL(hAPP_P159683425l_bool(typeSa1700205512_sconf(Pa,Ea),S)) <-> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,cOMBS_570216337l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,cOMBB_383678192on_val),hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,fconj),hconf_97414254t_char(Pa))),hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,cOMBC_832625297y_bool),lconf_496643946t_char(Pa))),Ea))),S)))) # label(fact_349_sconf__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 482 (all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> hBOOL(hext(Hb,H_b)))) # label(fact_350_red__hext__incr) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 483 (all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(wf_pro755087577t_char(wf_J_mdecl,Pa)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> (hBOOL(d_list_char(Eb,hAPP_f363827556r_bool(some_f80346385r_bool,dom_list_char_val(Lb)))) -> hBOOL(d_list_char(E_b,hAPP_f363827556r_bool(some_f80346385r_bool,dom_list_char_val(L_b)))))))) # label(fact_351_red__preserves__defass) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 484 (all A all A_3 (hAPP_nat_option_nat(some_nat,A) = hAPP_nat_option_nat(some_nat,A_3) <-> A = A_3)) # label(fact_352_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 485 (all A all A_3 (hAPP_P1510515380on_val(some_P948696889on_val,A) = hAPP_P1510515380on_val(some_P948696889on_val,A_3) <-> A = A_3)) # label(fact_353_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 486 (all A all A_3 (hAPP_ty_option_ty(some_ty,A) = hAPP_ty_option_ty(some_ty,A_3) <-> A = A_3)) # label(fact_354_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 487 (all A all A_3 (hAPP_f363827556r_bool(some_f80346385r_bool,A) = hAPP_f363827556r_bool(some_f80346385r_bool,A_3) <-> A = A_3)) # label(fact_355_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 488 (all A all A_3 (hAPP_val_option_val(some_val,A) = hAPP_val_option_val(some_val,A_3) <-> A = A_3)) # label(fact_356_option_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 489 (all F_1 all A all B (hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B)))) # label(fact_357_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 490 (all F_1 all A all B (hBOOL(hAPP_P828904212r_bool(F_1,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))) -> hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(produc2116052801r_bool(F_1),A),B)))) # label(fact_358_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 491 (all F_1 all A all B (hBOOL(hAPP_P659547099r_bool(F_1,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))) -> hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(produc266042248r_bool(F_1),A),B)))) # label(fact_359_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 492 (all F_1 all A all B (hBOOL(hAPP_P1680401186r_bool(F_1,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))) -> hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(produc1588781647r_bool(F_1),A),B)))) # label(fact_360_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 493 (all F_1 all A all B (hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B)))) # label(fact_361_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 494 (all F_1 all A all B (hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B)))) # label(fact_362_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 495 (all F_1 all A all B (hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B)))) # label(fact_363_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 496 (all F_1 all A all B (hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B)))) # label(fact_364_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 497 (all F_1 all A all B (hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))) -> hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B)))) # label(fact_365_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 498 (all F_1 all A all B (hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))) -> hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B)))) # label(fact_366_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 499 (all F_1 all A all B (hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))) -> hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B)))) # label(fact_367_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 500 (all F_1 all A all B (hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))) -> hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B)))) # label(fact_368_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 501 (all F_1 all A all B (hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B)))) # label(fact_369_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 502 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B)))) # label(fact_370_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 503 (all F_1 all A all B (hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B)))) # label(fact_371_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 504 (all F_1 all A all B (hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B)))) # label(fact_372_curryI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 505 (all L_0 all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_ad325961431ar_val(L_0,Lb)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),map_ad325961431ar_val(L_0,L_b))))),red(Pa))))) # label(fact_373_red__lcl__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 506 (all Va_1 all Va all Ta all Pa all Hb all Lb all Ea (hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea)) -> (hBOOL(conf_P373316194t_char(Pa,Hb,Va,Ta)) -> (hAPP_l512744617ion_ty(Ea,Va_1) = hAPP_ty_option_ty(some_ty,Ta) -> hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va))),Ea)))))) # label(fact_374_lconf__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 507 (all Va_1 all Va all Ta all Pa all Hb all Lb all Ea (hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea)) -> (hBOOL(conf_P373316194t_char(Pa,Hb,Va,Ta)) -> hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va))),fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,Ta))))))) # label(fact_375_lconf__upd2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 508 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_3),B_3))),lex_pr1541028704on_val(R_1,S))) <-> hBOOL(hAPP_f1734260017l_bool(hAPP_P53416969l_bool(member894971540t_char,hAPP_l1648260346t_char(hAPP_l1105836155t_char(produc1237966615t_char,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,B),B_3)),S)))) # label(fact_376_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 509 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_3),B_3))),lex_pr69619957on_val(R_1,S))) <-> hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,B),B_3)),S)))) # label(fact_377_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 510 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_3),B_3))),lex_pr1787105337t_char(R_1,S))) <-> hBOOL(hAPP_f479632753l_bool(hAPP_P153687689l_bool(member817832404t_char,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,B),B_3)),S)))) # label(fact_378_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 511 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_3),B_3))),lex_pr213428520t_char(R_1,S))) <-> hBOOL(hAPP_f288221747l_bool(hAPP_P569585933l_bool(member520253462har_ty,hAPP_l1294856089har_ty(hAPP_l1657578379har_ty(produc1860789535har_ty,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f1748390065l_bool(hAPP_P1503283977l_bool(member1580476948t_char,hAPP_l1334098948t_char(hAPP_l1450984463t_char(produc436875159t_char,B),B_3)),S)))) # label(fact_379_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 512 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_3),B_3))),lex_pr167435119t_char(R_1,S))) <-> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,B),B_3)),S)))) # label(fact_380_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 513 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_3),B_3))),lex_pr1668767798t_char(R_1,S))) <-> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,B),B_3)),S)))) # label(fact_381_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 514 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_3),B_3))),lex_pr307591827t_char(R_1,S))) <-> hBOOL(hAPP_f348753975l_bool(hAPP_P1033205013l_bool(member273646106st_val,hAPP_l1249476511st_val(hAPP_l103437071st_val(produc2078839843st_val,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f588675559l_bool(hAPP_P1860450421l_bool(member1199939018t_char,hAPP_e817857447t_char(hAPP_e1376201919t_char(produc943465171t_char,B),B_3)),S)))) # label(fact_382_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 515 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_3),B_3))),lex_pr1588300168t_char(R_1,S))) <-> hBOOL(hAPP_f433445541l_bool(hAPP_P1019319281l_bool(member104734088ist_ty,hAPP_l1319068228ist_ty(hAPP_l1770520637ist_ty(produc512429457ist_ty,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,B),B_3)),S)))) # label(fact_383_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 516 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_3),B_3))),lex_pr1876288492t_char(R_1,S))) <-> hBOOL(hAPP_f479632753l_bool(hAPP_P153687689l_bool(member817832404t_char,hAPP_l1883348915t_char(hAPP_l2019537453t_char(produc2035944023t_char,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,B),B_3)),S)))) # label(fact_384_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 517 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_3),B_3))),lex_pr2110711565on_val(R_1,S))) <-> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),B_3)),S)))) # label(fact_385_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 518 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_3),B_3))),lex_prod_val_val(R_1,S))) <-> hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),B_3)),S)))) # label(fact_386_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 519 (all A all B all A_3 all B_3 all R_1 all S (is_bop(A) & is_bop(A_3) -> (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_3),B_3))),lex_pr1932514710al_val(R_1,S))) <-> hBOOL(hAPP_f1854361213l_bool(hAPP_P1034346913l_bool(member978285664op_bop,hAPP_b1909667208op_bop(hAPP_b1058859669op_bop(product_Pair_bop_bop,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,B),B_3)),S))))) # label(fact_387_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 520 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_3),B_3))),lex_pr280535005t_char(R_1,S))) <-> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),B_3)),S)))) # label(fact_388_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 521 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_3),B_3))),lex_pr1971266694on_val(R_1,S))) <-> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f983152497l_bool(hAPP_P1953134729l_bool(member781783252on_val,hAPP_f1146435765on_val(hAPP_f1744304433on_val(produc1618304727on_val,B),B_3)),S)))) # label(fact_389_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 522 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_3),B_3))),lex_pr731210613on_val(R_1,S))) <-> hBOOL(hAPP_f1754555101l_bool(hAPP_P1679186017l_bool(member1337019328on_val,hAPP_f368284312on_val(hAPP_f1805337205on_val(produc1712663241on_val,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f1661305905l_bool(hAPP_P1878549513l_bool(member490182804on_val,hAPP_f1741070310on_val(hAPP_f864891091on_val(produc1960514199on_val,B),B_3)),S)))) # label(fact_390_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 523 (all A all B all A_3 all B_3 all R_1 all S (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_3),B_3))),lex_pr1038007919on_val(R_1,S))) <-> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),A_3)),R_1)) | A = A_3 & hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),B_3)),S)))) # label(fact_391_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 524 (all F1 all A all B (hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(F1,A),B)) -> hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))))) # label(fact_392_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 525 (all F1 all A all B (hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(F1,A),B)) -> hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))))) # label(fact_393_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 526 (all F1 all A all B (hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(F1,A),B)) -> hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))))) # label(fact_394_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 527 (all F1 all A all B (hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(F1,A),B)) -> hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))))) # label(fact_395_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 528 (all F1 all A all B (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(F1,A),B)) -> hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))))) # label(fact_396_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 529 (all F1 all A all B (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(F1,A),B)) -> hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))))) # label(fact_397_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 530 (all F1 all A all B (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(F1,A),B)) -> hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))))) # label(fact_398_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 531 (all F1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(F1,A),B)) -> hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))))) # label(fact_399_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 532 (all F1 all A all B (hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(F1,A),B)) -> hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))))) # label(fact_400_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 533 (all F1 all A all B (hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(F1,A),B)) -> hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))))) # label(fact_401_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 534 (all F1 all A all B (hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(F1,A),B)) -> hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))))) # label(fact_402_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 535 (all F1 all A all B (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(F1,A),B)) -> hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))))) # label(fact_403_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 536 (all F1 all A all B (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(F1,A),B)) -> hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))))) # label(fact_404_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 537 (all F1 all A all B (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A),B)) -> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))))) # label(fact_405_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 538 (all F1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F1,A),B)) -> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))))) # label(fact_406_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 539 (all F1 all A all B (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F1,A),B)) -> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))))) # label(fact_407_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 540 (all F_1 all A all B (hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(F_1,A),B)) -> hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))))) # label(fact_408_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 541 (all F_1 all A all B (hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(F_1,A),B)) -> hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))))) # label(fact_409_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 542 (all F_1 all A all B (hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(F_1,A),B)) -> hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))))) # label(fact_410_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 543 (all F_1 all A all B (hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(F_1,A),B)) -> hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))))) # label(fact_411_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 544 (all F_1 all A all B (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(F_1,A),B)) -> hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))))) # label(fact_412_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 545 (all F_1 all A all B (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(F_1,A),B)) -> hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))))) # label(fact_413_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 546 (all F_1 all A all B (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(F_1,A),B)) -> hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))))) # label(fact_414_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 547 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(F_1,A),B)) -> hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))))) # label(fact_415_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 548 (all F_1 all A all B (hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(F_1,A),B)) -> hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))))) # label(fact_416_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 549 (all F_1 all A all B (hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(F_1,A),B)) -> hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))))) # label(fact_417_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 550 (all F_1 all A all B (hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(F_1,A),B)) -> hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))))) # label(fact_418_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 551 (all F_1 all A all B (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(F_1,A),B)) -> hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))))) # label(fact_419_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 552 (all F_1 all A all B (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(F_1,A),B)) -> hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))))) # label(fact_420_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 553 (all F_1 all A all B (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F_1,A),B)) -> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))))) # label(fact_421_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 554 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F_1,A),B)) -> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))))) # label(fact_422_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 555 (all F_1 all A all B (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F_1,A),B)) -> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))))) # label(fact_423_splitI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 556 (all L1 all M_1 all L2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,M_1),dom_na996029170on_val(L2))) -> hAPP_n546249108on_val(map_ad61982421on_val(L1,L2),M_1) = hAPP_n546249108on_val(L2,M_1))) # label(fact_424_map__add__dom__app__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 557 (all L1 all M_1 all L2 (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_val(L2))) -> hAPP_l207779698on_val(map_ad325961431ar_val(L1,L2),M_1) = hAPP_l207779698on_val(L2,M_1))) # label(fact_425_map__add__dom__app__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 558 (all C_2 all P_1 all Q_2 (P_1 = Q_2 -> hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,C_2),P_1) = hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,C_2),Q_2))) # label(fact_426_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 559 (all C_2 all P_1 all Q_2 (P_1 = Q_2 -> (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_2),P_1)) <-> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_2),Q_2))))) # label(fact_427_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 560 (all L1 all M_1 all L2 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,M_1),dom_na996029170on_val(L2))) -> hAPP_n546249108on_val(map_ad61982421on_val(L1,L2),M_1) = hAPP_n546249108on_val(L1,M_1))) # label(fact_428_map__add__dom__app__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 561 (all L1 all M_1 all L2 (-hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_val(L2))) -> hAPP_l207779698on_val(map_ad325961431ar_val(L1,L2),M_1) = hAPP_l207779698on_val(L1,M_1))) # label(fact_429_map__add__dom__app__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 562 (all L2 all M_1 all L1 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,M_1),dom_na996029170on_val(L1))) -> hAPP_n546249108on_val(map_ad61982421on_val(L1,L2),M_1) = hAPP_n546249108on_val(L2,M_1))) # label(fact_430_map__add__dom__app__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 563 (all L2 all M_1 all L1 (-hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_val(L1))) -> hAPP_l207779698on_val(map_ad325961431ar_val(L1,L2),M_1) = hAPP_l207779698on_val(L2,M_1))) # label(fact_431_map__add__dom__app__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 564 (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_432_map__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 565 (all F_1 hAPP_f46308763ion_ty(produc907433735ion_ty,produc1675615144ion_ty(F_1)) = F_1) # label(fact_433_split__curry) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 566 (all F_1 hAPP_f2121594859l_bool(produc1958875245l_bool,produc2062775566l_bool(F_1)) = F_1) # label(fact_434_split__curry) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 567 (all F_1 produc1675615144ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,F_1)) = F_1) # label(fact_435_curry__split) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 568 (all F_1 produc2062775566l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F_1)) = F_1) # label(fact_436_curry__split) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 569 (all Pa all Q_1 all X_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,hAPP_f1863694447l_bool(cOMBB_383678192on_val,hAPP_b589554111l_bool(fconj,Pa))),Q_1)),X_1)) <-> hBOOL(Pa) & hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Q_1),X_1)))) # label(fact_437_split__part) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 570 (all Va_1 all Ta all Va all U all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),hAPP_v834067052t_char(val_list_char,U)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,U)),S))),red(Pa)))) # label(fact_438_red__reds_ORedInitBlock) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 571 (all T_a all Pa all Hb all Va all Ta (hBOOL(conf_P373316194t_char(Pa,Hb,Va,Ta)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),Ta),T_a)) -> hBOOL(conf_P373316194t_char(Pa,Hb,Va,T_a))))) # label(fact_439_conf__widen) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 572 (all F_1 all A all B (hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,F_1),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(F_1,A),B)))) # label(fact_440_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 573 (all F_1 all A all B (hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,F_1),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))) -> hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(F_1,A),B)))) # label(fact_441_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 574 (all F_1 all A all B (hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,F_1),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))) -> hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(F_1,A),B)))) # label(fact_442_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 575 (all F_1 all A all B (hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,F_1),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))) -> hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(F_1,A),B)))) # label(fact_443_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 576 (all F_1 all A all B (hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,F_1),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(F_1,A),B)))) # label(fact_444_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 577 (all F_1 all A all B (hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,F_1),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(F_1,A),B)))) # label(fact_445_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 578 (all F_1 all A all B (hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,F_1),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(F_1,A),B)))) # label(fact_446_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 579 (all F_1 all A all B (hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,F_1),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(F_1,A),B)))) # label(fact_447_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 580 (all F_1 all A all B (hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,F_1),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))) -> hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(F_1,A),B)))) # label(fact_448_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 581 (all F_1 all A all B (hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,F_1),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))) -> hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(F_1,A),B)))) # label(fact_449_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 582 (all F_1 all A all B (hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,F_1),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))) -> hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(F_1,A),B)))) # label(fact_450_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 583 (all F_1 all A all B (hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,F_1),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))) -> hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(F_1,A),B)))) # label(fact_451_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 584 (all F_1 all A all B (hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,F_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(F_1,A),B)))) # label(fact_452_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 585 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F_1,A),B)))) # label(fact_453_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 586 (all F_1 all A all B (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,F_1),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(F_1,A),B)))) # label(fact_454_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 587 (all F_1 all A all B (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,F_1),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(F_1,A),B)))) # label(fact_455_splitD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 588 (all H_b all Pa all Hb all Lb all Ea (hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea)) -> (hBOOL(hext(Hb,H_b)) -> hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),Lb),Ea))))) # label(fact_456_lconf__hext) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 589 (all Va all E_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(hAPP_v834067052t_char(val_list_char,Va),E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S))),red(Pa)))) # label(fact_457_red__reds_ORedSeq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 590 (all E1 all U1 all M_1 all E2 (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,M_1),dom_na996029170on_val(E2))) -> map_ad61982421on_val(fun_up2041264236on_val(E1,M_1,hAPP_P1510515380on_val(some_P948696889on_val,U1)),E2) = fun_up2041264236on_val(map_ad61982421on_val(E1,E2),M_1,hAPP_P1510515380on_val(some_P948696889on_val,U1)))) # label(fact_458_map__add__upd__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 591 (all E1 all U1 all M_1 all E2 (-hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_val(E2))) -> map_ad325961431ar_val(fun_up1149430426on_val(E1,M_1,hAPP_val_option_val(some_val,U1)),E2) = fun_up1149430426on_val(map_ad325961431ar_val(E1,E2),M_1,hAPP_val_option_val(some_val,U1)))) # label(fact_459_map__add__upd__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 592 (all E1 all U1 all M_1 all E2 (-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,M_1),dom_Pr695701035ar_val(E2))) -> map_ad1185064968ar_val(fun_up204312361on_val(E1,M_1,hAPP_val_option_val(some_val,U1)),E2) = fun_up204312361on_val(map_ad1185064968ar_val(E1,E2),M_1,hAPP_val_option_val(some_val,U1)))) # label(fact_460_map__add__upd__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 593 (all E1 all U1 all M_1 all E2 (-hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,M_1),dom_list_char_ty(E2))) -> map_add_list_char_ty(fun_up424764369ion_ty(E1,M_1,hAPP_ty_option_ty(some_ty,U1)),E2) = fun_up424764369ion_ty(map_add_list_char_ty(E1,E2),M_1,hAPP_ty_option_ty(some_ty,U1)))) # label(fact_461_map__add__upd__left) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 594 (all Va_1 all Ta all U all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,hAPP_v834067052t_char(val_list_char,U))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,U)),S))),red(Pa)))) # label(fact_462_red__reds_ORedBlock) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 595 (all M_1 all A all B (hAPP_n546249108on_val(M_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,B) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A),dom_na996029170on_val(M_1))))) # label(fact_463_domI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 596 (all M_1 all A all B (hAPP_l207779698on_val(M_1,A) = hAPP_val_option_val(some_val,B) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,A),dom_list_char_val(M_1))))) # label(fact_464_domI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 597 (all Ta all V_a all Eb all Hb all Lb all Va_1 all Va all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> (hAPP_l207779698on_val(L_b,Va_1) = hAPP_val_option_val(some_val,V_a) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),red(Pa)))))) # label(fact_465_red__reds_OInitBlockRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 598 (all F1 all A all B hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,F1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)) = hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(F1,A),B)) # label(fact_466_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 599 (all F1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) <-> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F1,A),B)))) # label(fact_467_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 600 (all F_1 all A all B hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,F_1),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B)) = hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(F_1,A),B)) # label(fact_468_split__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 601 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,F_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))) <-> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F_1,A),B)))) # label(fact_469_split__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 602 (all M_1 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_1,N),K) = hAPP_val_option_val(some_val,Xx))) # label(fact_470_map__add__find__right) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 603 (all X_2 all A_2 (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),A_2)) <-> hBOOL(hAPP_P1384137393r_bool(A_2,X_2)))) # label(fact_471_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 604 (all X_2 all A_2 (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),A_2)) <-> hBOOL(hAPP_P1680401186r_bool(A_2,X_2)))) # label(fact_472_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 605 (all X_2 all A_2 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),A_2)) <-> hBOOL(hAPP_P1333315679l_bool(A_2,X_2)))) # label(fact_473_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 606 (all X_2 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2)) <-> hBOOL(hAPP_nat_bool(A_2,X_2)))) # label(fact_474_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 607 (all X_2 all A_2 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),A_2)) <-> hBOOL(hAPP_P449474095r_bool(A_2,X_2)))) # label(fact_475_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 608 (all X_2 all A_2 (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),A_2)) <-> hBOOL(hAPP_list_char_bool(A_2,X_2)))) # label(fact_476_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 609 (all X_2 all A_2 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),A_2)) <-> hBOOL(hAPP_P282169671l_bool(A_2,X_2)))) # label(fact_477_mem__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 610 (all F_1 hAPP_f46308763ion_ty(produc907433735ion_ty,hAPP_f802560783ion_ty(hAPP_f7643013ion_ty(cOMBB_864319000t_char,hAPP_f69964139ion_ty(cOMBB_2041093409on_val,F_1)),produc823076510on_val)) = F_1) # label(fact_478_split__eta) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 611 (all F_1 hAPP_f2121594859l_bool(produc1958875245l_bool,hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,hAPP_f2057883639l_bool(cOMBB_1750801836on_val,F_1)),produc899768717on_val)) = F_1) # label(fact_479_split__eta) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 612 (all Va_1 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,E_b)),S_2))),red(Pa))))) # label(fact_480_red__reds_OLAssRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 613 (all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_b,E_2)),S_2))),red(Pa))))) # label(fact_481_red__reds_OSeqRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 614 (all F_1 all A all B (hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B)) -> hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))))) # label(fact_482_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 615 (all F_1 all A all B (hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(produc2116052801r_bool(F_1),A),B)) -> hBOOL(hAPP_P828904212r_bool(F_1,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))))) # label(fact_483_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 616 (all F_1 all A all B (hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(produc266042248r_bool(F_1),A),B)) -> hBOOL(hAPP_P659547099r_bool(F_1,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))))) # label(fact_484_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 617 (all F_1 all A all B (hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(produc1588781647r_bool(F_1),A),B)) -> hBOOL(hAPP_P1680401186r_bool(F_1,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))))) # label(fact_485_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 618 (all F_1 all A all B (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B)) -> hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))))) # label(fact_486_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 619 (all F_1 all A all B (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B)) -> hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))))) # label(fact_487_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 620 (all F_1 all A all B (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B)) -> hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))))) # label(fact_488_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 621 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B)) -> hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))))) # label(fact_489_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 622 (all F_1 all A all B (hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B)) -> hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))))) # label(fact_490_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 623 (all F_1 all A all B (hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B)) -> hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))))) # label(fact_491_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 624 (all F_1 all A all B (hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B)) -> hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))))) # label(fact_492_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 625 (all F_1 all A all B (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B)) -> hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))))) # label(fact_493_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 626 (all F_1 all A all B (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B)) -> hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))))) # label(fact_494_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 627 (all F_1 all A all B (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B)) -> hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))))) # label(fact_495_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 628 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B)) -> hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))))) # label(fact_496_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 629 (all F_1 all A all B (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B)) -> hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))))) # label(fact_497_curryE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 630 (all F_1 all A all B (hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(produc288369490r_bool(F_1),A),B)) -> hBOOL(hAPP_P2014166431r_bool(F_1,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A),B))))) # label(fact_498_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 631 (all F_1 all A all B (hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(produc2116052801r_bool(F_1),A),B)) -> hBOOL(hAPP_P828904212r_bool(F_1,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A),B))))) # label(fact_499_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 632 (all F_1 all A all B (hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(produc266042248r_bool(F_1),A),B)) -> hBOOL(hAPP_P659547099r_bool(F_1,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A),B))))) # label(fact_500_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 633 (all F_1 all A all B (hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(produc1588781647r_bool(F_1),A),B)) -> hBOOL(hAPP_P1680401186r_bool(F_1,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A),B))))) # label(fact_501_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 634 (all F_1 all A all B (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(produc550034914r_bool(F_1),A),B)) -> hBOOL(hAPP_P2118621157r_bool(F_1,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A),B))))) # label(fact_502_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 635 (all F_1 all A all B (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(produc156891095r_bool(F_1),A),B)) -> hBOOL(hAPP_P1907982426r_bool(F_1,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A),B))))) # label(fact_503_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 636 (all F_1 all A all B (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(produc1574020101r_bool(F_1),A),B)) -> hBOOL(hAPP_P92196306r_bool(F_1,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A),B))))) # label(fact_504_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 637 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(produc1838470831l_bool(F_1),A),B)) -> hBOOL(hAPP_P71593144l_bool(F_1,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A),B))))) # label(fact_505_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 638 (all F_1 all A all B (hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(produc2053127004l_bool(F_1),A),B)) -> hBOOL(hAPP_P1333315679l_bool(F_1,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B))))) # label(fact_506_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 639 (all F_1 all A all B (hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(produc886919678l_bool(F_1),A),B)) -> hBOOL(hAPP_P929938951l_bool(F_1,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B))))) # label(fact_507_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 640 (all F_1 all A all B (hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(produc1555310053l_bool(F_1),A),B)) -> hBOOL(hAPP_P943837928l_bool(F_1,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A),B))))) # label(fact_508_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 641 (all F_1 all A all B (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(produc95371820r_bool(F_1),A),B)) -> hBOOL(hAPP_P449474095r_bool(F_1,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B))))) # label(fact_509_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 642 (all F_1 all A all B (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(produc481748255l_bool(F_1),A),B)) -> hBOOL(hAPP_P1235399154l_bool(F_1,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A),B))))) # label(fact_510_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 643 (all F_1 all A all B (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(produc2062775566l_bool(F_1),A),B)) -> hBOOL(hAPP_P159683425l_bool(F_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A),B))))) # label(fact_511_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.47 644 (all F_1 all A all B (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(produc1911975310l_bool(F_1),A),B)) -> hBOOL(hAPP_P1708370145l_bool(F_1,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A),B))))) # label(fact_512_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 645 (all F_1 all A all B (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(produc1159035454l_bool(F_1),A),B)) -> hBOOL(hAPP_P282169671l_bool(F_1,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B))))) # label(fact_513_curryD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 646 (all F_1 all G all X_2 all Y_2 map_ad1185064968ar_val(F_1,fun_up204312361on_val(G,X_2,hAPP_val_option_val(some_val,Y_2))) = fun_up204312361on_val(map_ad1185064968ar_val(F_1,G),X_2,hAPP_val_option_val(some_val,Y_2))) # label(fact_514_map__add__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 647 (all F_1 all G all X_2 all Y_2 map_ad61982421on_val(F_1,fun_up2041264236on_val(G,X_2,hAPP_P1510515380on_val(some_P948696889on_val,Y_2))) = fun_up2041264236on_val(map_ad61982421on_val(F_1,G),X_2,hAPP_P1510515380on_val(some_P948696889on_val,Y_2))) # label(fact_515_map__add__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 648 (all F_1 all G all X_2 all Y_2 map_add_list_char_ty(F_1,fun_up424764369ion_ty(G,X_2,hAPP_ty_option_ty(some_ty,Y_2))) = fun_up424764369ion_ty(map_add_list_char_ty(F_1,G),X_2,hAPP_ty_option_ty(some_ty,Y_2))) # label(fact_516_map__add__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 649 (all F_1 all G all X_2 all Y_2 map_ad325961431ar_val(F_1,fun_up1149430426on_val(G,X_2,hAPP_val_option_val(some_val,Y_2))) = fun_up1149430426on_val(map_ad325961431ar_val(F_1,G),X_2,hAPP_val_option_val(some_val,Y_2))) # label(fact_517_map__add__upd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 650 (all Pa all Hb all Ea all Va_1 all Ta all Eb all T_a (hBOOL(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,Ta)),Eb,T_a)) -> hBOOL(wTrt_1(Pa,Hb,Ea,block_list_char(Va_1,Ta,Eb),T_a)))) # label(fact_520_WTrtBlock) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 651 (all C_2 all P_1 (hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,X_1),Y_1) -> -hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(C_2,X_1),Y_1)))))) # label(fact_521_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 652 (all C_2 all P_1 (hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,X_1),Y_1) -> -hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(C_2,X_1),Y_1)))))) # label(fact_522_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 653 (all C_2 all P_1 (hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,X_1),Y_1) -> -hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(C_2,X_1),Y_1)))))) # label(fact_523_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 654 (all C_2 all P_1 (hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,X_1),Y_1) -> -hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(C_2,X_1),Y_1)))))) # label(fact_524_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 655 (all C_2 all P_1 (hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,X_1),Y_1) -> -hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(C_2,X_1),Y_1)))))) # label(fact_525_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 656 (all C_2 all P_1 (hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,X_1),Y_1) -> -hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(C_2,X_1),Y_1)))))) # label(fact_526_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 657 (all C_2 all P_1 (hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,X_1),Y_1) -> -hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(C_2,X_1),Y_1)))))) # label(fact_527_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 658 (all C_2 all P_1 (hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Y_1) -> -hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(C_2,X_1),Y_1)))))) # label(fact_528_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 659 (all C_2 all P_1 (hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_1),Y_1) -> -hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(C_2,X_1),Y_1)))))) # label(fact_529_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 660 (all C_2 all P_1 (hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_1),Y_1) -> -hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(C_2,X_1),Y_1)))))) # label(fact_530_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 661 (all C_2 all P_1 (hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,C_2),P_1)) -> -(all X_1 all Y_1 (is_bop(X_1) -> (P_1 = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,X_1),Y_1) -> -hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(C_2,X_1),Y_1))))))) # label(fact_531_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 662 (all C_2 all P_1 (hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_1),Y_1) -> -hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(C_2,X_1),Y_1)))))) # label(fact_532_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 663 (all C_2 all P_1 (hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_1) -> -hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(C_2,X_1),Y_1)))))) # label(fact_533_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 664 (all C_2 all P_1 (hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_1) -> -hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C_2,X_1),Y_1)))))) # label(fact_534_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 665 (all C_2 all P_1 (hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Y_1) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C_2,X_1),Y_1)))))) # label(fact_535_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 666 (all C_2 all P_1 (hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C_2),P_1)) -> -(all X_1 all Y_1 (P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_1),Y_1) -> -hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C_2,X_1),Y_1)))))) # label(fact_536_splitE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 667 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2) -> hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P2014166431r_bool(hAPP_f1484794973r_bool(produc1732333873r_bool,C_2),P_1)))) # label(fact_537_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 668 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2) -> hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P828904212r_bool(hAPP_f895126887r_bool(produc1596557472r_bool,C_2),P_1)))) # label(fact_538_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 669 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2) -> hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P659547099r_bool(hAPP_f252398939r_bool(produc1324280167r_bool,C_2),P_1)))) # label(fact_539_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 670 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2) -> hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P1680401186r_bool(hAPP_f952817385r_bool(produc723279022r_bool,C_2),P_1)))) # label(fact_540_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 671 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P2118621157r_bool(hAPP_f1697332217r_bool(produc21910851r_bool,C_2),P_1)))) # label(fact_541_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 672 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P1907982426r_bool(hAPP_f102021095r_bool(produc154616760r_bool,C_2),P_1)))) # label(fact_542_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 673 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P92196306r_bool(hAPP_f1613448899r_bool(produc2027921764r_bool,C_2),P_1)))) # label(fact_543_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 674 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P71593144l_bool(hAPP_f1634841927l_bool(produc1491230096l_bool,C_2),P_1)))) # label(fact_544_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 675 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2) -> hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P1333315679l_bool(hAPP_f1525114763l_bool(produc70644925l_bool,C_2),P_1)))) # label(fact_545_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 676 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2) -> hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P929938951l_bool(hAPP_f1534412387l_bool(produc769963999l_bool,C_2),P_1)))) # label(fact_546_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 677 (all C_2 all P_1 ((all A_1 all B_2 (is_bop(A_1) -> (P_1 = hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2) -> hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(C_2,A_1),B_2))))) -> hBOOL(hAPP_P943837928l_bool(hAPP_f340876351l_bool(produc1326056646l_bool,C_2),P_1)))) # label(fact_547_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 678 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2) -> hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P449474095r_bool(hAPP_f2132060507r_bool(produc1704639885r_bool,C_2),P_1)))) # label(fact_548_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 679 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P1235399154l_bool(hAPP_f1443410953l_bool(produc392960766l_bool,C_2),P_1)))) # label(fact_549_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 680 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,C_2),P_1)))) # label(fact_550_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 681 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_f1930574389l_bool(produc1815960045l_bool,C_2),P_1)))) # label(fact_551_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 682 (all C_2 all P_1 ((all A_1 all B_2 (P_1 = hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(C_2,A_1),B_2)))) -> hBOOL(hAPP_P282169671l_bool(hAPP_f635218277l_bool(produc1911463199l_bool,C_2),P_1)))) # label(fact_552_splitI2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 683 (all E_2 all T_2_2 all Pa all Hb all Ea all E_1_1 all T_1_1 (hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,T_1_1)) -> (hBOOL(wTrt_1(Pa,Hb,Ea,E_2,T_2_2)) -> hBOOL(wTrt_1(Pa,Hb,Ea,seq_list_char(E_1_1,E_2),T_2_2))))) # label(fact_553_WTrtSeq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 684 (all Pa all Hb all Lb all Ea (hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea)) <-> (all V_3 all V_2 (hAPP_l207779698on_val(Lb,V_3) = hAPP_val_option_val(some_val,V_2) -> (exists T_4 (hAPP_l512744617ion_ty(Ea,V_3) = hAPP_ty_option_ty(some_ty,T_4) & hBOOL(conf_P373316194t_char(Pa,Hb,V_2,T_4)))))))) # label(fact_554_lconf__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 685 (all Va_1 all Va all Hb all Lb all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va)))))),red(Pa)))) # label(fact_555_red__reds_ORedLAss) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 686 (all Hb hBOOL(hext(Hb,Hb))) # label(fact_556_hext__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 687 (all F_1 all G ((all X_1 all Y_1 hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(F_1,X_1),Y_1) = hAPP_P1228500987ion_ty(G,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_1))) -> hAPP_f46308763ion_ty(produc907433735ion_ty,F_1) = G)) # label(fact_557_cond__split__eta) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 688 (all G all F_1 ((all X_1 all Y_1 (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(F_1,X_1),Y_1)) <-> hBOOL(hAPP_P159683425l_bool(G,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_1))))) -> hAPP_f2121594859l_bool(produc1958875245l_bool,F_1) = G)) # label(fact_558_cond__split__eta) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 689 (all A all M_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A),dom_na996029170on_val(M_1))) -> (exists B_2 hAPP_n546249108on_val(M_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,B_2)))) # label(fact_559_domD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 690 (all A all M_1 (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,A),dom_list_char_val(M_1))) -> (exists B_2 hAPP_l207779698on_val(M_1,A) = hAPP_val_option_val(some_val,B_2)))) # label(fact_560_domD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 691 (all Q_1 all Pa all Z_1 (hBOOL(hAPP_option_ty_bool(Q_1,hAPP_P1228500987ion_ty(hAPP_f46308763ion_ty(produc907433735ion_ty,Pa),Z_1))) -> -(all X_1 all Y_1 (Z_1 = hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Y_1) -> -hBOOL(hAPP_option_ty_bool(Q_1,hAPP_f652398900ion_ty(hAPP_l2000496933ion_ty(Pa,X_1),Y_1))))))) # label(fact_561_splitE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 692 (all Q_1 all Pa all Z_1 (hBOOL(hAPP_bool_bool(Q_1,hAPP_P159683425l_bool(hAPP_f2121594859l_bool(produc1958875245l_bool,Pa),Z_1))) -> -(all X_1 all Y_1 (Z_1 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,X_1),Y_1) -> -hBOOL(hAPP_bool_bool(Q_1,hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,X_1),Y_1))))))) # label(fact_562_splitE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 693 (all H_b all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(hext(Hb,H_b)) -> hBOOL(wTrt_1(Pa,H_b,Ea,Eb,Ta))))) # label(fact_563_WTrt__hext__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 694 (all Fs_2 all Hb all A all C all Fs (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> hBOOL(hext(Hb,fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))))))) # label(fact_564_hext__upd__obj) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 695 (all H_4 all Hb all H_b (hBOOL(hext(Hb,H_b)) -> (hBOOL(hext(H_b,H_4)) -> hBOOL(hext(Hb,H_4))))) # label(fact_565_hext__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 696 (all A all C all Fs all Hb all H_b (hBOOL(hext(Hb,H_b)) -> (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (exists Fs_3 hAPP_n546249108on_val(H_b,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_3)))))) # label(fact_566_hext__objD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 697 (all Hb all H_b (hBOOL(hext(Hb,H_b)) <-> (all A_1 all C_1 all Fs_1 (hAPP_n546249108on_val(Hb,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_1),Fs_1)) -> (exists Fs_3 hAPP_n546249108on_val(H_b,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_1),Fs_3))))))) # label(fact_567_hext__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 698 (all Va_1 all Eb all A_2 (hBOOL(d_list_char(lAss_list_char(Va_1,Eb),A_2)) <-> hBOOL(d_list_char(Eb,A_2)))) # label(fact_568__092_060D_062___092_060D_062s_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 699 (all A_17 all Ty_7 all Exp_13 all A_16 all Exp_12 block_list_char(A_17,Ty_7,Exp_13) != lAss_list_char(A_16,Exp_12)) # label(fact_569_exp_Osimps_I143_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 700 (all A_15 all Ty_6 all Exp_11 all Exp1_7 all Exp2_7 block_list_char(A_15,Ty_6,Exp_11) != seq_list_char(Exp1_7,Exp2_7)) # label(fact_570_exp_Osimps_I196_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 701 (all A_14 all Exp_10 all A_13 all Ty_5 all Exp_9 lAss_list_char(A_14,Exp_10) != block_list_char(A_13,Ty_5,Exp_9)) # label(fact_571_exp_Osimps_I142_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 702 (all Val_7 all Val_6 (hAPP_v834067052t_char(val_list_char,Val_7) = hAPP_v834067052t_char(val_list_char,Val_6) <-> Val_7 = Val_6)) # label(fact_572_exp_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 703 (all Exp1_6 all Exp2_6 all Exp1_5 all Exp2_5 (seq_list_char(Exp1_6,Exp2_6) = seq_list_char(Exp1_5,Exp2_5) <-> Exp1_6 = Exp1_5 & Exp2_6 = Exp2_5)) # label(fact_573_exp_Osimps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 704 (all A all Exp_8 all A_3 all Exp_7 (lAss_list_char(A,Exp_8) = lAss_list_char(A_3,Exp_7) <-> A = A_3 & Exp_8 = Exp_7)) # label(fact_574_exp_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 705 (all A all Ty_4 all Exp_8 all A_3 all Ty_3 all Exp_7 (block_list_char(A,Ty_4,Exp_8) = block_list_char(A_3,Ty_3,Exp_7) <-> A = A_3 & Ty_4 = Ty_3 & Exp_8 = Exp_7)) # label(fact_575_exp_Osimps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 706 (all Val_5 all Exp1_4 all Exp2_4 hAPP_v834067052t_char(val_list_char,Val_5) != seq_list_char(Exp1_4,Exp2_4)) # label(fact_576_exp_Osimps_I84_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 707 (all Val_4 all A_12 all Exp_6 hAPP_v834067052t_char(val_list_char,Val_4) != lAss_list_char(A_12,Exp_6)) # label(fact_577_exp_Osimps_I74_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 708 (all Exp1_3 all Exp2_3 all Val_3 seq_list_char(Exp1_3,Exp2_3) != hAPP_v834067052t_char(val_list_char,Val_3)) # label(fact_578_exp_Osimps_I85_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 709 (all A_11 all Exp_5 all Val_2 lAss_list_char(A_11,Exp_5) != hAPP_v834067052t_char(val_list_char,Val_2)) # label(fact_579_exp_Osimps_I75_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 710 (all Val_1 all A_10 all Ty_2 all Exp_4 hAPP_v834067052t_char(val_list_char,Val_1) != block_list_char(A_10,Ty_2,Exp_4)) # label(fact_580_exp_Osimps_I82_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 711 (all A_9 all Ty_1 all Exp_3 all Val block_list_char(A_9,Ty_1,Exp_3) != hAPP_v834067052t_char(val_list_char,Val)) # label(fact_581_exp_Osimps_I83_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 712 (all Va all A_2 hBOOL(d_list_char(hAPP_v834067052t_char(val_list_char,Va),A_2))) # label(fact_582__092_060D_062___092_060D_062s_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 713 (all Exp1_2 all Exp2_2 all A_8 all Exp_2 seq_list_char(Exp1_2,Exp2_2) != lAss_list_char(A_8,Exp_2)) # label(fact_583_exp_Osimps_I145_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 714 (all A_7 all Exp_1 all Exp1_1 all Exp2_1 lAss_list_char(A_7,Exp_1) != seq_list_char(Exp1_1,Exp2_1)) # label(fact_584_exp_Osimps_I144_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 715 (all Exp1 all Exp2 all A_6 all Ty all Exp seq_list_char(Exp1,Exp2) != block_list_char(A_6,Ty,Exp)) # label(fact_585_exp_Osimps_I197_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 716 (all Fs_2 all A all C all Fs all Pa all Hb (hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb)) -> (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))) -> hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))))))))) # label(fact_586_hconf__upd__obj) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 717 (all Ta all V_a all Pa all Eb all Hb all Lb all Va_1 all Va all E_b all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va)))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (hAPP_l207779698on_val(L_b,Va_1) = hAPP_val_option_val(some_val,V_a) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,V_a)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))))) # label(fact_587_redp__redsp_OInitBlockRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 718 (all Ta all Va all Eb all Hb all Lb all Va_1 all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> (hAPP_l207779698on_val(L_b,Va_1) = hAPP_val_option_val(some_val,Va) -> (-hBOOL(assigned(Va_1,Eb)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),red(Pa))))))) # label(fact_588_red__reds_OBlockRedSome) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 719 (all Pa all Hb all Eb all T_a all Ea all Va_1 all Ta (hAPP_l512744617ion_ty(Ea,Va_1) = hAPP_ty_option_ty(some_ty,Ta) -> (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_a)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_a),Ta)) -> hBOOL(wTrt_1(Pa,Hb,Ea,lAss_list_char(Va_1,Eb),void)))))) # label(fact_589_WTrtLAss) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 720 (all Va_1 all Eb all S all Va all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_val_option_val(some_val,Va)))))),transi2024712006on_val(red(Pa)))))) # label(fact_590_LAssRedsVal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 721 (all H_b all Hb ((all A_1 all C_1 all Fs_1 (hAPP_n546249108on_val(Hb,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_1),Fs_1)) -> (exists Fs_3 hAPP_n546249108on_val(H_b,A_1) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C_1),Fs_3))))) -> hBOOL(hext(Hb,H_b)))) # label(fact_591_hextI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 722 (all Pa all Va_1 all Va all Hb all Lb hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va)))))) # label(fact_592_redp__redsp_ORedLAss) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 723 (all Eb all H_0 all L_0 all E_b all H_1 all L_1_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))),red(Pa))) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_0)),dom_list_char_val(L_1_1))))) # label(fact_593_red__lcl__incr) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 724 (all Pa all Hb all Ea hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val)),Ea))) # label(fact_594_lconf__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 725 (all Q_1 all Pa all X_2 (hBOOL(hAPP_list_char_bool(Pa,X_2)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Pa),Q_1)) -> hBOOL(hAPP_list_char_bool(Q_1,X_2))))) # label(fact_595_rev__predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 726 (all X_2 all Pa all Q_1 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Pa),Q_1)) -> (hBOOL(hAPP_list_char_bool(Pa,X_2)) -> hBOOL(hAPP_list_char_bool(Q_1,X_2))))) # label(fact_596_predicate1D) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 727 (all R_2 all S_4 (hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,member1601084734t_char),R_2)),hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,member1601084734t_char),S_4))) <-> hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(R_2),S_4)))) # label(fact_597_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 728 (all R_2 all S_4 (hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,member1467889965t_char),R_2)),hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,member1467889965t_char),S_4))) <-> hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(R_2),S_4)))) # label(fact_598_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 729 (all R_2 all S_4 (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,member875476972on_val),R_2)),hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,member875476972on_val),S_4))) <-> hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_2),S_4)))) # label(fact_599_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 730 (all R_2 all S_4 (hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_2)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_4))) <-> hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(R_2),S_4)))) # label(fact_600_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 731 (all R_2 all S_4 (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,member1251428284t_char),R_2)),hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,member1251428284t_char),S_4))) <-> hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_2),S_4)))) # label(fact_601_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 732 (all R_2 all S_4 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,member_list_char),R_2)),hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,member_list_char),S_4))) <-> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(R_2),S_4)))) # label(fact_602_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 733 (all R_2 all S_4 (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,member773094996on_val),R_2)),hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,member773094996on_val),S_4))) <-> hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_2),S_4)))) # label(fact_603_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 734 (all A_5 none_nat != hAPP_nat_option_nat(some_nat,A_5)) # label(fact_604_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 735 (all A_5 none_ty != hAPP_ty_option_ty(some_ty,A_5)) # label(fact_605_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 736 (all A_3 none_P179726773on_val != hAPP_P1510515380on_val(some_P948696889on_val,A_3)) # label(fact_606_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 737 (all A_5 none_val != hAPP_val_option_val(some_val,A_5)) # label(fact_607_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 738 (all A_3 none_f478147469r_bool != hAPP_f363827556r_bool(some_f80346385r_bool,A_3)) # label(fact_608_option_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 739 (all A_4 hAPP_nat_option_nat(some_nat,A_4) != none_nat) # label(fact_609_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 740 (all A_4 hAPP_ty_option_ty(some_ty,A_4) != none_ty) # label(fact_610_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 741 (all A_3 hAPP_P1510515380on_val(some_P948696889on_val,A_3) != none_P179726773on_val) # label(fact_611_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 742 (all A_4 hAPP_val_option_val(some_val,A_4) != none_val) # label(fact_612_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 743 (all A_3 hAPP_f363827556r_bool(some_f80346385r_bool,A_3) != none_f478147469r_bool) # label(fact_613_option_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 744 (all X_2 ((all Y_1 X_2 != hAPP_nat_option_nat(some_nat,Y_1)) <-> X_2 = none_nat)) # label(fact_614_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 745 (all X_2 ((all Y_1 X_2 != hAPP_ty_option_ty(some_ty,Y_1)) <-> X_2 = none_ty)) # label(fact_615_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 746 (all X_2 ((all Y_1 X_2 != hAPP_P1510515380on_val(some_P948696889on_val,Y_1)) <-> X_2 = none_P179726773on_val)) # label(fact_616_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 747 (all X_2 ((all Y_1 X_2 != hAPP_val_option_val(some_val,Y_1)) <-> X_2 = none_val)) # label(fact_617_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 748 (all X_2 ((all Y_1 X_2 != hAPP_f363827556r_bool(some_f80346385r_bool,Y_1)) <-> X_2 = none_f478147469r_bool)) # label(fact_618_not__Some__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 749 (all X_2 (X_2 != none_nat <-> (exists Y_1 X_2 = hAPP_nat_option_nat(some_nat,Y_1)))) # label(fact_619_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 750 (all X_2 (X_2 != none_ty <-> (exists Y_1 X_2 = hAPP_ty_option_ty(some_ty,Y_1)))) # label(fact_620_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 751 (all X_2 (X_2 != none_P179726773on_val <-> (exists Y_1 X_2 = hAPP_P1510515380on_val(some_P948696889on_val,Y_1)))) # label(fact_621_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 752 (all X_2 (X_2 != none_val <-> (exists Y_1 X_2 = hAPP_val_option_val(some_val,Y_1)))) # label(fact_622_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 753 (all X_2 (X_2 != none_f478147469r_bool <-> (exists Y_1 X_2 = hAPP_f363827556r_bool(some_f80346385r_bool,Y_1)))) # label(fact_623_not__None__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 754 (all Va_1 all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(Va_1,Eb),S),lAss_list_char(Va_1,E_b)),S_2)))) # label(fact_624_redp__redsp_OLAssRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 755 (all E_2 all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(Eb,E_2),S),seq_list_char(E_b,E_2)),S_2)))) # label(fact_625_redp__redsp_OSeqRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 756 (all M_1 dom_na996029170on_val(M_1) = collect_nat(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,fNot),hAPP_o1566711458t_bool(hAPP_f489569861t_bool(cOMBC_229530231l_bool,hAPP_f1677329295l_bool(hAPP_f1611569977l_bool(cOMBB_731867268ol_nat,fequal1937332960on_val),M_1)),none_P179726773on_val)))) # label(fact_626_dom__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 757 (all M_1 dom_list_char_val(M_1) = collect_list_char(hAPP_f1371002581r_bool(hAPP_f1861125939r_bool(cOMBB_1091123364t_char,fNot),hAPP_o453398608r_bool(hAPP_f399018025r_bool(cOMBC_442485623l_bool,hAPP_f396807521l_bool(hAPP_f926979333l_bool(cOMBB_1112666310t_char,fequal_option_val),M_1)),none_val)))) # label(fact_627_dom__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 758 (all A all M_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A),dom_na996029170on_val(M_1))) <-> hAPP_n546249108on_val(M_1,A) != none_P179726773on_val)) # label(fact_628_domIff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 759 (all A all M_1 (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,A),dom_list_char_val(M_1))) <-> hAPP_l207779698on_val(M_1,A) != none_val)) # label(fact_629_domIff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 760 (all Ta all Pa all Eb all Hb all Lb all Va_1 all E_b all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (hAPP_l207779698on_val(L_b,Va_1) = none_val -> (-hBOOL(assigned(Va_1,Eb)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))))))) # label(fact_630_redp__redsp_OBlockRedNone) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 761 (all M_1 all N all K (hAPP_l207779698on_val(map_ad325961431ar_val(M_1,N),K) = none_val <-> hAPP_l207779698on_val(N,K) = none_val & hAPP_l207779698on_val(M_1,K) = none_val)) # label(fact_631_map__add__None) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 762 (all X_2 all X_1 hAPP_P2094403585on_val(fun_up204312361on_val(hAPP_o1269033393on_val(cOMBK_1867744698t_char,none_val),X_2,none_val),X_1) = none_val) # label(fact_632_empty__upd__none) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 763 (all X_2 all X_1 hAPP_n546249108on_val(fun_up2041264236on_val(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,none_P179726773on_val),X_2,none_P179726773on_val),X_1) = none_P179726773on_val) # label(fact_633_empty__upd__none) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 764 (all X_2 all X_1 hAPP_l512744617ion_ty(fun_up424764369ion_ty(hAPP_o1240645474ion_ty(cOMBK_1294242658t_char,none_ty),X_2,none_ty),X_1) = none_ty) # label(fact_634_empty__upd__none) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 765 (all X_2 all X_1 hAPP_l207779698on_val(fun_up1149430426on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val),X_2,none_val),X_1) = none_val) # label(fact_635_empty__upd__none) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 766 (all M_1 map_ad325961431ar_val(M_1,hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val)) = M_1) # label(fact_636_map__add__empty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 767 (all M_1 map_ad325961431ar_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val),M_1) = M_1) # label(fact_637_empty__map__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 768 (all Pa all Va all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(hAPP_v834067052t_char(val_list_char,Va),E_2),S),E_2),S))) # label(fact_638_redp__redsp_ORedSeq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 769 (all T_2 all K all X_2 -(all X_1 hAPP_P2094403585on_val(fun_up204312361on_val(T_2,K,hAPP_val_option_val(some_val,X_2)),X_1) = none_val)) # label(fact_639_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 770 (all T_2 all K all X_2 -(all X_1 hAPP_n546249108on_val(fun_up2041264236on_val(T_2,K,hAPP_P1510515380on_val(some_P948696889on_val,X_2)),X_1) = none_P179726773on_val)) # label(fact_640_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 771 (all T_2 all K all X_2 -(all X_1 hAPP_l512744617ion_ty(fun_up424764369ion_ty(T_2,K,hAPP_ty_option_ty(some_ty,X_2)),X_1) = none_ty)) # label(fact_641_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 772 (all T_2 all K all X_2 -(all X_1 hAPP_l207779698on_val(fun_up1149430426on_val(T_2,K,hAPP_val_option_val(some_val,X_2)),X_1) = none_val)) # label(fact_642_map__upd__nonempty) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 773 (all Pa all Va_1 all Ta all U all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,hAPP_v834067052t_char(val_list_char,U)),S),hAPP_v834067052t_char(val_list_char,U)),S))) # label(fact_643_redp__redsp_ORedBlock) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 774 (all M_1 all N all K all X_2 (hAPP_l207779698on_val(map_ad325961431ar_val(M_1,N),K) = hAPP_val_option_val(some_val,X_2) -> hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,X_2) | hAPP_l207779698on_val(N,K) = none_val & hAPP_l207779698on_val(M_1,K) = hAPP_val_option_val(some_val,X_2))) # label(fact_644_map__add__SomeD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 775 (all M_1 all N all K all X_2 (hAPP_l207779698on_val(map_ad325961431ar_val(M_1,N),K) = hAPP_val_option_val(some_val,X_2) <-> hAPP_l207779698on_val(N,K) = hAPP_val_option_val(some_val,X_2) | hAPP_l207779698on_val(N,K) = none_val & hAPP_l207779698on_val(M_1,K) = hAPP_val_option_val(some_val,X_2))) # label(fact_645_map__add__Some__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 776 (all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_b,E_2)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_646_SeqReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 777 (all Va_1 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,E_b)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_647_LAssReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 778 (all Ta all Va all Pa all Eb all Hb all Lb all Va_1 all E_b all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (hAPP_l207779698on_val(L_b,Va_1) = hAPP_val_option_val(some_val,Va) -> (-hBOOL(assigned(Va_1,Eb)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1))))))))) # label(fact_648_redp__redsp_OBlockRedSome) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 779 (all E_2 all E_2_1 all S_2_1 all E_1_1 all S_0 all V_1_2 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),S_2_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(E_1_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_649_SeqReds2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 780 (all Pa all X_1 all Xa all Xb all Xc (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,X_1,Xa),Xb),Xc)) <-> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,X_1),Xa)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xb),Xc))),red(Pa))))) # label(fact_650_redp__red__eq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 781 (all A all Obj all Pa all Hb (hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb)) -> (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,Obj) -> hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),Obj))))) # label(fact_651_hconfD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 782 (all Pa all Va_1 all Ta all Va all U all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),hAPP_v834067052t_char(val_list_char,U))),S),hAPP_v834067052t_char(val_list_char,U)),S))) # label(fact_652_redp__redsp_ORedInitBlock) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 783 (all Ta all Eb all Hb all Lb all Va_1 all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,none_val)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> (hAPP_l207779698on_val(L_b,Va_1) = none_val -> (-hBOOL(assigned(Va_1,Eb)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,Eb)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,E_b)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),red(Pa))))))) # label(fact_653_red__reds_OBlockRedNone) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 784 (all L_0 all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_ad325961431ar_val(L_0,Lb)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),map_ad325961431ar_val(L_0,L_b))))),transi2024712006on_val(red(Pa)))))) # label(fact_654_Red__lcl__add) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 785 (all Pa all Hb all Ea all Va all Eb all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,lAss_list_char(Va,Eb),Ta)) -> -(Ta = void -> (all T_4 (hAPP_l512744617ion_ty(Ea,Va) = hAPP_ty_option_ty(some_ty,T_4) -> (all T_5 (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_5)) -> -hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_5),T_4))))))))) # label(fact_655_WTrt__elim__cases_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 786 (all Ta all Eb all Hb all Lb all Va_1 all Va all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,hAPP_option_val_val(the_val,hAPP_l207779698on_val(L_b,Va_1)))),E_b))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),transi2024712006on_val(red(Pa)))))) # label(fact_656_InitBlockReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 787 (all Ta all Eb all Hb all Lb all Va_1 all Va all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),transi2024712006on_val(red(Pa)))) -> (hBOOL(final_list_char(E_b)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),Eb))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),fun_up1149430426on_val(L_b,Va_1,hAPP_l207779698on_val(Lb,Va_1)))))),transi2024712006on_val(red(Pa))))))) # label(fact_657_InitBlockRedsFinal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 788 (all Va_1 all Eb (hBOOL(assigned(Va_1,Eb)) <-> (exists V_2 exists E_1 Eb = seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,V_2)),E_1)))) # label(fact_658_assigned__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 789 (all A all R_1 hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),A)),transi374442731on_val(R_1)))) # label(fact_659_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 790 (all A all R_1 hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),A)),transi1395422419t_char(R_1)))) # label(fact_660_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 791 (all A all R_1 hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),A)),transi2024712006on_val(R_1)))) # label(fact_661_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 792 (all A all R_1 hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),A)),transi935034983cl_val(R_1)))) # label(fact_662_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 793 (all Ta all H_0 all L_0 all Va_1 all E_0 all S_0 all E_2 all H_2 all L_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_0),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))),transi2024712006on_val(red(Pa)))) -> (hBOOL(final_list_char(E_2)) -> (S_0 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),fun_up1149430426on_val(L_0,Va_1,none_val)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,E_0)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,Va_1,hAPP_l207779698on_val(L_0,Va_1)))))),transi2024712006on_val(red(Pa)))))))) # label(fact_663_BlockRedsFinal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 794 (all Fs all Hb all Va all Pa all C all F all Ta all D (hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D)) -> (hBOOL(conf_P373316194t_char(Pa,Hb,Va,Ta)) -> (hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs))) -> hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,Va))))))))) # label(fact_664_oconf__fupd) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 795 (all P_1 all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,P_1),R_1)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,P_1),transi374442731on_val(R_1))))) # label(fact_665_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 796 (all P_1 all R_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,P_1),R_1)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,P_1),transi1395422419t_char(R_1))))) # label(fact_666_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 797 (all P_1 all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,P_1),R_1)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,P_1),transi2024712006on_val(R_1))))) # label(fact_667_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 798 (all A_2 all B_1 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),A_2)) -> A_2 = B_1))) # label(fact_668_equalityI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 799 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1)) -> (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),A_2)) -> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),B_1))))) # label(fact_669_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 800 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1)) -> (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),A_2)) -> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),B_1))))) # label(fact_670_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 801 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1)) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),A_2)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),B_1))))) # label(fact_671_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 802 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_1))))) # label(fact_672_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 803 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),A_2)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),B_1))))) # label(fact_673_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 804 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) -> (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),A_2)) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),B_1))))) # label(fact_674_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 805 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),A_2)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),B_1))))) # label(fact_675_subsetD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 806 (all R_1 all S (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_1),S)) -> hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(transi374442731on_val(R_1)),transi374442731on_val(S))))) # label(fact_676_rtrancl__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 807 (all R_1 all S (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_1),S)) -> hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(transi1395422419t_char(R_1)),transi1395422419t_char(S))))) # label(fact_677_rtrancl__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 808 (all R_1 all S (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_1),S)) -> hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(transi2024712006on_val(R_1)),transi2024712006on_val(S))))) # label(fact_678_rtrancl__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 809 (all R_2 all S_4 (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_2),S_4)) -> (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(S_4),transi374442731on_val(R_2))) -> transi374442731on_val(S_4) = transi374442731on_val(R_2)))) # label(fact_679_rtrancl__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 810 (all R_2 all S_4 (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_2),S_4)) -> (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(S_4),transi1395422419t_char(R_2))) -> transi1395422419t_char(S_4) = transi1395422419t_char(R_2)))) # label(fact_680_rtrancl__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 811 (all R_2 all S_4 (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_2),S_4)) -> (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(S_4),transi2024712006on_val(R_2))) -> transi2024712006on_val(S_4) = transi2024712006on_val(R_2)))) # label(fact_681_rtrancl__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 812 (all R_1 all S (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_1),transi374442731on_val(S))) -> hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(transi374442731on_val(R_1)),transi374442731on_val(S))))) # label(fact_682_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 813 (all R_1 all S (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_1),transi1395422419t_char(S))) -> hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(transi1395422419t_char(R_1)),transi1395422419t_char(S))))) # label(fact_683_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 814 (all R_1 all S (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_1),transi2024712006on_val(S))) -> hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(transi2024712006on_val(R_1)),transi2024712006on_val(S))))) # label(fact_684_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 815 (all X_3 hAPP_option_val_val(the_val,hAPP_val_option_val(some_val,X_3)) = X_3) # label(fact_685_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 816 (all X_3 hAPP_option_nat_nat(the_nat,hAPP_nat_option_nat(some_nat,X_3)) = X_3) # label(fact_686_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 817 (all X_2 hAPP_o1977518472on_val(the_Pr431167171on_val,hAPP_P1510515380on_val(some_P948696889on_val,X_2)) = X_2) # label(fact_687_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 818 (all X_3 hAPP_option_ty_ty(the_ty,hAPP_ty_option_ty(some_ty,X_3)) = X_3) # label(fact_688_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 819 (all X_2 hAPP_o285151112r_bool(the_fu297177755r_bool,hAPP_f363827556r_bool(some_f80346385r_bool,X_2)) = X_2) # label(fact_689_the_Osimps) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 820 (all A_2 hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),A_2))) # label(fact_690_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 821 (all A_2 all B_1 (A_2 = B_1 <-> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) & hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),A_2)))) # label(fact_691_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 822 (all A_2 all B_1 (A_2 = B_1 -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)))) # label(fact_692_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 823 (all A_2 all B_1 (A_2 = B_1 -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),A_2)))) # label(fact_693_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 824 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1)) -> (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),A_2)) -> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),B_1))))) # label(fact_694_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.48 825 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1)) -> (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),A_2)) -> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),B_1))))) # label(fact_695_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 826 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1)) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),A_2)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),B_1))))) # label(fact_696_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 827 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1))))) # label(fact_697_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 828 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),A_2)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),B_1))))) # label(fact_698_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 829 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) -> (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),A_2)) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),B_1))))) # label(fact_699_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 830 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),A_2)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),B_1))))) # label(fact_700_in__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 831 (all B_1 all X_2 all A_2 (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),A_2)) -> (hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1)) -> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),B_1))))) # label(fact_701_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 832 (all B_1 all X_2 all A_2 (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),A_2)) -> (hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1)) -> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),B_1))))) # label(fact_702_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 833 (all B_1 all X_2 all A_2 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),A_2)) -> (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),B_1))))) # label(fact_703_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 834 (all B_1 all X_2 all A_2 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2)) -> (hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1))))) # label(fact_704_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 835 (all B_1 all X_2 all A_2 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),A_2)) -> (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),B_1))))) # label(fact_705_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 836 (all B_1 all X_2 all A_2 (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),A_2)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),B_1))))) # label(fact_706_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 837 (all B_1 all X_2 all A_2 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),A_2)) -> (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),B_1))))) # label(fact_707_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 838 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1)) -> (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),A_2)) -> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_2),B_1))))) # label(fact_708_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 839 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1)) -> (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),A_2)) -> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_2),B_1))))) # label(fact_709_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 840 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1)) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),A_2)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_2),B_1))))) # label(fact_710_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 841 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1)) -> (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_1))))) # label(fact_711_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 842 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),A_2)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_2),B_1))))) # label(fact_712_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 843 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) -> (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),A_2)) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_2),B_1))))) # label(fact_713_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 844 (all X_2 all A_2 all B_1 (hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),A_2)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_2),B_1))))) # label(fact_714_set__mp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 845 (all C all A_2 all B_1 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),C)) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),C))))) # label(fact_715_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 846 (all A_2 all B_1 (A_2 = B_1 -> -(hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)) -> -hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B_1),A_2))))) # label(fact_716_equalityE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 847 (all X_2 all Hb all A (hAPP_n546249108on_val(Hb,A) = none_P179726773on_val -> hBOOL(hext(Hb,fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,X_2)))))) # label(fact_717_hext__new) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 848 (all R_1 transi374442731on_val(transi374442731on_val(R_1)) = transi374442731on_val(R_1)) # label(fact_718_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 849 (all R_1 transi1395422419t_char(transi1395422419t_char(R_1)) = transi1395422419t_char(R_1)) # label(fact_719_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 850 (all R_1 transi2024712006on_val(transi2024712006on_val(R_1)) = transi2024712006on_val(R_1)) # label(fact_720_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 851 (all Obj all A all Pa all Hb (hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb)) -> (hAPP_n546249108on_val(Hb,A) = none_P179726773on_val -> (hBOOL(hAPP_P1235399154l_bool(oconf_1869808039t_char(Pa,Hb),Obj)) -> hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,Obj)))))))) # label(fact_721_hconf__new) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 852 (all C_2 all A all B all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),R_1)) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2)),transi374442731on_val(R_1))) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_2)),transi374442731on_val(R_1)))))) # label(fact_722_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 853 (all C_2 all A all B all R_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),R_1)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2)),transi1395422419t_char(R_1))) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_2)),transi1395422419t_char(R_1)))))) # label(fact_723_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 854 (all C_2 all A all B all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),R_1)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2)),transi2024712006on_val(R_1))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_2)),transi2024712006on_val(R_1)))))) # label(fact_724_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 855 (all C_2 all A all B all R_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),R_1)) -> (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2)),transi935034983cl_val(R_1))) -> hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_2)),transi935034983cl_val(R_1)))))) # label(fact_725_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 856 (all C_2 all A all B all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),transi374442731on_val(R_1))) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2)),R_1)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_2)),transi374442731on_val(R_1)))))) # label(fact_726_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 857 (all C_2 all A all B all R_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),transi1395422419t_char(R_1))) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2)),R_1)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_2)),transi1395422419t_char(R_1)))))) # label(fact_727_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 858 (all C_2 all A all B all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2)),R_1)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_2)),transi2024712006on_val(R_1)))))) # label(fact_728_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 859 (all C_2 all A all B all R_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),transi935034983cl_val(R_1))) -> (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2)),R_1)) -> hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_2)),transi935034983cl_val(R_1)))))) # label(fact_729_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 860 (all C_2 all A all B all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),transi374442731on_val(R_1))) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,B),C_2)),transi374442731on_val(R_1))) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),C_2)),transi374442731on_val(R_1)))))) # label(fact_730_rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 861 (all C_2 all A all B all R_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),transi1395422419t_char(R_1))) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,B),C_2)),transi1395422419t_char(R_1))) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),C_2)),transi1395422419t_char(R_1)))))) # label(fact_731_rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 862 (all C_2 all A all B all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,B),C_2)),transi2024712006on_val(R_1))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),C_2)),transi2024712006on_val(R_1)))))) # label(fact_732_rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 863 (all C_2 all A all B all R_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),transi935034983cl_val(R_1))) -> (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,B),C_2)),transi935034983cl_val(R_1))) -> hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),C_2)),transi935034983cl_val(R_1)))))) # label(fact_733_rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 864 (all B_1 all A_2 ((all X_1 (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_1),A_2)) -> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,X_1),B_1)))) -> hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(A_2),B_1)))) # label(fact_734_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 865 (all B_1 all A_2 ((all X_1 (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_1),A_2)) -> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,X_1),B_1)))) -> hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(A_2),B_1)))) # label(fact_735_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 866 (all B_1 all A_2 ((all X_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_1),A_2)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,X_1),B_1)))) -> hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(A_2),B_1)))) # label(fact_736_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 867 (all B_1 all A_2 ((all X_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B_1)))) -> hBOOL(hAPP_f54304608l_bool(ord_le1568362934t_bool(A_2),B_1)))) # label(fact_737_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 868 (all B_1 all A_2 ((all X_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_1),A_2)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,X_1),B_1)))) -> hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(A_2),B_1)))) # label(fact_738_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 869 (all B_1 all A_2 ((all X_1 (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_1),A_2)) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_1),B_1)))) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A_2),B_1)))) # label(fact_739_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 870 (all B_1 all A_2 ((all X_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_1),A_2)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,X_1),B_1)))) -> hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(A_2),B_1)))) # label(fact_740_subsetI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 871 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Xa_1),Xb_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Za),Zb))),transi374442731on_val(R_1))) -> (hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Xa_1),Xb_1) != hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Xa_1),Xb_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Za),Zb))),transi374442731on_val(R_1)))))))) # label(fact_741_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 872 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xa_1),Xb_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Za),Zb))),transi2024712006on_val(R_1))) -> (hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xa_1),Xb_1) != hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Xa_1),Xb_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Za),Zb))),transi2024712006on_val(R_1)))))))) # label(fact_742_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 873 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Xa_1),Xb_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Za),Zb))),transi198989188t_char(R_1))) -> (hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Xa_1),Xb_1) != hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Xa_1),Xb_1)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Za),Zb))),transi198989188t_char(R_1)))))))) # label(fact_743_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 874 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Xa_1),Xb_1)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Za),Zb))),transi772168185t_char(R_1))) -> (hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Xa_1),Xb_1) != hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Xa_1),Xb_1)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Za),Zb))),transi772168185t_char(R_1)))))))) # label(fact_744_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 875 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Xa_1),Xb_1)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Za),Zb))),transi2005320128t_char(R_1))) -> (hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Xa_1),Xb_1) != hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Xa_1),Xb_1)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Za),Zb))),transi2005320128t_char(R_1)))))))) # label(fact_745_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 876 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Xa_1),Xb_1)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Za),Zb))),transi1123801095t_char(R_1))) -> (hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Xa_1),Xb_1) != hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Xa_1),Xb_1)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Za),Zb))),transi1123801095t_char(R_1)))))))) # label(fact_746_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 877 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Xa_1),Xb_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Za),Zb))),transi1789604888t_char(R_1))) -> (hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Xa_1),Xb_1) != hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Xa_1),Xb_1)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Za),Zb))),transi1789604888t_char(R_1)))))))) # label(fact_747_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 878 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Xa_1),Xb_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Za),Zb))),transi1257872013t_char(R_1))) -> (hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Xa_1),Xb_1) != hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Xa_1),Xb_1)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Za),Zb))),transi1257872013t_char(R_1)))))))) # label(fact_748_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 879 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Xa_1),Xb_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Za),Zb))),transi122195895t_char(R_1))) -> (hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Xa_1),Xb_1) != hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Xa_1),Xb_1)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Za),Zb))),transi122195895t_char(R_1)))))))) # label(fact_749_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 880 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Xa_1),Xb_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Za),Zb))),transi208336786on_val(R_1))) -> (hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Xa_1),Xb_1) != hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Xa_1),Xb_1)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Za),Zb))),transi208336786on_val(R_1)))))))) # label(fact_750_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 881 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Xa_1),Xb_1)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Za),Zb))),transi1423755450al_val(R_1))) -> (hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Xa_1),Xb_1) != hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Xa_1),Xb_1)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Za),Zb))),transi1423755450al_val(R_1)))))))) # label(fact_751_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 882 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Xa_1),Xb_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Za),Zb))),transi1906258203al_val(R_1))) -> (hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Xa_1),Xb_1) != hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Za),Zb) -> -(all A_1 all B_2 (is_bop(A_1) -> (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Xa_1),Xb_1)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Za),Zb))),transi1906258203al_val(R_1))))))))) # label(fact_752_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 883 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Xa_1),Xb_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Za),Zb))),transi1095029602t_char(R_1))) -> (hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Xa_1),Xb_1) != hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Xa_1),Xb_1)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Za),Zb))),transi1095029602t_char(R_1)))))))) # label(fact_753_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 884 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Xa_1),Xb_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Za),Zb))),transi61620055on_val(R_1))) -> (hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Xa_1),Xb_1) != hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Xa_1),Xb_1)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Za),Zb))),transi61620055on_val(R_1)))))))) # label(fact_754_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 885 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Xa_1),Xb_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Za),Zb))),transi921647814on_val(R_1))) -> (hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Xa_1),Xb_1) != hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Xa_1),Xb_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Za),Zb))),transi921647814on_val(R_1)))))))) # label(fact_755_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 886 (all Xa_1 all Xb_1 all Za all Zb all R_1 (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Xa_1),Xb_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Za),Zb))),transi910771962on_val(R_1))) -> (hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Xa_1),Xb_1) != hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Za),Zb) -> -(all A_1 all B_2 (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Xa_1),Xb_1)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2))),R_1)) -> -hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Za),Zb))),transi910771962on_val(R_1)))))))) # label(fact_756_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 887 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Ax),Ay)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Bx),By))),transi374442731on_val(R_1))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Bx),By))),transi374442731on_val(R_1))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay)))))) # label(fact_757_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 888 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ax),Ay)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Bx),By))),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Bx),By))),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)))))) # label(fact_758_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 889 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Ax),Ay)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Bx),By))),transi198989188t_char(R_1))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Bx),By))),transi198989188t_char(R_1))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay)))))) # label(fact_759_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 890 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Ax),Ay)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Bx),By))),transi772168185t_char(R_1))) -> (hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Aa),Ba)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Bx),By))),transi772168185t_char(R_1))) -> (hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Ax),Ay)))))) # label(fact_760_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 891 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Ax),Ay)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Bx),By))),transi2005320128t_char(R_1))) -> (hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Aa),Ba)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Bx),By))),transi2005320128t_char(R_1))) -> (hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Ax),Ay)))))) # label(fact_761_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 892 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Ax),Ay)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Bx),By))),transi1123801095t_char(R_1))) -> (hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Aa),Ba)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Bx),By))),transi1123801095t_char(R_1))) -> (hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Ax),Ay)))))) # label(fact_762_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 893 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Ax),Ay)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Bx),By))),transi1789604888t_char(R_1))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Bx),By))),transi1789604888t_char(R_1))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)))))) # label(fact_763_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 894 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ax),Ay)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Bx),By))),transi1257872013t_char(R_1))) -> (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Bx),By))),transi1257872013t_char(R_1))) -> (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)))))) # label(fact_764_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 895 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Ax),Ay)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Bx),By))),transi122195895t_char(R_1))) -> (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Bx),By))),transi122195895t_char(R_1))) -> (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)))))) # label(fact_765_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 896 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Ax),Ay)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Bx),By))),transi208336786on_val(R_1))) -> (hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Bx),By))),transi208336786on_val(R_1))) -> (hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay)))))) # label(fact_766_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 897 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Ax),Ay)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Bx),By))),transi1423755450al_val(R_1))) -> (hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Aa),Ba)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Bx),By))),transi1423755450al_val(R_1))) -> (hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay)))))) # label(fact_767_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 898 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Ax),Ay)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bx),By))),transi1906258203al_val(R_1))) -> (hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (is_bop(A_1) & is_bop(Aa) -> (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bx),By))),transi1906258203al_val(R_1))) -> (hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_1),B_2))))))) -> hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay)))))) # label(fact_768_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 899 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Ax),Ay)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Bx),By))),transi1095029602t_char(R_1))) -> (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Bx),By))),transi1095029602t_char(R_1))) -> (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay)))))) # label(fact_769_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 900 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Ax),Ay)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Bx),By))),transi61620055on_val(R_1))) -> (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Bx),By))),transi61620055on_val(R_1))) -> (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)))))) # label(fact_770_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 901 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ax),Ay)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Bx),By))),transi921647814on_val(R_1))) -> (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Bx),By))),transi921647814on_val(R_1))) -> (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)))))) # label(fact_771_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 902 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Ax),Ay)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Bx),By))),transi910771962on_val(R_1))) -> (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Bx),By))),transi910771962on_val(R_1))) -> (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_1),B_2)))))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)))))) # label(fact_772_converse__rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 903 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Ax),Ay)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Bx),By))),transi374442731on_val(R_1))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Ax),Ay)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2))),transi374442731on_val(R_1))) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,A_1),B_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(Pa,Bx),By)))))) # label(fact_773_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 904 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ax),Ay)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Bx),By))),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ax),Ay)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2))),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,A_1),B_2)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(Pa,Bx),By)))))) # label(fact_774_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 905 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Ax),Ay)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Bx),By))),transi198989188t_char(R_1))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Ax),Ay)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2))),transi198989188t_char(R_1))) -> (hBOOL(hAPP_f595031537l_bool(hAPP_P1862681481l_bool(member1999287380t_char,hAPP_P1342907945t_char(hAPP_P91410073t_char(produc1897818327t_char,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,A_1),B_2)),hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l214204733r_bool(Pa,Bx),By)))))) # label(fact_775_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 906 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Ax),Ay)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Bx),By))),transi772168185t_char(R_1))) -> (hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Ax),Ay)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2))),transi772168185t_char(R_1))) -> (hBOOL(hAPP_f126445617l_bool(hAPP_P1313790473l_bool(member1551446420t_char,hAPP_P1247668062t_char(hAPP_P1756548163t_char(produc635935767t_char,hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,A_1),B_2)),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_l902158906r_bool(hAPP_l24694616r_bool(Pa,Bx),By)))))) # label(fact_776_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 907 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Ax),Ay)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Bx),By))),transi2005320128t_char(R_1))) -> (hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Ax),Ay)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2))),transi2005320128t_char(R_1))) -> (hBOOL(hAPP_f272179441l_bool(hAPP_P396425609l_bool(member1607118676t_char,hAPP_P579374437t_char(hAPP_P777914897t_char(produc1431439831t_char,hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,A_1),B_2)),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P828904212r_bool(hAPP_l1342015621r_bool(Pa,Bx),By)))))) # label(fact_777_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.49 908 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Ax),Ay)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Bx),By))),transi1123801095t_char(R_1))) -> (hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Ax),Ay)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2))),transi1123801095t_char(R_1))) -> (hBOOL(hAPP_f538118321l_bool(hAPP_P1390376713l_bool(member162552852t_char,hAPP_P991802092t_char(hAPP_P1958775007t_char(produc1641293463t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,A_1),B_2)),hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P659547099r_bool(hAPP_l2140727500r_bool(Pa,Bx),By)))))) # label(fact_778_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 909 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Ax),Ay)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Bx),By))),transi1789604888t_char(R_1))) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Ax),Ay)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2))),transi1789604888t_char(R_1))) -> (hBOOL(hAPP_f1145574243l_bool(hAPP_P2139822957l_bool(member1161907014t_char,hAPP_P1220989409t_char(hAPP_P1668407995t_char(produc1299387215t_char,hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,A_1),B_2)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_e544220455r_bool(hAPP_l1062423959r_bool(Pa,Bx),By)))))) # label(fact_779_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 910 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ax),Ay)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Bx),By))),transi1257872013t_char(R_1))) -> (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ax),Ay)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2))),transi1257872013t_char(R_1))) -> (hBOOL(hAPP_f258424141l_bool(hAPP_P409642305l_bool(member125098544t_char,hAPP_P1333668416t_char(hAPP_P1859316965t_char(produc57279289t_char,hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,A_1),B_2)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P2118621157r_bool(hAPP_l1987619678r_bool(Pa,Bx),By)))))) # label(fact_780_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 911 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Ax),Ay)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Bx),By))),transi122195895t_char(R_1))) -> (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Ax),Ay)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2))),transi122195895t_char(R_1))) -> (hBOOL(hAPP_f528956081l_bool(hAPP_P325013257l_bool(member1420286996t_char,hAPP_P1539798428t_char(hAPP_P719127871t_char(produc24551831t_char,hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,A_1),B_2)),hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P1907982426r_bool(hAPP_l217977712r_bool(Pa,Bx),By)))))) # label(fact_781_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 912 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Ax),Ay)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Bx),By))),transi208336786on_val(R_1))) -> (hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Ax),Ay)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2))),transi208336786on_val(R_1))) -> (hBOOL(hAPP_f1980787287l_bool(hAPP_P274544981l_bool(member88670778on_val,hAPP_P1758592847on_val(hAPP_P2015431471on_val(produc1951691075on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A_1),B_2)),hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P71593144l_bool(hAPP_P1183008383l_bool(Pa,Bx),By)))))) # label(fact_782_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 913 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Ax),Ay)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Bx),By))),transi1423755450al_val(R_1))) -> (hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Ax),Ay)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2))),transi1423755450al_val(R_1))) -> (hBOOL(hAPP_f2129782055l_bool(hAPP_P124661l_bool(member837208074al_val,hAPP_P47773639al_val(hAPP_P1874979071al_val(produc1244920211al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A_1),B_2)),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(Pa,Bx),By)))))) # label(fact_783_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 914 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Ax),Ay)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bx),By))),transi1906258203al_val(R_1))) -> (hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (is_bop(A_1) & is_bop(Aa) -> (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Ax),Ay)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2))),transi1906258203al_val(R_1))) -> (hBOOL(hAPP_f126136681l_bool(hAPP_P982127993l_bool(member1732271180al_val,hAPP_P2123720426al_val(hAPP_P1538518401al_val(produc1924279125al_val,hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,A_1),B_2)),hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Aa),Ba))))))) -> hBOOL(hAPP_P929938951l_bool(hAPP_b97269396l_bool(Pa,Bx),By)))))) # label(fact_784_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 915 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Ax),Ay)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Bx),By))),transi1095029602t_char(R_1))) -> (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Ax),Ay)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2))),transi1095029602t_char(R_1))) -> (hBOOL(hAPP_f851858423l_bool(hAPP_P786771093l_bool(member794220506t_char,hAPP_P1657265855t_char(hAPP_P1071727823t_char(produc2080520419t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A_1),B_2)),hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Aa),Ba))),R_1)) -> (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(Pa,Bx),By)))))) # label(fact_785_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 916 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Ax),Ay)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Bx),By))),transi61620055on_val(R_1))) -> (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Ax),Ay)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2))),transi61620055on_val(R_1))) -> (hBOOL(hAPP_f665343921l_bool(hAPP_P502294281l_bool(member1322055188on_val,hAPP_P330218428on_val(hAPP_P1875010047on_val(produc499151895on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,A_1),B_2)),hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_f1715346603l_bool(hAPP_l465799708l_bool(Pa,Bx),By)))))) # label(fact_786_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 917 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ax),Ay)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Bx),By))),transi921647814on_val(R_1))) -> (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Ax),Ay)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2))),transi921647814on_val(R_1))) -> (hBOOL(hAPP_f1297673713l_bool(hAPP_P240409993l_bool(member563141460on_val,hAPP_P291613419on_val(hAPP_P265246237on_val(produc870913623on_val,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,A_1),B_2)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_f1033709212l_bool(hAPP_f1175813647l_bool(Pa,Bx),By)))))) # label(fact_787_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 918 (all Pa all Ax all Ay all Bx all By all R_1 (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Ax),Ay)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Bx),By))),transi910771962on_val(R_1))) -> (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Ax),Ay)) -> ((all A_1 all B_2 all Aa all Ba (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Ax),Ay)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2))),transi910771962on_val(R_1))) -> (hBOOL(hAPP_f1261741735l_bool(hAPP_P1362631157l_bool(member808015754on_val,hAPP_P1486793863on_val(hAPP_P2077211775on_val(produc1564932627on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A_1),B_2)),hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Aa),Ba))),R_1)) -> (hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,A_1),B_2)) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Aa),Ba)))))) -> hBOOL(hAPP_P1708370145l_bool(hAPP_P1116729363l_bool(Pa,Bx),By)))))) # label(fact_788_rtrancl__induct2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 919 (all Lb all Ea all Eb all Ta all Hb all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb)) -> (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(d_list_char(Eb,hAPP_f363827556r_bool(some_f80346385r_bool,dom_list_char_val(Lb)))) -> (-hBOOL(final_list_char(Eb)) -> (exists E_1 exists S_5 hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1),S_5))),red(Pa)))))))))) # label(fact_789_progress) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 920 (all Y_3 (Y_3 != none_nat -> -(all A_1 Y_3 != hAPP_nat_option_nat(some_nat,A_1)))) # label(fact_790_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 921 (all Y_3 (Y_3 != none_ty -> -(all A_1 Y_3 != hAPP_ty_option_ty(some_ty,A_1)))) # label(fact_791_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 922 (all Y_2 (Y_2 != none_P179726773on_val -> -(all A_1 Y_2 != hAPP_P1510515380on_val(some_P948696889on_val,A_1)))) # label(fact_792_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 923 (all Y_3 (Y_3 != none_val -> -(all A_1 Y_3 != hAPP_val_option_val(some_val,A_1)))) # label(fact_793_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 924 (all Y_2 (Y_2 != none_f478147469r_bool -> -(all A_1 Y_2 != hAPP_f363827556r_bool(some_f80346385r_bool,A_1)))) # label(fact_794_option_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 925 (all X_2 hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),X_2))) # label(fact_795_order__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 926 (all Pa all A all B all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),transi374442731on_val(R_1))) -> (hBOOL(hAPP_P71593144l_bool(Pa,A)) -> ((all Y_1 all Z (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),Y_1)),transi374442731on_val(R_1))) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),Z)),R_1)) -> (hBOOL(hAPP_P71593144l_bool(Pa,Y_1)) -> hBOOL(hAPP_P71593144l_bool(Pa,Z)))))) -> hBOOL(hAPP_P71593144l_bool(Pa,B)))))) # label(fact_796_rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 927 (all Pa all A all B all R_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),transi1395422419t_char(R_1))) -> (hBOOL(hAPP_list_char_bool(Pa,A)) -> ((all Y_1 all Z (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),Y_1)),transi1395422419t_char(R_1))) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),Z)),R_1)) -> (hBOOL(hAPP_list_char_bool(Pa,Y_1)) -> hBOOL(hAPP_list_char_bool(Pa,Z)))))) -> hBOOL(hAPP_list_char_bool(Pa,B)))))) # label(fact_797_rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 928 (all Pa all A all B all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_P1708370145l_bool(Pa,A)) -> ((all Y_1 all Z (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),Y_1)),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),Z)),R_1)) -> (hBOOL(hAPP_P1708370145l_bool(Pa,Y_1)) -> hBOOL(hAPP_P1708370145l_bool(Pa,Z)))))) -> hBOOL(hAPP_P1708370145l_bool(Pa,B)))))) # label(fact_798_rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 929 (all Pa all A all B all R_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),transi935034983cl_val(R_1))) -> (hBOOL(hAPP_val_bool(Pa,A)) -> ((all Y_1 all Z (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),Y_1)),transi935034983cl_val(R_1))) -> (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),Z)),R_1)) -> (hBOOL(hAPP_val_bool(Pa,Y_1)) -> hBOOL(hAPP_val_bool(Pa,Z)))))) -> hBOOL(hAPP_val_bool(Pa,B)))))) # label(fact_799_rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 930 (all R_2 all S_4 (hBOOL(hAPP_f1931964053l_bool(ord_le2008677227r_bool(hAPP_f1209019955r_bool(hAPP_f521496323r_bool(cOMBC_654453230r_bool,hAPP_f732843907r_bool(hAPP_f1563448447r_bool(cOMBB_1490692730t_char,cOMBC_390659185l_bool),hAPP_f1868463117l_bool(hAPP_f1365840271l_bool(cOMBB_1705938036t_char,hAPP_f1937828171l_bool(cOMBB_1681501894t_char,member1601084734t_char)),produc1331140167t_char))),R_2)),hAPP_f1209019955r_bool(hAPP_f521496323r_bool(cOMBC_654453230r_bool,hAPP_f732843907r_bool(hAPP_f1563448447r_bool(cOMBB_1490692730t_char,cOMBC_390659185l_bool),hAPP_f1868463117l_bool(hAPP_f1365840271l_bool(cOMBB_1705938036t_char,hAPP_f1937828171l_bool(cOMBB_1681501894t_char,member1601084734t_char)),produc1331140167t_char))),S_4))) <-> hBOOL(hAPP_f483496539l_bool(ord_le1987888477r_bool(R_2),S_4)))) # label(fact_800_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 931 (all R_2 all S_4 (hBOOL(hAPP_f1795246582l_bool(ord_le735260024r_bool(hAPP_f2025561243r_bool(hAPP_f1500560577r_bool(cOMBC_1784597444r_bool,hAPP_f29105311r_bool(hAPP_f953097879r_bool(cOMBB_672864638t_char,cOMBC_1338332465l_bool),hAPP_f333583909l_bool(hAPP_f1407048615l_bool(cOMBB_741416308t_char,hAPP_f937861397l_bool(cOMBB_1520154591t_char,member1467889965t_char)),produc822965838t_char))),R_2)),hAPP_f2025561243r_bool(hAPP_f1500560577r_bool(cOMBC_1784597444r_bool,hAPP_f29105311r_bool(hAPP_f953097879r_bool(cOMBB_672864638t_char,cOMBC_1338332465l_bool),hAPP_f333583909l_bool(hAPP_f1407048615l_bool(cOMBB_741416308t_char,hAPP_f937861397l_bool(cOMBB_1520154591t_char,member1467889965t_char)),produc822965838t_char))),S_4))) <-> hBOOL(hAPP_f515912112l_bool(ord_le117566470r_bool(R_2),S_4)))) # label(fact_801_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 932 (all R_2 all S_4 (hBOOL(hAPP_f861853459l_bool(ord_le1270183657l_bool(hAPP_f447422815l_bool(hAPP_f2052909183l_bool(cOMBC_766524526l_bool,hAPP_f1427871743l_bool(hAPP_f32926423l_bool(cOMBB_779086262on_val,cOMBC_1491642377l_bool),hAPP_f1082373989l_bool(hAPP_f869803751l_bool(cOMBB_555068556on_val,hAPP_f810261999l_bool(cOMBB_1034324152on_val,member875476972on_val)),produc1611380469on_val))),R_2)),hAPP_f447422815l_bool(hAPP_f2052909183l_bool(cOMBC_766524526l_bool,hAPP_f1427871743l_bool(hAPP_f32926423l_bool(cOMBB_779086262on_val,cOMBC_1491642377l_bool),hAPP_f1082373989l_bool(hAPP_f869803751l_bool(cOMBB_555068556on_val,hAPP_f810261999l_bool(cOMBB_1034324152on_val,member875476972on_val)),produc1611380469on_val))),S_4))) <-> hBOOL(hAPP_f458849545l_bool(ord_le1438917387l_bool(R_2),S_4)))) # label(fact_802_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 933 (all R_2 all S_4 (hBOOL(hAPP_f1776419603l_bool(ord_le1871967977r_bool(hAPP_f344506159r_bool(hAPP_f447563647r_bool(cOMBC_389248878r_bool,hAPP_f1032444159r_bool(hAPP_f254182519r_bool(cOMBB_1551681790t_char,cOMBC_1603044337l_bool),hAPP_f1764180741l_bool(hAPP_f247798919l_bool(cOMBB_526805108t_char,hAPP_f144783951l_bool(cOMBB_1586673472t_char,member1251428284t_char)),produc5062597t_char))),R_2)),hAPP_f344506159r_bool(hAPP_f447563647r_bool(cOMBC_389248878r_bool,hAPP_f1032444159r_bool(hAPP_f254182519r_bool(cOMBB_1551681790t_char,cOMBC_1603044337l_bool),hAPP_f1764180741l_bool(hAPP_f247798919l_bool(cOMBB_526805108t_char,hAPP_f144783951l_bool(cOMBB_1586673472t_char,member1251428284t_char)),produc5062597t_char))),S_4))) <-> hBOOL(hAPP_f2106398425l_bool(ord_le640323803r_bool(R_2),S_4)))) # label(fact_803_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 934 (all R_2 all S_4 (hBOOL(hAPP_f434955681l_bool(ord_le1050317687l_bool(hAPP_f1200025813l_bool(hAPP_f1089788553l_bool(cOMBC_967917532l_bool,hAPP_f2095325577l_bool(hAPP_f1135930489l_bool(cOMBB_1223415373on_val,cOMBC_1608987946l_bool),hAPP_f1204100177l_bool(hAPP_f2026692601l_bool(cOMBB_1977588741on_val,hAPP_f1510763001l_bool(cOMBB_565412073on_val,member773094996on_val)),produc1441475159on_val))),R_2)),hAPP_f1200025813l_bool(hAPP_f1089788553l_bool(cOMBC_967917532l_bool,hAPP_f2095325577l_bool(hAPP_f1135930489l_bool(cOMBB_1223415373on_val,cOMBC_1608987946l_bool),hAPP_f1204100177l_bool(hAPP_f2026692601l_bool(cOMBB_1977588741on_val,hAPP_f1510763001l_bool(cOMBB_565412073on_val,member773094996on_val)),produc1441475159on_val))),S_4))) <-> hBOOL(hAPP_f1453283057l_bool(ord_le1776148979l_bool(R_2),S_4)))) # label(fact_804_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 935 (all R_2 all S_4 (hBOOL(hAPP_f539072365l_bool(ord_le176694639r_bool(hAPP_f2091926485r_bool(hAPP_f1820115955r_bool(cOMBC_790582442r_bool,hAPP_f2059406941r_bool(hAPP_f108089737r_bool(cOMBB_2143526097t_char,cOMBC_220519196l_bool),hAPP_f165071409l_bool(hAPP_f1174637065l_bool(cOMBB_33167485t_char,hAPP_f380623487l_bool(cOMBB_1033145403t_char,member1840112042t_char)),produc1147572817t_char))),R_2)),hAPP_f2091926485r_bool(hAPP_f1820115955r_bool(cOMBC_790582442r_bool,hAPP_f2059406941r_bool(hAPP_f108089737r_bool(cOMBB_2143526097t_char,cOMBC_220519196l_bool),hAPP_f165071409l_bool(hAPP_f1174637065l_bool(cOMBB_33167485t_char,hAPP_f380623487l_bool(cOMBB_1033145403t_char,member1840112042t_char)),produc1147572817t_char))),S_4))) <-> hBOOL(hAPP_f82569901l_bool(ord_le715555971r_bool(R_2),S_4)))) # label(fact_805_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 936 (all R_2 all S_4 (hBOOL(hAPP_f1409772418l_bool(ord_le458107652r_bool(hAPP_f306469557r_bool(hAPP_f197435839r_bool(cOMBC_886773442r_bool,hAPP_f1749915625r_bool(hAPP_f842743203r_bool(cOMBB_657296617har_ty,cOMBC_1407716098l_bool),hAPP_f935003377l_bool(hAPP_f162154931l_bool(cOMBB_859890145har_ty,hAPP_f1847120981l_bool(cOMBB_1035649854t_char,member1379348767t_char)),produc1152259904t_char))),R_2)),hAPP_f306469557r_bool(hAPP_f197435839r_bool(cOMBC_886773442r_bool,hAPP_f1749915625r_bool(hAPP_f842743203r_bool(cOMBB_657296617har_ty,cOMBC_1407716098l_bool),hAPP_f935003377l_bool(hAPP_f162154931l_bool(cOMBB_859890145har_ty,hAPP_f1847120981l_bool(cOMBB_1035649854t_char,member1379348767t_char)),produc1152259904t_char))),S_4))) <-> hBOOL(hAPP_f1161798306l_bool(ord_le1734858744r_bool(R_2),S_4)))) # label(fact_806_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 937 (all R_2 all S_4 (hBOOL(hAPP_f1520735791l_bool(ord_le1151384881r_bool(hAPP_f719350875r_bool(hAPP_f2133563379r_bool(cOMBC_1025440566r_bool,hAPP_f1957374161r_bool(hAPP_f304993943r_bool(cOMBB_847828016t_char,cOMBC_516637475l_bool),hAPP_f1817350437l_bool(hAPP_f614662951l_bool(cOMBB_1558246132t_char,hAPP_f251669717l_bool(cOMBB_773661144t_char,member1771544038t_char)),produc1483578759t_char))),R_2)),hAPP_f719350875r_bool(hAPP_f2133563379r_bool(cOMBC_1025440566r_bool,hAPP_f1957374161r_bool(hAPP_f304993943r_bool(cOMBB_847828016t_char,cOMBC_516637475l_bool),hAPP_f1817350437l_bool(hAPP_f614662951l_bool(cOMBB_1558246132t_char,hAPP_f251669717l_bool(cOMBB_773661144t_char,member1771544038t_char)),produc1483578759t_char))),S_4))) <-> hBOOL(hAPP_f2050077417l_bool(ord_le725666495r_bool(R_2),S_4)))) # label(fact_807_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 938 (all R_2 all S_4 (hBOOL(hAPP_f1118567467l_bool(ord_le989574145r_bool(hAPP_f1051205629r_bool(hAPP_f987862447r_bool(cOMBC_1387630958r_bool,hAPP_f1449341487r_bool(hAPP_f1823921107r_bool(cOMBB_308691073st_val,cOMBC_818212448l_bool),hAPP_f2118054305l_bool(hAPP_f1687138147l_bool(cOMBB_2078271971st_val,hAPP_f1612138403l_bool(cOMBB_961360819t_char,member699351154t_char)),produc1916172923t_char))),R_2)),hAPP_f1051205629r_bool(hAPP_f987862447r_bool(cOMBC_1387630958r_bool,hAPP_f1449341487r_bool(hAPP_f1823921107r_bool(cOMBB_308691073st_val,cOMBC_818212448l_bool),hAPP_f2118054305l_bool(hAPP_f1687138147l_bool(cOMBB_2078271971st_val,hAPP_f1612138403l_bool(cOMBB_961360819t_char,member699351154t_char)),produc1916172923t_char))),S_4))) <-> hBOOL(hAPP_f1314764175l_bool(ord_le1852058257r_bool(R_2),S_4)))) # label(fact_808_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 939 (all R_2 all S_4 (hBOOL(hAPP_f1889282162l_bool(ord_le1449176264r_bool(hAPP_f2071340985r_bool(hAPP_f133320957r_bool(cOMBC_1127703214r_bool,hAPP_f1608277885r_bool(hAPP_f1134248971r_bool(cOMBB_338473166ist_ty,cOMBC_1365742487l_bool),hAPP_f2047757465l_bool(hAPP_f466945179l_bool(cOMBB_68065882ist_ty,hAPP_f693085049l_bool(cOMBB_147773915t_char,member140606439t_char)),produc1909267824t_char))),R_2)),hAPP_f2071340985r_bool(hAPP_f133320957r_bool(cOMBC_1127703214r_bool,hAPP_f1608277885r_bool(hAPP_f1134248971r_bool(cOMBB_338473166ist_ty,cOMBC_1365742487l_bool),hAPP_f2047757465l_bool(hAPP_f466945179l_bool(cOMBB_68065882ist_ty,hAPP_f693085049l_bool(cOMBB_147773915t_char,member140606439t_char)),produc1909267824t_char))),S_4))) <-> hBOOL(hAPP_f1746574980l_bool(ord_le1218729222r_bool(R_2),S_4)))) # label(fact_809_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 940 (all R_2 all S_4 (hBOOL(hAPP_f998390560l_bool(ord_le817953186r_bool(hAPP_f1044627221r_bool(hAPP_f308875635r_bool(cOMBC_1718404842r_bool,hAPP_f531187933r_bool(hAPP_f179418505r_bool(cOMBB_550632017t_char,cOMBC_407285762l_bool),hAPP_f1136362289l_bool(hAPP_f1736484361l_bool(cOMBB_2042763133t_char,hAPP_f1715733055l_bool(cOMBB_123628846t_char,member133545693t_char)),produc921874948t_char))),R_2)),hAPP_f1044627221r_bool(hAPP_f308875635r_bool(cOMBC_1718404842r_bool,hAPP_f531187933r_bool(hAPP_f179418505r_bool(cOMBB_550632017t_char,cOMBC_407285762l_bool),hAPP_f1136362289l_bool(hAPP_f1736484361l_bool(cOMBB_2042763133t_char,hAPP_f1715733055l_bool(cOMBB_123628846t_char,member133545693t_char)),produc921874948t_char))),S_4))) <-> hBOOL(hAPP_f1780084320l_bool(ord_le1579844278r_bool(R_2),S_4)))) # label(fact_810_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 941 (all R_2 all S_4 (hBOOL(hAPP_f2041029616l_bool(ord_le285175110l_bool(hAPP_f844901525l_bool(hAPP_f348508809l_bool(cOMBC_622308798l_bool,hAPP_f1149562121l_bool(hAPP_f1850037271l_bool(cOMBB_773375802t_char,cOMBC_2141828763l_bool),hAPP_f1752856401l_bool(hAPP_f552300311l_bool(cOMBB_1270208498t_char,hAPP_f1564338425l_bool(cOMBB_1078680455on_val,member1972431429on_val)),produc379668296on_val))),R_2)),hAPP_f844901525l_bool(hAPP_f348508809l_bool(cOMBC_622308798l_bool,hAPP_f1149562121l_bool(hAPP_f1850037271l_bool(cOMBB_773375802t_char,cOMBC_2141828763l_bool),hAPP_f1752856401l_bool(hAPP_f552300311l_bool(cOMBB_1270208498t_char,hAPP_f1564338425l_bool(cOMBB_1078680455on_val,member1972431429on_val)),produc379668296on_val))),S_4))) <-> hBOOL(hAPP_f837795298l_bool(ord_le1461833060l_bool(R_2),S_4)))) # label(fact_811_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 942 (all R_2 all S_4 (hBOOL(hAPP_f2071159779l_bool(ord_le408082617l_bool(hAPP_f198821591l_bool(hAPP_f1880802701l_bool(cOMBC_1979963740l_bool,hAPP_f1859053709l_bool(hAPP_f400269243l_bool(cOMBB_1701031980ol_val,cOMBC_331963401l_bool),hAPP_f293485653l_bool(hAPP_f565735867l_bool(cOMBB_815843940ol_val,hAPP_f183649339l_bool(cOMBB_2078984970ol_val,member649088532al_val)),product_Pair_val_val))),R_2)),hAPP_f198821591l_bool(hAPP_f1880802701l_bool(cOMBC_1979963740l_bool,hAPP_f1859053709l_bool(hAPP_f400269243l_bool(cOMBB_1701031980ol_val,cOMBC_331963401l_bool),hAPP_f293485653l_bool(hAPP_f565735867l_bool(cOMBB_815843940ol_val,hAPP_f183649339l_bool(cOMBB_2078984970ol_val,member649088532al_val)),product_Pair_val_val))),S_4))) <-> hBOOL(hAPP_f2028441009l_bool(ord_le310098611l_bool(R_2),S_4)))) # label(fact_812_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 943 (all R_2 all S_4 (hBOOL(hAPP_f1776070952l_bool(ord_le1725884030l_bool(hAPP_f257113085l_bool(hAPP_f1100052969l_bool(cOMBC_199425070l_bool,hAPP_f2100207721l_bool(hAPP_f1374595987l_bool(cOMBB_761748254ol_bop,cOMBC_813705475l_bool),hAPP_f866074145l_bool(hAPP_f877616419l_bool(cOMBB_1458388806ol_bop,hAPP_f62511709l_bool(cOMBB_2139740953al_val,member1417904245al_val)),produc621191550al_val))),R_2)),hAPP_f257113085l_bool(hAPP_f1100052969l_bool(cOMBC_199425070l_bool,hAPP_f2100207721l_bool(hAPP_f1374595987l_bool(cOMBB_761748254ol_bop,cOMBC_813705475l_bool),hAPP_f866074145l_bool(hAPP_f877616419l_bool(cOMBB_1458388806ol_bop,hAPP_f62511709l_bool(cOMBB_2139740953al_val,member1417904245al_val)),produc621191550al_val))),S_4))) <-> hBOOL(hAPP_f742333458l_bool(ord_le1467847572l_bool(R_2),S_4)))) # label(fact_813_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 944 (all R_2 all S_4 (hBOOL(hAPP_f678833350l_bool(ord_le188521288l_bool(hAPP_f2080627739l_bool(hAPP_f350189921l_bool(cOMBC_1535683812l_bool,hAPP_f1094343359l_bool(hAPP_f876671127l_bool(cOMBB_1200577438t_char,cOMBC_317789649l_bool),hAPP_f1370205989l_bool(hAPP_f1406462375l_bool(cOMBB_109816436t_char,hAPP_f919000597l_bool(cOMBB_1153773871on_val,member1542417277on_val)),produc823076510on_val))),R_2)),hAPP_f2080627739l_bool(hAPP_f350189921l_bool(cOMBC_1535683812l_bool,hAPP_f1094343359l_bool(hAPP_f876671127l_bool(cOMBB_1200577438t_char,cOMBC_317789649l_bool),hAPP_f1370205989l_bool(hAPP_f1406462375l_bool(cOMBB_109816436t_char,hAPP_f919000597l_bool(cOMBB_1153773871on_val,member1542417277on_val)),produc823076510on_val))),S_4))) <-> hBOOL(hAPP_f1134950784l_bool(ord_le1744419030l_bool(R_2),S_4)))) # label(fact_814_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 945 (all R_2 all S_4 (hBOOL(hAPP_f1450446905l_bool(ord_le125655867l_bool(hAPP_f47713631l_bool(hAPP_f77033475l_bool(cOMBC_1317565126l_bool,hAPP_f1250221913l_bool(hAPP_f1860331535l_bool(cOMBB_2084052674on_val,cOMBC_1518234801l_bool),hAPP_f1670595613l_bool(hAPP_f1472899487l_bool(cOMBB_588525814on_val,hAPP_f1168269397l_bool(cOMBB_1293776864on_val,member763590124on_val)),produc899768717on_val))),R_2)),hAPP_f47713631l_bool(hAPP_f77033475l_bool(cOMBC_1317565126l_bool,hAPP_f1250221913l_bool(hAPP_f1860331535l_bool(cOMBB_2084052674on_val,cOMBC_1518234801l_bool),hAPP_f1670595613l_bool(hAPP_f1472899487l_bool(cOMBB_588525814on_val,hAPP_f1168269397l_bool(cOMBB_1293776864on_val,member763590124on_val)),produc899768717on_val))),S_4))) <-> hBOOL(hAPP_f966411375l_bool(ord_le1908998213l_bool(R_2),S_4)))) # label(fact_815_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 946 (all R_2 all S_4 (hBOOL(hAPP_f570766339l_bool(ord_le1080391173l_bool(hAPP_f989077673l_bool(hAPP_f40682957l_bool(cOMBC_562612496l_bool,hAPP_f1475571983l_bool(hAPP_f1946480059l_bool(cOMBB_673739729t_char,cOMBC_1585774710l_bool),hAPP_f1614195593l_bool(hAPP_f705562443l_bool(cOMBB_507006011t_char,hAPP_f1639555093l_bool(cOMBB_985659173on_val,member840932460on_val)),produc1259058957on_val))),R_2)),hAPP_f989077673l_bool(hAPP_f40682957l_bool(cOMBC_562612496l_bool,hAPP_f1475571983l_bool(hAPP_f1946480059l_bool(cOMBB_673739729t_char,cOMBC_1585774710l_bool),hAPP_f1614195593l_bool(hAPP_f705562443l_bool(cOMBB_507006011t_char,hAPP_f1639555093l_bool(cOMBB_985659173on_val,member840932460on_val)),produc1259058957on_val))),S_4))) <-> hBOOL(hAPP_f91506671l_bool(ord_le1668954565l_bool(R_2),S_4)))) # label(fact_816_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 947 (all Z_1 all Y_2 all X_2 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Z_1),Y_2)) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Z_1),X_2))))) # label(fact_817_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 948 (all Y_2 all X_2 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2)) -> X_2 = Y_2))) # label(fact_818_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 949 (all Z_1 all X_2 all Y_2 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),Z_1)) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Z_1))))) # label(fact_819_order__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 950 (all X_2 all Y_2 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2)) -> X_2 = Y_2))) # label(fact_820_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 951 (all C_2 all B all A (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B),A)) -> (B = C_2 -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(C_2),A))))) # label(fact_821_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 952 (all C_2 all A all B (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A),B)) -> (B = C_2 -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A),C_2))))) # label(fact_822_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 953 (all C_2 all A all B (A = B -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(C_2),B)) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(C_2),A))))) # label(fact_823_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 954 (all C_2 all A all B (A = B -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(B),C_2)) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(A),C_2))))) # label(fact_824_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 955 (all Y_2 all X_2 (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2)) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2)) <-> X_2 = Y_2))) # label(fact_825_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 956 (all X_2 all Y_2 (X_2 = Y_2 -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2)))) # label(fact_826_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 957 (all X_2 all Y_2 (X_2 = Y_2 <-> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(X_2),Y_2)) & hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(Y_2),X_2)))) # label(fact_827_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 958 (all X_2 all F_1 all G (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(F_1),G)) -> hBOOL(hAPP_bool_bool(ord_less_eq_bool(hAPP_list_char_bool(F_1,X_2)),hAPP_list_char_bool(G,X_2))))) # label(fact_828_le__funE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 959 (all X_2 all F_1 all G (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(F_1),G)) -> hBOOL(hAPP_bool_bool(ord_less_eq_bool(hAPP_list_char_bool(F_1,X_2)),hAPP_list_char_bool(G,X_2))))) # label(fact_829_le__funD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 960 (all F_1 all G (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(F_1),G)) <-> (all X_1 hBOOL(hAPP_bool_bool(ord_less_eq_bool(hAPP_list_char_bool(F_1,X_1)),hAPP_list_char_bool(G,X_1)))))) # label(fact_830_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 961 (all Pa (hBOOL(wf_pro755087577t_char(wf_J_mdecl,Pa)) -> hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)))) # label(fact_831_wf__prog__wwf__prog) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 962 (all P all C_3 all Md (hBOOL(hAPP_P1384137393r_bool(hAPP_l2054741776r_bool(hAPP_l2138409430r_bool(wf_J_mdecl,P),C_3),Md)) -> hBOOL(hAPP_P1384137393r_bool(hAPP_l2054741776r_bool(hAPP_l2138409430r_bool(wwf_J_mdecl,P),C_3),Md)))) # label(fact_832_wf__mdecl__wwf__mdecl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 963 (all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(fv(E_b)),fv(Eb)))))) # label(fact_833_Red__fv) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 964 (all A all B all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),transi374442731on_val(R_1))) -> (A != B -> -(all Y_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),Y_1)),transi374442731on_val(R_1))) -> -hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),B)),R_1))))))) # label(fact_834_rtranclE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 965 (all A all B all R_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),transi1395422419t_char(R_1))) -> (A != B -> -(all Y_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),Y_1)),transi1395422419t_char(R_1))) -> -hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),B)),R_1))))))) # label(fact_835_rtranclE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 966 (all A all B all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),transi2024712006on_val(R_1))) -> (A != B -> -(all Y_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),Y_1)),transi2024712006on_val(R_1))) -> -hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),B)),R_1))))))) # label(fact_836_rtranclE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 967 (all A all B all R_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),transi935034983cl_val(R_1))) -> (A != B -> -(all Y_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),Y_1)),transi935034983cl_val(R_1))) -> -hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),B)),R_1))))))) # label(fact_837_rtranclE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 968 (all X_2 all Z_1 all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_2),Z_1)),transi374442731on_val(R_1))) -> (X_2 != Z_1 -> -(all Y_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,X_2),Y_1)),R_1)) -> -hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),Z_1)),transi374442731on_val(R_1)))))))) # label(fact_838_converse__rtranclE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 969 (all X_2 all Z_1 all R_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_2),Z_1)),transi1395422419t_char(R_1))) -> (X_2 != Z_1 -> -(all Y_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,X_2),Y_1)),R_1)) -> -hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),Z_1)),transi1395422419t_char(R_1)))))))) # label(fact_839_converse__rtranclE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 970 (all X_2 all Z_1 all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_2),Z_1)),transi2024712006on_val(R_1))) -> (X_2 != Z_1 -> -(all Y_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,X_2),Y_1)),R_1)) -> -hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),Z_1)),transi2024712006on_val(R_1)))))))) # label(fact_840_converse__rtranclE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 971 (all X_2 all Z_1 all R_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_2),Z_1)),transi935034983cl_val(R_1))) -> (X_2 != Z_1 -> -(all Y_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,X_2),Y_1)),R_1)) -> -hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),Z_1)),transi935034983cl_val(R_1)))))))) # label(fact_841_converse__rtranclE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 972 (all Pa all A all B all R_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,A),B)),transi374442731on_val(R_1))) -> (hBOOL(hAPP_P71593144l_bool(Pa,B)) -> ((all Y_1 all Z (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Y_1),Z)),R_1)) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,Z),B)),transi374442731on_val(R_1))) -> (hBOOL(hAPP_P71593144l_bool(Pa,Z)) -> hBOOL(hAPP_P71593144l_bool(Pa,Y_1)))))) -> hBOOL(hAPP_P71593144l_bool(Pa,A)))))) # label(fact_842_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 973 (all Pa all A all B all R_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,A),B)),transi1395422419t_char(R_1))) -> (hBOOL(hAPP_list_char_bool(Pa,B)) -> ((all Y_1 all Z (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Y_1),Z)),R_1)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,Z),B)),transi1395422419t_char(R_1))) -> (hBOOL(hAPP_list_char_bool(Pa,Z)) -> hBOOL(hAPP_list_char_bool(Pa,Y_1)))))) -> hBOOL(hAPP_list_char_bool(Pa,A)))))) # label(fact_843_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 974 (all Pa all A all B all R_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,A),B)),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_P1708370145l_bool(Pa,B)) -> ((all Y_1 all Z (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Y_1),Z)),R_1)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,Z),B)),transi2024712006on_val(R_1))) -> (hBOOL(hAPP_P1708370145l_bool(Pa,Z)) -> hBOOL(hAPP_P1708370145l_bool(Pa,Y_1)))))) -> hBOOL(hAPP_P1708370145l_bool(Pa,A)))))) # label(fact_844_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 975 (all Pa all A all B all R_1 (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,A),B)),transi935034983cl_val(R_1))) -> (hBOOL(hAPP_val_bool(Pa,B)) -> ((all Y_1 all Z (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Y_1),Z)),R_1)) -> (hBOOL(hAPP_f2028441009l_bool(hAPP_P530382601l_bool(member649088532al_val,hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,Z),B)),transi935034983cl_val(R_1))) -> (hBOOL(hAPP_val_bool(Pa,Z)) -> hBOOL(hAPP_val_bool(Pa,Y_1)))))) -> hBOOL(hAPP_val_bool(Pa,A)))))) # label(fact_845_converse__rtrancl__induct) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 976 (all F_1 all G ((all X_1 hBOOL(hAPP_bool_bool(ord_less_eq_bool(hAPP_list_char_bool(F_1,X_1)),hAPP_list_char_bool(G,X_1)))) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(F_1),G)))) # label(fact_846_le__funI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 977 (all Eb all S all E_b all S_2 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)) <-> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) & hBOOL(final_list_char(E_b))))) # label(fact_847_big__iff__small) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 978 (all Va_1 all Pa all Eb all Hb all Lb all E_b all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (-hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,Va_1),fv(Eb))) -> hAPP_l207779698on_val(L_b,Va_1) = hAPP_l207779698on_val(Lb,Va_1)))) # label(fact_848_eval__notfree__unchanged) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 979 (all E_b all S_2 all Eb all S all E_5 all S_3 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_5),S_3))),red(Pa))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_5,S_3),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)))))) # label(fact_849_extend__1__eval) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 980 (all Eb all S all E_b all S_2 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa))))))) # label(fact_850_big__by__small) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 981 (all E_b all S_2 all Eb all S all E_5 all S_3 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_5),S_3))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_5,S_3),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)))))) # label(fact_851_extend__eval) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 982 (all Eb all S all E_b all S_2 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> (hBOOL(final_list_char(E_b)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)))))) # label(fact_852_small__by__big) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 983 (all L_b all Va_1 all Pa all Eb all S_0 all Va all Hb all Lb (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) -> (L_b = fun_up1149430426on_val(Lb,Va_1,hAPP_val_option_val(some_val,Va)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(Va_1,Eb),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),L_b)))))) # label(fact_853_LAss) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 984 (all Ta all Pa all E_0 all H_0 all L_0 all Va_1 all E_1_1 all H_1 all L_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),fun_up1149430426on_val(L_0,Va_1,none_val))),E_1_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(Va_1,Ta,E_0),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),E_1_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,Va_1,hAPP_l207779698on_val(L_0,Va_1))))))) # label(fact_854_Block) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 985 (all Pa all Eb all H_0 all L_0 all E_b all H_1 all L_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_0)),dom_list_char_val(L_1_1))))) # label(fact_855_eval__lcl__incr) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 986 (all Pa all Eb all Hb all Lb all E_b all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> hBOOL(hext(Hb,H_b)))) # label(fact_856_eval__hext) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 987 (all E_1_1 all E_2 all S_2_1 all Pa all E_0 all S_0 all Va all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),hAPP_v834067052t_char(val_list_char,Va)),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1),E_2),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1_1),S_0),E_2),S_2_1))))) # label(fact_857_Seq) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 988 (all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_b)),semila919158006r_bool(dom_list_char_val(Lb),fv(Eb))))))) # label(fact_858_Reds__dom__lcl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 989 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),semila1731249415r_bool(A_2,B_1))) -> (-hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),A_2)) -> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),B_1))))) # label(fact_859_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 990 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),semila1346223580r_bool(A_2,B_1))) -> (-hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),A_2)) -> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),B_1))))) # label(fact_860_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 991 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),semila449273525l_bool(A_2,B_1))) -> (-hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),A_2)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),B_1))))) # label(fact_861_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 992 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),semila465093516t_bool(A_2,B_1))) -> (-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_2)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_1))))) # label(fact_862_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 993 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),semila1168318597r_bool(A_2,B_1))) -> (-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),A_2)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),B_1))))) # label(fact_863_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 994 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),semila919158006r_bool(A_2,B_1))) -> (-hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),A_2)) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),B_1))))) # label(fact_864_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 995 (all C_2 all A_2 all B_1 (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),semila751111325l_bool(A_2,B_1))) -> (-hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),A_2)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),B_1))))) # label(fact_865_UnE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 996 (all A_2 all C_2 all B_1 ((-hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),B_1)) -> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),A_2))) -> hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,C_2),semila1731249415r_bool(A_2,B_1))))) # label(fact_866_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 997 (all A_2 all C_2 all B_1 ((-hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),B_1)) -> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),A_2))) -> hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,C_2),semila1346223580r_bool(A_2,B_1))))) # label(fact_867_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 998 (all A_2 all C_2 all B_1 ((-hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),B_1)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),A_2))) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,C_2),semila449273525l_bool(A_2,B_1))))) # label(fact_868_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 999 (all A_2 all C_2 all B_1 ((-hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),B_1)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),A_2))) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_2),semila465093516t_bool(A_2,B_1))))) # label(fact_869_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1000 (all A_2 all C_2 all B_1 ((-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),B_1)) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),A_2))) -> hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,C_2),semila1168318597r_bool(A_2,B_1))))) # label(fact_870_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1001 (all A_2 all C_2 all B_1 ((-hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),B_1)) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),A_2))) -> hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C_2),semila919158006r_bool(A_2,B_1))))) # label(fact_871_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1002 (all A_2 all C_2 all B_1 ((-hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),B_1)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),A_2))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,C_2),semila751111325l_bool(A_2,B_1))))) # label(fact_872_UnCI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1003 (all A_2 all B_1 all X_2 (hBOOL(hAPP_list_char_bool(semila919158006r_bool(A_2,B_1),X_2)) -> (-hBOOL(hAPP_list_char_bool(A_2,X_2)) -> hBOOL(hAPP_list_char_bool(B_1,X_2))))) # label(fact_873_sup1E) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1004 (all A_2 all B_1 all X_2 ((-hBOOL(hAPP_list_char_bool(B_1,X_2)) -> hBOOL(hAPP_list_char_bool(A_2,X_2))) -> hBOOL(hAPP_list_char_bool(semila919158006r_bool(A_2,B_1),X_2)))) # label(fact_874_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1005 (all A_2 semila919158006r_bool(A_2,A_2) = A_2) # label(fact_875_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1006 (all A_2 all B_1 semila1731249415r_bool(A_2,B_1) = collec1387638140t_char(cOMBS_1743887558l_bool(hAPP_f1985672189l_bool(hAPP_f1169733153l_bool(cOMBB_565990871t_char,fdisj),hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,member1601084734t_char),A_2)),hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,member1601084734t_char),B_1)))) # label(fact_876_Un__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1007 (all A_2 all B_1 semila1346223580r_bool(A_2,B_1) = collec1583467887t_char(cOMBS_635570165l_bool(hAPP_f561246575l_bool(hAPP_f321462169l_bool(cOMBB_808210516t_char,fdisj),hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,member1467889965t_char),A_2)),hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,member1467889965t_char),B_1)))) # label(fact_877_Un__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1008 (all A_2 all B_1 semila449273525l_bool(A_2,B_1) = collec2087910442on_val(cOMBS_1218320756l_bool(hAPP_f914702973l_bool(hAPP_f1600936353l_bool(cOMBB_1617503877on_val,fdisj),hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,member875476972on_val),A_2)),hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,member875476972on_val),B_1)))) # label(fact_878_Un__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1009 (all A_2 all B_1 semila465093516t_bool(A_2,B_1) = collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,fdisj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),A_2)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),B_1)))) # label(fact_879_Un__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1010 (all A_2 all B_1 semila1168318597r_bool(A_2,B_1) = collec1797130234t_char(cOMBS_350755140l_bool(hAPP_f644972157l_bool(hAPP_f722872225l_bool(cOMBB_1643767893t_char,fdisj),hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,member1251428284t_char),A_2)),hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,member1251428284t_char),B_1)))) # label(fact_880_Un__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1011 (all A_2 all B_1 semila919158006r_bool(A_2,B_1) = collect_list_char(cOMBS_1502238389l_bool(hAPP_f1163760061l_bool(hAPP_f1157863905l_bool(cOMBB_984708934t_char,fdisj),hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,member_list_char),A_2)),hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,member_list_char),B_1)))) # label(fact_881_Un__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1012 (all A_2 all B_1 semila751111325l_bool(A_2,B_1) = collec718040978on_val(cOMBS_1319864284l_bool(hAPP_f379976829l_bool(hAPP_f606945057l_bool(cOMBB_705522285on_val,fdisj),hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,member773094996on_val),A_2)),hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,member773094996on_val),B_1)))) # label(fact_882_Un__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1013 (all A_2 all B_1 semila919158006r_bool(A_2,B_1) = semila919158006r_bool(B_1,A_2)) # label(fact_883_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1014 (all E_1_1 all E_2 fv(seq_list_char(E_1_1,E_2)) = semila919158006r_bool(fv(E_1_1),fv(E_2))) # label(fact_884_fv__fvs_Osimps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1015 (all Pa all Va all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,Va),S),E_b),S_2)) -> -(E_b = hAPP_v834067052t_char(val_list_char,Va) -> S_2 != S))) # label(fact_885_eval__cases_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1016 (all Pa all Va all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,hAPP_v834067052t_char(val_list_char,Va),S),hAPP_v834067052t_char(val_list_char,Va)),S))) # label(fact_886_Val) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1017 (all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),red(Pa))) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_b)),semila919158006r_bool(dom_list_char_val(Lb),fv(Eb)))))) # label(fact_887_Red__dom__lcl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1018 (all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),E_b),S_2)) -> hBOOL(final_list_char(E_b)))) # label(fact_888_eval__final) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1019 (all Pa all S all Eb (hBOOL(final_list_char(Eb)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),Eb),S)))) # label(fact_889_eval__finalId) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1020 (all Pa all Va_1 all Ta all E_1_1 all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,block_list_char(Va_1,Ta,E_1_1),S),E_b),S_2)) -> -(all H_0_1 all L_0_1 (S = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),L_0_1) -> (all H_1_1 all L_1_2 (S_2 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),fun_up1149430426on_val(L_1_2,Va_1,hAPP_l207779698on_val(L_0_1,Va_1))) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0_1),fun_up1149430426on_val(L_0_1,Va_1,none_val))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1_1),L_1_2))))))))) # label(fact_890_eval__cases_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1021 (all W all Eb all Hb all Lb all E_b all H_b all L_b all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(fv(Eb)),W)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),restri761823004ar_val(Lb,W))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),restri761823004ar_val(L_b,W)))))))) # label(fact_891_eval__restrict__lcl) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1022 (all F all D all C all Fs all E_2 all Va all H_2 all L_2 all E_1_1 all S_0 all A all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))),transi2024712006on_val(red(Pa)))) -> (hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) = hAPP_n546249108on_val(H_2,A) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1_1,F,D,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,fun_up2041264236on_val(H_2,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,Va)))))),L_2)))),transi2024712006on_val(red(Pa)))))))) # label(fact_892_FAssRedsVal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1023 (all F all D all E_2 all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(Eb,F,D,E_2),S),fAss_list_char(E_b,F,D,E_2)),S_2)))) # label(fact_893_redp__redsp_OFAssRed1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1024 (all Va all F all D all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,Eb),S),fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,E_b)),S_2)))) # label(fact_894_redp__redsp_OFAssRed2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1025 (all E_1_1 all F all D all E_2 fv(fAss_list_char(E_1_1,F,D,E_2)) = semila919158006r_bool(fv(E_1_1),fv(E_2))) # label(fact_895_fv__fvs_Osimps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1026 (all F all D all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Eb,F,D,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_b,F,D,E_2)),S_2))),red(Pa))))) # label(fact_896_red__reds_OFAssRed1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1027 (all Va all F all D all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,E_b)),S_2))),red(Pa))))) # label(fact_897_red__reds_OFAssRed2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.50 1028 (all F all D all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Eb,F,D,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_b,F,D,E_2)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_898_FAssReds1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1029 (all Va all F all D all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,E_b)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_899_FAssReds2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1030 (all H_2_1 all Fs_2 all F all D all C all Fs all E_2 all Va all H_2 all L_2 all Pa all E_1_1 all S_0 all A all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),hAPP_v834067052t_char(val_list_char,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))) -> (hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (Fs_2 = fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,Va)) -> (H_2_1 = fun_up2041264236on_val(H_2,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2),S_0),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2_1),L_2))))))))) # label(fact_900_FAss) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1031 (all Pa all F all D all Va all Lb all Hb all A all C all Fs (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D,hAPP_v834067052t_char(val_list_char,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,Va)))))),Lb))))) # label(fact_901_redp__redsp_ORedFAss) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1032 (all F all D all Va all Lb all Pa all Hb all A all C all Fs (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D,hAPP_v834067052t_char(val_list_char,Va))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),fun_up204312361on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D),hAPP_val_option_val(some_val,Va)))))),Lb)))),red(Pa))))) # label(fact_902_red__reds_ORedFAss) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1033 (all F all D all Va all C all Fs all Eb all S all A all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_2))),transi2024712006on_val(red(Pa)))) -> (hAPP_n546249108on_val(hp(S_2),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,Va) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_2))),transi2024712006on_val(red(Pa)))))))) # label(fact_903_FAccRedsVal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1034 (all Pa all F all D all Va all S all A all C all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,Va) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S))),red(Pa)))))) # label(fact_904_red__reds_ORedFAcc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1035 (all Pa all F all D all Va all S all A all C all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,Va) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),F,D),S),hAPP_v834067052t_char(val_list_char,Va)),S))))) # label(fact_905_redp__redsp_ORedFAcc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1036 (all F all D all Va all C all Fs all Pa all Eb all S_0 all A all Hb all Lb (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) -> (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hAPP_P2094403585on_val(Fs,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,F),D)) = hAPP_val_option_val(some_val,Va) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Eb,F,D),S_0),hAPP_v834067052t_char(val_list_char,Va)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))))))) # label(fact_906_FAcc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1037 (all Va_1 all Ta all Va all A all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S))),red(Pa)))) # label(fact_907_red__reds_OInitBlockThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1038 (all Pa all Eb all F all D all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(throw_list_char(Eb),F,D),S),throw_list_char(Eb)),S))) # label(fact_908_redp__redsp_OFAccThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1039 (all F all D all Pa all Eb all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Eb,F,D),S_0),throw_list_char(E_b)),S_1)))) # label(fact_909_eval__evals_OFAccThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1040 (all Pa all Eb all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Eb),S_0),throw_list_char(E_b)),S_1)))) # label(fact_910_eval__evals_OThrowThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1041 (all Pa all Eb all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(throw_list_char(Eb)),S),throw_list_char(Eb)),S))) # label(fact_911_redp__redsp_OThrowThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1042 (all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(Eb),S),throw_list_char(E_b)),S_2)))) # label(fact_912_redp__redsp_OThrowRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1043 (all Eb fv(throw_list_char(Eb)) = fv(Eb)) # label(fact_913_fv__fvs_Osimps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1044 (all F all D all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(Eb,F,D),S),fAcc_list_char(E_b,F,D)),S_2)))) # label(fact_914_redp__redsp_OFAccRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1045 (all Eb all F all D fv(fAcc_list_char(Eb,F,D)) = fv(Eb)) # label(fact_915_fv__fvs_Osimps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1046 (all Eb all F all D all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(throw_list_char(Eb),F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_916_red__reds_OFAccThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1047 (all F all D all Eb all S all A all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_917_FAccRedsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1048 (all E_1_1 all Pa all E_0 all S_0 all Eb all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_0,S_0),throw_list_char(Eb)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_0,E_1_1),S_0),throw_list_char(Eb)),S_1)))) # label(fact_918_eval__evals_OSeqThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1049 (all Va_1 all Pa all Eb all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(Va_1,Eb),S_0),throw_list_char(E_b)),S_1)))) # label(fact_919_eval__evals_OLAssThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1050 (all F all D all E_2 all Pa all E_1_1 all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2),S_0),throw_list_char(E_b)),S_1)))) # label(fact_920_eval__evals_OFAssThrow1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1051 (all Pa all Eb all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,seq_list_char(throw_list_char(Eb),E_2),S),throw_list_char(Eb)),S))) # label(fact_921_redp__redsp_OSeqThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1052 (all Pa all Va_1 all Eb all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,lAss_list_char(Va_1,throw_list_char(Eb)),S),throw_list_char(Eb)),S))) # label(fact_922_redp__redsp_OLAssThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1053 (all Pa all Eb all F all D all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(throw_list_char(Eb),F,D,E_2),S),throw_list_char(Eb)),S))) # label(fact_923_redp__redsp_OFAssThrow1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1054 (all Eb all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_924_red__reds_OThrowThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1055 (all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),red(Pa))))) # label(fact_925_red__reds_OThrowRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1056 (all Pa all Eb all S_0 all A all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Eb),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S_1)))) # label(fact_926_Throw) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1057 (all F all D all E_2 all E_b all S_2_1 all Pa all E_1_1 all S_0 all Va all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,Va)),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),throw_list_char(E_b)),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2),S_0),throw_list_char(E_b)),S_2_1))))) # label(fact_927_eval__evals_OFAssThrow2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1058 (all F all D all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(E_b,F,D)),S_2))),red(Pa))))) # label(fact_928_red__reds_OFAccRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1059 (all Pa all Va all F all D all Eb all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,throw_list_char(Eb)),S),throw_list_char(Eb)),S))) # label(fact_929_redp__redsp_OFAssThrow2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1060 (all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_930_ThrowReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1061 (all Eb all S all A all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_931_ThrowRedsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1062 (all Va_1 all Eb all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_932_red__reds_OLAssThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1063 (all Eb all E_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(throw_list_char(Eb),E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_933_red__reds_OSeqThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1064 (all Eb all F all D all E_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(throw_list_char(Eb),F,D,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_934_red__reds_OFAssThrow1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1065 (all Pa all Va_1 all Ta all A all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S))) # label(fact_935_redp__redsp_OBlockThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1066 (all F all D all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(E_b,F,D)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_936_FAccReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1067 (all Va all F all D all Eb all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,Va),F,D,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_937_red__reds_OFAssThrow2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1068 (all Va_1 all Eb all S all A all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,lAss_list_char(Va_1,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_938_LAssRedsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1069 (all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,seq_list_char(Eb,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_939_SeqRedsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1070 (all F all D all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(Eb,F,D,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_940_FAssRedsThrow1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1071 (all F all D all E_2 all Eb all S_2_1 all E_1_1 all S_0 all Va all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1_1,F,D,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_941_FAssRedsThrow2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1072 (all Va_1 all Ta all A all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,Ta,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S))),red(Pa)))) # label(fact_942_red__reds_OBlockThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1073 (all Pa all Va_1 all Ta all Va all A all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))))),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S))) # label(fact_943_redp__redsp_OInitBlockThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1074 (all Pa all Va_1 all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,lAss_list_char(Va_1,Eb),S),E_b),S_2)) -> ((E_b = hAPP_v834067052t_char(val_list_char,unit) -> (all V_2 all H all L_4 (S_2 = hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),fun_up1149430426on_val(L_4,Va_1,hAPP_val_option_val(some_val,V_2))) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,V_2)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H),L_4)))))) -> -(all E_1 (E_b = throw_list_char(E_1) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E_1)),S_2))))))) # label(fact_944_eval__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1075 (all Pa all E_1_1 all E_2 all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,seq_list_char(E_1_1,E_2),S),E_b),S_2)) -> ((all V_2 all S_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),hAPP_v834067052t_char(val_list_char,V_2)),S_1_1)) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),E_b),S_2)))) -> -(all E_4 (E_b = throw_list_char(E_4) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),throw_list_char(E_4)),S_2))))))) # label(fact_945_eval__cases_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1076 (all Nat_1 unit != addr(Nat_1)) # label(fact_946_val_Osimps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1077 (all Nat_1 addr(Nat_1) != unit) # label(fact_947_val_Osimps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1078 (all Nat_2 all Nat (addr(Nat_2) = addr(Nat) <-> Nat_2 = Nat)) # label(fact_948_val_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1079 (all E_2 all Va_1 all E_2_1 all H_2 all L_2 all C all D all Fs all E_1_1 all S_0 all A all H_1 all L_1_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1)))),transi2024712006on_val(red(Pa)))) -> (hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,Va_1,hAPP_val_option_val(some_val,addr(A)))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))),transi2024712006on_val(red(Pa)))) -> (hBOOL(final_list_char(E_2_1)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_1_1,C,Va_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,Va_1,hAPP_l207779698on_val(L_1_1,Va_1)))))),transi2024712006on_val(red(Pa)))))))))) # label(fact_949_TryCatchRedsFinal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1080 (all Ta all Pa all Hb all Ea all Eb all T_r (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_r)) -> (hBOOL(is_refT(T_r)) -> hBOOL(wTrt_1(Pa,Hb,Ea,throw_list_char(Eb),Ta))))) # label(fact_950_WTrtThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1081 (all Bop all E_2 all Eb all S_2_1 all E_1_1 all S_0 all V_1_2 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_1_1,Bop,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_951_BinOpRedsThrow2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1082 (all Va_1 all E_2 all C all D all Fs all E_1_1 all S all A all Hb all Lb all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))),transi2024712006on_val(red(Pa)))) -> (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_1_1,C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))),transi2024712006on_val(red(Pa)))))))) # label(fact_952_TryRedsFail) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1083 (all Bop all E_2 all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(Eb,Bop,E_2),S),binOp_list_char(E_b,Bop,E_2)),S_2)))) # label(fact_953_redp__redsp_OBinOpRed1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1084 (all C all Va_1 all E_2 all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(Eb,C,Va_1,E_2),S),tryCatch_list_char(E_b,C,Va_1,E_2)),S_2)))) # label(fact_954_redp__redsp_OTryRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1085 (all Bop all E_2 all Pa all E_1_1 all S_0 all Eb all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(Eb)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2),S_0),throw_list_char(Eb)),S_1)))) # label(fact_955_eval__evals_OBinOpThrow1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1086 (all V_1_2 all Bop all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,Eb),S),binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,E_b)),S_2)))) # label(fact_956_redp__redsp_OBinOpRed2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1087 (all Pa all Eb all Bop all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(throw_list_char(Eb),Bop,E_2),S),throw_list_char(Eb)),S))) # label(fact_957_redp__redsp_OBinOpThrow1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1088 (all C all Va_1 all E_2 all Pa all E_1_1 all S_0 all V_1_2 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,Va_1,E_2),S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)))) # label(fact_958_Try) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1089 (all Pa all Va all C all Va_1 all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(hAPP_v834067052t_char(val_list_char,Va),C,Va_1,E_2),S),hAPP_v834067052t_char(val_list_char,Va)),S))) # label(fact_959_redp__redsp_ORedTry) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1090 (all E_1_1 all Bop all E_2 fv(binOp_list_char(E_1_1,Bop,E_2)) = semila919158006r_bool(fv(E_1_1),fv(E_2))) # label(fact_960_fv__fvs_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1091 (all Bop all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(Eb,Bop,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_b,Bop,E_2)),S_2))),red(Pa))))) # label(fact_961_red__reds_OBinOpRed1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1092 (all Bop all E_2 all Eb all S_2_1 all Pa all E_1_1 all S_0 all V_1_2 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),throw_list_char(Eb)),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2),S_0),throw_list_char(Eb)),S_2_1))))) # label(fact_962_eval__evals_OBinOpThrow2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1093 (all Pa all V_1_2 all Bop all Eb all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,throw_list_char(Eb)),S),throw_list_char(Eb)),S))) # label(fact_963_redp__redsp_OBinOpThrow2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1094 (all C all Va_1 all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Eb,C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_b,C,Va_1,E_2)),S_2))),red(Pa))))) # label(fact_964_red__reds_OTryRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1095 (all V_1_2 all Bop all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,E_b)),S_2))),red(Pa))))) # label(fact_965_red__reds_OBinOpRed2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1096 (all Eb all Bop all E_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(throw_list_char(Eb),Bop,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_966_red__reds_OBinOpThrow1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1097 (all Bop all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(Eb,Bop,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_b,Bop,E_2)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_967_BinOp1Reds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1098 (all Va all C all Va_1 all E_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(hAPP_v834067052t_char(val_list_char,Va),C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S))),red(Pa)))) # label(fact_968_red__reds_ORedTry) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1099 (all C all Va_1 all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Eb,C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(E_b,C,Va_1,E_2)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_969_TryReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1100 (all Va_1 all E_2 all C all D all Fs all Pa all E_1_1 all S_0 all A all H_1 all L_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))) -> (hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,Va_1,E_2),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))))))) # label(fact_970_TryThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1101 (all V_1_2 all Bop all Eb all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_971_red__reds_OBinOpThrow2) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1102 (all Va all Bop all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,Va),Bop,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,Va),Bop,E_b)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_972_BinOp2Reds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1103 (all Bop all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(Eb,Bop,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(E_b)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_973_BinOpRedsThrow1) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1104 (all C all Va_1 all E_2 all Eb all S all Va all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(Eb,C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_974_TryRedsVal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1105 (all Va_1 all E_2 all C all Pa all S all A all D all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S))),red(Pa)))))) # label(fact_975_red__reds_ORedTryFail) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1106 (all E_2 all Va_1 all E_2_1 all H_2 all L_2 all C all D all Fs all Pa all E_1_1 all S_0 all A all H_1 all L_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))) -> (hAPP_n546249108on_val(H_1,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),fun_up1149430426on_val(L_1_1,Va_1,hAPP_val_option_val(some_val,addr(A))))),E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,tryCatch_list_char(E_1_1,C,Va_1,E_2),S_0),E_2_1),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),fun_up1149430426on_val(L_2,Va_1,hAPP_l207779698on_val(L_1_1,Va_1)))))))))) # label(fact_976_TryCatch) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1107 (all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,throw_list_char(Eb),Ta)) -> -(all T_r_1 (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_r_1)) -> -hBOOL(is_refT(T_r_1)))))) # label(fact_977_WTrt__elim__cases_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1108 (all X_2 all A all Hb (hBOOL(preallocated(Hb)) -> (hAPP_n546249108on_val(Hb,A) = none_P179726773on_val -> hBOOL(preallocated(fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,X_2))))))) # label(fact_978_preallocated__new) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1109 (all Va_1 all E_2 all C all Pa all S all A all D all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,Va_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,block_list_char(Va_1,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,addr(A))),E_2))),S))),red(Pa)))))) # label(fact_979_red__reds_ORedTryCatch) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1110 (all Fs_2 all A all C all Fs all Hb (hBOOL(preallocated(Hb)) -> (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> hBOOL(preallocated(fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_2)))))))) # label(fact_980_preallocated__upd__obj) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1111 (all C all D all Fs all Eb all S all A all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_2))),transi2024712006on_val(red(Pa)))) -> (hAPP_n546249108on_val(hp(S_2),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_2))),transi2024712006on_val(red(Pa)))))))) # label(fact_981_CastRedsAddr) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1112 (all Va_1 all C all E_2 all T_2_2 all Pa all Hb all Ea all E_1_1 all T_1_1 (hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,T_1_1)) -> (hBOOL(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,T_2_2)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_2)) -> hBOOL(wTrt_1(Pa,Hb,Ea,tryCatch_list_char(E_1_1,C,Va_1,E_2),T_2_2)))))) # label(fact_982_WTrtTry) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1113 (all C all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,Eb),S),cast_list_char(C,E_b)),S_2)))) # label(fact_983_redp__redsp_OCastRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1114 (all C all Eb fv(cast_list_char(C,Eb)) = fv(Eb)) # label(fact_984_fv__fvs_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1115 (all C all Pa all Eb all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),throw_list_char(E_b)),S_1)))) # label(fact_985_eval__evals_OCastThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1116 (all Pa all C all Eb all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,throw_list_char(Eb)),S),throw_list_char(Eb)),S))) # label(fact_986_redp__redsp_OCastThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1117 (all F all Ta all D all Pa all Hb all Ea all Eb all C (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C))) -> (hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D)) -> hBOOL(wTrt_1(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta))))) # label(fact_987_WTrtFAcc) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1118 (all C all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,E_b)),S_2))),red(Pa))))) # label(fact_988_red__reds_OCastRed) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1119 (all C all Eb all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,throw_list_char(Eb))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_989_red__reds_OCastThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1120 (all C all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,E_b)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_990_CastReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1121 (all E_2 all T_2_2 all F all Ta all D all Pa all Hb all Ea all E_1_1 all C (hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,hAPP_list_char_ty(class,C))) -> (hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D)) -> (hBOOL(wTrt_1(Pa,Hb,Ea,E_2,T_2_2)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),Ta)) -> hBOOL(wTrt_1(Pa,Hb,Ea,fAss_list_char(E_1_1,F,D,E_2),void))))))) # label(fact_991_WTrtFAss) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1122 (all C all Eb all S all A all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_992_CastRedsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1123 (all H_b all Hb (hBOOL(preallocated(Hb)) -> (hBOOL(hext(Hb,H_b)) -> hBOOL(preallocated(H_b))))) # label(fact_993_preallocated__hext) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1124 (all C all D all Fs all Pa all Eb all S_0 all A all Hb all Lb (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) -> (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))))))) # label(fact_994_Cast) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1125 (all C all Pa all S all A all D all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S))),red(Pa)))))) # label(fact_995_red__reds_ORedCast) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1126 (all Pa all Hb all Ea all E_1_1 all C all Va_1 all E_2 all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,tryCatch_list_char(E_1_1,C,Va_1,E_2),Ta)) -> -(all T_1_2 (hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,T_1_2)) -> (hBOOL(wTrt_1(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,Ta)) -> -hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_2),Ta))))))) # label(fact_996_WTrt__elim__cases_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1127 (all Pa all Hb all Ea all Eb all C (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C))) -> (hBOOL(final_list_char(Eb)) -> ((all A_1 Eb != hAPP_v834067052t_char(val_list_char,addr(A_1))) -> -(all A_1 Eb != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))))))) # label(fact_997_final__addrE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1128 (all Bop all Va all E_2 all V_2_1 all S_2_1 all E_1_1 all S_0 all V_1_2 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_2_1)),S_2_1))),transi2024712006on_val(red(Pa)))) -> (binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2_1))) = hAPP_val_option_val(some_val,Va) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(E_1_1,Bop,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_2_1))),transi2024712006on_val(red(Pa)))))))) # label(fact_998_BinOpRedsVal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1129 (all C all D all Fs all Eb all S all A all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_2))),transi2024712006on_val(red(Pa)))) -> (hAPP_n546249108on_val(hp(S_2),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S_2))),transi2024712006on_val(red(Pa)))))))) # label(fact_999_CastRedsFail) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1130 (all Bop all Va all E_2 all V_2_1 all S_2_1 all Pa all E_1_1 all S_0 all V_1_2 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,V_1_2)),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),hAPP_v834067052t_char(val_list_char,V_2_1)),S_2_1)) -> (binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2_1))) = hAPP_val_option_val(some_val,Va) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2),S_0),hAPP_v834067052t_char(val_list_char,Va)),S_2_1)))))) # label(fact_1000_BinOp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1131 (all Pa all S all Bop all V_1_2 all V_2_1 all Va (binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2_1))) = hAPP_val_option_val(some_val,Va) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,hAPP_v834067052t_char(val_list_char,V_2_1)),S),hAPP_v834067052t_char(val_list_char,Va)),S)))) # label(fact_1001_redp__redsp_ORedBinOp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1132 (all C all D all Fs all Pa all Eb all S_0 all A all Hb all Lb (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))) -> (hAPP_n546249108on_val(Hb,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))))))) # label(fact_1002_CastFail) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1133 (all C all Pa all S all A all D all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (-hBOOL(hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(member1251428284t_char,hAPP_l2100324114t_char(hAPP_l208357873t_char(produc5062597t_char,D),C)),transi1395422419t_char(subcls851966956t_char(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A)))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S))),red(Pa)))))) # label(fact_1003_red__reds_ORedCastFail) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1134 (all S all Pa all Bop all V_1_2 all V_2_1 all Va (binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2_1))) = hAPP_val_option_val(some_val,Va) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,binOp_list_char(hAPP_v834067052t_char(val_list_char,V_1_2),Bop,hAPP_v834067052t_char(val_list_char,V_2_1))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S))),red(Pa))))) # label(fact_1004_red__reds_ORedBinOp) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1135 (all Pa all E_1_1 all Bop all E_2 all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,binOp_list_char(E_1_1,Bop,E_2),S),E_b),S_2)) -> ((all V_1_1 all S_1_1 all V_2_3 all V_2 (E_b = hAPP_v834067052t_char(val_list_char,V_2) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),hAPP_v834067052t_char(val_list_char,V_2_3)),S_2)) -> binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,Bop),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_1),V_2_3))) != hAPP_val_option_val(some_val,V_2))))) -> ((all E_4 (E_b = throw_list_char(E_4) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),throw_list_char(E_4)),S_2)))) -> -(all V_1_1 all S_1_1 all E_4 (E_b = throw_list_char(E_4) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S),hAPP_v834067052t_char(val_list_char,V_1_1)),S_1_1)) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),throw_list_char(E_4)),S_2))))))))) # label(fact_1005_eval__cases_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.51 1136 (all V_1_3 binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),unit))) = none_val) # label(fact_1006_binop_Osimps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1137 (all V_2_2 binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,unit),V_2_2))) = none_val) # label(fact_1007_binop_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1138 (all Hb (hBOOL(preallocated(Hb)) -> hAPP_val_option_ty(typeof_h(Hb),addr(addr_of_sys_xcpt(classCast))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,classCast)))) # label(fact_1008_typeof__ClassCast) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1139 (all Pa all Ea all Hb all Va all Ta (hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,Ta) -> hBOOL(wTrt_1(Pa,Hb,Ea,hAPP_v834067052t_char(val_list_char,Va),Ta)))) # label(fact_1009_WTrtVal) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1140 (all Va all Ta all Hb all H_b (hBOOL(hext(Hb,H_b)) -> (hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,Ta) -> hAPP_val_option_ty(typeof_h(H_b),Va) = hAPP_ty_option_ty(some_ty,Ta)))) # label(fact_1010_hext__typeof__mono) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1141 (all Hb all Va all Ta (hAPP_val_option_ty(typeof_h(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,none_P179726773on_val)),Va) = hAPP_ty_option_ty(some_ty,Ta) -> hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,Ta))) # label(fact_1011_typeof__lit__typeof) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1142 (all Hb hAPP_val_option_ty(typeof_h(Hb),unit) = hAPP_ty_option_ty(some_ty,void)) # label(fact_1012_typeof__h_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1143 (all V all V_2_2 binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,addr(V)),V_2_2))) = none_val) # label(fact_1013_binop_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1144 (all V_1_3 all V binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),addr(V)))) = none_val) # label(fact_1014_binop_Osimps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1145 (all Hb (hBOOL(preallocated(Hb)) -> hAPP_val_option_ty(typeof_h(Hb),addr(addr_of_sys_xcpt(outOfMemory))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,outOfMemory)))) # label(fact_1015_typeof__OutOfMemory) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1146 (all Hb (hBOOL(preallocated(Hb)) -> hAPP_val_option_ty(typeof_h(Hb),addr(addr_of_sys_xcpt(nullPointer))) = hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,nullPointer)))) # label(fact_1016_typeof__NullPointer) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1147 (all Hb all A hAPP_val_option_ty(typeof_h(Hb),addr(A)) = option1388193227on_val(none_ty,hAPP_f46308763ion_ty(produc907433735ion_ty,hAPP_f451501457ion_ty(hAPP_f509342689ion_ty(cOMBB_352765746t_char,cOMBK_184479553on_val),hAPP_f359949478ion_ty(hAPP_f1243585741ion_ty(cOMBB_1888336841t_char,some_ty),class))),hAPP_n546249108on_val(Hb,A))) # label(fact_1017_typeof__h_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1148 (all Ea all Va_1 all E_2 all T_2_2 all Pa all Ta all Hb all Va all T_1_1 (hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,T_1_1) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),Ta)) -> (hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,Ta)),E_2,T_2_2)) -> hBOOL(wTrt(Pa,Hb,Ea,block_list_char(Va_1,Ta,seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,Va)),E_2)),T_2_2)))))) # label(fact_1018_WTrt_H__WTrts_H_Ointros_I16_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1149 (all Pa all Ea all Hb all Va all Ta (hAPP_val_option_ty(typeof_h(Hb),Va) = hAPP_ty_option_ty(some_ty,Ta) -> hBOOL(wTrt(Pa,Hb,Ea,hAPP_v834067052t_char(val_list_char,Va),Ta)))) # label(fact_1019_WTrt_H__WTrts_H_Ointros_I3_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1150 (all E_2 all T_2_2 all Pa all Hb all Ea all E_1_1 all T_1_1 (hBOOL(wTrt(Pa,Hb,Ea,E_1_1,T_1_1)) -> (hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2_2)) -> hBOOL(wTrt(Pa,Hb,Ea,seq_list_char(E_1_1,E_2),T_2_2))))) # label(fact_1020_WTrt_H__WTrts_H_Ointros_I18_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1151 (all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) -> hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta)))) # label(fact_1021_wt__wt_H) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1152 (all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta)) -> hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)))) # label(fact_1022_wt_H__wt) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1153 (all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta)) <-> hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)))) # label(fact_1023_wt_H__iff__wt) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1154 (all Ta all Pa all Hb all Ea all Eb all T_r (hBOOL(wTrt(Pa,Hb,Ea,Eb,T_r)) -> (hBOOL(is_refT(T_r)) -> hBOOL(wTrt(Pa,Hb,Ea,throw_list_char(Eb),Ta))))) # label(fact_1024_WTrt_H__WTrts_H_Ointros_I21_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1155 (all F all Ta all D all Pa all Hb all Ea all Eb all C (hBOOL(wTrt(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C))) -> (hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D)) -> hBOOL(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta))))) # label(fact_1025_WTrt_H__WTrts_H_Ointros_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1156 (all Pa all Hb all Ea all Va_1 all Ta all Eb all T_a (hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,Ta)),Eb,T_a)) -> (-hBOOL(assigned(Va_1,Eb)) -> hBOOL(wTrt(Pa,Hb,Ea,block_list_char(Va_1,Ta,Eb),T_a))))) # label(fact_1026_WTrt_H__WTrts_H_Ointros_I17_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1157 (all Va_1 all C all E_2 all T_2_2 all Pa all Hb all Ea all E_1_1 all T_1_1 (hBOOL(wTrt(Pa,Hb,Ea,E_1_1,T_1_1)) -> (hBOOL(wTrt(Pa,Hb,fun_up424764369ion_ty(Ea,Va_1,hAPP_ty_option_ty(some_ty,hAPP_list_char_ty(class,C))),E_2,T_2_2)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_1_1),T_2_2)) -> hBOOL(wTrt(Pa,Hb,Ea,tryCatch_list_char(E_1_1,C,Va_1,E_2),T_2_2)))))) # label(fact_1027_WTrt_H__WTrts_H_Ointros_I22_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1158 (all E_2 all T_2_2 all F all Ta all D all Pa all Hb all Ea all E_1_1 all C (hBOOL(wTrt(Pa,Hb,Ea,E_1_1,hAPP_list_char_ty(class,C))) -> (hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C,F,Ta),D)) -> (hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2_2)) -> (hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_2),Ta)) -> hBOOL(wTrt(Pa,Hb,Ea,fAss_list_char(E_1_1,F,D,E_2),void))))))) # label(fact_1028_WTrt_H__WTrts_H_Ointros_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1159 (all F all D all Eb all S all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(Eb,F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1029_FAccRedsNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1160 (all F all D all E_2 all Va all S_2_1 all E_1_1 all S_0 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_2_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(E_1_1,F,D,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_1030_FAssRedsNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1161 (all F all D all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S))),red(Pa)))) # label(fact_1031_red__reds_ORedFAccNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1162 (all Nat_1 null != addr(Nat_1)) # label(fact_1034_val_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1163 (all Nat_1 addr(Nat_1) != null) # label(fact_1035_val_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1164 (all C all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cast_list_char(C,Eb),S_0),hAPP_v834067052t_char(val_list_char,null)),S_1)))) # label(fact_1036_CastNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1165 (all Pa all C all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,null)),S),hAPP_v834067052t_char(val_list_char,null)),S))) # label(fact_1037_redp__redsp_ORedCastNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1166 (all C all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,hAPP_v834067052t_char(val_list_char,null))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S))),red(Pa)))) # label(fact_1038_red__reds_ORedCastNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1167 (all C all Eb all S all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cast_list_char(C,Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1039_CastRedsNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1168 (all V_1_3 binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_3),null))) = none_val) # label(fact_1040_binop_Osimps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1169 (all V_2_2 binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,null),V_2_2))) = none_val) # label(fact_1041_binop_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1170 (all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Eb),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)))) # label(fact_1042_ThrowNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1171 (all Pa all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,throw_list_char(hAPP_v834067052t_char(val_list_char,null)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S))) # label(fact_1043_redp__redsp_ORedThrowNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1172 (all F all D all E_2 all Va all S_2_1 all Pa all E_1_1 all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),hAPP_v834067052t_char(val_list_char,Va)),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAss_list_char(E_1_1,F,D,E_2),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1))))) # label(fact_1044_FAssNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1173 (all F all D all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,fAcc_list_char(Eb,F,D),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_1)))) # label(fact_1045_FAccNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1174 (all Pa all F all D all Va all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,Va)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S))) # label(fact_1046_redp__redsp_ORedFAssNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1175 (all Pa all F all D all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,fAcc_list_char(hAPP_v834067052t_char(val_list_char,null),F,D),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S))) # label(fact_1047_redp__redsp_ORedFAccNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1176 (all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,null))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S))),red(Pa)))) # label(fact_1048_red__reds_ORedThrowNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1177 (all Eb all S all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1049_ThrowRedsNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1178 (all F all D all Va all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,fAss_list_char(hAPP_v834067052t_char(val_list_char,null),F,D,hAPP_v834067052t_char(val_list_char,Va))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S))),red(Pa)))) # label(fact_1050_red__reds_ORedFAssNull) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1179 (all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(is_refT(Ta)) -> (hBOOL(final_list_char(Eb)) -> (Eb != hAPP_v834067052t_char(val_list_char,null) -> (((exists A_1 Eb = hAPP_v834067052t_char(val_list_char,addr(A_1))) -> (all C_1 Ta != hAPP_list_char_ty(class,C_1))) -> -(all A_1 Eb != throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1)))))))))) # label(fact_1051_finalRefE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1180 (all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(Eb),S),E_b),S_2)) -> ((all A_1 (E_b = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A_1))) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,addr(A_1))),S_2)))) -> ((E_b = throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer)))) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,null)),S_2))) -> -(all E_1 (E_b = throw_list_char(E_1) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E_1)),S_2)))))))) # label(fact_1052_eval__cases_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1181 (all Va_1 all E_2 all Pa all C all S all A all D all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,Va_1,E_2),S),block_list_char(Va_1,hAPP_list_char_ty(class,C),seq_list_char(lAss_list_char(Va_1,hAPP_v834067052t_char(val_list_char,addr(A))),E_2))),S))))) # label(fact_1053_redp__redsp_ORedTryCatch) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1182 (all Pa all C all S all A all D all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A))),S),hAPP_v834067052t_char(val_list_char,addr(A))),S))))) # label(fact_1054_redp__redsp_ORedCast) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1183 (all Va_1 all E_2 all Pa all C all S all A all D all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (-hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,tryCatch_list_char(throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A))),C,Va_1,E_2),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(A)))),S))))) # label(fact_1055_redp__redsp_ORedTryFail) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1184 (all Pa all C all S all A all D all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,D),Fs)) -> (-hBOOL(hAPP_list_char_bool(hAPP_l1361600383r_bool(transi1065307915t_char(subcls744239332t_char(Pa)),D),C)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cast_list_char(C,hAPP_v834067052t_char(val_list_char,addr(A))),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(classCast))))),S))))) # label(fact_1056_redp__redsp_ORedCastFail) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1185 (all C all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(is_refT(Ta)) -> (hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C)) -> hBOOL(wTrt_1(Pa,Hb,Ea,cast_list_char(C,Eb),hAPP_list_char_ty(class,C))))))) # label(fact_1057_WTrtCast) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1186 (all List hAPP_list_char_ty(class,List) != void) # label(fact_1058_ty_Osimps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1187 (all List void != hAPP_list_char_ty(class,List)) # label(fact_1059_ty_Osimps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1188 (all List_2 all List_1 (hAPP_list_char_ty(class,List_2) = hAPP_list_char_ty(class,List_1) <-> List_2 = List_1)) # label(fact_1060_ty_Oinject) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1189 (all C all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(is_refT(Ta)) -> (hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C)) -> hBOOL(wTrt(Pa,Hb,Ea,cast_list_char(C,Eb),hAPP_list_char_ty(class,C))))))) # label(fact_1061_WTrt_H__WTrts_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1190 (all Pa all Hb all Ea all D all Eb all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,cast_list_char(D,Eb),Ta)) -> -(Ta = hAPP_list_char_ty(class,D) -> (all T_4 (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,T_4)) -> (hBOOL(is_refT(T_4)) -> -hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),D)))))))) # label(fact_1062_WTrt__elim__cases_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1191 (all Pa all C (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C),sys_xcpts)) -> (hBOOL(hAPP_list_char_bool(Pa,nullPointer)) -> (hBOOL(hAPP_list_char_bool(Pa,outOfMemory)) -> (hBOOL(hAPP_list_char_bool(Pa,classCast)) -> hBOOL(hAPP_list_char_bool(Pa,C))))))) # label(fact_1063_sys__xcpts__cases) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1192 (all V_1_2 all Va binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),bool(Va)))) = none_val) # label(fact_1064_binop_Osimps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1193 (all Nat all Bool_1 addr(Nat) != bool(Bool_1)) # label(fact_1065_val_Osimps_I21_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1194 (all Bool_1 all Nat bool(Bool_1) != addr(Nat)) # label(fact_1066_val_Osimps_I20_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1195 (all Bool_1 all Bool (bool(Bool_1) = bool(Bool) <-> (hBOOL(Bool_1) <-> hBOOL(Bool)))) # label(fact_1067_val_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1196 (all Bool unit != bool(Bool)) # label(fact_1068_val_Osimps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1197 (all Bool bool(Bool) != unit) # label(fact_1069_val_Osimps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1198 (all Bool null != bool(Bool)) # label(fact_1070_val_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1199 (all Bool bool(Bool) != null) # label(fact_1071_val_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1200 (all C all Hb (hBOOL(preallocated(Hb)) -> (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C),sys_xcpts)) -> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,addr_of_sys_xcpt(C)),dom_na996029170on_val(Hb)))))) # label(fact_1072_preallocated__dom) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1201 (all Va all V_2_1 binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,add),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,bool(Va)),V_2_1))) = none_val) # label(fact_1073_binop_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1202 (all Pa all C all Hb (hBOOL(preallocated(Hb)) -> (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C),sys_xcpts)) -> ((all Fs_1 (hAPP_n546249108on_val(Hb,addr_of_sys_xcpt(C)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)) -> hBOOL(hAPP_list_char_bool(hAPP_f388705405r_bool(Pa,Hb),C)))) -> hBOOL(hAPP_list_char_bool(hAPP_f388705405r_bool(Pa,Hb),C)))))) # label(fact_1074_preallocatedE) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1203 (all C all Hb (hBOOL(preallocated(Hb)) -> (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,C),sys_xcpts)) -> (exists Fs_1 hAPP_n546249108on_val(Hb,addr_of_sys_xcpt(C)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs_1)))))) # label(fact_1075_preallocatedD) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1204 (all Hb (hBOOL(preallocated(Hb)) <-> (all X_1 (hBOOL(hAPP_f986089162l_bool(hAPP_l1903254203l_bool(member_list_char,X_1),sys_xcpts)) -> (exists Fs_1 hAPP_n546249108on_val(Hb,addr_of_sys_xcpt(X_1)) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,X_1),Fs_1))))))) # label(fact_1076_preallocated__def) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1205 (all V_1_2 all V_2_1 binop(hAPP_P929466802al_val(hAPP_b1229254591al_val(produc621191550al_val,c_Expr_Obop_OEq),hAPP_v852496844al_val(hAPP_v1519391al_val(product_Pair_val_val,V_1_2),V_2_1))) = hAPP_val_option_val(some_val,bool(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,V_1_2),V_2_1)))) # label(fact_1077_binop_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1206 (all C_2 all B all S all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool(fFalse))),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,unit)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1078_WhileFReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1207 (all C_2 all Pa all Eb all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_2),S_0),throw_list_char(E_b)),S_1)))) # label(fact_1079_WhileCondThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1208 (all Y (is_bop(Y) -> (Y != c_Expr_Obop_OEq -> Y = add))) # label(fact_1080_bop_Oexhaust) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1209 (all B all Eb fv(while_list_char(B,Eb)) = semila919158006r_bool(fv(B),fv(Eb))) # label(fact_1083_fv__fvs_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1210 (all E_3 all S_3_1 all C_2 all V_1_2 all S_2_1 all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1),hAPP_v834067052t_char(val_list_char,V_1_2)),S_2_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_2),S_2_1),E_3),S_3_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_2),S_0),E_3),S_3_1)))))) # label(fact_1084_WhileT) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1211 (all C_2 all E_b all S_2_1 all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1),throw_list_char(E_b)),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_2),S_0),throw_list_char(E_b)),S_2_1))))) # label(fact_1085_WhileBodyThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1212 (all C_2 all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool(fFalse))),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(Eb,C_2),S_0),hAPP_v834067052t_char(val_list_char,unit)),S_1)))) # label(fact_1086_WhileF) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1213 (all C_2 all B all S all Eb all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1087_WhileRedsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1214 (all Eb all S_3_1 all C_2 all V_1_2 all S_2_1 all B all S_0 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,V_1_2)),S_2_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_2_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_3_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_3_1))),transi2024712006on_val(red(Pa)))))))) # label(fact_1088_WhileTReds) # label(axiom) # label(non_clause). [assumption].
% 2.24/2.52 1215 (all C_2 all Eb all S_2_1 all B all S_0 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,B),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,C_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_1089_WhileTRedsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1216 (all Pa all B all C_2 all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_2),S),E_b),S_2)) -> ((E_b = hAPP_v834067052t_char(val_list_char,unit) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),hAPP_v834067052t_char(val_list_char,bool(fFalse))),S_2))) -> ((all S_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1_1)) -> (all V_1_1 all S_2_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1_1),hAPP_v834067052t_char(val_list_char,V_1_1)),S_2_2)) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_2),S_2_2),E_b),S_2)))))) -> ((all E_1 (E_b = throw_list_char(E_1) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),throw_list_char(E_1)),S_2)))) -> -(all S_1_1 all E_1 (E_b = throw_list_char(E_1) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,B,S),hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1_1)) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,C_2,S_1_1),throw_list_char(E_1)),S_2)))))))))) # label(fact_1090_eval__cases_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1217 (all B all C_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,while_list_char(B,C_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit))),S))),red(Pa)))) # label(fact_1091_red__reds_ORedWhile) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1218 (all E_1_1 all E_2 all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(Eb,E_1_1,E_2),S),cond_list_char(E_b,E_1_1,E_2)),S_2)))) # label(fact_1092_redp__redsp_OCondRed) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1219 (all E_1_1 all E_2 all Pa all Eb all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1_1,E_2),S_0),throw_list_char(E_b)),S_1)))) # label(fact_1093_eval__evals_OCondThrow) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1220 (all Pa all Eb all E_1_1 all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(throw_list_char(Eb),E_1_1,E_2),S),throw_list_char(Eb)),S))) # label(fact_1094_redp__redsp_OCondThrow) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1221 (all B all E_1_1 all E_2 fv(cond_list_char(B,E_1_1,E_2)) = semila919158006r_bool(semila919158006r_bool(fv(B),fv(E_1_1)),fv(E_2))) # label(fact_1095_fv__fvs_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1222 (all E_1_1 all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(E_b,E_1_1,E_2)),S_2))),red(Pa))))) # label(fact_1096_red__reds_OCondRed) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1223 (all E_1_1 all E_2 all E_b all S_2_1 all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool(fFalse))),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1),E_b),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1_1,E_2),S_0),E_b),S_2_1))))) # label(fact_1097_CondF) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1224 (all E_2 all E_1_1 all E_b all S_2_1 all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1),E_b),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1_1,E_2),S_0),E_b),S_2_1))))) # label(fact_1098_CondT) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1225 (all Pa all E_1_1 all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(hAPP_v834067052t_char(val_list_char,bool(fFalse)),E_1_1,E_2),S),E_2),S))) # label(fact_1099_redp__redsp_ORedCondF) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1226 (all Pa all E_1_1 all E_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,cond_list_char(hAPP_v834067052t_char(val_list_char,bool(fTrue)),E_1_1,E_2),S),E_1_1),S))) # label(fact_1100_redp__redsp_ORedCondT) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1227 (all Eb all E_1_1 all E_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(throw_list_char(Eb),E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_1101_red__reds_OCondThrow) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1228 (all E_1_1 all E_2 all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(E_b,E_1_1,E_2)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1102_CondReds) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1229 (all E_1_1 all E_2 all Eb all S all A all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1103_CondRedsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1230 (all E_1_1 all E_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(hAPP_v834067052t_char(val_list_char,bool(fTrue)),E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S))),red(Pa)))) # label(fact_1104_red__reds_ORedCondT) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1231 (all E_1_1 all E_2 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(hAPP_v834067052t_char(val_list_char,bool(fFalse)),E_1_1,E_2)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S))),red(Pa)))) # label(fact_1105_red__reds_ORedCondF) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1232 (all Pa all B all C_2 all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,while_list_char(B,C_2),S),E_b),S_2)) <-> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit)),S),E_b),S_2)))) # label(fact_1106_unfold__while) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1233 (all Pa all B all C_2 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,while_list_char(B,C_2),S),cond_list_char(B,seq_list_char(C_2,while_list_char(B,C_2)),hAPP_v834067052t_char(val_list_char,unit))),S))) # label(fact_1107_redp__redsp_ORedWhile) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1234 (all E_2 all E_1_1 all E_b all S_2_1 all Eb all S_0 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_1_1),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_1108_CondReds2T) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1235 (all E_1_1 all E_2 all E_b all S_2_1 all Eb all S_0 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,bool(fFalse))),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_2),S_1)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,cond_list_char(Eb,E_1_1,E_2)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_1109_CondReds2F) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1236 (all List nt != hAPP_list_char_ty(class,List)) # label(fact_1110_ty_Osimps_I20_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1237 (all List hAPP_list_char_ty(class,List) != nt) # label(fact_1111_ty_Osimps_I21_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1238 (all F all D all Ta all Pa all Hb all Ea all Eb (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,nt)) -> hBOOL(wTrt_1(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta)))) # label(fact_1114_WTrtFAccNT) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1239 (all F all D all Ta all Pa all Hb all Ea all Eb (hBOOL(wTrt(Pa,Hb,Ea,Eb,nt)) -> hBOOL(wTrt(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta)))) # label(fact_1115_WTrt_H__WTrts_H_Ointros_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1240 (all Ta (hBOOL(is_refT(Ta)) <-> Ta = nt | (exists C_1 Ta = hAPP_list_char_ty(class,C_1)))) # label(fact_1116_is__refT__def) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1241 (all F all D all E_2 all T_2_2 all Pa all Hb all Ea all E_1_1 (hBOOL(wTrt_1(Pa,Hb,Ea,E_1_1,nt)) -> (hBOOL(wTrt_1(Pa,Hb,Ea,E_2,T_2_2)) -> hBOOL(wTrt_1(Pa,Hb,Ea,fAss_list_char(E_1_1,F,D,E_2),void))))) # label(fact_1117_WTrtFAssNT) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1242 (all F all D all E_2 all T_2_2 all Pa all Hb all Ea all E_1_1 (hBOOL(wTrt(Pa,Hb,Ea,E_1_1,nt)) -> (hBOOL(wTrt(Pa,Hb,Ea,E_2,T_2_2)) -> hBOOL(wTrt(Pa,Hb,Ea,fAss_list_char(E_1_1,F,D,E_2),void))))) # label(fact_1118_WTrt_H__WTrts_H_Ointros_I11_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1243 (all Hb hAPP_val_option_ty(typeof_h(Hb),null) = hAPP_ty_option_ty(some_ty,nt)) # label(fact_1119_typeof__h_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1244 (all Pa all Hb all Ea all Eb all F all D all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,fAcc_list_char(Eb,F,D),Ta)) -> ((all C_1 (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C_1))) -> -hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_1,F,Ta),D)))) -> hBOOL(wTrt_1(Pa,Hb,Ea,Eb,nt))))) # label(fact_1120_WTrt__elim__cases_I7_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1245 (all Pa all Hb all Ea all Eb all F all D all Va all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,fAss_list_char(Eb,F,D,Va),Ta)) -> ((Ta = void -> (all C_1 (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C_1))) -> (all T_4 (hBOOL(hAPP_list_char_bool(has_fi1183600461t_char(Pa,C_1,F,T_4),D)) -> (all T_2_1 (hBOOL(wTrt_1(Pa,Hb,Ea,Va,T_2_1)) -> -hBOOL(hAPP_ty_bool(hAPP_ty_fun_ty_bool(widen_2090681816t_char(Pa),T_2_1),T_4))))))))) -> -(Ta = void -> (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,nt)) -> (all T_2_1 -hBOOL(wTrt_1(Pa,Hb,Ea,Va,T_2_1)))))))) # label(fact_1121_WTrt__elim__cases_I8_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1246 (all T (hBOOL(is_refT(T)) -> (T != nt -> -(all C_1 T != hAPP_list_char_ty(class,C_1))))) # label(fact_1122_refTE) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1247 (all Pa all Eb all E_1_1 all E_2 all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,cond_list_char(Eb,E_1_1,E_2),S),E_b),S_2)) -> ((all S_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,bool(fTrue))),S_1_1)) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_1_1,S_1_1),E_b),S_2)))) -> ((all S_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,bool(fFalse))),S_1_1)) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,E_2,S_1_1),E_b),S_2)))) -> -(all E_1 (E_b = throw_list_char(E_1) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E_1)),S_2)))))))) # label(fact_1123_eval__cases_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1248 (all C all Lb all Pa all Hb (new_Addr(Hb) = none_nat -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,new_list_char(C)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))),red(Pa))))) # label(fact_1124_red__reds_ORedNewFail) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1249 (all Hb all Ea all Pa all C (hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C)) -> hBOOL(wTrt_1(Pa,Hb,Ea,new_list_char(C),hAPP_list_char_ty(class,C))))) # label(fact_1125_WTrtNew) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1250 (all Pa all Hb all Ea all C all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,new_list_char(C),Ta)) -> -(Ta = hAPP_list_char_ty(class,C) -> -hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C))))) # label(fact_1126_WTrt__elim__cases_I10_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1251 (all Hb all A (new_Addr(Hb) = hAPP_nat_option_nat(some_nat,A) -> hAPP_n546249108on_val(Hb,A) = none_P179726773on_val)) # label(fact_1127_new__Addr__SomeD) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1252 (all Hb all Ea all Pa all C (hBOOL(hAPP_list_char_bool(is_cla570604648t_char(Pa),C)) -> hBOOL(wTrt(Pa,Hb,Ea,new_list_char(C),hAPP_list_char_ty(class,C))))) # label(fact_1128_WTrt_H__WTrts_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1253 (all Pa all C all Lb all Hb (new_Addr(Hb) = none_nat -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))))) # label(fact_1129_NewFail) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1254 (all Pa all C all Lb all Hb (new_Addr(Hb) = none_nat -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(outOfMemory))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))))) # label(fact_1130_redp__redsp_ORedNewFail) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1255 (all Lb all H_b all Pa all C all FDTs all Hb all A (new_Addr(Hb) = hAPP_nat_option_nat(some_nat,A) -> (hBOOL(fields1147507508t_char(Pa,C,FDTs)) -> (H_b = fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),init_fields(FDTs)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,new_list_char(C)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),Lb)))),red(Pa))))))) # label(fact_1131_red__reds_ORedNew) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1256 (all Lb all H_b all Pa all C all FDTs all Hb all A (new_Addr(Hb) = hAPP_nat_option_nat(some_nat,A) -> (hBOOL(fields1147507508t_char(Pa,C,FDTs)) -> (H_b = fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),init_fields(FDTs)))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),Lb))))))) # label(fact_1132_redp__redsp_ORedNew) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1257 (all Lb all H_b all Pa all C all FDTs all Hb all A (new_Addr(Hb) = hAPP_nat_option_nat(some_nat,A) -> (hBOOL(fields1147507508t_char(Pa,C,FDTs)) -> (H_b = fun_up2041264236on_val(Hb,A,hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),init_fields(FDTs)))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,new_list_char(C),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),hAPP_v834067052t_char(val_list_char,addr(A))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),Lb))))))) # label(fact_1133_New) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1258 (all M all Vs_1 all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,null),M,map_va1934808527t_char(val_list_char,Vs_1))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S))),red(Pa)))) # label(fact_1134_red__reds_ORedCallNull) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1259 (all Pa all M all Vs_1 all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,null),M,map_va1934808527t_char(val_list_char,Vs_1)),S),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S))) # label(fact_1135_redp__redsp_ORedCallNull) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1260 (all M all Ps all Pa all Eb all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Eb,M,Ps),S_0),throw_list_char(E_b)),S_1)))) # label(fact_1136_CallObjThrow) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1261 (all M all Esa all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(Eb,M,Esa),S),call_list_char(E_b,M,Esa)),S_2)))) # label(fact_1137_redp__redsp_OCallObj) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1262 (all Pa all Eb all M all Esa all S hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(throw_list_char(Eb),M,Esa),S),throw_list_char(Eb)),S))) # label(fact_1138_redp__redsp_OCallThrowObj) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1263 (all M all Esa all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Eb,M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(E_b,M,Esa)),S_2))),red(Pa))))) # label(fact_1139_red__reds_OCallObj) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1264 (all Eb all M all Esa all S all Pa hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(throw_list_char(Eb),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa)))) # label(fact_1140_red__reds_OCallThrowObj) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1265 (all M all Esa all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Eb,M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(E_b,M,Esa)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1141_CallRedsObj) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1266 (all M all Esa all Eb all S0 all A all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_1))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Eb,M,Esa)),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_1))),transi2024712006on_val(red(Pa)))))) # label(fact_1142_CallRedsThrowObj) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1267 (all M all Esa all Vs_1 all S_2_1 all Eb all S_0 all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,null)),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,map_va1934808527t_char(val_list_char,Vs_1)),S_2_1))),transi374442731on_val(reds(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Eb,M,Esa)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_1143_CallRedsNull) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1268 (all M all Ps all Vs_1 all S_2_1 all Pa all Eb all S_0 all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,null)),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1),map_va1934808527t_char(val_list_char,Vs_1)),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Eb,M,Ps),S_0),throw_list_char(hAPP_v834067052t_char(val_list_char,addr(addr_of_sys_xcpt(nullPointer))))),S_2_1))))) # label(fact_1144_CallNull) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1269 (all Es_a all T_3 all Esa all T_2 all Es_1 all T_1 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),T_2)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),T_1))),reds(Pa))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,T_1),Es_a),T_3)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,T_2),Es_a),T_3)))))) # label(fact_1145_extend__1__evals) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1270 (all Es_a all S_2 all Esa all S all Es_1 all S_3 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_1),S_3))),transi374442731on_val(reds(Pa)))) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Es_1,S_3),Es_a),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S),Es_a),S_2)))))) # label(fact_1146_extend__evals) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1271 (all Esa all S all Es_a all S_2 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S),Es_a),S_2)) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2))),transi374442731on_val(reds(Pa))))))) # label(fact_1147_bigs__by__smalls) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1272 (all Pa all Esa all Hb all Lb all Es_a all H_b all L_b (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> hBOOL(hext(Hb,H_b)))) # label(fact_1148_evals__hext) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1273 (all Esa all Hb all Lb all Es_a all H_b all L_b all Pa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),reds(Pa))) -> hBOOL(hext(Hb,H_b)))) # label(fact_1149_reds__hext__incr) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1274 (all Pa all Esa all H_0 all L_0 all Es_a all H_1 all L_1_1 (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_0),L_0)),Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_1),L_1_1))) -> hBOOL(hAPP_f986089162l_bool(ord_le2092826700r_bool(dom_list_char_val(L_0)),dom_list_char_val(L_1_1))))) # label(fact_1150_evals__lcl__incr) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1275 (all Va all M all Esa all S all Es_a all S_2 all Pa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2))),reds(Pa))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Es_a)),S_2))),red(Pa))))) # label(fact_1151_red__reds_OCallParams) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.52 1276 (all Va all M all Esa all S all Es_a all S_2 all Pa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2))),transi374442731on_val(reds(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Es_a)),S_2))),transi2024712006on_val(red(Pa)))))) # label(fact_1152_CallRedsParams) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1277 (all M all Esa all Vs_1_1 all A all Es_2 all S_2_1 all Eb all S0 all Va all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1_1),cons_exp_list_char(throw_list_char(A),Es_2))),S_2_1))),transi374442731on_val(reds(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Eb,M,Esa)),S0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(A)),S_2_1))),transi2024712006on_val(red(Pa))))))) # label(fact_1153_CallRedsThrowParams) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1278 (all Eb all M all Esa fv(call_list_char(Eb,M,Esa)) = semila919158006r_bool(fv(Eb),fvs(Esa))) # label(fact_1154_fv__fvs_Osimps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1279 (all Eb all Esa fvs(cons_exp_list_char(Eb,Esa)) = semila919158006r_bool(fv(Eb),fvs(Esa))) # label(fact_1155_fv__fvs_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1280 (all Esa all Es_a all S_2_1 all Pa all Eb all S_0 all Va all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,Va)),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),Es_a),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Eb,Esa),S_0),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Es_a)),S_2_1))))) # label(fact_1156_eval__evals_OCons) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1281 (all Esa all Pa all Eb all S_0 all E_b all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),throw_list_char(E_b)),S_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Eb,Esa),S_0),cons_exp_list_char(throw_list_char(E_b),Esa)),S_1)))) # label(fact_1157_ConsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1282 (all Va all Esa all S all Es_a all S_2 all Pa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2))),reds(Pa))) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Es_a)),S_2))),reds(Pa))))) # label(fact_1158_red__reds_OListRed2) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1283 (all Pa all Va all M all S all Esa all Vs_1 all Eb all Es_a (Esa = append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(throw_list_char(Eb),Es_a)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Esa),S),throw_list_char(Eb)),S)))) # label(fact_1159_redp__redsp_OCallThrowParams) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1284 (all Vs_1 all Es_a all Pa all X_2 all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,throw_list_char(X_2),S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(throw_list_char(X_2),Es_a)),S),append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(E_b,Es_a))),S_2)))) # label(fact_1160_list__eval__Throw) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1285 (all Va all Esa all S all Es_a all S_2 all Pa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2))),transi374442731on_val(reds(Pa)))) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Es_a)),S_2))),transi374442731on_val(reds(Pa)))))) # label(fact_1161_ListReds2) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1286 (all Esa all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),red(Pa))) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(Eb,Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(E_b,Esa)),S_2))),reds(Pa))))) # label(fact_1162_red__reds_OListRed1) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1287 (all M all Esa all Vs_1 all Ex all Es_a all S_2_1 all Pa all Eb all S_0 all Va all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,Va)),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1),append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(throw_list_char(Ex),Es_a))),S_2_1)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Eb,M,Esa),S_0),throw_list_char(Ex)),S_2_1))))) # label(fact_1163_CallParamsThrow) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1288 (all Va all M all S all Pa all Esa all Vs_1 all Eb all Es_a (Esa = append_exp_list_char(map_va1934808527t_char(val_list_char,Vs_1),cons_exp_list_char(throw_list_char(Eb),Es_a)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Esa)),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,throw_list_char(Eb)),S))),red(Pa))))) # label(fact_1164_red__reds_OCallThrowParams) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1289 (all Esa all Eb all S all E_b all S_2 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),S_2))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(Eb,Esa)),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(E_b,Esa)),S_2))),transi374442731on_val(reds(Pa)))))) # label(fact_1165_ListReds1) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1290 (all Esa all Es_a all S_2_1 all Eb all S_0 all Va all S_1 all Pa (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,Va)),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2_1))),transi374442731on_val(reds(Pa)))) -> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(Eb,Esa)),S_0)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Es_a)),S_2_1))),transi374442731on_val(reds(Pa))))))) # label(fact_1166_ListRedsVal) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1291 (all Pa all Eb all Esa all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,cons_exp_list_char(Eb,Esa),S),E_b),S_2)) -> ((all V_2 all S_1_1 all Es (E_b = cons_exp_list_char(hAPP_v834067052t_char(val_list_char,V_2),Es) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),hAPP_v834067052t_char(val_list_char,V_2)),S_1_1)) -> -hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S_1_1),Es),S_2))))) -> -(all E_1 (E_b = cons_exp_list_char(throw_list_char(E_1),Esa) -> -hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S),throw_list_char(E_1)),S_2))))))) # label(fact_1167_evals__cases_I2_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1292 (all Pa all Esa all S all Es_a all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S),Es_a),S_2)) -> hBOOL(finals_list_char(Es_a)))) # label(fact_1168_evals__final) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1293 (all Pa all S all Esa (hBOOL(finals_list_char(Esa)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Esa,S),Esa),S)))) # label(fact_1169_eval__finalsId) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1294 (all Ea all Ts all Esa all S all Es_a all S_2 all Pa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),S_2))),reds(Pa))) -> (hBOOL(wTrts_1(Pa,hp(S),Ea,Esa,Ts)) -> (hBOOL(hAPP_P159683425l_bool(typeSa1700205512_sconf(Pa,Ea),S)) -> hBOOL(hAPP_P159683425l_bool(typeSa1700205512_sconf(Pa,Ea),S_2)))))) # label(fact_1170_reds__preserves__sconf) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1295 (all Esa all Ts all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) -> hBOOL(wTrts_1(Pa,Hb,Ea,cons_exp_list_char(Eb,Esa),cons_ty(Ta,Ts)))))) # label(fact_1171_WTrtCons) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1296 (all H_b all Pa all Hb all Ea all Esa all Ts (hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) -> (hBOOL(hext(Hb,H_b)) -> hBOOL(wTrts_1(Pa,H_b,Ea,Esa,Ts))))) # label(fact_1172_WTrts__hext__mono) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1297 (all M all Ta all Esa all Ts all Pa all Hb all Ea all Eb (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,nt)) -> (hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) -> hBOOL(wTrt_1(Pa,Hb,Ea,call_list_char(Eb,M,Esa),Ta))))) # label(fact_1173_WTrtCallNT) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1298 (all Pa all Hb all Ea all Vs_1 all Ts (hBOOL(wTrts_1(Pa,Hb,Ea,map_va1934808527t_char(val_list_char,Vs_1),Ts)) <-> map_val_option_ty(typeof_h(Hb),Vs_1) = map_ty_option_ty(some_ty,Ts))) # label(fact_1174_WTrts__Val) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1299 (all Ea all Ts all Esa all Hb all Lb all Es_a all H_b all L_b all Pa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),reds(Pa))) -> (hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) -> (hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),Hb)) -> hBOOL(hAPP_f61040418l_bool(hconf_97414254t_char(Pa),H_b)))))) # label(fact_1175_reds__preserves__hconf) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1300 (all Ea all Ts all Esa all Hb all Lb all Es_a all H_b all L_b all Pa (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Es_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),reds(Pa))) -> (hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) -> (hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),Hb),Lb),Ea)) -> hBOOL(hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(hAPP_f1213370163y_bool(lconf_496643946t_char(Pa),H_b),L_b),Ea)))))) # label(fact_1176_reds__preserves__lconf) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1301 (all Pa all X_1 all Xa all Xb all Xc (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,X_1,Xa),Xb),Xc)) <-> hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,X_1),Xa)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Xb),Xc))),reds(Pa))))) # label(fact_1177_redsp__reds__eq) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1302 (all V_1 all Vs_3 all T all Ts_3 all V all Vs_2 all E blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,cons_list_char(V_1,Vs_3)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,cons_ty(T,Ts_3)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(V,Vs_2)),E)))) = block_list_char(V_1,T,seq_list_char(lAss_list_char(V_1,hAPP_v834067052t_char(val_list_char,V)),blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs_3),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts_3),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_2),E))))))) # label(fact_1178_blocks_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1303 (all Va all Pa all Esa all S all Es_a all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Esa,S),Es_a),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Esa),S),cons_exp_list_char(hAPP_v834067052t_char(val_list_char,Va),Es_a)),S_2)))) # label(fact_1179_redp__redsp_OListRed2) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1304 (all Esa all Pa all Eb all S all E_b all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,Eb,S),E_b),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,cons_exp_list_char(Eb,Esa),S),cons_exp_list_char(E_b,Esa)),S_2)))) # label(fact_1180_redp__redsp_OListRed1) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1305 (all Va all M all Pa all Esa all S all Es_a all S_2 (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(redsp(Pa,Esa,S),Es_a),S_2)) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Esa),S),call_list_char(hAPP_v834067052t_char(val_list_char,Va),M,Es_a)),S_2)))) # label(fact_1181_redp__redsp_OCallParams) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1306 (all Jmdcl all C all D all Fds all Mths all Pa (hBOOL(wf_pro755087577t_char(wf_J_mdecl,Pa)) -> (hBOOL(hAPP_f515912112l_bool(hAPP_P205570445l_bool(member1467889965t_char,hAPP_P1224499548t_char(hAPP_l902950593t_char(produc822965838t_char,C),hAPP_P1423780764t_char(hAPP_l309186817t_char(produc1483578759t_char,D),hAPP_l277216047t_char(hAPP_l352172327t_char(produc1152259904t_char,Fds),Mths)))),set_Pr1494163115t_char(Pa))) -> (hBOOL(hAPP_f483496539l_bool(hAPP_P7095645l_bool(member1601084734t_char,Jmdcl),set_Pr2033386304t_char(Mths))) -> hBOOL(hAPP_P1384137393r_bool(hAPP_l2054741776r_bool(hAPP_l2138409430r_bool(wf_J_mdecl,Pa),C),Jmdcl)))))) # label(fact_1182_wf__J__prog__wf__J__mdecl) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1307 (all Ef all H_3 all L_3 all L_2_1 all M all Ts all Ta all Pns all Body all D all C all Fs all Esa all Vs_1 all H_2 all L_2 all Eb all S_0 all A all S_1 all Pa (hBOOL(wf_pro755087577t_char(wwf_J_mdecl,Pa)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,hAPP_v834067052t_char(val_list_char,addr(A))),S_1))),transi2024712006on_val(red(Pa)))) -> (hBOOL(hAPP_f458849545l_bool(hAPP_P126004409l_bool(member875476972on_val,hAPP_P658340954on_val(hAPP_P1526035745on_val(produc1611380469on_val,hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,Esa),S_1)),hAPP_P1963616220on_val(hAPP_l1275479261on_val(produc379668296on_val,map_va1934808527t_char(val_list_char,Vs_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2)))),transi374442731on_val(reds(Pa)))) -> (hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D)) -> (size_size_list_val(Vs_1) = size_s2113983095t_char(Pns) -> (L_2_1 = map_up1085636310ar_val(fun_up1149430426on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val),this,hAPP_val_option_val(some_val,addr(A))),Pns,Vs_1) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Body),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2_1))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ef),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_3)))),transi2024712006on_val(red(Pa)))) -> (hBOOL(final_list_char(Ef)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(Eb,M,Esa)),S_0)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Ef),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_2)))),transi2024712006on_val(red(Pa)))))))))))))) # label(fact_1183_CallRedsFinal) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1308 (all E_b all H_3 all L_3 all L_2_1 all M all Ts all Ta all Pns all Body all D all C all Fs all Ps all Vs_1 all H_2 all L_2 all Pa all Eb all S_0 all A all S_1 (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,S_0),hAPP_v834067052t_char(val_list_char,addr(A))),S_1)) -> (hBOOL(hAPP_P159683425l_bool(hAPP_l146377954l_bool(evals(Pa,Ps,S_1),map_va1934808527t_char(val_list_char,Vs_1)),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2))) -> (hAPP_n546249108on_val(H_2,A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D)) -> (size_size_list_val(Vs_1) = size_s2113983095t_char(Pns) -> (L_2_1 = map_up1085636310ar_val(fun_up1149430426on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,none_val),this,hAPP_val_option_val(some_val,addr(A))),Pns,Vs_1) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Body,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_2),L_2_1)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_3))) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,call_list_char(Eb,M,Ps),S_0),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_3),L_2))))))))))) # label(fact_1184_Call) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1309 (all Vs_1 all Pa all M all Ts all Ta all Pns all Body all D all S all A all C all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D)) -> (size_size_list_val(Vs_1) = size_s2113983095t_char(Pns) -> (size_size_list_ty(Ts) = size_s2113983095t_char(Pns) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,call_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),M,map_va1934808527t_char(val_list_char,Vs_1))),S)),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,cons_list_char(this,Pns)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,cons_ty(hAPP_list_char_ty(class,D),Ts)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(addr(A),Vs_1)),Body))))),S))),red(Pa)))))))) # label(fact_1185_red__reds_ORedCall) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1310 (all Vs_1 all Pa all M all Ts all Ta all Pns all Body all D all S all A all C all Fs (hAPP_n546249108on_val(hp(S),A) = hAPP_P1510515380on_val(some_P948696889on_val,hAPP_f900686428on_val(hAPP_l1786340417on_val(produc823076510on_val,C),Fs)) -> (hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D)) -> (size_size_list_val(Vs_1) = size_s2113983095t_char(Pns) -> (size_size_list_ty(Ts) = size_s2113983095t_char(Pns) -> hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(redp(Pa,call_list_char(hAPP_v834067052t_char(val_list_char,addr(A)),M,map_va1934808527t_char(val_list_char,Vs_1)),S),blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,cons_list_char(this,Pns)),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,cons_ty(hAPP_list_char_ty(class,D),Ts)),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,cons_val(addr(A),Vs_1)),Body))))),S))))))) # label(fact_1186_redp__redsp_ORedCall) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1311 (all Pa all Hb all Ea all Esa all Ts (hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) -> size_s1143674878t_char(Esa) = size_size_list_ty(Ts))) # label(fact_1187_WTrts__same__length) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1312 (all Hb all Lb all Pa all Eb all Vs_1 all Vs all Ts (size_s2113983095t_char(Vs) = size_size_list_ty(Ts) -> (size_size_list_val(Vs_1) = size_size_list_ty(Ts) -> (hBOOL(final_list_char(Eb)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)))),transi2024712006on_val(red(Pa)))))))) # label(fact_1188_blocksFinal) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1313 (all Pa all Eb all Hb all Lb all E_b all H_b all L_b all Vs_1 all Ps all Ts (size_s2113983095t_char(Ps) = size_size_list_ty(Ts) -> (size_s2113983095t_char(Ps) = size_size_list_val(Vs_1) -> (hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Ps),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb)))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb)),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b))) -> (exists L_1 hBOOL(hAPP_P159683425l_bool(hAPP_e1833980889l_bool(eval(Pa,Eb,hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_up1085636310ar_val(Lb,Ps,Vs_1))),E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_1)))))))) # label(fact_1189_blocksEval) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1314 (all Pa all Hb all Ea all Eb all Ta all Vs_1 all Vs all Ts (size_s2113983095t_char(Vs) = size_size_list_ty(Ts) -> (size_size_list_val(Vs_1) = size_size_list_ty(Ts) -> (hBOOL(wTrt_1(Pa,Hb,Ea,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb)))),Ta)) <-> hBOOL(wTrt_1(Pa,Hb,map_up891053837har_ty(Ea,Vs,Ts),Eb,Ta)) & (exists Ts_2 (map_val_option_ty(typeof_h(Hb),Vs_1) = map_ty_option_ty(some_ty,Ts_2) & hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_2,Ts)))))))) # label(fact_1190_wt__blocks) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1315 (all Esa all Ts_1 all M all Ts all Ta all Pns all Body all D all Pa all Hb all Ea all Eb all C (hBOOL(wTrt_1(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C))) -> (hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D)) -> (hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts_1)) -> (hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Ts)) -> hBOOL(wTrt_1(Pa,Hb,Ea,call_list_char(Eb,M,Esa),Ta))))))) # label(fact_1191_WTrtCall) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1316 (all Esa all Ts_1 all M all Ts all Ta all Pns all Body all D all Pa all Hb all Ea all Eb all C (hBOOL(wTrt(Pa,Hb,Ea,Eb,hAPP_list_char_ty(class,C))) -> (hBOOL(hAPP_list_char_bool(method1809630380t_char(Pa,C,M,Ts,Ta,hAPP_e952791821t_char(hAPP_l796364813t_char(produc1147572817t_char,Pns),Body)),D)) -> (hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts_1)) -> (hBOOL(list_all2_ty_ty(widen_2090681816t_char(Pa),Ts_1,Ts)) -> hBOOL(wTrt(Pa,Hb,Ea,call_list_char(Eb,M,Esa),Ta))))))) # label(fact_1192_WTrt_H__WTrts_H_Ointros_I12_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1317 (all Pa all Hb all Ea all Esa all Ts (hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts)) <-> hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)))) # label(fact_1193_wts_H__iff__wts) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1318 (all Pa all Hb all Ea all Esa all Ts (hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts)) -> hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)))) # label(fact_1194_wts_H__wts) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1319 (all Pa all Hb all Ea all Esa all Ts (hBOOL(wTrts_1(Pa,Hb,Ea,Esa,Ts)) -> hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts)))) # label(fact_1195_wts__wts_H) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1320 (all M all Ta all Esa all Ts all Pa all Hb all Ea all Eb (hBOOL(wTrt(Pa,Hb,Ea,Eb,nt)) -> (hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts)) -> hBOOL(wTrt(Pa,Hb,Ea,call_list_char(Eb,M,Esa),Ta))))) # label(fact_1196_WTrt_H__WTrts_H_Ointros_I13_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1321 (all Esa all Ts all Pa all Hb all Ea all Eb all Ta (hBOOL(wTrt(Pa,Hb,Ea,Eb,Ta)) -> (hBOOL(wTrts(Pa,Hb,Ea,Esa,Ts)) -> hBOOL(wTrts(Pa,Hb,Ea,cons_exp_list_char(Eb,Esa),cons_ty(Ta,Ts)))))) # label(fact_1197_WTrt_H__WTrts_H_Ointros_I15_J) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1322 (all L all Eb all Hb all Lb all E_b all H_b all L_b all Pa all Vs_1 all Vs all Ts (size_s2113983095t_char(Vs) = size_size_list_ty(Ts) -> (size_size_list_val(Vs_1) = size_size_list_ty(Ts) -> (hBOOL(distinct_list_char(Vs)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_up1085636310ar_val(Lb,Vs,Vs_1)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),transi2024712006on_val(red(Pa)))) -> (hBOOL(final_list_char(E_b)) -> (L = overri2012515291on_val(L_b,Lb,set_list_char(Vs)) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L)))),transi2024712006on_val(red(Pa))))))))))) # label(fact_1198_blocksRedsFinal) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1323 (all Eb all Hb all Lb all E_b all H_b all L_b all Pa all Vs_1 all Vs all Ts (size_s2113983095t_char(Vs) = size_size_list_ty(Ts) -> (size_size_list_val(Vs_1) = size_size_list_ty(Ts) -> (hBOOL(distinct_list_char(Vs)) -> (hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,Eb),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),map_up1085636310ar_val(Lb,Vs,Vs_1)))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,E_b),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),L_b)))),transi2024712006on_val(red(Pa)))) -> hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,Vs_1),Eb))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,Hb),Lb))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,blocks(hAPP_P767818445t_char(hAPP_l1873467853t_char(produc921874948t_char,Vs),hAPP_P1392904962t_char(hAPP_l14371579t_char(produc1909267824t_char,Ts),hAPP_e1752110927t_char(hAPP_l1859255743t_char(produc1916172923t_char,map_list_char_val(comp_o1129292306t_char(the_val,L_b),Vs)),E_b))))),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,H_b),overri2012515291on_val(L_b,Lb,set_list_char(Vs)))))),transi2024712006on_val(red(Pa))))))))) # label(fact_1199_blocksReds) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1324 (all P (-hBOOL(hAPP_bool_bool(fNot,P)) | -hBOOL(P))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1325 (all P (hBOOL(P) | hBOOL(hAPP_bool_bool(fNot,P)))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1326 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1327 (all Q all P (-hBOOL(P) | -hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1328 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(P))) # label(help_fconj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1329 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) | hBOOL(Q))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1330 (all Q all P (-hBOOL(P) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1331 (all P all Q (-hBOOL(Q) | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)))) # label(help_fdisj_2_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1332 (all P all Q (-hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) | hBOOL(P) | hBOOL(Q))) # label(help_fdisj_3_1_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1333 (all P (is_bool(P) -> P = fTrue | P = fFalse)) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1334 (all X all Y (-hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Value__Oval_T) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1335 (all X all Y (X != Y | hBOOL(hAPP_val_bool(hAPP_v1392248405l_bool(fequal_val,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Value__Oval_T) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1336 (all X all Y (-hBOOL(hAPP_option_val_bool(hAPP_o586881855l_bool(fequal_option_val,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1337 (all X all Y (X != Y | hBOOL(hAPP_option_val_bool(hAPP_o586881855l_bool(fequal_option_val,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1338 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f894608603t_bool(cOMBB_bool_bool_nat,P),Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1339 (all P all Q all R hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1340 (all P all Q all R hAPP_list_char_bool(hAPP_f1371002581r_bool(hAPP_f1861125939r_bool(cOMBB_1091123364t_char,P),Q),R) = hAPP_bool_bool(P,hAPP_list_char_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1341 (all P all Q all R hAPP_list_char_bool(cOMBS_1502238389l_bool(P,Q),R) = hAPP_bool_bool(hAPP_l2010421276l_bool(P,R),hAPP_list_char_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__String__Ochar_J_000tc__HOL__Obool_0) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1342 (all P all Q all R hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1343 (all P all Q all R hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(hAPP_f1080886329l_bool(cOMBB_1015721476ol_nat,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1344 (all P all Q hAPP_l512744617ion_ty(hAPP_o1240645474ion_ty(cOMBK_1294242658t_char,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__List__Olist_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1345 (all P all Q hAPP_l207779698on_val(hAPP_o538043682on_val(cOMBK_1097134891t_char,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1346 (all P all Q all R hAPP_l512744617ion_ty(hAPP_f359949478ion_ty(hAPP_f1243585741ion_ty(cOMBB_1888336841t_char,P),Q),R) = hAPP_ty_option_ty(P,hAPP_list_char_ty(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Type__Oty_000tc__Option__Ooption_Itc__Type__Oty_J_00) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1347 (all P all Q all R hAPP_list_char_bool(hAPP_o453398608r_bool(hAPP_f399018025r_bool(cOMBC_442485623l_bool,P),Q),R) = hAPP_option_val_bool(hAPP_l1646953198l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__Option__Oopt) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1348 (all P all Q all R hAPP_l2010421276l_bool(hAPP_f1163760061l_bool(hAPP_f1157863905l_bool(cOMBB_984708934t_char,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_list_char_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_033) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1349 (all P all Q all R hAPP_val_bool(hAPP_f1728541444l_bool(hAPP_f1764548711l_bool(cOMBC_331963401l_bool,P),Q),R) = hAPP_f2028441009l_bool(hAPP_v3604996l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1350 (all P all Q all R hAPP_list_char_bool(hAPP_f1371002581r_bool(hAPP_f522372661r_bool(cOMBC_892477410l_bool,P),Q),R) = hAPP_f986089162l_bool(hAPP_l1903254203l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__Lis) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1351 (all P all Q all R hAPP_P449474095r_bool(cOMBS_350755140l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P1457625805l_bool(P,R),hAPP_P449474095r_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1352 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f1074020887l_bool(hAPP_f1863694447l_bool(cOMBB_383678192on_val,P),Q),R) = hAPP_bool_bool(P,hAPP_f1033709212l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1353 (all P all Q hAPP_P2094403585on_val(hAPP_o1269033393on_val(cOMBK_1867744698t_char,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__prod_Itc__) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1354 (all P all Q all R hAPP_v1392248405l_bool(hAPP_f198821591l_bool(hAPP_f1880802701l_bool(cOMBC_1979963740l_bool,P),Q),R) = hAPP_f1728541444l_bool(hAPP_v1988122071l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt_034) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1355 (all P all Q all R hAPP_l1646953198l_bool(hAPP_f396807521l_bool(hAPP_f926979333l_bool(cOMBB_1112666310t_char,P),Q),R) = hAPP_o586881855l_bool(P,hAPP_l207779698on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__fun_Itc__O) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1356 (all P all Q all R hAPP_P1457625805l_bool(hAPP_f644972157l_bool(hAPP_f722872225l_bool(cOMBB_1643767893t_char,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P449474095r_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_035) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1357 (all P all Q all R hAPP_v3604996l_bool(hAPP_f1394668591l_bool(hAPP_f183649339l_bool(cOMBB_2078984970ol_val,P),Q),R) = hAPP_P530382601l_bool(P,hAPP_v852496844al_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1358 (all P all Q all R hAPP_P929938951l_bool(hAPP_f1335946228l_bool(hAPP_f263393637l_bool(cOMBC_813705475l_bool,P),Q),R) = hAPP_f742333458l_bool(hAPP_P1614880106l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1359 (all P all Q all R hAPP_list_char_bool(hAPP_f335969926r_bool(hAPP_f1367982615r_bool(cOMBC_1603044337l_bool,P),Q),R) = hAPP_f2106398425l_bool(hAPP_l553007690l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1360 (all P all Q hAPP_f652398900ion_ty(hAPP_o534509643ion_ty(cOMBK_184479553on_val,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__pro) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1361 (all P all Q all R hAPP_b97269396l_bool(hAPP_f257113085l_bool(hAPP_f1100052969l_bool(cOMBC_199425070l_bool,P),Q),R) = hAPP_f1335946228l_bool(hAPP_b1257035143l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1362 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f603925568l_bool(hAPP_f181262431l_bool(cOMBC_832625297y_bool,P),Q),R) = hAPP_f1001225811y_bool(hAPP_f2060496320y_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1363 (all P all Q all R hAPP_e544220455r_bool(hAPP_f1724656343r_bool(hAPP_f388097003r_bool(cOMBC_818212448l_bool,P),Q),R) = hAPP_f1314764175l_bool(hAPP_e53687815l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1364 (all X all Y (-hBOOL(hAPP_o2007402111l_bool(hAPP_o1968908095l_bool(fequal1937332960on_val,X),Y)) | X = Y)) # label(help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1365 (all X all Y (X != Y | hBOOL(hAPP_o2007402111l_bool(hAPP_o1968908095l_bool(fequal1937332960on_val,X),Y)))) # label(help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1366 (all P all Q all R hAPP_l1361600383r_bool(hAPP_f344506159r_bool(hAPP_f447563647r_bool(cOMBC_389248878r_bool,P),Q),R) = hAPP_f335969926r_bool(hAPP_l1335043179r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_036) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1367 (all P all Q all R hAPP_v417179479l_bool(hAPP_f293485653l_bool(hAPP_f565735867l_bool(cOMBB_815843940ol_val,P),Q),R) = hAPP_f1394668591l_bool(P,hAPP_v1519391al_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1368 (all P all Q all R hAPP_P449474095r_bool(hAPP_f112056853r_bool(hAPP_f1876889431r_bool(cOMBC_148995234l_bool,P),Q),R) = hAPP_f2106398425l_bool(hAPP_P1180869721l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1369 (all P all Q all R hAPP_e544220455r_bool(hAPP_f1466436665r_bool(hAPP_f1766231913r_bool(cOMBC_220519196l_bool,P),Q),R) = hAPP_f82569901l_bool(hAPP_e1303556805l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_037) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1370 (all P all Q hAPP_n546249108on_val(hAPP_o1576581476on_val(cOMBK_1944287343al_nat,P),Q) = P) # label(help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__Stri) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1371 (all P all Q all R hAPP_nat_bool(hAPP_o1566711458t_bool(hAPP_f489569861t_bool(cOMBC_229530231l_bool,P),Q),R) = hAPP_o2007402111l_bool(hAPP_n95946796l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Option__Ooption_Itc__prod_Itc__List) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1372 (all P all Q all R hAPP_P1614880106l_bool(hAPP_f1646911885l_bool(hAPP_f62511709l_bool(cOMBB_2139740953al_val,P),Q),R) = hAPP_P1653675595l_bool(P,hAPP_P929466802al_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1373 (all P all Q all R hAPP_l1062423959r_bool(hAPP_f1051205629r_bool(hAPP_f987862447r_bool(cOMBC_1387630958r_bool,P),Q),R) = hAPP_f1724656343r_bool(hAPP_l296209613r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__prod_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1374 (all P all Q all R hAPP_l2000496933ion_ty(hAPP_f451501457ion_ty(hAPP_f509342689ion_ty(cOMBB_352765746t_char,P),Q),R) = hAPP_o534509643ion_ty(P,hAPP_l512744617ion_ty(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Type__Oty_J_000tc__fun_Itc__fun) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1375 (all P all Q all R hAPP_l553007690l_bool(hAPP_f558380429l_bool(hAPP_f144783951l_bool(cOMBB_1586673472t_char,P),Q),R) = hAPP_P1180869721l_bool(P,hAPP_l2100324114t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1376 (all P all Q all R hAPP_v1988122071l_bool(hAPP_f1859053709l_bool(hAPP_f400269243l_bool(cOMBB_1701031980ol_val,P),Q),R) = hAPP_f1764548711l_bool(P,hAPP_v417179479l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1377 (all P all Q all R hAPP_P1384137393r_bool(cOMBS_1743887558l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P415257547l_bool(P,R),hAPP_P1384137393r_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1378 (all P all Q all R hAPP_l214204733r_bool(hAPP_f2091926485r_bool(hAPP_f1820115955r_bool(cOMBC_790582442r_bool,P),Q),R) = hAPP_f1466436665r_bool(hAPP_l753659065r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1379 (all P all Q all R hAPP_f1145256474l_bool(hAPP_f1452292669l_bool(hAPP_f1977633121l_bool(cOMBB_1303934920on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_f61040418l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1380 (all P all Q all R hAPP_P2118621157r_bool(hAPP_f1298720864r_bool(hAPP_f225832321r_bool(cOMBC_1365742487l_bool,P),Q),R) = hAPP_f1746574980l_bool(hAPP_P2028292026l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1381 (all P all Q all R hAPP_P415257547l_bool(hAPP_f1985672189l_bool(hAPP_f1169733153l_bool(cOMBB_565990871t_char,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P1384137393r_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_039) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1382 (all P all Q all R hAPP_e53687815l_bool(hAPP_f361629773l_bool(hAPP_f1612138403l_bool(cOMBB_961360819t_char,P),Q),R) = hAPP_P845017029l_bool(P,hAPP_e1752110927t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1383 (all P all Q all R hAPP_b406740087l_bool(hAPP_f866074145l_bool(hAPP_f877616419l_bool(cOMBB_1458388806ol_bop,P),Q),R) = hAPP_f1646911885l_bool(P,hAPP_b1229254591al_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1384 (all P all Q all R hAPP_l1987619678r_bool(hAPP_f2071340985r_bool(hAPP_f133320957r_bool(cOMBC_1127703214r_bool,P),Q),R) = hAPP_f1298720864r_bool(hAPP_l96108383r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1385 (all P all Q all R hAPP_e1303556805l_bool(hAPP_f901718717l_bool(hAPP_f380623487l_bool(cOMBB_1033145403t_char,P),Q),R) = hAPP_P1293136973l_bool(P,hAPP_e952791821t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1386 (all P all Q all R hAPP_l1425867561l_bool(hAPP_f1764180741l_bool(hAPP_f247798919l_bool(cOMBB_526805108t_char,P),Q),R) = hAPP_f558380429l_bool(P,hAPP_l208357873t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1387 (all P all Q all R hAPP_f652398900ion_ty(hAPP_f2110071953ion_ty(hAPP_f69964139ion_ty(cOMBB_2041093409on_val,P),Q),R) = hAPP_P1228500987ion_ty(P,hAPP_f900686428on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1388 (all P all Q all R hAPP_f1715346603l_bool(hAPP_f1579743228l_bool(hAPP_f1166017719l_bool(cOMBC_317789649l_bool,P),Q),R) = hAPP_f1134950784l_bool(hAPP_f749178132l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1389 (all P all Q all R hAPP_b1257035143l_bool(hAPP_f2100207721l_bool(hAPP_f1374595987l_bool(cOMBB_761748254ol_bop,P),Q),R) = hAPP_f263393637l_bool(P,hAPP_b406740087l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt_040) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1390 (all P all Q all R hAPP_P1907982426r_bool(hAPP_f1874697593r_bool(hAPP_f1707979241r_bool(cOMBC_407285762l_bool,P),Q),R) = hAPP_f1780084320l_bool(hAPP_P1562529797l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1391 (all P all Q all R hAPP_l1335043179r_bool(hAPP_f1032444159r_bool(hAPP_f254182519r_bool(cOMBB_1551681790t_char,P),Q),R) = hAPP_f1367982615r_bool(P,hAPP_l1425867561l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1392 (all P all Q all R hAPP_l465799708l_bool(hAPP_f2080627739l_bool(hAPP_f350189921l_bool(cOMBC_1535683812l_bool,P),Q),R) = hAPP_f1579743228l_bool(hAPP_l1739862107l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_041) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1393 (all P all Q all R hAPP_l1842007287l_bool(hAPP_f2118054305l_bool(hAPP_f1687138147l_bool(cOMBB_2078271971st_val,P),Q),R) = hAPP_f361629773l_bool(P,hAPP_l1859255743t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1394 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f550652027l_bool(hAPP_f838396643l_bool(cOMBC_2027949654l_bool,P),Q),R) = hAPP_f603925568l_bool(hAPP_f1617787571l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1395 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f1008932791l_bool(hAPP_f2057883639l_bool(cOMBB_1750801836on_val,P),Q),R) = hAPP_P159683425l_bool(P,hAPP_f1727192346on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1396 (all P all Q all R hAPP_P2028292026l_bool(hAPP_f921434893l_bool(hAPP_f693085049l_bool(cOMBB_147773915t_char,P),Q),R) = hAPP_P1198052655l_bool(P,hAPP_P1392904962t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1397 (all P all Q all R hAPP_n95946796l_bool(hAPP_f1677329295l_bool(hAPP_f1611569977l_bool(cOMBB_731867268ol_nat,P),Q),R) = hAPP_o1968908095l_bool(P,hAPP_n546249108on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__Stri) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1398 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f555424277l_bool(hAPP_f1734879897l_bool(cOMBB_1522540928on_val,P),Q),R) = hAPP_f1074020887l_bool(P,hAPP_f1175813647l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1399 (all P all Q all R hAPP_f1175813647l_bool(cOMBS_570216337l_bool(P,Q),R) = hAPP_f1074020887l_bool(hAPP_f1492320500l_bool(P,R),hAPP_f1175813647l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1400 (all P all Q all R hAPP_f1033709212l_bool(hAPP_f33142364l_bool(hAPP_f510152537l_bool(cOMBC_1518234801l_bool,P),Q),R) = hAPP_f966411375l_bool(hAPP_f720086610l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio_042) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1401 (all P all Q all R hAPP_l217977712r_bool(hAPP_f1044627221r_bool(hAPP_f308875635r_bool(cOMBC_1718404842r_bool,P),Q),R) = hAPP_f1874697593r_bool(hAPP_l1783480313r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__043) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1402 (all P all Q all R hAPP_l296209613r_bool(hAPP_f1449341487r_bool(hAPP_f1823921107r_bool(cOMBB_308691073st_val,P),Q),R) = hAPP_f388097003r_bool(P,hAPP_l1842007287l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_044) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1403 (all P all Q all R hAPP_P1187139874r_bool(hAPP_f279818502r_bool(hAPP_f1419180947r_bool(cOMBC_390659185l_bool,P),Q),R) = hAPP_f483496539l_bool(hAPP_P1383068750l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc_045) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1404 (all P all Q all R hAPP_l551544901l_bool(hAPP_f165071409l_bool(hAPP_f1174637065l_bool(cOMBB_33167485t_char,P),Q),R) = hAPP_f901718717l_bool(P,hAPP_l796364813t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_046) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1405 (all P all Q all R hAPP_P1680401186r_bool(cOMBS_635570165l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P1552072218l_bool(P,R),hAPP_P1680401186r_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_047) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1406 (all P all Q all R hAPP_P1552072218l_bool(hAPP_f561246575l_bool(hAPP_f321462169l_bool(cOMBB_808210516t_char,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P1680401186r_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_048) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1407 (all P all Q all R hAPP_f1492320500l_bool(hAPP_f1523875321l_bool(hAPP_f592397849l_bool(cOMBB_1718333400on_val,P),Q),R) = hAPP_f1863694447l_bool(P,hAPP_f1145256474l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1408 (all P all Q all R hAPP_l165010689r_bool(hAPP_f1209019955r_bool(hAPP_f521496323r_bool(cOMBC_654453230r_bool,P),Q),R) = hAPP_f279818502r_bool(hAPP_l2053770731r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_049) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1409 (all P all Q all R hAPP_P1384137393r_bool(hAPP_f1853572245r_bool(hAPP_f1933376467r_bool(cOMBC_36589090l_bool,P),Q),R) = hAPP_f483496539l_bool(hAPP_P7095645l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1410 (all P all Q all R hAPP_l753659065r_bool(hAPP_f2059406941r_bool(hAPP_f108089737r_bool(cOMBB_2143526097t_char,P),Q),R) = hAPP_f1766231913r_bool(P,hAPP_l551544901l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_050) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1411 (all P all Q all R hAPP_l2000496933ion_ty(hAPP_f802560783ion_ty(hAPP_f7643013ion_ty(cOMBB_864319000t_char,P),Q),R) = hAPP_f2110071953ion_ty(P,hAPP_l1786340417on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1412 (all P all Q all R hAPP_f749178132l_bool(hAPP_f1099622285l_bool(hAPP_f919000597l_bool(cOMBB_1153773871on_val,P),Q),R) = hAPP_P1217996045l_bool(P,hAPP_f900686428on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun__051) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1413 (all P all Q all R hAPP_l1117138611l_bool(hAPP_f2047757465l_bool(hAPP_f466945179l_bool(cOMBB_68065882ist_ty,P),Q),R) = hAPP_f921434893l_bool(P,hAPP_l14371579t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1414 (all P all Q all R hAPP_P1562529797l_bool(hAPP_f1233028029l_bool(hAPP_f1715733055l_bool(cOMBB_123628846t_char,P),Q),R) = hAPP_P1472618637l_bool(P,hAPP_P767818445t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___052) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1415 (all P all Q all R hAPP_f1617787571l_bool(hAPP_f857351829l_bool(hAPP_f348318673l_bool(cOMBB_1518282696on_val,P),Q),R) = hAPP_f181262431l_bool(P,hAPP_f1213370163y_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_053) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1416 (all P all Q all R hAPP_l96108383r_bool(hAPP_f1608277885r_bool(hAPP_f1134248971r_bool(cOMBB_338473166ist_ty,P),Q),R) = hAPP_f225832321r_bool(P,hAPP_l1117138611l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt_054) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1417 (all P all Q all R hAPP_l902158906r_bool(hAPP_f605643693r_bool(hAPP_f841257045r_bool(cOMBC_1407716098l_bool,P),Q),R) = hAPP_f1161798306l_bool(hAPP_l213519975l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1418 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f47713631l_bool(hAPP_f77033475l_bool(cOMBC_1317565126l_bool,P),Q),R) = hAPP_f33142364l_bool(hAPP_f893576377l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_055) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1419 (all P all Q all R hAPP_P1383068750l_bool(hAPP_f1239832973l_bool(hAPP_f1937828171l_bool(cOMBB_1681501894t_char,P),Q),R) = hAPP_P7095645l_bool(P,hAPP_P242904598t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1420 (all P all Q all R hAPP_l24694616r_bool(hAPP_f306469557r_bool(hAPP_f197435839r_bool(cOMBC_886773442r_bool,P),Q),R) = hAPP_f605643693r_bool(hAPP_l1129005983r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___056) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1421 (all P all Q all R hAPP_l2111308793l_bool(hAPP_f1370205989l_bool(hAPP_f1406462375l_bool(cOMBB_109816436t_char,P),Q),R) = hAPP_f1099622285l_bool(P,hAPP_l1786340417on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__057) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1422 (all P all Q all R hAPP_P159683425l_bool(hAPP_f1175362209l_bool(hAPP_f101237475l_bool(cOMBC_1585774710l_bool,P),Q),R) = hAPP_f91506671l_bool(hAPP_P1609485901l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1423 (all P all Q all R hAPP_f1175813647l_bool(hAPP_f1363667773l_bool(hAPP_f1050935001l_bool(cOMBB_1153617344on_val,P),Q),R) = hAPP_f1008932791l_bool(P,hAPP_f1849790461on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_058) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1424 (all P all Q all R hAPP_P159683425l_bool(hAPP_f1526206996l_bool(hAPP_f1467537159l_bool(cOMBC_2141828763l_bool,P),Q),R) = hAPP_f837795298l_bool(hAPP_P594889876l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_059) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1425 (all P all Q all R hAPP_P828904212r_bool(hAPP_f764724814r_bool(hAPP_f1410576713r_bool(cOMBC_516637475l_bool,P),Q),R) = hAPP_f2050077417l_bool(hAPP_P1418247892l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1426 (all P all Q all R hAPP_f720086610l_bool(hAPP_f292637069l_bool(hAPP_f1168269397l_bool(cOMBB_1293776864on_val,P),Q),R) = hAPP_P998768845l_bool(P,hAPP_f1727192346on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_060) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1427 (all P all Q all R hAPP_l1739862107l_bool(hAPP_f1094343359l_bool(hAPP_f876671127l_bool(cOMBB_1200577438t_char,P),Q),R) = hAPP_f1166017719l_bool(P,hAPP_l2111308793l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__061) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1428 (all P all Q all R hAPP_e1833980889l_bool(hAPP_f989077673l_bool(hAPP_f40682957l_bool(cOMBC_562612496l_bool,P),Q),R) = hAPP_f1175362209l_bool(hAPP_e1705922617l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_062) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1429 (all P all Q all R hAPP_P282169671l_bool(cOMBS_1319864284l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P1402001845l_bool(P,R),hAPP_P282169671l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1430 (all P all Q all R hAPP_l1342015621r_bool(hAPP_f719350875r_bool(hAPP_f2133563379r_bool(cOMBC_1025440566r_bool,P),Q),R) = hAPP_f764724814r_bool(hAPP_l1988620845r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_063) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1431 (all P all Q all R hAPP_l1571522437l_bool(hAPP_f1136362289l_bool(hAPP_f1736484361l_bool(cOMBB_2042763133t_char,P),Q),R) = hAPP_f1233028029l_bool(P,hAPP_l1873467853t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1432 (all P all Q all R hAPP_P1402001845l_bool(hAPP_f379976829l_bool(hAPP_f606945057l_bool(cOMBB_705522285on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P282169671l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_064) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1433 (all P all Q all R hAPP_l146377954l_bool(hAPP_f844901525l_bool(hAPP_f348508809l_bool(cOMBC_622308798l_bool,P),Q),R) = hAPP_f1526206996l_bool(hAPP_l177734933l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1434 (all P all Q all R hAPP_P1333315679l_bool(cOMBS_1218320756l_bool(P,Q),R) = hAPP_bool_bool(hAPP_P895943837l_bool(P,R),hAPP_P1333315679l_bool(Q,R))) # label(help_COMBS_1_1_COMBS_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1435 (all P all Q all R hAPP_P659547099r_bool(hAPP_f658521820r_bool(hAPP_f454222487r_bool(cOMBC_1338332465l_bool,P),Q),R) = hAPP_f515912112l_bool(hAPP_P780018708l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_065) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1436 (all P all Q all R hAPP_P895943837l_bool(hAPP_f914702973l_bool(hAPP_f1600936353l_bool(cOMBB_1617503877on_val,P),Q),R) = hAPP_b589554111l_bool(P,hAPP_P1333315679l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_066) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1437 (all P all Q all R hAPP_l1783480313r_bool(hAPP_f531187933r_bool(hAPP_f179418505r_bool(cOMBB_550632017t_char,P),Q),R) = hAPP_f1707979241r_bool(P,hAPP_l1571522437l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__067) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1438 (all P all Q all R hAPP_l2140727500r_bool(hAPP_f2025561243r_bool(hAPP_f1500560577r_bool(cOMBC_1784597444r_bool,P),Q),R) = hAPP_f658521820r_bool(hAPP_l923073979r_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_068) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1439 (all P all Q all R hAPP_P1680401186r_bool(hAPP_f1666729379r_bool(hAPP_f1020753317r_bool(cOMBC_1297648632l_bool,P),Q),R) = hAPP_f515912112l_bool(hAPP_P205570445l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_069) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1440 (all P all Q all R hAPP_l1845912621l_bool(hAPP_f1868463117l_bool(hAPP_f1365840271l_bool(cOMBB_1705938036t_char,P),Q),R) = hAPP_f1239832973l_bool(P,hAPP_l1388836853t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__070) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1441 (all P all Q all R hAPP_l213519975l_bool(hAPP_f156692813l_bool(hAPP_f1847120981l_bool(cOMBB_1035649854t_char,P),Q),R) = hAPP_P1327510541l_bool(P,hAPP_l277216047t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1442 (all P all Q all R hAPP_l2053770731r_bool(hAPP_f732843907r_bool(hAPP_f1563448447r_bool(cOMBB_1490692730t_char,P),Q),R) = hAPP_f1419180947r_bool(P,hAPP_l1845912621l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__071) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1443 (all P all Q all R hAPP_f613075253l_bool(hAPP_f1670595613l_bool(hAPP_f1472899487l_bool(cOMBB_588525814on_val,P),Q),R) = hAPP_f292637069l_bool(P,hAPP_f1849790461on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_072) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1444 (all P all Q all R hAPP_P1609485901l_bool(hAPP_f826324045l_bool(hAPP_f1639555093l_bool(cOMBB_985659173on_val,P),Q),R) = hAPP_P2015860941l_bool(P,hAPP_P604205461on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1445 (all P all Q all R hAPP_f893576377l_bool(hAPP_f1250221913l_bool(hAPP_f1860331535l_bool(cOMBB_2084052674on_val,P),Q),R) = hAPP_f510152537l_bool(P,hAPP_f613075253l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_073) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.53 1446 (all P all Q all R hAPP_P1418247892l_bool(hAPP_f2037329933l_bool(hAPP_f251669717l_bool(cOMBB_773661144t_char,P),Q),R) = hAPP_P1517699917l_bool(P,hAPP_P1423780764t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_074) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1447 (all P all Q all R hAPP_P594889876l_bool(hAPP_f375531599l_bool(hAPP_f1564338425l_bool(cOMBB_1078680455on_val,P),Q),R) = hAPP_P483670507l_bool(P,hAPP_P1963616220on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1448 (all P all Q all R hAPP_P1708370145l_bool(hAPP_f973018659l_bool(hAPP_f961387813l_bool(cOMBC_1608987946l_bool,P),Q),R) = hAPP_f1453283057l_bool(hAPP_P638161699l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1449 (all P all Q all R hAPP_P71593144l_bool(hAPP_f1317381998l_bool(hAPP_f1734997943l_bool(cOMBC_1491642377l_bool,P),Q),R) = hAPP_f458849545l_bool(hAPP_P88824722l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1450 (all P all Q all R hAPP_P780018708l_bool(hAPP_f1107475085l_bool(hAPP_f937861397l_bool(cOMBB_1520154591t_char,P),Q),R) = hAPP_P205570445l_bool(P,hAPP_P1224499548t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_075) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1451 (all P all Q all R hAPP_l1536299231l_bool(hAPP_f935003377l_bool(hAPP_f162154931l_bool(cOMBB_859890145har_ty,P),Q),R) = hAPP_f156692813l_bool(P,hAPP_l352172327t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1452 (all P all Q all R hAPP_l1129005983r_bool(hAPP_f1749915625r_bool(hAPP_f842743203r_bool(cOMBB_657296617har_ty,P),Q),R) = hAPP_f841257045r_bool(P,hAPP_l1536299231l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__076) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1453 (all P all Q all R hAPP_e286792811l_bool(hAPP_f1614195593l_bool(hAPP_f705562443l_bool(cOMBB_507006011t_char,P),Q),R) = hAPP_f826324045l_bool(P,hAPP_e1659493427on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1454 (all P all Q all R hAPP_l810309945l_bool(hAPP_f1817350437l_bool(hAPP_f614662951l_bool(cOMBB_1558246132t_char,P),Q),R) = hAPP_f2037329933l_bool(P,hAPP_l309186817t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1455 (all P all Q all R hAPP_e1705922617l_bool(hAPP_f1475571983l_bool(hAPP_f1946480059l_bool(cOMBB_673739729t_char,P),Q),R) = hAPP_f101237475l_bool(P,hAPP_e286792811l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_077) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1456 (all P all Q all R hAPP_l232580245l_bool(hAPP_f1752856401l_bool(hAPP_f552300311l_bool(cOMBB_1270208498t_char,P),Q),R) = hAPP_f375531599l_bool(P,hAPP_l1275479261on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_078) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1457 (all P all Q all R hAPP_P1116729363l_bool(hAPP_f1200025813l_bool(hAPP_f1089788553l_bool(cOMBC_967917532l_bool,P),Q),R) = hAPP_f973018659l_bool(hAPP_P609938901l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_079) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1458 (all P all Q all R hAPP_P282169671l_bool(hAPP_f2036784149l_bool(hAPP_f1720452391l_bool(cOMBC_1021753250l_bool,P),Q),R) = hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.54 1459 (all P all Q all R hAPP_l1988620845r_bool(hAPP_f1957374161r_bool(hAPP_f304993943r_bool(cOMBB_847828016t_char,P),Q),R) = hAPP_f1410576713r_bool(P,hAPP_l810309945l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List___080) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1460 (all P all Q all R hAPP_l177734933l_bool(hAPP_f1149562121l_bool(hAPP_f1850037271l_bool(cOMBB_773375802t_char,P),Q),R) = hAPP_f1467537159l_bool(P,hAPP_l232580245l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_081) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1461 (all P all Q all R hAPP_P1183008383l_bool(hAPP_f447422815l_bool(hAPP_f2052909183l_bool(cOMBC_766524526l_bool,P),Q),R) = hAPP_f1317381998l_bool(hAPP_P768428603l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli_082) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1462 (all P all Q all R hAPP_P1333315679l_bool(hAPP_f1856968213l_bool(hAPP_f677078775l_bool(cOMBC_475083938l_bool,P),Q),R) = hAPP_f458849545l_bool(hAPP_P126004409l_bool(P,R),Q)) # label(help_COMBC_1_1_COMBC_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1463 (all P all Q all R hAPP_l1591404153l_bool(hAPP_f333583909l_bool(hAPP_f1407048615l_bool(cOMBB_741416308t_char,P),Q),R) = hAPP_f1107475085l_bool(P,hAPP_l902950593t_char(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1464 (all P all Q all R hAPP_l923073979r_bool(hAPP_f29105311r_bool(hAPP_f953097879r_bool(cOMBB_672864638t_char,P),Q),R) = hAPP_f454222487r_bool(P,hAPP_l1591404153l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__083) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1465 (all P all Q all R hAPP_P638161699l_bool(hAPP_f762728813l_bool(hAPP_f1510763001l_bool(cOMBB_565412073on_val,P),Q),R) = hAPP_P1303341961l_bool(P,hAPP_P1886180715on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1466 (all P all Q all R hAPP_P88824722l_bool(hAPP_f1776493709l_bool(hAPP_f810261999l_bool(cOMBB_1034324152on_val,P),Q),R) = hAPP_P126004409l_bool(P,hAPP_P658340954on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1467 (all P all Q all R hAPP_P527298901l_bool(hAPP_f1204100177l_bool(hAPP_f2026692601l_bool(cOMBB_1977588741on_val,P),Q),R) = hAPP_f762728813l_bool(P,hAPP_P1870962205on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1468 (all P all Q all R hAPP_P609938901l_bool(hAPP_f2095325577l_bool(hAPP_f1135930489l_bool(cOMBB_1223415373on_val,P),Q),R) = hAPP_f961387813l_bool(P,hAPP_P527298901l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___084) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1469 (all P all Q all R hAPP_P76086873l_bool(hAPP_f1082373989l_bool(hAPP_f869803751l_bool(cOMBB_555068556on_val,P),Q),R) = hAPP_f1776493709l_bool(P,hAPP_P1526035745on_val(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39 1470 (all P all Q all R hAPP_P768428603l_bool(hAPP_f1427871743l_bool(hAPP_f32926423l_bool(cOMBB_779086262on_val,P),Q),R) = hAPP_f1734997943l_bool(P,hAPP_P76086873l_bool(Q,R))) # label(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc___085) # label(axiom) # label(non_clause). [assumption].
% 4.18/4.39
% 4.18/4.39 ============================== end of process non-clausal formulas ===
% 4.18/4.39
% 4.18/4.39 ============================== PROCESS INITIAL CLAUSES ===============
% 4.18/4.39
% 4.18/4.39 ============================== PREDICATE ELIMINATION =================
% 4.18/4.39
% 4.18/4.39 ============================== end predicate elimination =============
% 4.18/4.39
% 4.18/4.39 Auto_denials: (non-Horn, no changes).
% 4.18/4.39
% 4.18/4.39 Term ordering decisions:
% 4.18/4.39 Function symbol KB weights: produc1259058957on_val=1. val_list_char=1. produc1441475159on_val=1. member773094996on_val=1. produc899768717on_val=1. produc1611380469on_val=1. produc5062597t_char=1. produc823076510on_val=1. product_Pair_val_val=1. produc379668296on_val=1. produc621191550al_val=1. member875476972on_val=1. some_val=1. produc1909267824t_char=1. produc1916172923t_char=1. produc921874948t_char=1. member1251428284t_char=1. produc1483578759t_char=1. produc1152259904t_char=1. produc822965838t_char=1. produc1147572817t_char=1. some_P948696889on_val=1. some_ty=1. member649088532al_val=1. none_val=1. produc1924279125al_val=1. fTrue=1. member_list_char=1. member1467889965t_char=1. member1601084734t_char=1. produc1431439831t_char=1. produc1564932627on_val=1. produc1641293463t_char=1. produc1951691075on_val=1. produc24551831t_char=1. produc57279289t_char=1. produc870913623on_val=1. unit=1. produc1244920211al_val=1. produc1299387215t_char=1. produc635935767t_char=1. class=1. 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hAPP_f1200025813l_bool=1. hAPP_f1204100177l_bool=1. hAPP_f1209019955r_bool=1. hAPP_f1250221913l_bool=1. hAPP_f133320957r_bool=1. hAPP_f1365840271l_bool=1. hAPP_f1370205989l_bool=1. hAPP_f1374595987l_bool=1. hAPP_f1406462375l_bool=1. hAPP_f1407048615l_bool=1. hAPP_f1427871743l_bool=1. hAPP_f144783951l_bool=1. hAPP_f1449341487r_bool=1. hAPP_f1472899487l_bool=1. hAPP_f1475571983l_bool=1. hAPP_f1500560577r_bool=1. hAPP_f1510763001l_bool=1. hAPP_f1563448447r_bool=1. hAPP_f1564338425l_bool=1. hAPP_f1608277885r_bool=1. hAPP_f1612138403l_bool=1. hAPP_f1614195593l_bool=1. hAPP_f162154931l_bool=1. hAPP_f1639555093l_bool=1. hAPP_f165071409l_bool=1. hAPP_f1670595613l_bool=1. hAPP_f1687138147l_bool=1. hAPP_f1715733055l_bool=1. hAPP_f1736484361l_bool=1. hAPP_f1749915625r_bool=1. hAPP_f1752856401l_bool=1. hAPP_f1764180741l_bool=1. hAPP_f179418505r_bool=1. hAPP_f1817350437l_bool=1. hAPP_f1820115955r_bool=1. hAPP_f1823921107r_bool=1. hAPP_f183649339l_bool=1. hAPP_f1847120981l_bool=1. hAPP_f1850037271l_bool=1. hAPP_f1859053709l_bool=1. hAPP_f1860331535l_bool=1. hAPP_f1863694447l_bool=1. hAPP_f1868463117l_bool=1. hAPP_f1880802701l_bool=1. hAPP_f1937828171l_bool=1. hAPP_f1946480059l_bool=1. hAPP_f1957374161r_bool=1. hAPP_f197435839r_bool=1. hAPP_f198821591l_bool=1. hAPP_f2025561243r_bool=1. hAPP_f2026692601l_bool=1. hAPP_f2047757465l_bool=1. hAPP_f2052909183l_bool=1. hAPP_f2059406941r_bool=1. hAPP_f2071340985r_bool=1. hAPP_f2080627739l_bool=1. hAPP_f2091926485r_bool=1. hAPP_f2095325577l_bool=1. hAPP_f2100207721l_bool=1. hAPP_f2118054305l_bool=1. hAPP_f2133563379r_bool=1. hAPP_f247798919l_bool=1. hAPP_f251669717l_bool=1. hAPP_f254182519r_bool=1. hAPP_f257113085l_bool=1. hAPP_f29105311r_bool=1. hAPP_f293485653l_bool=1. hAPP_f304993943r_bool=1. hAPP_f306469557r_bool=1. hAPP_f308875635r_bool=1. hAPP_f32926423l_bool=1. hAPP_f333583909l_bool=1. hAPP_f344506159r_bool=1. hAPP_f348508809l_bool=1. hAPP_f350189921l_bool=1. hAPP_f380623487l_bool=1. hAPP_f400269243l_bool=1. hAPP_f40682957l_bool=1. hAPP_f447422815l_bool=1. hAPP_f447563647r_bool=1. hAPP_f466945179l_bool=1. hAPP_f47713631l_bool=1. hAPP_f521496323r_bool=1. hAPP_f531187933r_bool=1. hAPP_f552300311l_bool=1. hAPP_f565735867l_bool=1. hAPP_f614662951l_bool=1. hAPP_f62511709l_bool=1. hAPP_f693085049l_bool=1. hAPP_f705562443l_bool=1. hAPP_f719350875r_bool=1. hAPP_f732843907r_bool=1. hAPP_f77033475l_bool=1. hAPP_f810261999l_bool=1. hAPP_f842743203r_bool=1. hAPP_f844901525l_bool=1. hAPP_f866074145l_bool=1. hAPP_f869803751l_bool=1. hAPP_f876671127l_bool=1. hAPP_f877616419l_bool=1. hAPP_f919000597l_bool=1. hAPP_f935003377l_bool=1. hAPP_f937861397l_bool=1. hAPP_f953097879r_bool=1. hAPP_f987862447r_bool=1. hAPP_f989077673l_bool=1. oconf_1869808039t_char=1. hAPP_P1661798543t_char=1. hAPP_f1734879897l_bool=1. hAPP_f555424277l_bool=1. hAPP_o2007402111l_bool=1. hAPP_option_ty_bool=1. hAPP_option_val_bool=1. hAPP_t1369077401t_char=1. lex_pr1038007919on_val=1. lex_pr1541028704on_val=1. lex_pr1588300168t_char=1. lex_pr1668767798t_char=1. lex_pr167435119t_char=1. lex_pr1787105337t_char=1. lex_pr1876288492t_char=1. lex_pr1932514710al_val=1. lex_pr1971266694on_val=1. lex_pr2110711565on_val=1. lex_pr213428520t_char=1. lex_pr280535005t_char=1. lex_pr307591827t_char=1. lex_pr69619957on_val=1. lex_pr731210613on_val=1. lex_prod_val_val=1. map_ad1185064968ar_val=1. map_add_list_char_ty=1. map_ty_option_ty=1. map_val_option_ty=1. semila1168318597r_bool=1. semila1346223580r_bool=1. semila1731249415r_bool=1. semila449273525l_bool=1. semila465093516t_bool=1. semila751111325l_bool=1. cOMBS_570216337l_bool=1. cons_list_char=1. cons_val=1. hAPP_f1074020887l_bool=1. hAPP_f1118567467l_bool=1. hAPP_f1409772418l_bool=1. hAPP_f1450446905l_bool=1. hAPP_f1452292669l_bool=1. hAPP_f1520735791l_bool=1. hAPP_f1523875321l_bool=1. hAPP_f1776070952l_bool=1. hAPP_f1776419603l_bool=1. hAPP_f1795246582l_bool=1. hAPP_f1889282162l_bool=1. hAPP_f1931964053l_bool=1. hAPP_f1977633121l_bool=1. hAPP_f2041029616l_bool=1. hAPP_f2071159779l_bool=1. hAPP_f348318673l_bool=1. hAPP_f434955681l_bool=1. hAPP_f539072365l_bool=1. hAPP_f550652027l_bool=1. hAPP_f570766339l_bool=1. hAPP_f592397849l_bool=1. hAPP_f678833350l_bool=1. hAPP_f838396643l_bool=1. hAPP_f857351829l_bool=1. hAPP_f861853459l_bool=1. hAPP_f998390560l_bool=1. hAPP_l2054741776r_bool=1. hAPP_l2138409430r_bool=1. hAPP_o1576581476on_val=1. hAPP_o1968908095l_bool=1. hAPP_o586881855l_bool=1. cOMBS_1218320756l_bool=1. cOMBS_1319864284l_bool=1. cOMBS_1502238389l_bool=1. cOMBS_1743887558l_bool=1. cOMBS_350755140l_bool=1. cOMBS_635570165l_bool=1. cOMBS_nat_bool_bool=1. hAPP_P1187139874r_bool=1. hAPP_P1383068750l_bool=1. hAPP_P1402001845l_bool=1. hAPP_P1418247892l_bool=1. hAPP_P1457625805l_bool=1. hAPP_P1552072218l_bool=1. hAPP_P1562529797l_bool=1. hAPP_P1609485901l_bool=1. hAPP_P1614880106l_bool=1. hAPP_P2028292026l_bool=1. hAPP_P415257547l_bool=1. hAPP_P527298901l_bool=1. hAPP_P594889876l_bool=1. hAPP_P609938901l_bool=1. hAPP_P638161699l_bool=1. hAPP_P76086873l_bool=1. hAPP_P768428603l_bool=1. hAPP_P780018708l_bool=1. hAPP_P88824722l_bool=1. hAPP_P895943837l_bool=1. hAPP_b1257035143l_bool=1. hAPP_b406740087l_bool=1. hAPP_e1303556805l_bool=1. hAPP_e1705922617l_bool=1. hAPP_e286792811l_bool=1. hAPP_e53687815l_bool=1. hAPP_f1008932791l_bool=1. hAPP_f101237475l_bool=1. hAPP_f1050935001l_bool=1. hAPP_f1080886329l_bool=1. hAPP_f1099622285l_bool=1. hAPP_f1107475085l_bool=1. hAPP_f1145256474l_bool=1. hAPP_f1146629647l_bool=1. hAPP_f1157863905l_bool=1. hAPP_f1163760061l_bool=1. hAPP_f1166017719l_bool=1. hAPP_f1169733153l_bool=1. hAPP_f1175362209l_bool=1. hAPP_f1233028029l_bool=1. hAPP_f1239832973l_bool=1. hAPP_f1243585741ion_ty=1. hAPP_f1298720864r_bool=1. hAPP_f1317381998l_bool=1. hAPP_f1335946228l_bool=1. hAPP_f1363667773l_bool=1. hAPP_f1367982615r_bool=1. hAPP_f1394668591l_bool=1. hAPP_f1410576713r_bool=1. hAPP_f1419180947r_bool=1. hAPP_f1466436665r_bool=1. hAPP_f1467537159l_bool=1. hAPP_f1492320500l_bool=1. hAPP_f1526206996l_bool=1. hAPP_f156692813l_bool=1. hAPP_f1579743228l_bool=1. hAPP_f1600936353l_bool=1. hAPP_f1611569977l_bool=1. hAPP_f1617787571l_bool=1. hAPP_f1646911885l_bool=1. hAPP_f1677329295l_bool=1. hAPP_f1707979241r_bool=1. hAPP_f1724656343r_bool=1. hAPP_f1728541444l_bool=1. hAPP_f1734997943l_bool=1. hAPP_f1764548711l_bool=1. hAPP_f1766231913r_bool=1. hAPP_f1776493709l_bool=1. hAPP_f181262431l_bool=1. hAPP_f1861125939r_bool=1. hAPP_f1874697593r_bool=1. hAPP_f1985672189l_bool=1. hAPP_f2037329933l_bool=1. hAPP_f2057883639l_bool=1. hAPP_f2110071953ion_ty=1. hAPP_f225832321r_bool=1. hAPP_f263393637l_bool=1. hAPP_f279818502r_bool=1. hAPP_f292637069l_bool=1. hAPP_f321462169l_bool=1. hAPP_f33142364l_bool=1. hAPP_f335969926r_bool=1. hAPP_f359949478ion_ty=1. hAPP_f361629773l_bool=1. hAPP_f375531599l_bool=1. hAPP_f379976829l_bool=1. hAPP_f388097003r_bool=1. hAPP_f396807521l_bool=1. hAPP_f399018025r_bool=1. hAPP_f451501457ion_ty=1. hAPP_f454222487r_bool=1. hAPP_f489569861t_bool=1. hAPP_f509342689ion_ty=1. hAPP_f510152537l_bool=1. hAPP_f558380429l_bool=1. hAPP_f561246575l_bool=1. hAPP_f603925568l_bool=1. hAPP_f605643693r_bool=1. hAPP_f606945057l_bool=1. hAPP_f613075253l_bool=1. hAPP_f644972157l_bool=1. hAPP_f658521820r_bool=1. hAPP_f69964139ion_ty=1. hAPP_f720086610l_bool=1. hAPP_f722872225l_bool=1. hAPP_f749178132l_bool=1. hAPP_f762728813l_bool=1. hAPP_f7643013ion_ty=1. hAPP_f764724814r_bool=1. hAPP_f802560783ion_ty=1. hAPP_f826324045l_bool=1. hAPP_f841257045r_bool=1. hAPP_f893576377l_bool=1. hAPP_f894608603t_bool=1. hAPP_f901718717l_bool=1. hAPP_f914702973l_bool=1. hAPP_f921434893l_bool=1. hAPP_f926979333l_bool=1. hAPP_f961387813l_bool=1. hAPP_f973018659l_bool=1. hAPP_l1117138611l_bool=1. hAPP_l1129005983r_bool=1. hAPP_l1335043179r_bool=1. hAPP_l1425867561l_bool=1. hAPP_l1536299231l_bool=1. hAPP_l1571522437l_bool=1. hAPP_l1591404153l_bool=1. hAPP_l1646953198l_bool=1. hAPP_l1739862107l_bool=1. hAPP_l177734933l_bool=1. hAPP_l1783480313r_bool=1. hAPP_l1842007287l_bool=1. hAPP_l1845912621l_bool=1. hAPP_l1988620845r_bool=1. hAPP_l2010421276l_bool=1. hAPP_l2053770731r_bool=1. hAPP_l2111308793l_bool=1. hAPP_l213519975l_bool=1. hAPP_l232580245l_bool=1. hAPP_l296209613r_bool=1. hAPP_l551544901l_bool=1. hAPP_l553007690l_bool=1. hAPP_l753659065r_bool=1. hAPP_l810309945l_bool=1. hAPP_l923073979r_bool=1. hAPP_l96108383r_bool=1. hAPP_n1006566506l_bool=1. hAPP_n95946796l_bool=1. hAPP_o1240645474ion_ty=1. hAPP_o1269033393on_val=1. hAPP_o1566711458t_bool=1. hAPP_o453398608r_bool=1. hAPP_o534509643ion_ty=1. hAPP_option_val_val=1. hAPP_v1988122071l_bool=1. hAPP_v3604996l_bool=1. hAPP_v417179479l_bool=1. restri761823004ar_val=1. comp_o1129292306t_char=1. hAPP_f388705405r_bool=1. hAPP_l165010689r_bool=1. hAPP_o1977518472on_val=1. hAPP_o285151112r_bool=1. hAPP_option_nat_nat=1. hAPP_option_ty_ty=1. map_list_char_val=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f9=1. f10=1. f11=1. f12=1. 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. f52=1. f53=1. f54=1. f55=1. f56=1. f57=1. f58=1. f59=1. f60=1. f61=1. f62=1. f63=1. f64=1. f65=1. f66=1. f67=1. f68=1. f69=1. f70=1. f71=1. f72=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f82=1. f83=1. f84=1. f85=1. f86=1. f87=1. f88=1. f89=1. f90=1. f91=1. f92=1. f93=1. f94=1. f95=1. f96=1. f97=1. f98=1. f99=1. f352=1. f353=1. f354=1. f355=1. f356=1. f357=1. f358=1. f359=1. f360=1. f361=1. f362=1. f363=1. f364=1. f365=1. f366=1. f367=1. f368=1. f369=1. f370=1. f371=1. f372=1. f373=1. f374=1. f375=1. f376=1. f377=1. f378=1. f379=1. f380=1. f381=1. f382=1. f383=1. f384=1. f385=1. f386=1. f387=1. f388=1. f389=1. f390=1. f391=1. f392=1. f393=1. f394=1. f395=1. f396=1. f397=1. f398=1. f399=1. f400=1. f401=1. f402=1. f403=1. f404=1. f405=1. f406=1. f407=1. f408=1. f409=1. f410=1. f411=1. f412=1. f413=1. f414=1. f415=1. f416=1. f417=1. f418=1. f419=1. f420=1. f421=1. f422=1. f423=1. f424=1. f425=1. f426=1. f427=1. f428=1. f429=1. f430=1. f431=1. f432=1. f433=1. f434=1. f435=1. f436=1. f437=1. f438=1. f439=1. f440=1. f441=1. f442=1. f443=1. f444=1. f445=1. f446=1. f447=1. f448=1. f449=1. f450=1. f451=1. f452=1. f453=1. f454=1. f455=1. f456=1. f457=1. f458=1. f459=1. f460=1. f461=1. f462=1. f463=1. f464=1. f465=1. f466=1. f467=1. f468=1. f469=1. f470=1. f471=1. f472=1. f473=1. f474=1. f475=1. f476=1. f477=1. f478=1. f479=1. f592=1. f593=1. f594=1. f595=1. f596=1. f597=1. f598=1. f599=1. f600=1. f601=1. f602=1. f603=1. f604=1. f605=1. f606=1. f607=1. f608=1. f609=1. f610=1. f611=1. f612=1. f613=1. f614=1. f615=1. f616=1. f617=1. f618=1. f619=1. f620=1. f621=1. f622=1. f623=1. f624=1. f625=1. f626=1. f627=1. f628=1. f629=1. f630=1. f631=1. f632=1. f633=1. f634=1. f635=1. f636=1. f637=1. f638=1. f639=1. f640=1. f641=1. f642=1. f643=1. f644=1. f645=1. f646=1. f647=1. f648=1. f649=1. f650=1. f651=1. f652=1. f653=1. f654=1. f655=1. f659=1. f660=1. f661=1. f662=1. f663=1. f664=1. f671=1. f672=1. f673=1. f674=1. f675=1. f676=1. f693=1. f694=1. f695=1. f696=1. f697=1. f698=1. f699=1. f700=1. f701=1. f877=1. f894=1. f925=1. f926=1. throw_list_char=1. red=1. transi2024712006on_val=1. addr=1. bool=1. ord_le2092826700r_bool=1. transi374442731on_val=1. transi1395422419t_char=1. addr_of_sys_xcpt=1. fv=1. transi935034983cl_val=1. reds=1. dom_list_char_val=1. widen_2090681816t_char=1. binop=1. ord_le1438917387l_bool=1. ord_le1776148979l_bool=1. ord_le640323803r_bool=1. size_size_list_ty=1. transi1906258203al_val=1. hp=1. lconf_496643946t_char=1. typeof_h=1. final_list_char=1. preallocated=1. size_s2113983095t_char=1. blocks=1. is_refT=1. transi1095029602t_char=1. transi1123801095t_char=1. transi122195895t_char=1. transi1257872013t_char=1. transi1423755450al_val=1. transi1789604888t_char=1. transi198989188t_char=1. transi2005320128t_char=1. transi208336786on_val=1. transi61620055on_val=1. transi772168185t_char=1. transi910771962on_val=1. transi921647814on_val=1. hconf_97414254t_char=1. ord_le117566470r_bool=1. ord_le1987888477r_bool=1. size_size_list_val=1. subcls851966956t_char=1. new_list_char=1. ord_le1568362934t_bool=1. dom_na996029170on_val=1. new_Addr=1. is_cla570604648t_char=1. ord_less_eq_bool=1. produc2062775566l_bool=1. subcls744239332t_char=1. transi1065307915t_char=1. distinct_list_char=1. finals_list_char=1. fvs=1. init_fields=1. produc1159035454l_bool=1. produc1555310053l_bool=1. produc156891095r_bool=1. produc1574020101r_bool=1. produc1588781647r_bool=1. produc1838470831l_bool=1. produc1911975310l_bool=1. produc2053127004l_bool=1. produc2116052801r_bool=1. produc266042248r_bool=1. produc288369490r_bool=1. produc481748255l_bool=1. produc550034914r_bool=1. produc886919678l_bool=1. produc95371820r_bool=1. collect_list_char=1. collect_nat=1. ord_le1050317687l_bool=1. ord_le1080391173l_bool=1. ord_le1151384881r_bool=1. ord_le1218729222r_bool=1. ord_le125655867l_bool=1. ord_le1270183657l_bool=1. ord_le1449176264r_bool=1. ord_le1461833060l_bool=1. ord_le1467847572l_bool=1. ord_le1579844278r_bool=1. ord_le1668954565l_bool=1. ord_le1725884030l_bool=1. ord_le1734858744r_bool=1. ord_le1744419030l_bool=1. ord_le176694639r_bool=1. ord_le1852058257r_bool=1. ord_le1871967977r_bool=1. ord_le188521288l_bool=1. ord_le1908998213l_bool=1. ord_le2008677227r_bool=1. ord_le285175110l_bool=1. ord_le310098611l_bool=1. ord_le408082617l_bool=1. ord_le458107652r_bool=1. ord_le715555971r_bool=1. ord_le725666495r_bool=1. ord_le735260024r_bool=1. ord_le817953186r_bool=1. ord_le989574145r_bool=1. produc1675615144ion_ty=1. set_list_char=1. collec1387638140t_char=1. collec1583467887t_char=1. collec1797130234t_char=1. collec2087910442on_val=1. collec718040978on_val=1. dom_Pr695701035ar_val=1. dom_list_char_ty=1. set_Pr1494163115t_char=1. set_Pr2033386304t_char=1. size_s1143674878t_char=1. undefined_bop=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. f50=1. f51=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. f125=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. f182=1. f183=1. f184=1. f185=1. f186=1. f187=1. f188=1. f189=1. f190=1. f191=1. f192=1. f193=1. f194=1. f195=1. f196=1. f197=1. f198=1. f199=1. f200=1. f201=1. f202=1. f203=1. f204=1. f205=1. f206=1. f207=1. f208=1. f209=1. f210=1. f211=1. f212=1. f213=1. f214=1. f215=1. f216=1. f217=1. f218=1. f219=1. f220=1. f221=1. f222=1. f223=1. f224=1. f225=1. f226=1. f227=1. f228=1. f229=1. f230=1. f231=1. f232=1. f233=1. f234=1. f235=1. f236=1. f237=1. f238=1. f239=1. f240=1. f241=1. f242=1. f243=1. f244=1. f245=1. f246=1. f247=1. f248=1. f249=1. f250=1. f251=1. f252=1. f253=1. f254=1. f255=1. f256=1. f257=1. f258=1. f259=1. f260=1. f261=1. f262=1. f263=1. f264=1. f265=1. f266=1. f267=1. f268=1. f269=1. f270=1. f271=1. f272=1. f273=1. f274=1. f275=1. f276=1. f277=1. f278=1. f279=1. f280=1. f281=1. f282=1. f283=1. f284=1. f285=1. f286=1. f287=1. f288=1. f289=1. f290=1. f291=1. f292=1. f293=1. f294=1. f295=1. f296=1. f297=1. f298=1. f299=1. f300=1. f301=1. f302=1. f303=1. f304=1. f305=1. f306=1. f307=1. f308=1. f309=1. f310=1. f311=1. f312=1. f313=1. f314=1. f315=1. f316=1. f317=1. f318=1. f319=1. f320=1. f321=1. f322=1. f323=1. f324=1. f325=1. f326=1. f327=1. f328=1. f329=1. f330=1. f331=1. f332=1. f333=1. f334=1. f335=1. f336=1. f337=1. f338=1. f339=1. f340=1. f341=1. f342=1. f343=1. f344=1. f345=1. f346=1. f347=1. f348=1. f349=1. f350=1. f351=1. f480=1. f481=1. f482=1. f483=1. f484=1. f485=1. f486=1. f487=1. f488=1. f489=1. f490=1. f491=1. f492=1. f493=1. f494=1. f495=1. f496=1. f497=1. f498=1. f499=1. f500=1. f501=1. f502=1. f503=1. f504=1. f505=1. f506=1. f507=1. f508=1. f509=1. f510=1. f511=1. f512=1. f513=1. f514=1. f515=1. f516=1. f517=1. f518=1. f519=1. f520=1. f521=1. f522=1. f523=1. f524=1. f525=1. f526=1. f527=1. f528=1. f529=1. f530=1. f531=1. f532=1. f533=1. f534=1. f535=1. f536=1. f537=1. f538=1. f539=1. f540=1. f541=1. f542=1. f543=1. f544=1. f545=1. f546=1. f547=1. f548=1. f549=1. f550=1. f551=1. f552=1. f553=1. f554=1. f555=1. f556=1. f557=1. f558=1. f559=1. f560=1. f561=1. f562=1. f563=1. f564=1. f565=1. f566=1. f567=1. f568=1. f569=1. f570=1. f571=1. f572=1. f573=1. f574=1. f575=1. f576=1. f577=1. f578=1. f579=1. f580=1. f581=1. f582=1. f583=1. f584=1. f585=1. f586=1. f587=1. f588=1. f589=1. f590=1. f591=1. f677=1. f678=1. f679=1. f680=1. f681=1. f682=1. f683=1. f684=1. f685=1. f686=1. f864=1. f865=1. f866=1. f867=1. f868=1. f927=1. f934=1. f940=1. eval=1. redp=1. fun_up1149430426on_val=1. binOp_list_char=1. block_list_char=1. fun_up2041264236on_val=1. fun_up424764369ion_ty=1. fun_up204312361on_val=1. call_list_char=1. cond_list_char=1. fAcc_list_char=1. evals=1. redsp=1. list_all2_ty_ty=1. map_up1085636310ar_val=1. fields1147507508t_char=1. map_up891053837har_ty=1. overri2012515291on_val=1. option1388193227on_val=1. f665=1. f666=1. f667=1. f668=1. f687=1. f688=1. f689=1. f690=1. f878=1. f879=1. f880=1. f881=1. f882=1. f883=1. f884=1. f885=1. f924=1. fAss_list_char=1. tryCatch_list_char=1. conf_P373316194t_char=1. has_fi1183600461t_char=1. f657=1. f658=1. f869=1. f870=1. f871=1. f872=1. f873=1. f874=1. f875=1. f876=1. f886=1. f887=1. f888=1. f889=1. f890=1. f891=1. f892=1. f893=1. wTrt_1=1. wTrt=1. wTrts_1=1. wTrts=1. f669=1. f670=1. f702=1. f703=1. f704=1. f705=1. f706=1. f707=1. f708=1. f709=1. f710=1. f711=1. f712=1. f713=1. f714=1. f715=1. f716=1. f717=1. f718=1. f719=1. f720=1. f721=1. f722=1. f723=1. f724=1. f725=1. f726=1. f727=1. f728=1. f729=1. f730=1. f731=1. f732=1. f733=1. f906=1. f908=1. f909=1. f918=1. f919=1. f920=1. f921=1. f922=1. method1809630380t_char=1. f656=1. f691=1. f692=1. f734=1. f735=1. f736=1. f737=1. f738=1. f739=1. f740=1. f741=1. f742=1. f743=1. f744=1. f745=1. f746=1. f747=1. f748=1. f749=1. f750=1. f751=1. f752=1. f753=1. f754=1. f755=1. f756=1. f757=1. f758=1. f759=1. f760=1. f761=1. f762=1. f763=1. f764=1. f765=1. f766=1. f767=1. f768=1. f769=1. f770=1. f771=1. f772=1. f773=1. f774=1. f775=1. f776=1. f777=1. f778=1. f779=1. f780=1. f781=1. f782=1. f783=1. f784=1. f785=1. f786=1. f787=1. f788=1. f789=1. f790=1. f791=1. f792=1. f793=1. f794=1. f795=1. f796=1. f797=1. f798=1. f799=1. f800=1. f801=1. f802=1. f803=1. f804=1. f805=1. f806=1. f807=1. f808=1. f809=1. f810=1. f811=1. f812=1. f813=1. f814=1. f815=1. f816=1. f817=1. f818=1. f819=1. f820=1. f821=1. f822=1. f823=1. f824=1. f825=1. f826=1. f827=1. f828=1. f829=1. f830=1. f831=1. f832=1. f833=1. f834=1. f835=1. f836=1. f837=1. f838=1. f839=1. f840=1. f841=1. f842=1. f843=1. f844=1. f845=1. f846=1. f847=1. f848=1. f849=1. f850=1. f851=1. f852=1. f853=1. f854=1. f855=1. f856=1. f857=1. f858=1. f859=1. f860=1. f861=1. f862=1. f863=1. f899=1. f900=1. f901=1. f902=1. f903=1. f904=1. f905=1. f923=1. f928=1. f929=1. f930=1. f931=1. f932=1. f933=1. f944=1. f945=1. f946=1. f947=1. f895=1. f896=1. f897=1. f898=1. f910=1. f911=1. f912=1. f913=1. f914=1. f915=1. f916=1. f917=1. f935=1. f941=1. f942=1. f943=1. f907=1. f936=1. f937=1. f938=1. f939=1. f949=1. f948=1.
% 4.18/4.39
% 4.18/4.39 ============================== PROOF =================================
% 4.18/4.39 % SZS status Theorem
% 4.18/4.39 % SZS output start Refutation
% 4.18/4.39
% 4.18/4.39 % Proof 1 at 2.26 (+ 0.05) seconds.
% 4.18/4.39 % Length of proof is 3.
% 4.18/4.39 % Level of proof is 1.
% 4.18/4.39 % Maximum clause weight is 32.000.
% 4.18/4.39 % Given clauses 0.
% 4.18/4.39
% 4.18/4.39 1613 hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,hAPP_val_option_val(some_val,v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a)))),red(p))) # label(fact_1_InitBlockRed_I1_J) # label(axiom). [assumption].
% 4.18/4.39 3611 -hBOOL(hAPP_f1453283057l_bool(hAPP_P1303341961l_bool(member773094996on_val,hAPP_P1886180715on_val(hAPP_P1870962205on_val(produc1441475159on_val,hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,ea),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,ha),fun_up1149430426on_val(la,v_1,hAPP_val_option_val(some_val,v))))),hAPP_P604205461on_val(hAPP_e1659493427on_val(produc1259058957on_val,e_a),hAPP_f1727192346on_val(hAPP_f1849790461on_val(produc899768717on_val,h_a),l_a)))),red(p))) # label(conj_0) # label(negated_conjecture). [assumption].
% 4.18/4.39 3612 $F. [copy(3611),unit_del(a,1613)].
% 4.18/4.39
% 4.18/4.39 % SZS output end Refutation
% 4.18/4.39 ============================== end of proof ==========================
% 4.18/4.39
% 4.18/4.39 ============================== STATISTICS ============================
% 4.18/4.39
% 4.18/4.39 Given=0. Generated=2271. Kept=2053. proofs=1.
% 4.18/4.39 Usable=0. Sos=0. Demods=277. Limbo=2053, Disabled=2271. Hints=0.
% 4.18/4.39 Megabytes=115.49.
% 4.18/4.39 User_CPU=2.26, System_CPU=0.05, Wall_clock=2.
% 4.18/4.39
% 4.18/4.39 ============================== end of statistics =====================
% 4.18/4.39
% 4.18/4.39 ============================== end of search =========================
% 4.18/4.39
% 4.18/4.39 THEOREM PROVED
% 4.18/4.39 % SZS status Theorem
% 4.18/4.39
% 4.18/4.39 Exiting with 1 proof.
% 4.18/4.39
% 4.18/4.39 Process 30983 exit (max_proofs) Sat Jun 4 11:25:21 2022
% 4.18/4.39 Prover9 interrupted
%------------------------------------------------------------------------------